%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ALG276^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 10:08:45 AM UTC 2026
% Result : Theorem 141.38s 23.88s
% Output : CNFRefutation 141.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 7
% Syntax : Number of formulae : 127 ( 85 unt; 0 typ; 6 def)
% Number of atoms : 843 ( 621 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 2587 ( 694 ~; 232 |; 54 &;1597 @)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 8 con; 0-2 aty)
% Number of variables : 558 ( 9 ^; 512 !; 37 ?; 558 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_g,type,
g: $tType ).
thf(tp_cGROUP1,type,
cGROUP1: ( g > g > g ) > g > $o ).
thf(tp_cGROUP4,type,
cGROUP4: ( g > g > g ) > $o ).
thf(tp_cGRP_ASSOC,type,
cGRP_ASSOC: ( g > g > g ) > $o ).
thf(tp_cGRP_DIVISORS,type,
cGRP_DIVISORS: ( g > g > g ) > $o ).
thf(tp_cGRP_INVERSE,type,
cGRP_INVERSE: ( g > g > g ) > g > $o ).
thf(tp_cGRP_UNIT,type,
cGRP_UNIT: ( g > g > g ) > g > $o ).
thf(tp_sK10_SY86,type,
sK10_SY86: g > g > g ).
thf(tp_sK11_SY87,type,
sK11_SY87: g > g > g ).
thf(tp_sK12_SY88,type,
sK12_SY88: g > g ).
thf(tp_sK13_SY90,type,
sK13_SY90: g > g ).
thf(tp_sK14_SY77,type,
sK14_SY77: g > g ).
thf(tp_sK15_SY78,type,
sK15_SY78: g > g ).
thf(tp_sK1_SY0,type,
sK1_SY0: g > g > g ).
thf(tp_sK2_SX0,type,
sK2_SX0: g ).
thf(tp_sK3_SX0,type,
sK3_SX0: g ).
thf(tp_sK4_SY62,type,
sK4_SY62: g ).
thf(tp_sK5_SY64,type,
sK5_SY64: g ).
thf(tp_sK6_SX0,type,
sK6_SX0: g ).
thf(tp_sK7_SY66,type,
sK7_SY66: g ).
thf(tp_sK8_SY65,type,
sK8_SY65: g > g ).
thf(tp_sK9_SX1,type,
sK9_SX1: g > g ).
thf(cGROUP1,definition,
( cGROUP1
= ( ^ [Xf: g > g > g,Xe: g] :
( ( cGRP_ASSOC @ Xf )
& ( cGRP_UNIT @ Xf @ Xe )
& ( cGRP_INVERSE @ Xf @ Xe ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGROUP1_def) ).
thf(cGROUP4,definition,
( cGROUP4
= ( ^ [Xf: g > g > g] :
( ( cGRP_ASSOC @ Xf )
& ( cGRP_DIVISORS @ Xf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGROUP4_def) ).
thf(cGRP_ASSOC,definition,
( cGRP_ASSOC
= ( ^ [Xf: g > g > g] :
! [Xa: g,Xb: g,Xc: g] :
( ( Xf @ ( Xf @ Xa @ Xb ) @ Xc )
= ( Xf @ Xa @ ( Xf @ Xb @ Xc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_ASSOC_def) ).
thf(cGRP_DIVISORS,definition,
( cGRP_DIVISORS
= ( ^ [Xf: g > g > g] :
! [Xa: g,Xb: g] :
( ? [Xx: g] :
( ( Xf @ Xa @ Xx )
= Xb )
& ? [Xy: g] :
( ( Xf @ Xy @ Xa )
= Xb ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_DIVISORS_def) ).
thf(cGRP_INVERSE,definition,
( cGRP_INVERSE
= ( ^ [Xf: g > g > g,Xe: g] :
! [Xa: g] :
? [Xb: g] :
( ( ( Xf @ Xa @ Xb )
= Xe )
& ( ( Xf @ Xb @ Xa )
= Xe ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_INVERSE_def) ).
thf(cGRP_UNIT,definition,
( cGRP_UNIT
= ( ^ [Xf: g > g > g,Xe: g] :
! [Xa: g] :
( ( ( Xf @ Xe @ Xa )
= Xa )
& ( ( Xf @ Xa @ Xe )
= Xa ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_UNIT_def) ).
thf(1,conjecture,
! [Xf: g > g > g] :
( ? [Xe: g] : ( cGROUP1 @ Xf @ Xe )
<=> ( cGROUP4 @ Xf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEQUIV_01_04) ).
thf(2,negated_conjecture,
( ( ! [Xf: g > g > g] :
( ? [Xe: g] : ( cGROUP1 @ Xf @ Xe )
<=> ( cGROUP4 @ Xf ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: g > g > g] :
( ? [SY1: g] :
( ! [SY3: g,SY4: g,SY5: g] :
( ( SY0 @ ( SY0 @ SY3 @ SY4 ) @ SY5 )
= ( SY0 @ SY3 @ ( SY0 @ SY4 @ SY5 ) ) )
& ! [SY17: g] :
( ( ( SY0 @ SY1 @ SY17 )
= SY17 )
& ( ( SY0 @ SY17 @ SY1 )
= SY17 ) )
& ! [SY18: g] :
? [SY19: g] :
( ( ( SY0 @ SY18 @ SY19 )
= SY1 )
& ( ( SY0 @ SY19 @ SY18 )
= SY1 ) ) )
<=> ( ! [SY20: g,SY21: g,SY22: g] :
( ( SY0 @ ( SY0 @ SY20 @ SY21 ) @ SY22 )
= ( SY0 @ SY20 @ ( SY0 @ SY21 @ SY22 ) ) )
& ! [SY23: g,SY24: g] :
( ? [SY25: g] :
( ( SY0 @ SY23 @ SY25 )
= SY24 )
& ? [SY26: g] :
( ( SY0 @ SY26 @ SY23 )
= SY24 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,cGROUP1,cGROUP4,cGRP_ASSOC,cGRP_DIVISORS,cGRP_INVERSE,cGRP_UNIT]) ).
thf(4,plain,
( ( ? [SY42: g] :
( ! [SY43: g,SY44: g,SY45: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY43 @ SY44 ) @ SY45 )
= ( sK1_SY0 @ SY43 @ ( sK1_SY0 @ SY44 @ SY45 ) ) )
& ! [SY46: g] :
( ( ( sK1_SY0 @ SY42 @ SY46 )
= SY46 )
& ( ( sK1_SY0 @ SY46 @ SY42 )
= SY46 ) )
& ! [SY47: g] :
? [SY48: g] :
( ( ( sK1_SY0 @ SY47 @ SY48 )
= SY42 )
& ( ( sK1_SY0 @ SY48 @ SY47 )
= SY42 ) ) )
<=> ( ! [SY49: g,SY50: g,SY51: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY49 @ SY50 ) @ SY51 )
= ( sK1_SY0 @ SY49 @ ( sK1_SY0 @ SY50 @ SY51 ) ) )
& ! [SY52: g,SY53: g] :
( ? [SY54: g] :
( ( sK1_SY0 @ SY52 @ SY54 )
= SY53 )
& ? [SY55: g] :
( ( sK1_SY0 @ SY55 @ SY52 )
= SY53 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ? [SY42: g] :
( ! [SY43: g,SY44: g,SY45: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY43 @ SY44 ) @ SY45 )
= ( sK1_SY0 @ SY43 @ ( sK1_SY0 @ SY44 @ SY45 ) ) )
& ! [SY46: g] :
( ( ( sK1_SY0 @ SY42 @ SY46 )
= SY46 )
& ( ( sK1_SY0 @ SY46 @ SY42 )
= SY46 ) )
& ! [SY47: g] :
? [SY48: g] :
( ( ( sK1_SY0 @ SY47 @ SY48 )
= SY42 )
& ( ( sK1_SY0 @ SY48 @ SY47 )
= SY42 ) ) )
=> ( ! [SY49: g,SY50: g,SY51: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY49 @ SY50 ) @ SY51 )
= ( sK1_SY0 @ SY49 @ ( sK1_SY0 @ SY50 @ SY51 ) ) )
& ! [SY52: g,SY53: g] :
( ? [SY54: g] :
( ( sK1_SY0 @ SY52 @ SY54 )
= SY53 )
& ? [SY55: g] :
( ( sK1_SY0 @ SY55 @ SY52 )
= SY53 ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[4]) ).
