%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV031^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n016.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 10:49:24 AM UTC 2026
% Result : Theorem 0.44s 0.27s
% Output : CNFRefutation 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 1
% Syntax : Number of formulae : 151 ( 66 unt; 0 typ; 0 def)
% Number of atoms : 1096 ( 266 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 2383 ( 424 ~; 330 |; 48 &;1477 @)
% ( 0 <=>; 104 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 408 ( 408 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 588 ( 0 ^; 588 !; 0 ?; 588 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_b,type,
b: $tType ).
thf(tp_sK10_SY97,type,
sK10_SY97: a > b ).
thf(tp_sK11_SY103,type,
sK11_SY103: a ).
thf(tp_sK1_Xp,type,
sK1_Xp: a > $o ).
thf(tp_sK2_SY21,type,
sK2_SY21: a > ( a > b ) > ( a > b ) > $o ).
thf(tp_sK3_SX0,type,
sK3_SX0: a > b ).
thf(tp_sK4_SY66,type,
sK4_SY66: a ).
thf(tp_sK5_SX0,type,
sK5_SX0: a > b ).
thf(tp_sK6_SY77,type,
sK6_SY77: a > b ).
thf(tp_sK7_SY81,type,
sK7_SY81: a ).
thf(tp_sK8_SX0,type,
sK8_SX0: a > b ).
thf(tp_sK9_SY92,type,
sK9_SY92: a > b ).
thf(1,conjecture,
! [Xp: a > $o,Xe: a > ( a > b ) > ( a > b ) > $o] :
( ! [Xx: a] :
( ( Xp @ Xx )
=> ( ! [Xx0: a > b] : ( Xe @ Xx @ Xx0 @ Xx0 )
& ! [Xx0: a > b,Xy: a > b] :
( ( Xe @ Xx @ Xx0 @ Xy )
=> ( Xe @ Xx @ Xy @ Xx0 ) )
& ! [Xx0: a > b,Xy: a > b,Xz: a > b] :
( ( ( Xe @ Xx @ Xx0 @ Xy )
& ( Xe @ Xx @ Xy @ Xz ) )
=> ( Xe @ Xx @ Xx0 @ Xz ) ) ) )
=> ( ! [Xx: a > b,Xx0: a] :
( ( Xp @ Xx0 )
=> ( Xe @ Xx0 @ Xx @ Xx ) )
& ! [Xx: a > b,Xy: a > b] :
( ! [Xx0: a] :
( ( Xp @ Xx0 )
=> ( Xe @ Xx0 @ Xx @ Xy ) )
=> ! [Xx0: a] :
( ( Xp @ Xx0 )
=> ( Xe @ Xx0 @ Xy @ Xx ) ) )
& ! [Xx: a > b,Xy: a > b,Xz: a > b] :
( ( ! [Xx0: a] :
( ( Xp @ Xx0 )
=> ( Xe @ Xx0 @ Xx @ Xy ) )
& ! [Xx0: a] :
( ( Xp @ Xx0 )
=> ( Xe @ Xx0 @ Xy @ Xz ) ) )
=> ! [Xx0: a] :
( ( Xp @ Xx0 )
=> ( Xe @ Xx0 @ Xx @ Xz ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM512_pme) ).
thf(2,negated_conjecture,
( ( ! [Xp: a > $o,Xe: a > ( a > b ) > ( a > b ) > $o] :
( ! [Xx: a] :
( ( Xp @ Xx )
=> ( ! [Xx0: a > b] : ( Xe @ Xx @ Xx0 @ Xx0 )
& ! [Xx0: a > b,Xy: a > b] :
( ( Xe @ Xx @ Xx0 @ Xy )
=> ( Xe @ Xx @ Xy @ Xx0 ) )
& ! [Xx0: a > b,Xy: a > b,Xz: a > b] :
( ( ( Xe @ Xx @ Xx0 @ Xy )
& ( Xe @ Xx @ Xy @ Xz ) )
=> ( Xe @ Xx @ Xx0 @ Xz ) ) ) )
=> ( ! [Xx: a > b,Xx0: a] :
( ( Xp @ Xx0 )
=> ( Xe @ Xx0 @ Xx @ Xx ) )
& ! [Xx: a > b,Xy: a > b] :
( ! [Xx0: a] :
( ( Xp @ Xx0 )
=> ( Xe @ Xx0 @ Xx @ Xy ) )
=> ! [Xx0: a] :
( ( Xp @ Xx0 )
=> ( Xe @ Xx0 @ Xy @ Xx ) ) )
& ! [Xx: a > b,Xy: a > b,Xz: a > b] :
( ( ! [Xx0: a] :
( ( Xp @ Xx0 )
=> ( Xe @ Xx0 @ Xx @ Xy ) )
& ! [Xx0: a] :
( ( Xp @ Xx0 )
=> ( Xe @ Xx0 @ Xy @ Xz ) ) )
=> ! [Xx0: a] :
( ( Xp @ Xx0 )
=> ( Xe @ Xx0 @ Xx @ Xz ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xp: a > $o,Xe: a > ( a > b ) > ( a > b ) > $o] :
( ! [Xx: a] :
( ( Xp @ Xx )
=> ( ! [Xx0: a > b] : ( Xe @ Xx @ Xx0 @ Xx0 )
& ! [Xx0: a > b,Xy: a > b] :
( ( Xe @ Xx @ Xx0 @ Xy )
=> ( Xe @ Xx @ Xy @ Xx0 ) )
& ! [Xx0: a > b,Xy: a > b,Xz: a > b] :
( ( ( Xe @ Xx @ Xx0 @ Xy )
& ( Xe @ Xx @ Xy @ Xz ) )
=> ( Xe @ Xx @ Xx0 @ Xz ) ) ) )
=> ( ! [Xx: a > b,Xx0: a] :
( ( Xp @ Xx0 )
=> ( Xe @ Xx0 @ Xx @ Xx ) )
& ! [Xx: a > b,Xy: a > b] :
( ! [Xx0: a] :
( ( Xp @ Xx0 )
=> ( Xe @ Xx0 @ Xx @ Xy ) )
=> ! [Xx0: a] :
( ( Xp @ Xx0 )
=> ( Xe @ Xx0 @ Xy @ Xx ) ) )
& ! [Xx: a > b,Xy: a > b,Xz: a > b] :
( ( ! [Xx0: a] :
( ( Xp @ Xx0 )
=> ( Xe @ Xx0 @ Xx @ Xy ) )
& ! [Xx0: a] :
( ( Xp @ Xx0 )
=> ( Xe @ Xx0 @ Xy @ Xz ) ) )
=> ! [Xx0: a] :
( ( Xp @ Xx0 )
=> ( Xe @ Xx0 @ Xx @ Xz ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY21: a > ( a > b ) > ( a > b ) > $o] :
( ! [SY22: a] :
( ( sK1_Xp @ SY22 )
=> ( ! [Xx0: a > b] : ( SY21 @ SY22 @ Xx0 @ Xx0 )
& ! [Xx0: a > b,Xy: a > b] :
( ( SY21 @ SY22 @ Xx0 @ Xy )
=> ( SY21 @ SY22 @ Xy @ Xx0 ) )
& ! [Xx0: a > b,Xy: a > b,Xz: a > b] :
( ( ( SY21 @ SY22 @ Xx0 @ Xy )
& ( SY21 @ SY22 @ Xy @ Xz ) )
=> ( SY21 @ SY22 @ Xx0 @ Xz ) ) ) )
=> ( ! [SY29: a > b,SY30: a] :
( ( sK1_Xp @ SY30 )
=> ( SY21 @ SY30 @ SY29 @ SY29 ) )
& ! [SY31: a > b,SY32: a > b] :
( ! [SY33: a] :
( ( sK1_Xp @ SY33 )
=> ( SY21 @ SY33 @ SY31 @ SY32 ) )
=> ! [SY34: a] :
( ( sK1_Xp @ SY34 )
=> ( SY21 @ SY34 @ SY32 @ SY31 ) ) )
& ! [SY35: a > b,SY36: a > b,SY37: a > b] :
( ( ! [SY38: a] :
( ( sK1_Xp @ SY38 )
=> ( SY21 @ SY38 @ SY35 @ SY36 ) )
& ! [SY39: a] :
( ( sK1_Xp @ SY39 )
=> ( SY21 @ SY39 @ SY36 @ SY37 ) ) )
=> ! [SY40: a] :
( ( sK1_Xp @ SY40 )
=> ( SY21 @ SY40 @ SY35 @ SY37 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY41: a] :
( ( sK1_Xp @ SY41 )
=> ( ! [SY42: a > b] : ( sK2_SY21 @ SY41 @ SY42 @ SY42 )
& ! [SY43: a > b,SY44: a > b] :
( ( sK2_SY21 @ SY41 @ SY43 @ SY44 )
=> ( sK2_SY21 @ SY41 @ SY44 @ SY43 ) )
& ! [SY45: a > b,SY46: a > b,SY47: a > b] :
( ( ( sK2_SY21 @ SY41 @ SY45 @ SY46 )
& ( sK2_SY21 @ SY41 @ SY46 @ SY47 ) )
=> ( sK2_SY21 @ SY41 @ SY45 @ SY47 ) ) ) )
=> ( ! [SY48: a > b,SY49: a] :
( ( sK1_Xp @ SY49 )
=> ( sK2_SY21 @ SY49 @ SY48 @ SY48 ) )
& ! [SY50: a > b,SY51: a > b] :
( ! [SY52: a] :
( ( sK1_Xp @ SY52 )
=> ( sK2_SY21 @ SY52 @ SY50 @ SY51 ) )