thf(6,plain,
( ( ( ! [SY49: g,SY50: g,SY51: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY49 @ SY50 ) @ SY51 )
= ( sK1_SY0 @ SY49 @ ( sK1_SY0 @ SY50 @ SY51 ) ) )
& ! [SY52: g,SY53: g] :
( ? [SY54: g] :
( ( sK1_SY0 @ SY52 @ SY54 )
= SY53 )
& ? [SY55: g] :
( ( sK1_SY0 @ SY55 @ SY52 )
= SY53 ) ) )
=> ? [SY42: g] :
( ! [SY43: g,SY44: g,SY45: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY43 @ SY44 ) @ SY45 )
= ( sK1_SY0 @ SY43 @ ( sK1_SY0 @ SY44 @ SY45 ) ) )
& ! [SY46: g] :
( ( ( sK1_SY0 @ SY42 @ SY46 )
= SY46 )
& ( ( sK1_SY0 @ SY46 @ SY42 )
= SY46 ) )
& ! [SY47: g] :
? [SY48: g] :
( ( ( sK1_SY0 @ SY47 @ SY48 )
= SY42 )
& ( ( sK1_SY0 @ SY48 @ SY47 )
= SY42 ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[4]) ).
thf(7,plain,
( ( ~ ( ? [SY42: g] :
( ! [SY43: g,SY44: g,SY45: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY43 @ SY44 ) @ SY45 )
= ( sK1_SY0 @ SY43 @ ( sK1_SY0 @ SY44 @ SY45 ) ) )
& ! [SY46: g] :
( ( ( sK1_SY0 @ SY42 @ SY46 )
= SY46 )
& ( ( sK1_SY0 @ SY46 @ SY42 )
= SY46 ) )
& ! [SY47: g] :
? [SY48: g] :
( ( ( sK1_SY0 @ SY47 @ SY48 )
= SY42 )
& ( ( sK1_SY0 @ SY48 @ SY47 )
= SY42 ) ) )
=> ( ! [SY49: g,SY50: g,SY51: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY49 @ SY50 ) @ SY51 )
= ( sK1_SY0 @ SY49 @ ( sK1_SY0 @ SY50 @ SY51 ) ) )
& ! [SY52: g,SY53: g] :
( ? [SY54: g] :
( ( sK1_SY0 @ SY52 @ SY54 )
= SY53 )
& ? [SY55: g] :
( ( sK1_SY0 @ SY55 @ SY52 )
= SY53 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ( ( ! [SY49: g,SY50: g,SY51: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY49 @ SY50 ) @ SY51 )
= ( sK1_SY0 @ SY49 @ ( sK1_SY0 @ SY50 @ SY51 ) ) )
& ! [SY52: g,SY53: g] :
( ? [SY54: g] :
( ( sK1_SY0 @ SY52 @ SY54 )
= SY53 )
& ? [SY55: g] :
( ( sK1_SY0 @ SY55 @ SY52 )
= SY53 ) ) )
=> ? [SY42: g] :
( ! [SY43: g,SY44: g,SY45: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY43 @ SY44 ) @ SY45 )
= ( sK1_SY0 @ SY43 @ ( sK1_SY0 @ SY44 @ SY45 ) ) )
& ! [SY46: g] :
( ( ( sK1_SY0 @ SY42 @ SY46 )
= SY46 )
& ( ( sK1_SY0 @ SY46 @ SY42 )
= SY46 ) )
& ! [SY47: g] :
? [SY48: g] :
( ( ( sK1_SY0 @ SY47 @ SY48 )
= SY42 )
& ( ( sK1_SY0 @ SY48 @ SY47 )
= SY42 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ( ? [SY42: g] :
( ! [SY43: g,SY44: g,SY45: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY43 @ SY44 ) @ SY45 )
= ( sK1_SY0 @ SY43 @ ( sK1_SY0 @ SY44 @ SY45 ) ) )
& ! [SY46: g] :
( ( ( sK1_SY0 @ SY42 @ SY46 )
= SY46 )
& ( ( sK1_SY0 @ SY46 @ SY42 )
= SY46 ) )
& ! [SY47: g] :
? [SY48: g] :
( ( ( sK1_SY0 @ SY47 @ SY48 )
= SY42 )
& ( ( sK1_SY0 @ SY48 @ SY47 )
= SY42 ) ) )
=> ( ! [SY49: g,SY50: g,SY51: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY49 @ SY50 ) @ SY51 )
= ( sK1_SY0 @ SY49 @ ( sK1_SY0 @ SY50 @ SY51 ) ) )
& ! [SY52: g,SY53: g] :
( ? [SY54: g] :
( ( sK1_SY0 @ SY52 @ SY54 )
= SY53 )
& ? [SY55: g] :
( ( sK1_SY0 @ SY55 @ SY52 )
= SY53 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(10,plain,
( ( ~ ( ~ ~ ! [SX0: g] :
~ ~ ( ~ ~ ( ~ ! [SX1: g,SX2: g,SX3: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX1 @ SX2 ) @ SX3 )
= ( sK1_SY0 @ SX1 @ ( sK1_SY0 @ SX2 @ SX3 ) ) )
| ~ ! [SX1: g] :
~ ( ( ( sK1_SY0 @ SX0 @ SX1 )
!= SX1 )
| ( ( sK1_SY0 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ! [SX1: g] :
~ ! [SX2: g] :
~ ~ ( ( ( sK1_SY0 @ SX1 @ SX2 )
!= SX0 )
| ( ( sK1_SY0 @ SX2 @ SX1 )
!= SX0 ) ) )
| ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX0 @ SX1 ) @ SX2 )
= ( sK1_SY0 @ SX0 @ ( sK1_SY0 @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g,SX1: g] :
~ ( ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX0 @ SX2 )
!= SX1 )
| ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX2 @ SX0 )
!= SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,cGROUP1,cGROUP4,cGRP_ASSOC,cGRP_DIVISORS,cGRP_INVERSE,cGRP_UNIT]) ).
thf(11,plain,
( ( ~ ~ ! [SX0: g] :
~ ~ ( ~ ~ ( ~ ! [SX1: g,SX2: g,SX3: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX1 @ SX2 ) @ SX3 )
= ( sK1_SY0 @ SX1 @ ( sK1_SY0 @ SX2 @ SX3 ) ) )
| ~ ! [SX1: g] :
~ ( ( ( sK1_SY0 @ SX0 @ SX1 )
!= SX1 )
| ( ( sK1_SY0 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ! [SX1: g] :
~ ! [SX2: g] :
~ ~ ( ( ( sK1_SY0 @ SX1 @ SX2 )
!= SX0 )
| ( ( sK1_SY0 @ SX2 @ SX1 )
!= SX0 ) ) )
| ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX0 @ SX1 ) @ SX2 )
= ( sK1_SY0 @ SX0 @ ( sK1_SY0 @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g,SX1: g] :
~ ( ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX0 @ SX2 )
!= SX1 )
| ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX2 @ SX0 )
!= SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(12,plain,
( ( ~ ~ ! [SX0: g] :
~ ~ ( ~ ~ ( ~ ! [SX1: g,SX2: g,SX3: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX1 @ SX2 ) @ SX3 )
= ( sK1_SY0 @ SX1 @ ( sK1_SY0 @ SX2 @ SX3 ) ) )
| ~ ! [SX1: g] :
~ ( ( ( sK1_SY0 @ SX0 @ SX1 )
!= SX1 )
| ( ( sK1_SY0 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ! [SX1: g] :
~ ! [SX2: g] :
~ ~ ( ( ( sK1_SY0 @ SX1 @ SX2 )
!= SX0 )
| ( ( sK1_SY0 @ SX2 @ SX1 )
!= SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[11]) ).