=> ! [SY53: a] :
( ( sK1_Xp @ SY53 )
=> ( sK2_SY21 @ SY53 @ SY51 @ SY50 ) ) )
& ! [SY54: a > b,SY55: a > b,SY56: a > b] :
( ( ! [SY57: a] :
( ( sK1_Xp @ SY57 )
=> ( sK2_SY21 @ SY57 @ SY54 @ SY55 ) )
& ! [SY58: a] :
( ( sK1_Xp @ SY58 )
=> ( sK2_SY21 @ SY58 @ SY55 @ SY56 ) ) )
=> ! [SY59: a] :
( ( sK1_Xp @ SY59 )
=> ( sK2_SY21 @ SY59 @ SY54 @ SY56 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY41: a] :
( ( sK1_Xp @ SY41 )
=> ( ! [SY42: a > b] : ( sK2_SY21 @ SY41 @ SY42 @ SY42 )
& ! [SY43: a > b,SY44: a > b] :
( ( sK2_SY21 @ SY41 @ SY43 @ SY44 )
=> ( sK2_SY21 @ SY41 @ SY44 @ SY43 ) )
& ! [SY45: a > b,SY46: a > b,SY47: a > b] :
( ( ( sK2_SY21 @ SY41 @ SY45 @ SY46 )
& ( sK2_SY21 @ SY41 @ SY46 @ SY47 ) )
=> ( sK2_SY21 @ SY41 @ SY45 @ SY47 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SY48: a > b,SY49: a] :
( ( sK1_Xp @ SY49 )
=> ( sK2_SY21 @ SY49 @ SY48 @ SY48 ) )
& ! [SY50: a > b,SY51: a > b] :
( ! [SY52: a] :
( ( sK1_Xp @ SY52 )
=> ( sK2_SY21 @ SY52 @ SY50 @ SY51 ) )
=> ! [SY53: a] :
( ( sK1_Xp @ SY53 )
=> ( sK2_SY21 @ SY53 @ SY51 @ SY50 ) ) )
& ! [SY54: a > b,SY55: a > b,SY56: a > b] :
( ( ! [SY57: a] :
( ( sK1_Xp @ SY57 )
=> ( sK2_SY21 @ SY57 @ SY54 @ SY55 ) )
& ! [SY58: a] :
( ( sK1_Xp @ SY58 )
=> ( sK2_SY21 @ SY58 @ SY55 @ SY56 ) ) )
=> ! [SY59: a] :
( ( sK1_Xp @ SY59 )
=> ( sK2_SY21 @ SY59 @ SY54 @ SY56 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(8,plain,
( ( ! [SY48: a > b,SY49: a] :
( ( sK1_Xp @ SY49 )
=> ( sK2_SY21 @ SY49 @ SY48 @ SY48 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[7]) ).
thf(9,plain,
( ( ! [SY50: a > b,SY51: a > b] :
( ! [SY52: a] :
( ( sK1_Xp @ SY52 )
=> ( sK2_SY21 @ SY52 @ SY50 @ SY51 ) )
=> ! [SY53: a] :
( ( sK1_Xp @ SY53 )
=> ( sK2_SY21 @ SY53 @ SY51 @ SY50 ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[7]) ).
thf(10,plain,
( ( ! [SY54: a > b,SY55: a > b,SY56: a > b] :
( ( ! [SY57: a] :
( ( sK1_Xp @ SY57 )
=> ( sK2_SY21 @ SY57 @ SY54 @ SY55 ) )
& ! [SY58: a] :
( ( sK1_Xp @ SY58 )
=> ( sK2_SY21 @ SY58 @ SY55 @ SY56 ) ) )
=> ! [SY59: a] :
( ( sK1_Xp @ SY59 )
=> ( sK2_SY21 @ SY59 @ SY54 @ SY56 ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[7]) ).
thf(11,plain,
( ( ~ ! [SY48: a > b,SY49: a] :
( ( sK1_Xp @ SY49 )
=> ( sK2_SY21 @ SY49 @ SY48 @ SY48 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(12,plain,
( ( ~ ! [SY50: a > b,SY51: a > b] :
( ! [SY52: a] :
( ( sK1_Xp @ SY52 )
=> ( sK2_SY21 @ SY52 @ SY50 @ SY51 ) )
=> ! [SY53: a] :
( ( sK1_Xp @ SY53 )
=> ( sK2_SY21 @ SY53 @ SY51 @ SY50 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(13,plain,
( ( ~ ! [SY54: a > b,SY55: a > b,SY56: a > b] :
( ( ! [SY57: a] :
( ( sK1_Xp @ SY57 )
=> ( sK2_SY21 @ SY57 @ SY54 @ SY55 ) )
& ! [SY58: a] :
( ( sK1_Xp @ SY58 )
=> ( sK2_SY21 @ SY58 @ SY55 @ SY56 ) ) )
=> ! [SY59: a] :
( ( sK1_Xp @ SY59 )
=> ( sK2_SY21 @ SY59 @ SY54 @ SY56 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(14,plain,
( ( ! [SY41: a] :
( ( sK1_Xp @ SY41 )
=> ( ! [SY42: a > b] : ( sK2_SY21 @ SY41 @ SY42 @ SY42 )
& ! [SY43: a > b,SY44: a > b] :
( ( sK2_SY21 @ SY41 @ SY43 @ SY44 )
=> ( sK2_SY21 @ SY41 @ SY44 @ SY43 ) )
& ! [SY45: a > b,SY46: a > b,SY47: a > b] :
( ( ( sK2_SY21 @ SY41 @ SY45 @ SY46 )
& ( sK2_SY21 @ SY41 @ SY46 @ SY47 ) )
=> ( sK2_SY21 @ SY41 @ SY45 @ SY47 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(15,plain,
( ( ~ ! [SY48: a > b,SY49: a] :
( ( sK1_Xp @ SY49 )
=> ( sK2_SY21 @ SY49 @ SY48 @ SY48 ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(16,plain,
( ( ! [SX0: a] :
( ~ ( sK1_Xp @ SX0 )
| ~ ( ~ ~ ( ~ ! [SX1: a > b] : ( sK2_SY21 @ SX0 @ SX1 @ SX1 )
| ~ ! [SX1: a > b,SX2: a > b] :
( ~ ( sK2_SY21 @ SX0 @ SX1 @ SX2 )
| ( sK2_SY21 @ SX0 @ SX2 @ SX1 ) ) )
| ~ ! [SX1: a > b,SX2: a > b,SX3: a > b] :
( ~ ~ ( ~ ( sK2_SY21 @ SX0 @ SX1 @ SX2 )
| ~ ( sK2_SY21 @ SX0 @ SX2 @ SX3 ) )
| ( sK2_SY21 @ SX0 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ! [SX0: a > b,SX1: a] :
( ~ ( sK1_Xp @ SX1 )
| ( sK2_SY21 @ SX1 @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(18,plain,
! [SV1: a] :
( ( ~ ( sK1_Xp @ SV1 )
| ~ ( ~ ~ ( ~ ! [SY60: a > b] : ( sK2_SY21 @ SV1 @ SY60 @ SY60 )
| ~ ! [SY61: a > b,SY62: a > b] :
( ~ ( sK2_SY21 @ SV1 @ SY61 @ SY62 )
| ( sK2_SY21 @ SV1 @ SY62 @ SY61 ) ) )
| ~ ! [SY63: a > b,SY64: a > b,SY65: a > b] :
( ~ ~ ( ~ ( sK2_SY21 @ SV1 @ SY63 @ SY64 )
| ~ ( sK2_SY21 @ SV1 @ SY64 @ SY65 ) )
| ( sK2_SY21 @ SV1 @ SY63 @ SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ! [SX0: a > b,SX1: a] :
( ~ ( sK1_Xp @ SX1 )
| ( sK2_SY21 @ SX1 @ SX0 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(20,plain,
! [SV1: a] :
( ( ( ~ ( sK1_Xp @ SV1 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY60: a > b] : ( sK2_SY21 @ SV1 @ SY60 @ SY60 )
| ~ ! [SY61: a > b,SY62: a > b] :
( ~ ( sK2_SY21 @ SV1 @ SY61 @ SY62 )
| ( sK2_SY21 @ SV1 @ SY62 @ SY61 ) ) )
| ~ ! [SY63: a > b,SY64: a > b,SY65: a > b] :
( ~ ~ ( ~ ( sK2_SY21 @ SV1 @ SY63 @ SY64 )
| ~ ( sK2_SY21 @ SV1 @ SY64 @ SY65 ) )
| ( sK2_SY21 @ SV1 @ SY63 @ SY65 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(21,plain,
( ( ! [SY66: a] :
( ~ ( sK1_Xp @ SY66 )
| ( sK2_SY21 @ SY66 @ sK3_SX0 @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[19]) ).
thf(22,plain,
! [SV1: a] :
( ( ( sK1_Xp @ SV1 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY60: a > b] : ( sK2_SY21 @ SV1 @ SY60 @ SY60 )
| ~ ! [SY61: a > b,SY62: a > b] :
( ~ ( sK2_SY21 @ SV1 @ SY61 @ SY62 )
| ( sK2_SY21 @ SV1 @ SY62 @ SY61 ) ) )
| ~ ! [SY63: a > b,SY64: a > b,SY65: a > b] :
( ~ ~ ( ~ ( sK2_SY21 @ SV1 @ SY63 @ SY64 )
| ~ ( sK2_SY21 @ SV1 @ SY64 @ SY65 ) )
| ( sK2_SY21 @ SV1 @ SY63 @ SY65 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(23,plain,
( ( ~ ( sK1_Xp @ sK4_SY66 )
| ( sK2_SY21 @ sK4_SY66 @ sK3_SX0 @ sK3_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[21]) ).
thf(24,plain,
! [SV1: a] :
( ( ( ~ ~ ( ~ ! [SY60: a > b] : ( sK2_SY21 @ SV1 @ SY60 @ SY60 )
| ~ ! [SY61: a > b,SY62: a > b] :
( ~ ( sK2_SY21 @ SV1 @ SY61 @ SY62 )
| ( sK2_SY21 @ SV1 @ SY62 @ SY61 ) ) )
| ~ ! [SY63: a > b,SY64: a > b,SY65: a > b] :
( ~ ~ ( ~ ( sK2_SY21 @ SV1 @ SY63 @ SY64 )
| ~ ( sK2_SY21 @ SV1 @ SY64 @ SY65 ) )
| ( sK2_SY21 @ SV1 @ SY63 @ SY65 ) ) )
= $false )
| ( ( sK1_Xp @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(25,plain,
( ( ~ ( sK1_Xp @ sK4_SY66 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(26,plain,
( ( sK2_SY21 @ sK4_SY66 @ sK3_SX0 @ sK3_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(27,plain,
! [SV1: a] :
( ( ( ~ ~ ( ~ ! [SY60: a > b] : ( sK2_SY21 @ SV1 @ SY60 @ SY60 )
| ~ ! [SY61: a > b,SY62: a > b] :
( ~ ( sK2_SY21 @ SV1 @ SY61 @ SY62 )
| ( sK2_SY21 @ SV1 @ SY62 @ SY61 ) ) ) )
= $false )
| ( ( sK1_Xp @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(28,plain,
! [SV1: a] :
( ( ( ~ ! [SY63: a > b,SY64: a > b,SY65: a > b] :
( ~ ~ ( ~ ( sK2_SY21 @ SV1 @ SY63 @ SY64 )
| ~ ( sK2_SY21 @ SV1 @ SY64 @ SY65 ) )
| ( sK2_SY21 @ SV1 @ SY63 @ SY65 ) ) )
= $false )
| ( ( sK1_Xp @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(29,plain,
( ( sK1_Xp @ sK4_SY66 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(30,plain,
! [SV1: a] :
( ( ( ~ ( ~ ! [SY60: a > b] : ( sK2_SY21 @ SV1 @ SY60 @ SY60 )
| ~ ! [SY61: a > b,SY62: a > b] :
( ~ ( sK2_SY21 @ SV1 @ SY61 @ SY62 )
| ( sK2_SY21 @ SV1 @ SY62 @ SY61 ) ) ) )
= $true )
| ( ( sK1_Xp @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(31,plain,
! [SV1: a] :
( ( ( ! [SY63: a > b,SY64: a > b,SY65: a > b] :
( ~ ~ ( ~ ( sK2_SY21 @ SV1 @ SY63 @ SY64 )
| ~ ( sK2_SY21 @ SV1 @ SY64 @ SY65 ) )
| ( sK2_SY21 @ SV1 @ SY63 @ SY65 ) ) )
= $true )
| ( ( sK1_Xp @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(32,plain,
! [SV1: a] :
( ( ( ~ ! [SY60: a > b] : ( sK2_SY21 @ SV1 @ SY60 @ SY60 )
| ~ ! [SY61: a > b,SY62: a > b] :
( ~ ( sK2_SY21 @ SV1 @ SY61 @ SY62 )
| ( sK2_SY21 @ SV1 @ SY62 @ SY61 ) ) )
= $false )
| ( ( sK1_Xp @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(33,plain,
! [SV2: a > b,SV1: a] :
( ( ( ! [SY67: a > b,SY68: a > b] :
( ~ ~ ( ~ ( sK2_SY21 @ SV1 @ SV2 @ SY67 )
| ~ ( sK2_SY21 @ SV1 @ SY67 @ SY68 ) )
| ( sK2_SY21 @ SV1 @ SV2 @ SY68 ) ) )
= $true )
| ( ( sK1_Xp @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV1: a] :
( ( ( ~ ! [SY60: a > b] : ( sK2_SY21 @ SV1 @ SY60 @ SY60 ) )
= $false )
| ( ( sK1_Xp @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(35,plain,
! [SV1: a] :
( ( ( ~ ! [SY61: a > b,SY62: a > b] :
( ~ ( sK2_SY21 @ SV1 @ SY61 @ SY62 )
| ( sK2_SY21 @ SV1 @ SY62 @ SY61 ) ) )
= $false )
| ( ( sK1_Xp @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(36,plain,
! [SV3: a > b,SV2: a > b,SV1: a] :
( ( ( ! [SY69: a > b] :
( ~ ~ ( ~ ( sK2_SY21 @ SV1 @ SV2 @ SV3 )
| ~ ( sK2_SY21 @ SV1 @ SV3 @ SY69 ) )
| ( sK2_SY21 @ SV1 @ SV2 @ SY69 ) ) )
= $true )
| ( ( sK1_Xp @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV1: a] :
( ( ( ! [SY60: a > b] : ( sK2_SY21 @ SV1 @ SY60 @ SY60 ) )
= $true )
| ( ( sK1_Xp @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(38,plain,
! [SV1: a] :
( ( ( ! [SY61: a > b,SY62: a > b] :
( ~ ( sK2_SY21 @ SV1 @ SY61 @ SY62 )
| ( sK2_SY21 @ SV1 @ SY62 @ SY61 ) ) )
= $true )
| ( ( sK1_Xp @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(39,plain,
! [SV4: a > b,SV3: a > b,SV2: a > b,SV1: a] :
( ( ( ~ ~ ( ~ ( sK2_SY21 @ SV1 @ SV2 @ SV3 )
| ~ ( sK2_SY21 @ SV1 @ SV3 @ SV4 ) )
| ( sK2_SY21 @ SV1 @ SV2 @ SV4 ) )
= $true )
| ( ( sK1_Xp @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV5: a > b,SV1: a] :
( ( ( sK2_SY21 @ SV1 @ SV5 @ SV5 )
= $true )
| ( ( sK1_Xp @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV6: a > b,SV1: a] :
( ( ( ! [SY70: a > b] :
( ~ ( sK2_SY21 @ SV1 @ SV6 @ SY70 )
| ( sK2_SY21 @ SV1 @ SY70 @ SV6 ) ) )
= $true )
| ( ( sK1_Xp @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(42,plain,
! [SV4: a > b,SV3: a > b,SV2: a > b,SV1: a] :
( ( ( ~ ~ ( ~ ( sK2_SY21 @ SV1 @ SV2 @ SV3 )
| ~ ( sK2_SY21 @ SV1 @ SV3 @ SV4 ) ) )
= $true )
| ( ( sK2_SY21 @ SV1 @ SV2 @ SV4 )
= $true )
| ( ( sK1_Xp @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV7: a > b,SV6: a > b,SV1: a] :
( ( ( ~ ( sK2_SY21 @ SV1 @ SV6 @ SV7 )