thf(13,plain,
( ( ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX0 @ SX1 ) @ SX2 )
= ( sK1_SY0 @ SX0 @ ( sK1_SY0 @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g,SX1: g] :
~ ( ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX0 @ SX2 )
!= SX1 )
| ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX2 @ SX0 )
!= SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ! [SX0: g] :
~ ~ ( ~ ~ ( ~ ! [SX1: g,SX2: g,SX3: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX1 @ SX2 ) @ SX3 )
= ( sK1_SY0 @ SX1 @ ( sK1_SY0 @ SX2 @ SX3 ) ) )
| ~ ! [SX1: g] :
~ ( ( ( sK1_SY0 @ SX0 @ SX1 )
!= SX1 )
| ( ( sK1_SY0 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ! [SX1: g] :
~ ! [SX2: g] :
~ ~ ( ( ( sK1_SY0 @ SX1 @ SX2 )
!= SX0 )
| ( ( sK1_SY0 @ SX2 @ SX1 )
!= SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX0 @ SX1 ) @ SX2 )
= ( sK1_SY0 @ SX0 @ ( sK1_SY0 @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g,SX1: g] :
~ ( ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX0 @ SX2 )
!= SX1 )
| ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX2 @ SX0 )
!= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ! [SX0: g] :
~ ~ ( ~ ~ ( ~ ! [SX1: g,SX2: g,SX3: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX1 @ SX2 ) @ SX3 )
= ( sK1_SY0 @ SX1 @ ( sK1_SY0 @ SX2 @ SX3 ) ) )
| ~ ! [SX1: g] :
~ ( ( ( sK1_SY0 @ SX0 @ SX1 )
!= SX1 )
| ( ( sK1_SY0 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ! [SX1: g] :
~ ! [SX2: g] :
~ ~ ( ( ( sK1_SY0 @ SX1 @ SX2 )
!= SX0 )
| ( ( sK1_SY0 @ SX2 @ SX1 )
!= SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(17,plain,
( ( ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX0 @ SX1 ) @ SX2 )
= ( sK1_SY0 @ SX0 @ ( sK1_SY0 @ SX1 @ SX2 ) ) ) )
= $true )
| ( ( ~ ! [SX0: g,SX1: g] :
~ ( ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX0 @ SX2 )
!= SX1 )
| ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX2 @ SX0 )
!= SX1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX1: g,SX2: g,SX3: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX1 @ SX2 ) @ SX3 )
= ( sK1_SY0 @ SX1 @ ( sK1_SY0 @ SX2 @ SX3 ) ) )
| ~ ! [SY59: g] :
~ ( ( ( sK1_SY0 @ sK2_SX0 @ SY59 )
!= SY59 )
| ( ( sK1_SY0 @ SY59 @ sK2_SX0 )
!= SY59 ) ) )
| ~ ! [SY60: g] :
~ ! [SY61: g] :
~ ~ ( ( ( sK1_SY0 @ SY60 @ SY61 )
!= sK2_SX0 )
| ( ( sK1_SY0 @ SY61 @ SY60 )
!= sK2_SX0 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(19,plain,
( ( ( ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX0 @ SX1 ) @ SX2 )
= ( sK1_SY0 @ SX0 @ ( sK1_SY0 @ SX1 @ SX2 ) ) ) )
= $false )
| ( ( ~ ! [SX0: g,SX1: g] :
~ ( ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX0 @ SX2 )
!= SX1 )
| ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX2 @ SX0 )
!= SX1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ( ~ ~ ( ~ ! [SX1: g,SX2: g,SX3: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX1 @ SX2 ) @ SX3 )
= ( sK1_SY0 @ SX1 @ ( sK1_SY0 @ SX2 @ SX3 ) ) )
| ~ ! [SY59: g] :
~ ( ( ( sK1_SY0 @ sK2_SX0 @ SY59 )
!= SY59 )
| ( ( sK1_SY0 @ SY59 @ sK2_SX0 )
!= SY59 ) ) )
| ~ ! [SY60: g] :
~ ! [SY61: g] :
~ ~ ( ( ( sK1_SY0 @ SY60 @ SY61 )
!= sK2_SX0 )
| ( ( sK1_SY0 @ SY61 @ SY60 )
!= sK2_SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(21,plain,
( ( ( ! [SY62: g,SY63: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ sK3_SX0 @ SY62 ) @ SY63 )
= ( sK1_SY0 @ sK3_SX0 @ ( sK1_SY0 @ SY62 @ SY63 ) ) ) )
= $false )
| ( ( ~ ! [SX0: g,SX1: g] :
~ ( ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX0 @ SX2 )
!= SX1 )
| ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX2 @ SX0 )
!= SX1 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[19]) ).
thf(22,plain,
( ( ~ ~ ( ~ ! [SX1: g,SX2: g,SX3: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX1 @ SX2 ) @ SX3 )
= ( sK1_SY0 @ SX1 @ ( sK1_SY0 @ SX2 @ SX3 ) ) )
| ~ ! [SY59: g] :
~ ( ( ( sK1_SY0 @ sK2_SX0 @ SY59 )
!= SY59 )
| ( ( sK1_SY0 @ SY59 @ sK2_SX0 )
!= SY59 ) ) )
| ~ ! [SY60: g] :
~ ! [SY61: g] :
~ ~ ( ( ( sK1_SY0 @ SY60 @ SY61 )
!= sK2_SX0 )
| ( ( sK1_SY0 @ SY61 @ SY60 )
!= sK2_SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(23,plain,
( ( ( ! [SY64: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ sK3_SX0 @ sK4_SY62 ) @ SY64 )
= ( sK1_SY0 @ sK3_SX0 @ ( sK1_SY0 @ sK4_SY62 @ SY64 ) ) ) )
= $false )
| ( ( ~ ! [SX0: g,SX1: g] :
~ ( ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX0 @ SX2 )
!= SX1 )
| ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX2 @ SX0 )
!= SX1 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[21]) ).
thf(24,plain,
( ( ~ ~ ( ~ ! [SX1: g,SX2: g,SX3: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX1 @ SX2 ) @ SX3 )
= ( sK1_SY0 @ SX1 @ ( sK1_SY0 @ SX2 @ SX3 ) ) )
| ~ ! [SY59: g] :
~ ( ( ( sK1_SY0 @ sK2_SX0 @ SY59 )
!= SY59 )
| ( ( sK1_SY0 @ SY59 @ sK2_SX0 )
!= SY59 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(25,plain,
( ( ~ ! [SY60: g] :
~ ! [SY61: g] :
~ ~ ( ( ( sK1_SY0 @ SY60 @ SY61 )
!= sK2_SX0 )
| ( ( sK1_SY0 @ SY61 @ SY60 )
!= sK2_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(26,plain,
( ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK3_SX0 @ sK4_SY62 ) @ sK5_SY64 )
= ( sK1_SY0 @ sK3_SX0 @ ( sK1_SY0 @ sK4_SY62 @ sK5_SY64 ) ) )
= $false )
| ( ( ~ ! [SX0: g,SX1: g] :
~ ( ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX0 @ SX2 )
!= SX1 )
| ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX2 @ SX0 )
!= SX1 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[23]) ).
thf(27,plain,
( ( ~ ( ~ ! [SX1: g,SX2: g,SX3: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX1 @ SX2 ) @ SX3 )
= ( sK1_SY0 @ SX1 @ ( sK1_SY0 @ SX2 @ SX3 ) ) )
| ~ ! [SY59: g] :
~ ( ( ( sK1_SY0 @ sK2_SX0 @ SY59 )
!= SY59 )
| ( ( sK1_SY0 @ SY59 @ sK2_SX0 )
!= SY59 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(28,plain,
( ( ! [SY60: g] :
~ ! [SY61: g] :
~ ~ ( ( ( sK1_SY0 @ SY60 @ SY61 )
!= sK2_SX0 )
| ( ( sK1_SY0 @ SY61 @ SY60 )
!= sK2_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(29,plain,
( ( ( ! [SX0: g,SX1: g] :
~ ( ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX0 @ SX2 )
!= SX1 )
| ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX2 @ SX0 )
!= SX1 ) ) )
= $false )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK3_SX0 @ sK4_SY62 ) @ sK5_SY64 )
= ( sK1_SY0 @ sK3_SX0 @ ( sK1_SY0 @ sK4_SY62 @ sK5_SY64 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(30,plain,
( ( ~ ! [SX1: g,SX2: g,SX3: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX1 @ SX2 ) @ SX3 )
= ( sK1_SY0 @ SX1 @ ( sK1_SY0 @ SX2 @ SX3 ) ) )
| ~ ! [SY59: g] :
~ ( ( ( sK1_SY0 @ sK2_SX0 @ SY59 )
!= SY59 )
| ( ( sK1_SY0 @ SY59 @ sK2_SX0 )
!= SY59 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV1: g] :
( ( ~ ! [SY65: g] :
~ ~ ( ( ( sK1_SY0 @ SV1 @ SY65 )
!= sK2_SX0 )
| ( ( sK1_SY0 @ SY65 @ SV1 )
!= sK2_SX0 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(32,plain,
( ( ( ! [SY66: g] :
~ ( ~ ~ ! [SY67: g] :
( ( sK1_SY0 @ sK6_SX0 @ SY67 )
!= SY66 )
| ~ ~ ! [SY68: g] :
( ( sK1_SY0 @ SY68 @ sK6_SX0 )
!= SY66 ) ) )
= $false )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK3_SX0 @ sK4_SY62 ) @ sK5_SY64 )
= ( sK1_SY0 @ sK3_SX0 @ ( sK1_SY0 @ sK4_SY62 @ sK5_SY64 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[29]) ).
thf(33,plain,
( ( ~ ! [SX1: g,SX2: g,SX3: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX1 @ SX2 ) @ SX3 )
= ( sK1_SY0 @ SX1 @ ( sK1_SY0 @ SX2 @ SX3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(34,plain,
( ( ~ ! [SY59: g] :
~ ( ( ( sK1_SY0 @ sK2_SX0 @ SY59 )
!= SY59 )
| ( ( sK1_SY0 @ SY59 @ sK2_SX0 )
!= SY59 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(35,plain,
! [SV1: g] :
( ( ! [SY65: g] :
~ ~ ( ( ( sK1_SY0 @ SV1 @ SY65 )
!= sK2_SX0 )
| ( ( sK1_SY0 @ SY65 @ SV1 )
!= sK2_SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(36,plain,
( ( ( ~ ( ~ ~ ! [SY69: g] :
( ( sK1_SY0 @ sK6_SX0 @ SY69 )
!= sK7_SY66 )
| ~ ~ ! [SY70: g] :
( ( sK1_SY0 @ SY70 @ sK6_SX0 )
!= sK7_SY66 ) ) )
= $false )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK3_SX0 @ sK4_SY62 ) @ sK5_SY64 )
= ( sK1_SY0 @ sK3_SX0 @ ( sK1_SY0 @ sK4_SY62 @ sK5_SY64 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[32]) ).
thf(37,plain,
( ( ! [SX1: g,SX2: g,SX3: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX1 @ SX2 ) @ SX3 )
= ( sK1_SY0 @ SX1 @ ( sK1_SY0 @ SX2 @ SX3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(38,plain,
( ( ! [SY59: g] :
~ ( ( ( sK1_SY0 @ sK2_SX0 @ SY59 )
!= SY59 )
| ( ( sK1_SY0 @ SY59 @ sK2_SX0 )
!= SY59 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(39,plain,
! [SV1: g] :
( ( ~ ~ ( ( ( sK1_SY0 @ SV1 @ ( sK8_SY65 @ SV1 ) )
!= sK2_SX0 )
| ( ( sK1_SY0 @ ( sK8_SY65 @ SV1 ) @ SV1 )
!= sK2_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[35]) ).
thf(40,plain,
( ( ( ~ ~ ! [SY69: g] :
( ( sK1_SY0 @ sK6_SX0 @ SY69 )
!= sK7_SY66 )
| ~ ~ ! [SY70: g] :
( ( sK1_SY0 @ SY70 @ sK6_SX0 )
!= sK7_SY66 ) )
= $true )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK3_SX0 @ sK4_SY62 ) @ sK5_SY64 )
= ( sK1_SY0 @ sK3_SX0 @ ( sK1_SY0 @ sK4_SY62 @ sK5_SY64 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(41,plain,
! [SV2: g] :
( ( ! [SY71: g,SY72: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SV2 @ SY71 ) @ SY72 )
= ( sK1_SY0 @ SV2 @ ( sK1_SY0 @ SY71 @ SY72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV3: g] :
( ( ~ ( ( ( sK1_SY0 @ sK2_SX0 @ SV3 )
!= SV3 )
| ( ( sK1_SY0 @ SV3 @ sK2_SX0 )
!= SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV1: g] :
( ( ~ ( ( ( sK1_SY0 @ SV1 @ ( sK8_SY65 @ SV1 ) )
!= sK2_SX0 )
| ( ( sK1_SY0 @ ( sK8_SY65 @ SV1 ) @ SV1 )
!= sK2_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(44,plain,
( ( ( ~ ~ ! [SY69: g] :
( ( sK1_SY0 @ sK6_SX0 @ SY69 )
!= sK7_SY66 ) )
= $true )
| ( ( ~ ~ ! [SY70: g] :
( ( sK1_SY0 @ SY70 @ sK6_SX0 )
!= sK7_SY66 ) )
= $true )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK3_SX0 @ sK4_SY62 ) @ sK5_SY64 )
= ( sK1_SY0 @ sK3_SX0 @ ( sK1_SY0 @ sK4_SY62 @ sK5_SY64 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(45,plain,
! [SV4: g,SV2: g] :
( ( ! [SY73: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SV2 @ SV4 ) @ SY73 )
= ( sK1_SY0 @ SV2 @ ( sK1_SY0 @ SV4 @ SY73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(46,plain,
! [SV3: g] :
( ( ( ( sK1_SY0 @ sK2_SX0 @ SV3 )
!= SV3 )
| ( ( sK1_SY0 @ SV3 @ sK2_SX0 )
!= SV3 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(47,plain,
! [SV1: g] :
( ( ( ( sK1_SY0 @ SV1 @ ( sK8_SY65 @ SV1 ) )
!= sK2_SX0 )
| ( ( sK1_SY0 @ ( sK8_SY65 @ SV1 ) @ SV1 )
!= sK2_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(48,plain,
( ( ( ~ ! [SY69: g] :
( ( sK1_SY0 @ sK6_SX0 @ SY69 )
!= sK7_SY66 ) )
= $false )
| ( ( ~ ~ ! [SY70: g] :
( ( sK1_SY0 @ SY70 @ sK6_SX0 )
!= sK7_SY66 ) )
= $true )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK3_SX0 @ sK4_SY62 ) @ sK5_SY64 )
= ( sK1_SY0 @ sK3_SX0 @ ( sK1_SY0 @ sK4_SY62 @ sK5_SY64 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV5: g,SV4: g,SV2: g] :
( ( ( sK1_SY0 @ ( sK1_SY0 @ SV2 @ SV4 ) @ SV5 )
= ( sK1_SY0 @ SV2 @ ( sK1_SY0 @ SV4 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(50,plain,
! [SV3: g] :
( ( ( sK1_SY0 @ sK2_SX0 @ SV3 )
!= SV3 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(51,plain,
! [SV3: g] :
( ( ( sK1_SY0 @ SV3 @ sK2_SX0 )
!= SV3 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(52,plain,
! [SV1: g] :
( ( ( sK1_SY0 @ SV1 @ ( sK8_SY65 @ SV1 ) )
!= sK2_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(53,plain,
! [SV1: g] :
( ( ( sK1_SY0 @ ( sK8_SY65 @ SV1 ) @ SV1 )
!= sK2_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(54,plain,
( ( ( ! [SY69: g] :
( ( sK1_SY0 @ sK6_SX0 @ SY69 )
!= sK7_SY66 ) )
= $true )
| ( ( ~ ~ ! [SY70: g] :
( ( sK1_SY0 @ SY70 @ sK6_SX0 )
!= sK7_SY66 ) )
= $true )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK3_SX0 @ sK4_SY62 ) @ sK5_SY64 )
= ( sK1_SY0 @ sK3_SX0 @ ( sK1_SY0 @ sK4_SY62 @ sK5_SY64 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(55,plain,
! [SV3: g] :
( ( ( sK1_SY0 @ sK2_SX0 @ SV3 )
= SV3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(56,plain,
! [SV3: g] :
( ( ( sK1_SY0 @ SV3 @ sK2_SX0 )
= SV3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(57,plain,
! [SV1: g] :
( ( ( sK1_SY0 @ SV1 @ ( sK8_SY65 @ SV1 ) )
= sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(58,plain,
! [SV1: g] :
( ( ( sK1_SY0 @ ( sK8_SY65 @ SV1 ) @ SV1 )
= sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(59,plain,
! [SV6: g] :
( ( ( ( sK1_SY0 @ sK6_SX0 @ SV6 )
!= sK7_SY66 )
= $true )
| ( ( ~ ~ ! [SY70: g] :
( ( sK1_SY0 @ SY70 @ sK6_SX0 )
!= sK7_SY66 ) )
= $true )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK3_SX0 @ sK4_SY62 ) @ sK5_SY64 )
= ( sK1_SY0 @ sK3_SX0 @ ( sK1_SY0 @ sK4_SY62 @ sK5_SY64 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV6: g] :
( ( ( ( sK1_SY0 @ sK6_SX0 @ SV6 )
= sK7_SY66 )
= $false )
| ( ( ~ ~ ! [SY70: g] :
( ( sK1_SY0 @ SY70 @ sK6_SX0 )
!= sK7_SY66 ) )
= $true )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK3_SX0 @ sK4_SY62 ) @ sK5_SY64 )
= ( sK1_SY0 @ sK3_SX0 @ ( sK1_SY0 @ sK4_SY62 @ sK5_SY64 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(61,plain,
! [SV6: g] :
( ( ( ~ ! [SY70: g] :
( ( sK1_SY0 @ SY70 @ sK6_SX0 )
!= sK7_SY66 ) )
= $false )
| ( ( ( sK1_SY0 @ sK6_SX0 @ SV6 )
= sK7_SY66 )
= $false )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK3_SX0 @ sK4_SY62 ) @ sK5_SY64 )
= ( sK1_SY0 @ sK3_SX0 @ ( sK1_SY0 @ sK4_SY62 @ sK5_SY64 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(62,plain,
! [SV6: g] :
( ( ( ! [SY70: g] :
( ( sK1_SY0 @ SY70 @ sK6_SX0 )
!= sK7_SY66 ) )
= $true )
| ( ( ( sK1_SY0 @ sK6_SX0 @ SV6 )
= sK7_SY66 )
= $false )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK3_SX0 @ sK4_SY62 ) @ sK5_SY64 )
= ( sK1_SY0 @ sK3_SX0 @ ( sK1_SY0 @ sK4_SY62 @ sK5_SY64 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(63,plain,
! [SV6: g,SV7: g] :
( ( ( ( sK1_SY0 @ SV7 @ sK6_SX0 )
!= sK7_SY66 )
= $true )
| ( ( ( sK1_SY0 @ sK6_SX0 @ SV6 )
= sK7_SY66 )
= $false )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK3_SX0 @ sK4_SY62 ) @ sK5_SY64 )
= ( sK1_SY0 @ sK3_SX0 @ ( sK1_SY0 @ sK4_SY62 @ sK5_SY64 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(64,plain,
! [SV6: g,SV7: g] :
( ( ( ( sK1_SY0 @ SV7 @ sK6_SX0 )
= sK7_SY66 )
= $false )
| ( ( ( sK1_SY0 @ sK6_SX0 @ SV6 )
= sK7_SY66 )
= $false )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK3_SX0 @ sK4_SY62 ) @ sK5_SY64 )
= ( sK1_SY0 @ sK3_SX0 @ ( sK1_SY0 @ sK4_SY62 @ sK5_SY64 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(65,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[49,64,58,57,56,55]) ).