| ( sK2_SY21 @ SV1 @ SV7 @ SV6 ) )
= $true )
| ( ( sK1_Xp @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(44,plain,
! [SV4: a > b,SV3: a > b,SV2: a > b,SV1: a] :
( ( ( ~ ( ~ ( sK2_SY21 @ SV1 @ SV2 @ SV3 )
| ~ ( sK2_SY21 @ SV1 @ SV3 @ SV4 ) ) )
= $false )
| ( ( sK2_SY21 @ SV1 @ SV2 @ SV4 )
= $true )
| ( ( sK1_Xp @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(45,plain,
! [SV7: a > b,SV6: a > b,SV1: a] :
( ( ( ~ ( sK2_SY21 @ SV1 @ SV6 @ SV7 ) )
= $true )
| ( ( sK2_SY21 @ SV1 @ SV7 @ SV6 )
= $true )
| ( ( sK1_Xp @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(46,plain,
! [SV4: a > b,SV3: a > b,SV2: a > b,SV1: a] :
( ( ( ~ ( sK2_SY21 @ SV1 @ SV2 @ SV3 )
| ~ ( sK2_SY21 @ SV1 @ SV3 @ SV4 ) )
= $true )
| ( ( sK2_SY21 @ SV1 @ SV2 @ SV4 )
= $true )
| ( ( sK1_Xp @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(47,plain,
! [SV7: a > b,SV6: a > b,SV1: a] :
( ( ( sK2_SY21 @ SV1 @ SV6 @ SV7 )
= $false )
| ( ( sK2_SY21 @ SV1 @ SV7 @ SV6 )
= $true )
| ( ( sK1_Xp @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(48,plain,
! [SV4: a > b,SV3: a > b,SV2: a > b,SV1: a] :
( ( ( ~ ( sK2_SY21 @ SV1 @ SV2 @ SV3 ) )
= $true )
| ( ( ~ ( sK2_SY21 @ SV1 @ SV3 @ SV4 ) )
= $true )
| ( ( sK2_SY21 @ SV1 @ SV2 @ SV4 )
= $true )
| ( ( sK1_Xp @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(49,plain,
! [SV4: a > b,SV3: a > b,SV2: a > b,SV1: a] :
( ( ( sK2_SY21 @ SV1 @ SV2 @ SV3 )
= $false )
| ( ( ~ ( sK2_SY21 @ SV1 @ SV3 @ SV4 ) )
= $true )
| ( ( sK2_SY21 @ SV1 @ SV2 @ SV4 )
= $true )
| ( ( sK1_Xp @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(50,plain,
! [SV2: a > b,SV4: a > b,SV3: a > b,SV1: a] :
( ( ( sK2_SY21 @ SV1 @ SV3 @ SV4 )
= $false )
| ( ( sK2_SY21 @ SV1 @ SV2 @ SV3 )
= $false )
| ( ( sK2_SY21 @ SV1 @ SV2 @ SV4 )
= $true )
| ( ( sK1_Xp @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(51,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[26,50,47,40,29]) ).
thf(52,plain,
( ( ! [SY41: a] :
( ( sK1_Xp @ SY41 )
=> ( ! [SY42: a > b] : ( sK2_SY21 @ SY41 @ SY42 @ SY42 )
& ! [SY43: a > b,SY44: a > b] :
( ( sK2_SY21 @ SY41 @ SY43 @ SY44 )
=> ( sK2_SY21 @ SY41 @ SY44 @ SY43 ) )
& ! [SY45: a > b,SY46: a > b,SY47: a > b] :
( ( ( sK2_SY21 @ SY41 @ SY45 @ SY46 )
& ( sK2_SY21 @ SY41 @ SY46 @ SY47 ) )
=> ( sK2_SY21 @ SY41 @ SY45 @ SY47 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(53,plain,
( ( ~ ! [SY50: a > b,SY51: a > b] :
( ! [SY52: a] :
( ( sK1_Xp @ SY52 )
=> ( sK2_SY21 @ SY52 @ SY50 @ SY51 ) )
=> ! [SY53: a] :
( ( sK1_Xp @ SY53 )
=> ( sK2_SY21 @ SY53 @ SY51 @ SY50 ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(54,plain,
( ( ~ ! [SX0: a > b,SX1: a > b] :
( ~ ! [SX2: a] :
( ~ ( sK1_Xp @ SX2 )
| ( sK2_SY21 @ SX2 @ SX0 @ SX1 ) )
| ! [SX2: a] :
( ~ ( sK1_Xp @ SX2 )
| ( sK2_SY21 @ SX2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(55,plain,
( ( ! [SX0: a] :
( ~ ( sK1_Xp @ SX0 )
| ~ ( ~ ~ ( ~ ! [SX1: a > b] : ( sK2_SY21 @ SX0 @ SX1 @ SX1 )
| ~ ! [SX1: a > b,SX2: a > b] :
( ~ ( sK2_SY21 @ SX0 @ SX1 @ SX2 )
| ( sK2_SY21 @ SX0 @ SX2 @ SX1 ) ) )
| ~ ! [SX1: a > b,SX2: a > b,SX3: a > b] :
( ~ ~ ( ~ ( sK2_SY21 @ SX0 @ SX1 @ SX2 )
| ~ ( sK2_SY21 @ SX0 @ SX2 @ SX3 ) )
| ( sK2_SY21 @ SX0 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(56,plain,
( ( ! [SX0: a > b,SX1: a > b] :
( ~ ! [SX2: a] :
( ~ ( sK1_Xp @ SX2 )
| ( sK2_SY21 @ SX2 @ SX0 @ SX1 ) )
| ! [SX2: a] :
( ~ ( sK1_Xp @ SX2 )
| ( sK2_SY21 @ SX2 @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(57,plain,
! [SV8: a] :
( ( ~ ( sK1_Xp @ SV8 )
| ~ ( ~ ~ ( ~ ! [SY71: a > b] : ( sK2_SY21 @ SV8 @ SY71 @ SY71 )
| ~ ! [SY72: a > b,SY73: a > b] :
( ~ ( sK2_SY21 @ SV8 @ SY72 @ SY73 )
| ( sK2_SY21 @ SV8 @ SY73 @ SY72 ) ) )
| ~ ! [SY74: a > b,SY75: a > b,SY76: a > b] :
( ~ ~ ( ~ ( sK2_SY21 @ SV8 @ SY74 @ SY75 )
| ~ ( sK2_SY21 @ SV8 @ SY75 @ SY76 ) )
| ( sK2_SY21 @ SV8 @ SY74 @ SY76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(58,plain,
( ( ! [SY77: a > b] :
( ~ ! [SY78: a] :
( ~ ( sK1_Xp @ SY78 )
| ( sK2_SY21 @ SY78 @ sK5_SX0 @ SY77 ) )
| ! [SY79: a] :
( ~ ( sK1_Xp @ SY79 )
| ( sK2_SY21 @ SY79 @ SY77 @ sK5_SX0 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[56]) ).
thf(59,plain,
! [SV8: a] :
( ( ( ~ ( sK1_Xp @ SV8 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY71: a > b] : ( sK2_SY21 @ SV8 @ SY71 @ SY71 )
| ~ ! [SY72: a > b,SY73: a > b] :
( ~ ( sK2_SY21 @ SV8 @ SY72 @ SY73 )
| ( sK2_SY21 @ SV8 @ SY73 @ SY72 ) ) )
| ~ ! [SY74: a > b,SY75: a > b,SY76: a > b] :
( ~ ~ ( ~ ( sK2_SY21 @ SV8 @ SY74 @ SY75 )
| ~ ( sK2_SY21 @ SV8 @ SY75 @ SY76 ) )
| ( sK2_SY21 @ SV8 @ SY74 @ SY76 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(60,plain,
( ( ~ ! [SY80: a] :
( ~ ( sK1_Xp @ SY80 )
| ( sK2_SY21 @ SY80 @ sK5_SX0 @ sK6_SY77 ) )
| ! [SY81: a] :
( ~ ( sK1_Xp @ SY81 )
| ( sK2_SY21 @ SY81 @ sK6_SY77 @ sK5_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[58]) ).