thf(66,plain,
( ( ~ ( ( ! [SY49: g,SY50: g,SY51: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY49 @ SY50 ) @ SY51 )
= ( sK1_SY0 @ SY49 @ ( sK1_SY0 @ SY50 @ SY51 ) ) )
& ! [SY52: g,SY53: g] :
( ? [SY54: g] :
( ( sK1_SY0 @ SY52 @ SY54 )
= SY53 )
& ? [SY55: g] :
( ( sK1_SY0 @ SY55 @ SY52 )
= SY53 ) ) )
=> ? [SY42: g] :
( ! [SY43: g,SY44: g,SY45: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY43 @ SY44 ) @ SY45 )
= ( sK1_SY0 @ SY43 @ ( sK1_SY0 @ SY44 @ SY45 ) ) )
& ! [SY46: g] :
( ( ( sK1_SY0 @ SY42 @ SY46 )
= SY46 )
& ( ( sK1_SY0 @ SY46 @ SY42 )
= SY46 ) )
& ! [SY47: g] :
? [SY48: g] :
( ( ( sK1_SY0 @ SY47 @ SY48 )
= SY42 )
& ( ( sK1_SY0 @ SY48 @ SY47 )
= SY42 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(67,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX0 @ SX1 ) @ SX2 )
= ( sK1_SY0 @ SX0 @ ( sK1_SY0 @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g,SX1: g] :
~ ( ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX0 @ SX2 )
!= SX1 )
| ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX2 @ SX0 )
!= SX1 ) ) )
| ~ ! [SX0: g] :
~ ~ ( ~ ~ ( ~ ! [SX1: g,SX2: g,SX3: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX1 @ SX2 ) @ SX3 )
= ( sK1_SY0 @ SX1 @ ( sK1_SY0 @ SX2 @ SX3 ) ) )
| ~ ! [SX1: g] :
~ ( ( ( sK1_SY0 @ SX0 @ SX1 )
!= SX1 )
| ( ( sK1_SY0 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ! [SX1: g] :
~ ! [SX2: g] :
~ ~ ( ( ( sK1_SY0 @ SX1 @ SX2 )
!= SX0 )
| ( ( sK1_SY0 @ SX2 @ SX1 )
!= SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66,cGROUP1,cGROUP4,cGRP_ASSOC,cGRP_DIVISORS,cGRP_INVERSE,cGRP_UNIT]) ).
thf(68,plain,
( ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX0 @ SX1 ) @ SX2 )
= ( sK1_SY0 @ SX0 @ ( sK1_SY0 @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g,SX1: g] :
~ ( ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX0 @ SX2 )
!= SX1 )
| ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX2 @ SX0 )
!= SX1 ) ) )
| ~ ! [SX0: g] :
~ ~ ( ~ ~ ( ~ ! [SX1: g,SX2: g,SX3: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX1 @ SX2 ) @ SX3 )
= ( sK1_SY0 @ SX1 @ ( sK1_SY0 @ SX2 @ SX3 ) ) )
| ~ ! [SX1: g] :
~ ( ( ( sK1_SY0 @ SX0 @ SX1 )
!= SX1 )
| ( ( sK1_SY0 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ! [SX1: g] :
~ ! [SX2: g] :
~ ~ ( ( ( sK1_SY0 @ SX1 @ SX2 )
!= SX0 )
| ( ( sK1_SY0 @ SX2 @ SX1 )
!= SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(69,plain,
( ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX0 @ SX1 ) @ SX2 )
= ( sK1_SY0 @ SX0 @ ( sK1_SY0 @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g,SX1: g] :
~ ( ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX0 @ SX2 )
!= SX1 )
| ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX2 @ SX0 )
!= SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(70,plain,
( ( ~ ! [SX0: g] :
~ ~ ( ~ ~ ( ~ ! [SX1: g,SX2: g,SX3: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX1 @ SX2 ) @ SX3 )
= ( sK1_SY0 @ SX1 @ ( sK1_SY0 @ SX2 @ SX3 ) ) )
| ~ ! [SX1: g] :
~ ( ( ( sK1_SY0 @ SX0 @ SX1 )
!= SX1 )
| ( ( sK1_SY0 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ! [SX1: g] :
~ ! [SX2: g] :
~ ~ ( ( ( sK1_SY0 @ SX1 @ SX2 )
!= SX0 )
| ( ( sK1_SY0 @ SX2 @ SX1 )
!= SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(71,plain,
( ( ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX0 @ SX1 ) @ SX2 )
= ( sK1_SY0 @ SX0 @ ( sK1_SY0 @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g,SX1: g] :
~ ( ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX0 @ SX2 )
!= SX1 )
| ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX2 @ SX0 )
!= SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(72,plain,
( ( ! [SX0: g] :
~ ~ ( ~ ~ ( ~ ! [SX1: g,SX2: g,SX3: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX1 @ SX2 ) @ SX3 )
= ( sK1_SY0 @ SX1 @ ( sK1_SY0 @ SX2 @ SX3 ) ) )
| ~ ! [SX1: g] :
~ ( ( ( sK1_SY0 @ SX0 @ SX1 )
!= SX1 )
| ( ( sK1_SY0 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ! [SX1: g] :
~ ! [SX2: g] :
~ ~ ( ( ( sK1_SY0 @ SX1 @ SX2 )
!= SX0 )
| ( ( sK1_SY0 @ SX2 @ SX1 )
!= SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(73,plain,
( ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX0 @ SX1 ) @ SX2 )
= ( sK1_SY0 @ SX0 @ ( sK1_SY0 @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g,SX1: g] :
~ ( ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX0 @ SX2 )
!= SX1 )
| ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX2 @ SX0 )
!= SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(74,plain,
! [SV8: g] :
( ( ~ ~ ( ~ ~ ( ~ ! [SX1: g,SX2: g,SX3: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX1 @ SX2 ) @ SX3 )
= ( sK1_SY0 @ SX1 @ ( sK1_SY0 @ SX2 @ SX3 ) ) )
| ~ ! [SY77: g] :
~ ( ( ( sK1_SY0 @ SV8 @ SY77 )
!= SY77 )
| ( ( sK1_SY0 @ SY77 @ SV8 )
!= SY77 ) ) )
| ~ ! [SY78: g] :
~ ! [SY79: g] :
~ ~ ( ( ( sK1_SY0 @ SY78 @ SY79 )
!= SV8 )
| ( ( sK1_SY0 @ SY79 @ SY78 )
!= SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(75,plain,
( ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX0 @ SX1 ) @ SX2 )
= ( sK1_SY0 @ SX0 @ ( sK1_SY0 @ SX1 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(76,plain,
( ( ~ ! [SX0: g,SX1: g] :
~ ( ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX0 @ SX2 )
!= SX1 )
| ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX2 @ SX0 )
!= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(77,plain,
! [SV8: g] :
( ( ~ ( ~ ~ ( ~ ! [SX1: g,SX2: g,SX3: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX1 @ SX2 ) @ SX3 )
= ( sK1_SY0 @ SX1 @ ( sK1_SY0 @ SX2 @ SX3 ) ) )
| ~ ! [SY77: g] :
~ ( ( ( sK1_SY0 @ SV8 @ SY77 )
!= SY77 )
| ( ( sK1_SY0 @ SY77 @ SV8 )
!= SY77 ) ) )
| ~ ! [SY78: g] :
~ ! [SY79: g] :
~ ~ ( ( ( sK1_SY0 @ SY78 @ SY79 )
!= SV8 )
| ( ( sK1_SY0 @ SY79 @ SY78 )
!= SV8 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(78,plain,
( ( ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX0 @ SX1 ) @ SX2 )
= ( sK1_SY0 @ SX0 @ ( sK1_SY0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(79,plain,
( ( ! [SX0: g,SX1: g] :
~ ( ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX0 @ SX2 )
!= SX1 )
| ~ ~ ! [SX2: g] :
( ( sK1_SY0 @ SX2 @ SX0 )
!= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(80,plain,
! [SV8: g] :
( ( ~ ~ ( ~ ! [SX1: g,SX2: g,SX3: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX1 @ SX2 ) @ SX3 )
= ( sK1_SY0 @ SX1 @ ( sK1_SY0 @ SX2 @ SX3 ) ) )
| ~ ! [SY77: g] :
~ ( ( ( sK1_SY0 @ SV8 @ SY77 )
!= SY77 )
| ( ( sK1_SY0 @ SY77 @ SV8 )
!= SY77 ) ) )
| ~ ! [SY78: g] :
~ ! [SY79: g] :
~ ~ ( ( ( sK1_SY0 @ SY78 @ SY79 )
!= SV8 )
| ( ( sK1_SY0 @ SY79 @ SY78 )
!= SV8 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(81,plain,
! [SV9: g] :
( ( ! [SY80: g,SY81: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SV9 @ SY80 ) @ SY81 )
= ( sK1_SY0 @ SV9 @ ( sK1_SY0 @ SY80 @ SY81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(82,plain,
! [SV10: g] :
( ( ! [SY82: g] :
~ ( ~ ~ ! [SY83: g] :
( ( sK1_SY0 @ SV10 @ SY83 )
!= SY82 )
| ~ ~ ! [SY84: g] :
( ( sK1_SY0 @ SY84 @ SV10 )
!= SY82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(83,plain,
! [SV8: g] :
( ( ( ~ ~ ( ~ ! [SX1: g,SX2: g,SX3: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX1 @ SX2 ) @ SX3 )
= ( sK1_SY0 @ SX1 @ ( sK1_SY0 @ SX2 @ SX3 ) ) )
| ~ ! [SY77: g] :
~ ( ( ( sK1_SY0 @ SV8 @ SY77 )
!= SY77 )
| ( ( sK1_SY0 @ SY77 @ SV8 )
!= SY77 ) ) ) )
= $true )
| ( ( ~ ! [SY78: g] :
~ ! [SY79: g] :
~ ~ ( ( ( sK1_SY0 @ SY78 @ SY79 )
!= SV8 )
| ( ( sK1_SY0 @ SY79 @ SY78 )
!= SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(84,plain,
! [SV11: g,SV9: g] :
( ( ! [SY85: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SV9 @ SV11 ) @ SY85 )
= ( sK1_SY0 @ SV9 @ ( sK1_SY0 @ SV11 @ SY85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(85,plain,
! [SV12: g,SV10: g] :
( ( ~ ( ~ ~ ! [SY86: g] :
( ( sK1_SY0 @ SV10 @ SY86 )
!= SV12 )
| ~ ~ ! [SY87: g] :
( ( sK1_SY0 @ SY87 @ SV10 )
!= SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(86,plain,
! [SV8: g] :
( ( ( ~ ( ~ ! [SX1: g,SX2: g,SX3: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX1 @ SX2 ) @ SX3 )
= ( sK1_SY0 @ SX1 @ ( sK1_SY0 @ SX2 @ SX3 ) ) )
| ~ ! [SY77: g] :
~ ( ( ( sK1_SY0 @ SV8 @ SY77 )
!= SY77 )
| ( ( sK1_SY0 @ SY77 @ SV8 )
!= SY77 ) ) ) )
= $false )
| ( ( ~ ! [SY78: g] :
~ ! [SY79: g] :
~ ~ ( ( ( sK1_SY0 @ SY78 @ SY79 )
!= SV8 )
| ( ( sK1_SY0 @ SY79 @ SY78 )
!= SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(87,plain,
! [SV13: g,SV11: g,SV9: g] :
( ( ( sK1_SY0 @ ( sK1_SY0 @ SV9 @ SV11 ) @ SV13 )
= ( sK1_SY0 @ SV9 @ ( sK1_SY0 @ SV11 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(88,plain,
! [SV12: g,SV10: g] :
( ( ~ ~ ! [SY86: g] :
( ( sK1_SY0 @ SV10 @ SY86 )
!= SV12 )
| ~ ~ ! [SY87: g] :
( ( sK1_SY0 @ SY87 @ SV10 )
!= SV12 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(89,plain,
! [SV8: g] :
( ( ( ~ ! [SX1: g,SX2: g,SX3: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX1 @ SX2 ) @ SX3 )
= ( sK1_SY0 @ SX1 @ ( sK1_SY0 @ SX2 @ SX3 ) ) )
| ~ ! [SY77: g] :
~ ( ( ( sK1_SY0 @ SV8 @ SY77 )
!= SY77 )
| ( ( sK1_SY0 @ SY77 @ SV8 )
!= SY77 ) ) )
= $true )
| ( ( ~ ! [SY78: g] :
~ ! [SY79: g] :
~ ~ ( ( ( sK1_SY0 @ SY78 @ SY79 )
!= SV8 )
| ( ( sK1_SY0 @ SY79 @ SY78 )
!= SV8 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(90,plain,
! [SV12: g,SV10: g] :
( ( ~ ~ ! [SY86: g] :
( ( sK1_SY0 @ SV10 @ SY86 )
!= SV12 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(91,plain,
! [SV12: g,SV10: g] :
( ( ~ ~ ! [SY87: g] :
( ( sK1_SY0 @ SY87 @ SV10 )
!= SV12 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(92,plain,
! [SV8: g] :
( ( ( ~ ! [SX1: g,SX2: g,SX3: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX1 @ SX2 ) @ SX3 )
= ( sK1_SY0 @ SX1 @ ( sK1_SY0 @ SX2 @ SX3 ) ) ) )
= $true )
| ( ( ~ ! [SY77: g] :
~ ( ( ( sK1_SY0 @ SV8 @ SY77 )
!= SY77 )
| ( ( sK1_SY0 @ SY77 @ SV8 )
!= SY77 ) ) )
= $true )
| ( ( ~ ! [SY78: g] :
~ ! [SY79: g] :
~ ~ ( ( ( sK1_SY0 @ SY78 @ SY79 )
!= SV8 )
| ( ( sK1_SY0 @ SY79 @ SY78 )
!= SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(93,plain,
! [SV12: g,SV10: g] :
( ( ~ ! [SY86: g] :
( ( sK1_SY0 @ SV10 @ SY86 )
!= SV12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(94,plain,
! [SV12: g,SV10: g] :
( ( ~ ! [SY87: g] :
( ( sK1_SY0 @ SY87 @ SV10 )
!= SV12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(95,plain,
! [SV8: g] :
( ( ( ! [SX1: g,SX2: g,SX3: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX1 @ SX2 ) @ SX3 )
= ( sK1_SY0 @ SX1 @ ( sK1_SY0 @ SX2 @ SX3 ) ) ) )
= $false )
| ( ( ~ ! [SY77: g] :
~ ( ( ( sK1_SY0 @ SV8 @ SY77 )
!= SY77 )
| ( ( sK1_SY0 @ SY77 @ SV8 )
!= SY77 ) ) )
= $true )
| ( ( ~ ! [SY78: g] :
~ ! [SY79: g] :
~ ~ ( ( ( sK1_SY0 @ SY78 @ SY79 )
!= SV8 )
| ( ( sK1_SY0 @ SY79 @ SY78 )
!= SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(96,plain,
! [SV12: g,SV10: g] :
( ( ! [SY86: g] :
( ( sK1_SY0 @ SV10 @ SY86 )
!= SV12 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(97,plain,
! [SV12: g,SV10: g] :
( ( ! [SY87: g] :
( ( sK1_SY0 @ SY87 @ SV10 )
!= SV12 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(98,plain,
! [SV8: g] :
( ( ( ! [SY88: g,SY89: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ SY88 ) @ SY89 )
= ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK1_SY0 @ SY88 @ SY89 ) ) ) )
= $false )
| ( ( ~ ! [SY77: g] :
~ ( ( ( sK1_SY0 @ SV8 @ SY77 )
!= SY77 )
| ( ( sK1_SY0 @ SY77 @ SV8 )
!= SY77 ) ) )
= $true )
| ( ( ~ ! [SY78: g] :
~ ! [SY79: g] :
~ ~ ( ( ( sK1_SY0 @ SY78 @ SY79 )
!= SV8 )
| ( ( sK1_SY0 @ SY79 @ SY78 )
!= SV8 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[95]) ).