thf(61,plain,
! [SV8: a] :
( ( ( sK1_Xp @ SV8 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY71: a > b] : ( sK2_SY21 @ SV8 @ SY71 @ SY71 )
| ~ ! [SY72: a > b,SY73: a > b] :
( ~ ( sK2_SY21 @ SV8 @ SY72 @ SY73 )
| ( sK2_SY21 @ SV8 @ SY73 @ SY72 ) ) )
| ~ ! [SY74: a > b,SY75: a > b,SY76: a > b] :
( ~ ~ ( ~ ( sK2_SY21 @ SV8 @ SY74 @ SY75 )
| ~ ( sK2_SY21 @ SV8 @ SY75 @ SY76 ) )
| ( sK2_SY21 @ SV8 @ SY74 @ SY76 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(62,plain,
( ( ~ ! [SY80: a] :
( ~ ( sK1_Xp @ SY80 )
| ( sK2_SY21 @ SY80 @ sK5_SX0 @ sK6_SY77 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(63,plain,
( ( ! [SY81: a] :
( ~ ( sK1_Xp @ SY81 )
| ( sK2_SY21 @ SY81 @ sK6_SY77 @ sK5_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(64,plain,
! [SV8: a] :
( ( ( ~ ~ ( ~ ! [SY71: a > b] : ( sK2_SY21 @ SV8 @ SY71 @ SY71 )
| ~ ! [SY72: a > b,SY73: a > b] :
( ~ ( sK2_SY21 @ SV8 @ SY72 @ SY73 )
| ( sK2_SY21 @ SV8 @ SY73 @ SY72 ) ) )
| ~ ! [SY74: a > b,SY75: a > b,SY76: a > b] :
( ~ ~ ( ~ ( sK2_SY21 @ SV8 @ SY74 @ SY75 )
| ~ ( sK2_SY21 @ SV8 @ SY75 @ SY76 ) )
| ( sK2_SY21 @ SV8 @ SY74 @ SY76 ) ) )
= $false )
| ( ( sK1_Xp @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(65,plain,
( ( ! [SY80: a] :
( ~ ( sK1_Xp @ SY80 )
| ( sK2_SY21 @ SY80 @ sK5_SX0 @ sK6_SY77 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(66,plain,
( ( ~ ( sK1_Xp @ sK7_SY81 )
| ( sK2_SY21 @ sK7_SY81 @ sK6_SY77 @ sK5_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[63]) ).
thf(67,plain,
! [SV8: a] :
( ( ( ~ ~ ( ~ ! [SY71: a > b] : ( sK2_SY21 @ SV8 @ SY71 @ SY71 )
| ~ ! [SY72: a > b,SY73: a > b] :
( ~ ( sK2_SY21 @ SV8 @ SY72 @ SY73 )
| ( sK2_SY21 @ SV8 @ SY73 @ SY72 ) ) ) )
= $false )
| ( ( sK1_Xp @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(68,plain,
! [SV8: a] :
( ( ( ~ ! [SY74: a > b,SY75: a > b,SY76: a > b] :
( ~ ~ ( ~ ( sK2_SY21 @ SV8 @ SY74 @ SY75 )
| ~ ( sK2_SY21 @ SV8 @ SY75 @ SY76 ) )
| ( sK2_SY21 @ SV8 @ SY74 @ SY76 ) ) )
= $false )
| ( ( sK1_Xp @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(69,plain,
! [SV9: a] :
( ( ~ ( sK1_Xp @ SV9 )
| ( sK2_SY21 @ SV9 @ sK5_SX0 @ sK6_SY77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(70,plain,
( ( ~ ( sK1_Xp @ sK7_SY81 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(71,plain,
( ( sK2_SY21 @ sK7_SY81 @ sK6_SY77 @ sK5_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(72,plain,
! [SV8: a] :
( ( ( ~ ( ~ ! [SY71: a > b] : ( sK2_SY21 @ SV8 @ SY71 @ SY71 )
| ~ ! [SY72: a > b,SY73: a > b] :
( ~ ( sK2_SY21 @ SV8 @ SY72 @ SY73 )
| ( sK2_SY21 @ SV8 @ SY73 @ SY72 ) ) ) )
= $true )
| ( ( sK1_Xp @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(73,plain,
! [SV8: a] :
( ( ( ! [SY74: a > b,SY75: a > b,SY76: a > b] :
( ~ ~ ( ~ ( sK2_SY21 @ SV8 @ SY74 @ SY75 )
| ~ ( sK2_SY21 @ SV8 @ SY75 @ SY76 ) )
| ( sK2_SY21 @ SV8 @ SY74 @ SY76 ) ) )
= $true )
| ( ( sK1_Xp @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(74,plain,
! [SV9: a] :
( ( ( ~ ( sK1_Xp @ SV9 ) )
= $true )
| ( ( sK2_SY21 @ SV9 @ sK5_SX0 @ sK6_SY77 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(75,plain,
( ( sK1_Xp @ sK7_SY81 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(76,plain,
! [SV8: a] :
( ( ( ~ ! [SY71: a > b] : ( sK2_SY21 @ SV8 @ SY71 @ SY71 )
| ~ ! [SY72: a > b,SY73: a > b] :
( ~ ( sK2_SY21 @ SV8 @ SY72 @ SY73 )
| ( sK2_SY21 @ SV8 @ SY73 @ SY72 ) ) )
= $false )
| ( ( sK1_Xp @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(77,plain,
! [SV10: a > b,SV8: a] :
( ( ( ! [SY82: a > b,SY83: a > b] :
( ~ ~ ( ~ ( sK2_SY21 @ SV8 @ SV10 @ SY82 )
| ~ ( sK2_SY21 @ SV8 @ SY82 @ SY83 ) )
| ( sK2_SY21 @ SV8 @ SV10 @ SY83 ) ) )
= $true )
| ( ( sK1_Xp @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(78,plain,
! [SV9: a] :
( ( ( sK1_Xp @ SV9 )
= $false )
| ( ( sK2_SY21 @ SV9 @ sK5_SX0 @ sK6_SY77 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(79,plain,
! [SV8: a] :
( ( ( ~ ! [SY71: a > b] : ( sK2_SY21 @ SV8 @ SY71 @ SY71 ) )
= $false )
| ( ( sK1_Xp @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(80,plain,
! [SV8: a] :
( ( ( ~ ! [SY72: a > b,SY73: a > b] :
( ~ ( sK2_SY21 @ SV8 @ SY72 @ SY73 )
| ( sK2_SY21 @ SV8 @ SY73 @ SY72 ) ) )
= $false )
| ( ( sK1_Xp @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(81,plain,
! [SV11: a > b,SV10: a > b,SV8: a] :
( ( ( ! [SY84: a > b] :
( ~ ~ ( ~ ( sK2_SY21 @ SV8 @ SV10 @ SV11 )
| ~ ( sK2_SY21 @ SV8 @ SV11 @ SY84 ) )
| ( sK2_SY21 @ SV8 @ SV10 @ SY84 ) ) )
= $true )
| ( ( sK1_Xp @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(82,plain,
! [SV8: a] :
( ( ( ! [SY71: a > b] : ( sK2_SY21 @ SV8 @ SY71 @ SY71 ) )
= $true )
| ( ( sK1_Xp @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(83,plain,
! [SV8: a] :
( ( ( ! [SY72: a > b,SY73: a > b] :
( ~ ( sK2_SY21 @ SV8 @ SY72 @ SY73 )
| ( sK2_SY21 @ SV8 @ SY73 @ SY72 ) ) )
= $true )
| ( ( sK1_Xp @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(84,plain,
! [SV12: a > b,SV11: a > b,SV10: a > b,SV8: a] :
( ( ( ~ ~ ( ~ ( sK2_SY21 @ SV8 @ SV10 @ SV11 )
| ~ ( sK2_SY21 @ SV8 @ SV11 @ SV12 ) )
| ( sK2_SY21 @ SV8 @ SV10 @ SV12 ) )
= $true )
| ( ( sK1_Xp @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(85,plain,
! [SV13: a > b,SV8: a] :
( ( ( sK2_SY21 @ SV8 @ SV13 @ SV13 )
= $true )
| ( ( sK1_Xp @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(86,plain,
! [SV14: a > b,SV8: a] :
( ( ( ! [SY85: a > b] :
( ~ ( sK2_SY21 @ SV8 @ SV14 @ SY85 )
| ( sK2_SY21 @ SV8 @ SY85 @ SV14 ) ) )
= $true )
| ( ( sK1_Xp @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(87,plain,
! [SV12: a > b,SV11: a > b,SV10: a > b,SV8: a] :
( ( ( ~ ~ ( ~ ( sK2_SY21 @ SV8 @ SV10 @ SV11 )
| ~ ( sK2_SY21 @ SV8 @ SV11 @ SV12 ) ) )
= $true )
| ( ( sK2_SY21 @ SV8 @ SV10 @ SV12 )
= $true )
| ( ( sK1_Xp @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(88,plain,
! [SV15: a > b,SV14: a > b,SV8: a] :
( ( ( ~ ( sK2_SY21 @ SV8 @ SV14 @ SV15 )
| ( sK2_SY21 @ SV8 @ SV15 @ SV14 ) )
= $true )
| ( ( sK1_Xp @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(89,plain,
! [SV12: a > b,SV11: a > b,SV10: a > b,SV8: a] :
( ( ( ~ ( ~ ( sK2_SY21 @ SV8 @ SV10 @ SV11 )
| ~ ( sK2_SY21 @ SV8 @ SV11 @ SV12 ) ) )
= $false )
| ( ( sK2_SY21 @ SV8 @ SV10 @ SV12 )
= $true )
| ( ( sK1_Xp @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(90,plain,
! [SV15: a > b,SV14: a > b,SV8: a] :
( ( ( ~ ( sK2_SY21 @ SV8 @ SV14 @ SV15 ) )
= $true )
| ( ( sK2_SY21 @ SV8 @ SV15 @ SV14 )
= $true )
| ( ( sK1_Xp @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(91,plain,
! [SV12: a > b,SV11: a > b,SV10: a > b,SV8: a] :
( ( ( ~ ( sK2_SY21 @ SV8 @ SV10 @ SV11 )
| ~ ( sK2_SY21 @ SV8 @ SV11 @ SV12 ) )
= $true )
| ( ( sK2_SY21 @ SV8 @ SV10 @ SV12 )
= $true )
| ( ( sK1_Xp @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(92,plain,
! [SV15: a > b,SV14: a > b,SV8: a] :
( ( ( sK2_SY21 @ SV8 @ SV14 @ SV15 )
= $false )
| ( ( sK2_SY21 @ SV8 @ SV15 @ SV14 )
= $true )
| ( ( sK1_Xp @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(93,plain,
! [SV12: a > b,SV11: a > b,SV10: a > b,SV8: a] :
( ( ( ~ ( sK2_SY21 @ SV8 @ SV10 @ SV11 ) )
= $true )
| ( ( ~ ( sK2_SY21 @ SV8 @ SV11 @ SV12 ) )
= $true )
| ( ( sK2_SY21 @ SV8 @ SV10 @ SV12 )
= $true )
| ( ( sK1_Xp @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(94,plain,
! [SV12: a > b,SV11: a > b,SV10: a > b,SV8: a] :
( ( ( sK2_SY21 @ SV8 @ SV10 @ SV11 )
= $false )
| ( ( ~ ( sK2_SY21 @ SV8 @ SV11 @ SV12 ) )
= $true )
| ( ( sK2_SY21 @ SV8 @ SV10 @ SV12 )
= $true )
| ( ( sK1_Xp @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(95,plain,
! [SV10: a > b,SV12: a > b,SV11: a > b,SV8: a] :
( ( ( sK2_SY21 @ SV8 @ SV11 @ SV12 )
= $false )
| ( ( sK2_SY21 @ SV8 @ SV10 @ SV11 )
= $false )
| ( ( sK2_SY21 @ SV8 @ SV10 @ SV12 )
= $true )
| ( ( sK1_Xp @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(96,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[71,95,92,85,78,75]) ).
thf(97,plain,
( ( ! [SY41: a] :
( ( sK1_Xp @ SY41 )
=> ( ! [SY42: a > b] : ( sK2_SY21 @ SY41 @ SY42 @ SY42 )
& ! [SY43: a > b,SY44: a > b] :
( ( sK2_SY21 @ SY41 @ SY43 @ SY44 )
=> ( sK2_SY21 @ SY41 @ SY44 @ SY43 ) )
& ! [SY45: a > b,SY46: a > b,SY47: a > b] :
( ( ( sK2_SY21 @ SY41 @ SY45 @ SY46 )
& ( sK2_SY21 @ SY41 @ SY46 @ SY47 ) )
=> ( sK2_SY21 @ SY41 @ SY45 @ SY47 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(98,plain,
( ( ~ ! [SY54: a > b,SY55: a > b,SY56: a > b] :
( ( ! [SY57: a] :
( ( sK1_Xp @ SY57 )
=> ( sK2_SY21 @ SY57 @ SY54 @ SY55 ) )
& ! [SY58: a] :
( ( sK1_Xp @ SY58 )
=> ( sK2_SY21 @ SY58 @ SY55 @ SY56 ) ) )
=> ! [SY59: a] :
( ( sK1_Xp @ SY59 )
=> ( sK2_SY21 @ SY59 @ SY54 @ SY56 ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(99,plain,
( ( ! [SX0: a] :
( ~ ( sK1_Xp @ SX0 )
| ~ ( ~ ~ ( ~ ! [SX1: a > b] : ( sK2_SY21 @ SX0 @ SX1 @ SX1 )
| ~ ! [SX1: a > b,SX2: a > b] :
( ~ ( sK2_SY21 @ SX0 @ SX1 @ SX2 )
| ( sK2_SY21 @ SX0 @ SX2 @ SX1 ) ) )
| ~ ! [SX1: a > b,SX2: a > b,SX3: a > b] :
( ~ ~ ( ~ ( sK2_SY21 @ SX0 @ SX1 @ SX2 )
| ~ ( sK2_SY21 @ SX0 @ SX2 @ SX3 ) )
| ( sK2_SY21 @ SX0 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(100,plain,
( ( ~ ! [SX0: a > b,SX1: a > b,SX2: a > b] :
( ~ ~ ( ~ ! [SX3: a] :
( ~ ( sK1_Xp @ SX3 )
| ( sK2_SY21 @ SX3 @ SX0 @ SX1 ) )
| ~ ! [SX3: a] :
( ~ ( sK1_Xp @ SX3 )
| ( sK2_SY21 @ SX3 @ SX1 @ SX2 ) ) )
| ! [SX3: a] :
( ~ ( sK1_Xp @ SX3 )
| ( sK2_SY21 @ SX3 @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(101,plain,
! [SV16: a] :
( ( ~ ( sK1_Xp @ SV16 )
| ~ ( ~ ~ ( ~ ! [SY86: a > b] : ( sK2_SY21 @ SV16 @ SY86 @ SY86 )
| ~ ! [SY87: a > b,SY88: a > b] :
( ~ ( sK2_SY21 @ SV16 @ SY87 @ SY88 )
| ( sK2_SY21 @ SV16 @ SY88 @ SY87 ) ) )
| ~ ! [SY89: a > b,SY90: a > b,SY91: a > b] :
( ~ ~ ( ~ ( sK2_SY21 @ SV16 @ SY89 @ SY90 )
| ~ ( sK2_SY21 @ SV16 @ SY90 @ SY91 ) )
| ( sK2_SY21 @ SV16 @ SY89 @ SY91 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(102,plain,
( ( ! [SX0: a > b,SX1: a > b,SX2: a > b] :
( ~ ~ ( ~ ! [SX3: a] :
( ~ ( sK1_Xp @ SX3 )
| ( sK2_SY21 @ SX3 @ SX0 @ SX1 ) )
| ~ ! [SX3: a] :
( ~ ( sK1_Xp @ SX3 )
| ( sK2_SY21 @ SX3 @ SX1 @ SX2 ) ) )
| ! [SX3: a] :
( ~ ( sK1_Xp @ SX3 )
| ( sK2_SY21 @ SX3 @ SX0 @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(103,plain,
! [SV16: a] :
( ( ( ~ ( sK1_Xp @ SV16 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY86: a > b] : ( sK2_SY21 @ SV16 @ SY86 @ SY86 )
| ~ ! [SY87: a > b,SY88: a > b] :
( ~ ( sK2_SY21 @ SV16 @ SY87 @ SY88 )
| ( sK2_SY21 @ SV16 @ SY88 @ SY87 ) ) )
| ~ ! [SY89: a > b,SY90: a > b,SY91: a > b] :
( ~ ~ ( ~ ( sK2_SY21 @ SV16 @ SY89 @ SY90 )
| ~ ( sK2_SY21 @ SV16 @ SY90 @ SY91 ) )
| ( sK2_SY21 @ SV16 @ SY89 @ SY91 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(104,plain,
( ( ! [SY92: a > b,SY93: a > b] :
( ~ ~ ( ~ ! [SY94: a] :
( ~ ( sK1_Xp @ SY94 )
| ( sK2_SY21 @ SY94 @ sK8_SX0 @ SY92 ) )
| ~ ! [SX3: a] :
( ~ ( sK1_Xp @ SX3 )
| ( sK2_SY21 @ SX3 @ SY92 @ SY93 ) ) )
| ! [SY96: a] :
( ~ ( sK1_Xp @ SY96 )
| ( sK2_SY21 @ SY96 @ sK8_SX0 @ SY93 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[102]) ).