thf(99,plain,
! [SV12: g,SV10: g] :
( ( ( sK1_SY0 @ SV10 @ ( sK10_SY86 @ SV12 @ SV10 ) )
!= SV12 )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[96]) ).
thf(100,plain,
! [SV10: g,SV12: g] :
( ( ( sK1_SY0 @ ( sK11_SY87 @ SV12 @ SV10 ) @ SV10 )
!= SV12 )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[97]) ).
thf(101,plain,
! [SV8: g] :
( ( ( ! [SY90: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK12_SY88 @ SV8 ) ) @ SY90 )
= ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK1_SY0 @ ( sK12_SY88 @ SV8 ) @ SY90 ) ) ) )
= $false )
| ( ( ~ ! [SY77: g] :
~ ( ( ( sK1_SY0 @ SV8 @ SY77 )
!= SY77 )
| ( ( sK1_SY0 @ SY77 @ SV8 )
!= SY77 ) ) )
= $true )
| ( ( ~ ! [SY78: g] :
~ ! [SY79: g] :
~ ~ ( ( ( sK1_SY0 @ SY78 @ SY79 )
!= SV8 )
| ( ( sK1_SY0 @ SY79 @ SY78 )
!= SV8 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[98]) ).
thf(102,plain,
! [SV12: g,SV10: g] :
( ( ( sK1_SY0 @ SV10 @ ( sK10_SY86 @ SV12 @ SV10 ) )
= SV12 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(103,plain,
! [SV10: g,SV12: g] :
( ( ( sK1_SY0 @ ( sK11_SY87 @ SV12 @ SV10 ) @ SV10 )
= SV12 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(104,plain,
! [SV8: g] :
( ( ( ( sK1_SY0 @ ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK12_SY88 @ SV8 ) ) @ ( sK13_SY90 @ SV8 ) )
= ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK1_SY0 @ ( sK12_SY88 @ SV8 ) @ ( sK13_SY90 @ SV8 ) ) ) )
= $false )
| ( ( ~ ! [SY77: g] :
~ ( ( ( sK1_SY0 @ SV8 @ SY77 )
!= SY77 )
| ( ( sK1_SY0 @ SY77 @ SV8 )
!= SY77 ) ) )
= $true )
| ( ( ~ ! [SY78: g] :
~ ! [SY79: g] :
~ ~ ( ( ( sK1_SY0 @ SY78 @ SY79 )
!= SV8 )
| ( ( sK1_SY0 @ SY79 @ SY78 )
!= SV8 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[101]) ).
thf(105,plain,
! [SV8: g] :
( ( ( ! [SY77: g] :
~ ( ( ( sK1_SY0 @ SV8 @ SY77 )
!= SY77 )
| ( ( sK1_SY0 @ SY77 @ SV8 )
!= SY77 ) ) )
= $false )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK12_SY88 @ SV8 ) ) @ ( sK13_SY90 @ SV8 ) )
= ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK1_SY0 @ ( sK12_SY88 @ SV8 ) @ ( sK13_SY90 @ SV8 ) ) ) )
= $false )
| ( ( ~ ! [SY78: g] :
~ ! [SY79: g] :
~ ~ ( ( ( sK1_SY0 @ SY78 @ SY79 )
!= SV8 )
| ( ( sK1_SY0 @ SY79 @ SY78 )
!= SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(106,plain,
! [SV8: g] :
( ( ( ~ ( ( ( sK1_SY0 @ SV8 @ ( sK14_SY77 @ SV8 ) )
!= ( sK14_SY77 @ SV8 ) )
| ( ( sK1_SY0 @ ( sK14_SY77 @ SV8 ) @ SV8 )
!= ( sK14_SY77 @ SV8 ) ) ) )
= $false )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK12_SY88 @ SV8 ) ) @ ( sK13_SY90 @ SV8 ) )
= ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK1_SY0 @ ( sK12_SY88 @ SV8 ) @ ( sK13_SY90 @ SV8 ) ) ) )
= $false )
| ( ( ~ ! [SY78: g] :
~ ! [SY79: g] :
~ ~ ( ( ( sK1_SY0 @ SY78 @ SY79 )
!= SV8 )
| ( ( sK1_SY0 @ SY79 @ SY78 )
!= SV8 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[105]) ).
thf(107,plain,
! [SV8: g] :
( ( ( ( ( sK1_SY0 @ SV8 @ ( sK14_SY77 @ SV8 ) )
!= ( sK14_SY77 @ SV8 ) )
| ( ( sK1_SY0 @ ( sK14_SY77 @ SV8 ) @ SV8 )
!= ( sK14_SY77 @ SV8 ) ) )
= $true )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK12_SY88 @ SV8 ) ) @ ( sK13_SY90 @ SV8 ) )
= ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK1_SY0 @ ( sK12_SY88 @ SV8 ) @ ( sK13_SY90 @ SV8 ) ) ) )
= $false )
| ( ( ~ ! [SY78: g] :
~ ! [SY79: g] :
~ ~ ( ( ( sK1_SY0 @ SY78 @ SY79 )
!= SV8 )
| ( ( sK1_SY0 @ SY79 @ SY78 )
!= SV8 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(108,plain,
! [SV8: g] :
( ( ( ( sK1_SY0 @ SV8 @ ( sK14_SY77 @ SV8 ) )
!= ( sK14_SY77 @ SV8 ) )
= $true )
| ( ( ( sK1_SY0 @ ( sK14_SY77 @ SV8 ) @ SV8 )
!= ( sK14_SY77 @ SV8 ) )
= $true )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK12_SY88 @ SV8 ) ) @ ( sK13_SY90 @ SV8 ) )
= ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK1_SY0 @ ( sK12_SY88 @ SV8 ) @ ( sK13_SY90 @ SV8 ) ) ) )
= $false )
| ( ( ~ ! [SY78: g] :
~ ! [SY79: g] :
~ ~ ( ( ( sK1_SY0 @ SY78 @ SY79 )
!= SV8 )
| ( ( sK1_SY0 @ SY79 @ SY78 )
!= SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(109,plain,
! [SV8: g] :
( ( ( ( sK1_SY0 @ SV8 @ ( sK14_SY77 @ SV8 ) )
= ( sK14_SY77 @ SV8 ) )
= $false )
| ( ( ( sK1_SY0 @ ( sK14_SY77 @ SV8 ) @ SV8 )
!= ( sK14_SY77 @ SV8 ) )
= $true )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK12_SY88 @ SV8 ) ) @ ( sK13_SY90 @ SV8 ) )
= ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK1_SY0 @ ( sK12_SY88 @ SV8 ) @ ( sK13_SY90 @ SV8 ) ) ) )
= $false )
| ( ( ~ ! [SY78: g] :
~ ! [SY79: g] :
~ ~ ( ( ( sK1_SY0 @ SY78 @ SY79 )
!= SV8 )
| ( ( sK1_SY0 @ SY79 @ SY78 )
!= SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(110,plain,
! [SV8: g] :
( ( ( ( sK1_SY0 @ ( sK14_SY77 @ SV8 ) @ SV8 )
= ( sK14_SY77 @ SV8 ) )
= $false )
| ( ( ( sK1_SY0 @ SV8 @ ( sK14_SY77 @ SV8 ) )
= ( sK14_SY77 @ SV8 ) )
= $false )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK12_SY88 @ SV8 ) ) @ ( sK13_SY90 @ SV8 ) )
= ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK1_SY0 @ ( sK12_SY88 @ SV8 ) @ ( sK13_SY90 @ SV8 ) ) ) )
= $false )
| ( ( ~ ! [SY78: g] :
~ ! [SY79: g] :
~ ~ ( ( ( sK1_SY0 @ SY78 @ SY79 )
!= SV8 )
| ( ( sK1_SY0 @ SY79 @ SY78 )
!= SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(111,plain,
! [SV8: g] :
( ( ( ! [SY78: g] :
~ ! [SY79: g] :
~ ~ ( ( ( sK1_SY0 @ SY78 @ SY79 )
!= SV8 )
| ( ( sK1_SY0 @ SY79 @ SY78 )
!= SV8 ) ) )
= $false )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK12_SY88 @ SV8 ) ) @ ( sK13_SY90 @ SV8 ) )
= ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK1_SY0 @ ( sK12_SY88 @ SV8 ) @ ( sK13_SY90 @ SV8 ) ) ) )
= $false )
| ( ( ( sK1_SY0 @ SV8 @ ( sK14_SY77 @ SV8 ) )
= ( sK14_SY77 @ SV8 ) )
= $false )
| ( ( ( sK1_SY0 @ ( sK14_SY77 @ SV8 ) @ SV8 )
= ( sK14_SY77 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(112,plain,
! [SV8: g] :
( ( ( ~ ! [SY91: g] :
~ ~ ( ( ( sK1_SY0 @ ( sK15_SY78 @ SV8 ) @ SY91 )
!= SV8 )
| ( ( sK1_SY0 @ SY91 @ ( sK15_SY78 @ SV8 ) )
!= SV8 ) ) )
= $false )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK12_SY88 @ SV8 ) ) @ ( sK13_SY90 @ SV8 ) )
= ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK1_SY0 @ ( sK12_SY88 @ SV8 ) @ ( sK13_SY90 @ SV8 ) ) ) )
= $false )
| ( ( ( sK1_SY0 @ SV8 @ ( sK14_SY77 @ SV8 ) )
= ( sK14_SY77 @ SV8 ) )
= $false )
| ( ( ( sK1_SY0 @ ( sK14_SY77 @ SV8 ) @ SV8 )
= ( sK14_SY77 @ SV8 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[111]) ).