thf(105,plain,
! [SV16: a] :
( ( ( sK1_Xp @ SV16 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY86: a > b] : ( sK2_SY21 @ SV16 @ SY86 @ SY86 )
| ~ ! [SY87: a > b,SY88: a > b] :
( ~ ( sK2_SY21 @ SV16 @ SY87 @ SY88 )
| ( sK2_SY21 @ SV16 @ SY88 @ SY87 ) ) )
| ~ ! [SY89: a > b,SY90: a > b,SY91: a > b] :
( ~ ~ ( ~ ( sK2_SY21 @ SV16 @ SY89 @ SY90 )
| ~ ( sK2_SY21 @ SV16 @ SY90 @ SY91 ) )
| ( sK2_SY21 @ SV16 @ SY89 @ SY91 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(106,plain,
( ( ! [SY97: a > b] :
( ~ ~ ( ~ ! [SY98: a] :
( ~ ( sK1_Xp @ SY98 )
| ( sK2_SY21 @ SY98 @ sK8_SX0 @ sK9_SY92 ) )
| ~ ! [SY99: a] :
( ~ ( sK1_Xp @ SY99 )
| ( sK2_SY21 @ SY99 @ sK9_SY92 @ SY97 ) ) )
| ! [SY96: a] :
( ~ ( sK1_Xp @ SY96 )
| ( sK2_SY21 @ SY96 @ sK8_SX0 @ SY97 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[104]) ).
thf(107,plain,
! [SV16: a] :
( ( ( ~ ~ ( ~ ! [SY86: a > b] : ( sK2_SY21 @ SV16 @ SY86 @ SY86 )
| ~ ! [SY87: a > b,SY88: a > b] :
( ~ ( sK2_SY21 @ SV16 @ SY87 @ SY88 )
| ( sK2_SY21 @ SV16 @ SY88 @ SY87 ) ) )
| ~ ! [SY89: a > b,SY90: a > b,SY91: a > b] :
( ~ ~ ( ~ ( sK2_SY21 @ SV16 @ SY89 @ SY90 )
| ~ ( sK2_SY21 @ SV16 @ SY90 @ SY91 ) )
| ( sK2_SY21 @ SV16 @ SY89 @ SY91 ) ) )
= $false )
| ( ( sK1_Xp @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(108,plain,
( ( ~ ~ ( ~ ! [SY98: a] :
( ~ ( sK1_Xp @ SY98 )
| ( sK2_SY21 @ SY98 @ sK8_SX0 @ sK9_SY92 ) )
| ~ ! [SY102: a] :
( ~ ( sK1_Xp @ SY102 )
| ( sK2_SY21 @ SY102 @ sK9_SY92 @ sK10_SY97 ) ) )
| ! [SY103: a] :
( ~ ( sK1_Xp @ SY103 )
| ( sK2_SY21 @ SY103 @ sK8_SX0 @ sK10_SY97 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[106]) ).
thf(109,plain,
! [SV16: a] :
( ( ( ~ ~ ( ~ ! [SY86: a > b] : ( sK2_SY21 @ SV16 @ SY86 @ SY86 )
| ~ ! [SY87: a > b,SY88: a > b] :
( ~ ( sK2_SY21 @ SV16 @ SY87 @ SY88 )
| ( sK2_SY21 @ SV16 @ SY88 @ SY87 ) ) ) )
= $false )
| ( ( sK1_Xp @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(110,plain,
! [SV16: a] :
( ( ( ~ ! [SY89: a > b,SY90: a > b,SY91: a > b] :
( ~ ~ ( ~ ( sK2_SY21 @ SV16 @ SY89 @ SY90 )
| ~ ( sK2_SY21 @ SV16 @ SY90 @ SY91 ) )
| ( sK2_SY21 @ SV16 @ SY89 @ SY91 ) ) )
= $false )
| ( ( sK1_Xp @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(111,plain,
( ( ~ ~ ( ~ ! [SY98: a] :
( ~ ( sK1_Xp @ SY98 )
| ( sK2_SY21 @ SY98 @ sK8_SX0 @ sK9_SY92 ) )
| ~ ! [SY102: a] :
( ~ ( sK1_Xp @ SY102 )
| ( sK2_SY21 @ SY102 @ sK9_SY92 @ sK10_SY97 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(112,plain,
( ( ! [SY103: a] :
( ~ ( sK1_Xp @ SY103 )
| ( sK2_SY21 @ SY103 @ sK8_SX0 @ sK10_SY97 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(113,plain,
! [SV16: a] :
( ( ( ~ ( ~ ! [SY86: a > b] : ( sK2_SY21 @ SV16 @ SY86 @ SY86 )
| ~ ! [SY87: a > b,SY88: a > b] :
( ~ ( sK2_SY21 @ SV16 @ SY87 @ SY88 )
| ( sK2_SY21 @ SV16 @ SY88 @ SY87 ) ) ) )
= $true )
| ( ( sK1_Xp @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(114,plain,
! [SV16: a] :
( ( ( ! [SY89: a > b,SY90: a > b,SY91: a > b] :
( ~ ~ ( ~ ( sK2_SY21 @ SV16 @ SY89 @ SY90 )
| ~ ( sK2_SY21 @ SV16 @ SY90 @ SY91 ) )
| ( sK2_SY21 @ SV16 @ SY89 @ SY91 ) ) )
= $true )
| ( ( sK1_Xp @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(115,plain,
( ( ~ ( ~ ! [SY98: a] :
( ~ ( sK1_Xp @ SY98 )
| ( sK2_SY21 @ SY98 @ sK8_SX0 @ sK9_SY92 ) )
| ~ ! [SY102: a] :
( ~ ( sK1_Xp @ SY102 )
| ( sK2_SY21 @ SY102 @ sK9_SY92 @ sK10_SY97 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(116,plain,
( ( ~ ( sK1_Xp @ sK11_SY103 )
| ( sK2_SY21 @ sK11_SY103 @ sK8_SX0 @ sK10_SY97 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[112]) ).
thf(117,plain,
! [SV16: a] :
( ( ( ~ ! [SY86: a > b] : ( sK2_SY21 @ SV16 @ SY86 @ SY86 )
| ~ ! [SY87: a > b,SY88: a > b] :
( ~ ( sK2_SY21 @ SV16 @ SY87 @ SY88 )
| ( sK2_SY21 @ SV16 @ SY88 @ SY87 ) ) )
= $false )
| ( ( sK1_Xp @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(118,plain,
! [SV17: a > b,SV16: a] :
( ( ( ! [SY104: a > b,SY105: a > b] :
( ~ ~ ( ~ ( sK2_SY21 @ SV16 @ SV17 @ SY104 )
| ~ ( sK2_SY21 @ SV16 @ SY104 @ SY105 ) )
| ( sK2_SY21 @ SV16 @ SV17 @ SY105 ) ) )
= $true )
| ( ( sK1_Xp @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(119,plain,
( ( ~ ! [SY98: a] :
( ~ ( sK1_Xp @ SY98 )
| ( sK2_SY21 @ SY98 @ sK8_SX0 @ sK9_SY92 ) )
| ~ ! [SY102: a] :
( ~ ( sK1_Xp @ SY102 )
| ( sK2_SY21 @ SY102 @ sK9_SY92 @ sK10_SY97 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(120,plain,
( ( ~ ( sK1_Xp @ sK11_SY103 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(121,plain,
( ( sK2_SY21 @ sK11_SY103 @ sK8_SX0 @ sK10_SY97 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(122,plain,
! [SV16: a] :
( ( ( ~ ! [SY86: a > b] : ( sK2_SY21 @ SV16 @ SY86 @ SY86 ) )
= $false )
| ( ( sK1_Xp @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(123,plain,
! [SV16: a] :
( ( ( ~ ! [SY87: a > b,SY88: a > b] :
( ~ ( sK2_SY21 @ SV16 @ SY87 @ SY88 )
| ( sK2_SY21 @ SV16 @ SY88 @ SY87 ) ) )
= $false )
| ( ( sK1_Xp @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(124,plain,
! [SV18: a > b,SV17: a > b,SV16: a] :
( ( ( ! [SY106: a > b] :
( ~ ~ ( ~ ( sK2_SY21 @ SV16 @ SV17 @ SV18 )
| ~ ( sK2_SY21 @ SV16 @ SV18 @ SY106 ) )
| ( sK2_SY21 @ SV16 @ SV17 @ SY106 ) ) )
= $true )
| ( ( sK1_Xp @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(125,plain,
( ( ~ ! [SY98: a] :
( ~ ( sK1_Xp @ SY98 )
| ( sK2_SY21 @ SY98 @ sK8_SX0 @ sK9_SY92 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[119]) ).
thf(126,plain,
( ( ~ ! [SY102: a] :
( ~ ( sK1_Xp @ SY102 )
| ( sK2_SY21 @ SY102 @ sK9_SY92 @ sK10_SY97 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[119]) ).
thf(127,plain,
( ( sK1_Xp @ sK11_SY103 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(128,plain,
! [SV16: a] :
( ( ( ! [SY86: a > b] : ( sK2_SY21 @ SV16 @ SY86 @ SY86 ) )
= $true )
| ( ( sK1_Xp @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(129,plain,
! [SV16: a] :
( ( ( ! [SY87: a > b,SY88: a > b] :
( ~ ( sK2_SY21 @ SV16 @ SY87 @ SY88 )
| ( sK2_SY21 @ SV16 @ SY88 @ SY87 ) ) )
= $true )
| ( ( sK1_Xp @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(130,plain,
! [SV19: a > b,SV18: a > b,SV17: a > b,SV16: a] :
( ( ( ~ ~ ( ~ ( sK2_SY21 @ SV16 @ SV17 @ SV18 )
| ~ ( sK2_SY21 @ SV16 @ SV18 @ SV19 ) )
| ( sK2_SY21 @ SV16 @ SV17 @ SV19 ) )
= $true )
| ( ( sK1_Xp @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(131,plain,
( ( ! [SY98: a] :
( ~ ( sK1_Xp @ SY98 )
| ( sK2_SY21 @ SY98 @ sK8_SX0 @ sK9_SY92 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(132,plain,
( ( ! [SY102: a] :
( ~ ( sK1_Xp @ SY102 )
| ( sK2_SY21 @ SY102 @ sK9_SY92 @ sK10_SY97 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(133,plain,
! [SV20: a > b,SV16: a] :
( ( ( sK2_SY21 @ SV16 @ SV20 @ SV20 )
= $true )
| ( ( sK1_Xp @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(134,plain,
! [SV21: a > b,SV16: a] :
( ( ( ! [SY107: a > b] :
( ~ ( sK2_SY21 @ SV16 @ SV21 @ SY107 )
| ( sK2_SY21 @ SV16 @ SY107 @ SV21 ) ) )
= $true )
| ( ( sK1_Xp @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(135,plain,
! [SV19: a > b,SV18: a > b,SV17: a > b,SV16: a] :
( ( ( ~ ~ ( ~ ( sK2_SY21 @ SV16 @ SV17 @ SV18 )
| ~ ( sK2_SY21 @ SV16 @ SV18 @ SV19 ) ) )
= $true )
| ( ( sK2_SY21 @ SV16 @ SV17 @ SV19 )
= $true )
| ( ( sK1_Xp @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(136,plain,
! [SV22: a] :
( ( ~ ( sK1_Xp @ SV22 )
| ( sK2_SY21 @ SV22 @ sK8_SX0 @ sK9_SY92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(137,plain,
! [SV23: a] :
( ( ~ ( sK1_Xp @ SV23 )
| ( sK2_SY21 @ SV23 @ sK9_SY92 @ sK10_SY97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(138,plain,
! [SV24: a > b,SV21: a > b,SV16: a] :
( ( ( ~ ( sK2_SY21 @ SV16 @ SV21 @ SV24 )
| ( sK2_SY21 @ SV16 @ SV24 @ SV21 ) )
= $true )
| ( ( sK1_Xp @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(139,plain,
! [SV19: a > b,SV18: a > b,SV17: a > b,SV16: a] :
( ( ( ~ ( ~ ( sK2_SY21 @ SV16 @ SV17 @ SV18 )
| ~ ( sK2_SY21 @ SV16 @ SV18 @ SV19 ) ) )
= $false )
| ( ( sK2_SY21 @ SV16 @ SV17 @ SV19 )
= $true )
| ( ( sK1_Xp @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(140,plain,
! [SV22: a] :
( ( ( ~ ( sK1_Xp @ SV22 ) )
= $true )
| ( ( sK2_SY21 @ SV22 @ sK8_SX0 @ sK9_SY92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(141,plain,
! [SV23: a] :
( ( ( ~ ( sK1_Xp @ SV23 ) )
= $true )
| ( ( sK2_SY21 @ SV23 @ sK9_SY92 @ sK10_SY97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(142,plain,
! [SV24: a > b,SV21: a > b,SV16: a] :
( ( ( ~ ( sK2_SY21 @ SV16 @ SV21 @ SV24 ) )
= $true )
| ( ( sK2_SY21 @ SV16 @ SV24 @ SV21 )
= $true )
| ( ( sK1_Xp @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(143,plain,
! [SV19: a > b,SV18: a > b,SV17: a > b,SV16: a] :
( ( ( ~ ( sK2_SY21 @ SV16 @ SV17 @ SV18 )
| ~ ( sK2_SY21 @ SV16 @ SV18 @ SV19 ) )
= $true )
| ( ( sK2_SY21 @ SV16 @ SV17 @ SV19 )
= $true )
| ( ( sK1_Xp @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(144,plain,
! [SV22: a] :
( ( ( sK1_Xp @ SV22 )
= $false )
| ( ( sK2_SY21 @ SV22 @ sK8_SX0 @ sK9_SY92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(145,plain,
! [SV23: a] :
( ( ( sK1_Xp @ SV23 )
= $false )
| ( ( sK2_SY21 @ SV23 @ sK9_SY92 @ sK10_SY97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(146,plain,
! [SV24: a > b,SV21: a > b,SV16: a] :
( ( ( sK2_SY21 @ SV16 @ SV21 @ SV24 )
= $false )
| ( ( sK2_SY21 @ SV16 @ SV24 @ SV21 )
= $true )
| ( ( sK1_Xp @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(147,plain,
! [SV19: a > b,SV18: a > b,SV17: a > b,SV16: a] :
( ( ( ~ ( sK2_SY21 @ SV16 @ SV17 @ SV18 ) )
= $true )
| ( ( ~ ( sK2_SY21 @ SV16 @ SV18 @ SV19 ) )
= $true )
| ( ( sK2_SY21 @ SV16 @ SV17 @ SV19 )
= $true )
| ( ( sK1_Xp @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(148,plain,
! [SV19: a > b,SV18: a > b,SV17: a > b,SV16: a] :
( ( ( sK2_SY21 @ SV16 @ SV17 @ SV18 )
= $false )
| ( ( ~ ( sK2_SY21 @ SV16 @ SV18 @ SV19 ) )
= $true )
| ( ( sK2_SY21 @ SV16 @ SV17 @ SV19 )
= $true )
| ( ( sK1_Xp @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(149,plain,
! [SV17: a > b,SV19: a > b,SV18: a > b,SV16: a] :
( ( ( sK2_SY21 @ SV16 @ SV18 @ SV19 )
= $false )
| ( ( sK2_SY21 @ SV16 @ SV17 @ SV18 )
= $false )
| ( ( sK2_SY21 @ SV16 @ SV17 @ SV19 )
= $true )
| ( ( sK1_Xp @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(150,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[121,149,146,145,144,133,127]) ).
thf(151,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[150,51,96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV031^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n016.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 15:44:30 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.44/0.27
% 0.44/0.27 No.of.Axioms: 0
% 0.44/0.27
% 0.44/0.27 Length.of.Defs: 0
% 0.44/0.27
% 0.44/0.27 Contains.Choice.Funs: false
% 0.44/0.27 .....
% 0.44/0.27
% 0.44/0.27 ********************************
% 0.44/0.27 * All subproblems solved! *
% 0.44/0.27 ********************************
% 0.44/0.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:1,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:150,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.44/0.27
% 0.44/0.27 %**** Beginning of derivation protocol ****
% 0.44/0.27 % SZS output start CNFRefutation
% See solution above
% 0.44/0.27
% 0.44/0.27 %**** End of derivation protocol ****
% 0.44/0.27 %**** no. of clauses in derivation: 151 ****
% 0.44/0.27 %**** clause counter: 150 ****
% 0.44/0.27
% 0.44/0.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:1,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:150,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------