thf(113,plain,
! [SV8: g] :
( ( ( ! [SY91: g] :
~ ~ ( ( ( sK1_SY0 @ ( sK15_SY78 @ SV8 ) @ SY91 )
!= SV8 )
| ( ( sK1_SY0 @ SY91 @ ( sK15_SY78 @ SV8 ) )
!= SV8 ) ) )
= $true )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK12_SY88 @ SV8 ) ) @ ( sK13_SY90 @ SV8 ) )
= ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK1_SY0 @ ( sK12_SY88 @ SV8 ) @ ( sK13_SY90 @ SV8 ) ) ) )
= $false )
| ( ( ( sK1_SY0 @ SV8 @ ( sK14_SY77 @ SV8 ) )
= ( sK14_SY77 @ SV8 ) )
= $false )
| ( ( ( sK1_SY0 @ ( sK14_SY77 @ SV8 ) @ SV8 )
= ( sK14_SY77 @ SV8 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(114,plain,
! [SV14: g,SV8: g] :
( ( ( ~ ~ ( ( ( sK1_SY0 @ ( sK15_SY78 @ SV8 ) @ SV14 )
!= SV8 )
| ( ( sK1_SY0 @ SV14 @ ( sK15_SY78 @ SV8 ) )
!= SV8 ) ) )
= $true )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK12_SY88 @ SV8 ) ) @ ( sK13_SY90 @ SV8 ) )
= ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK1_SY0 @ ( sK12_SY88 @ SV8 ) @ ( sK13_SY90 @ SV8 ) ) ) )
= $false )
| ( ( ( sK1_SY0 @ SV8 @ ( sK14_SY77 @ SV8 ) )
= ( sK14_SY77 @ SV8 ) )
= $false )
| ( ( ( sK1_SY0 @ ( sK14_SY77 @ SV8 ) @ SV8 )
= ( sK14_SY77 @ SV8 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(115,plain,
! [SV14: g,SV8: g] :
( ( ( ~ ( ( ( sK1_SY0 @ ( sK15_SY78 @ SV8 ) @ SV14 )
!= SV8 )
| ( ( sK1_SY0 @ SV14 @ ( sK15_SY78 @ SV8 ) )
!= SV8 ) ) )
= $false )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK12_SY88 @ SV8 ) ) @ ( sK13_SY90 @ SV8 ) )
= ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK1_SY0 @ ( sK12_SY88 @ SV8 ) @ ( sK13_SY90 @ SV8 ) ) ) )
= $false )
| ( ( ( sK1_SY0 @ SV8 @ ( sK14_SY77 @ SV8 ) )
= ( sK14_SY77 @ SV8 ) )
= $false )
| ( ( ( sK1_SY0 @ ( sK14_SY77 @ SV8 ) @ SV8 )
= ( sK14_SY77 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(116,plain,
! [SV14: g,SV8: g] :
( ( ( ( ( sK1_SY0 @ ( sK15_SY78 @ SV8 ) @ SV14 )
!= SV8 )
| ( ( sK1_SY0 @ SV14 @ ( sK15_SY78 @ SV8 ) )
!= SV8 ) )
= $true )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK12_SY88 @ SV8 ) ) @ ( sK13_SY90 @ SV8 ) )
= ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK1_SY0 @ ( sK12_SY88 @ SV8 ) @ ( sK13_SY90 @ SV8 ) ) ) )
= $false )
| ( ( ( sK1_SY0 @ SV8 @ ( sK14_SY77 @ SV8 ) )
= ( sK14_SY77 @ SV8 ) )
= $false )
| ( ( ( sK1_SY0 @ ( sK14_SY77 @ SV8 ) @ SV8 )
= ( sK14_SY77 @ SV8 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(117,plain,
! [SV14: g,SV8: g] :
( ( ( ( sK1_SY0 @ ( sK15_SY78 @ SV8 ) @ SV14 )
!= SV8 )
= $true )
| ( ( ( sK1_SY0 @ SV14 @ ( sK15_SY78 @ SV8 ) )
!= SV8 )
= $true )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK12_SY88 @ SV8 ) ) @ ( sK13_SY90 @ SV8 ) )
= ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK1_SY0 @ ( sK12_SY88 @ SV8 ) @ ( sK13_SY90 @ SV8 ) ) ) )
= $false )
| ( ( ( sK1_SY0 @ SV8 @ ( sK14_SY77 @ SV8 ) )
= ( sK14_SY77 @ SV8 ) )
= $false )
| ( ( ( sK1_SY0 @ ( sK14_SY77 @ SV8 ) @ SV8 )
= ( sK14_SY77 @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(118,plain,
! [SV14: g,SV8: g] :
( ( ( ( sK1_SY0 @ ( sK15_SY78 @ SV8 ) @ SV14 )
= SV8 )
= $false )
| ( ( ( sK1_SY0 @ SV14 @ ( sK15_SY78 @ SV8 ) )
!= SV8 )
= $true )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK12_SY88 @ SV8 ) ) @ ( sK13_SY90 @ SV8 ) )
= ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK1_SY0 @ ( sK12_SY88 @ SV8 ) @ ( sK13_SY90 @ SV8 ) ) ) )
= $false )
| ( ( ( sK1_SY0 @ SV8 @ ( sK14_SY77 @ SV8 ) )
= ( sK14_SY77 @ SV8 ) )
= $false )
| ( ( ( sK1_SY0 @ ( sK14_SY77 @ SV8 ) @ SV8 )
= ( sK14_SY77 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(119,plain,
! [SV8: g,SV14: g] :
( ( ( ( sK1_SY0 @ SV14 @ ( sK15_SY78 @ SV8 ) )
= SV8 )
= $false )
| ( ( ( sK1_SY0 @ ( sK15_SY78 @ SV8 ) @ SV14 )
= SV8 )
= $false )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK12_SY88 @ SV8 ) ) @ ( sK13_SY90 @ SV8 ) )
= ( sK1_SY0 @ ( sK9_SX1 @ SV8 ) @ ( sK1_SY0 @ ( sK12_SY88 @ SV8 ) @ ( sK13_SY90 @ SV8 ) ) ) )
= $false )
| ( ( ( sK1_SY0 @ SV8 @ ( sK14_SY77 @ SV8 ) )
= ( sK14_SY77 @ SV8 ) )
= $false )
| ( ( ( sK1_SY0 @ ( sK14_SY77 @ SV8 ) @ SV8 )
= ( sK14_SY77 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(120,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[87,119,103,102]) ).
thf(121,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[120,65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG276^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.21 % Computer : n004.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Tue Oct 6 18:09:54 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 141.38/23.88
% 141.38/23.88 No.of.Axioms: 0
% 141.38/23.88
% 141.38/23.88 Length.of.Defs: 1211
% 141.38/23.88
% 141.38/23.88 Contains.Choice.Funs: false
% 141.38/23.88 .....
% 141.38/23.88
% 141.38/23.88 ********************************
% 141.38/23.88 * All subproblems solved! *
% 141.38/23.88 ********************************
% 141.38/23.88 % 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:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:120,loop_count:0,foatp_calls:1,translation:fof_full)
% 141.38/23.88
% 141.38/23.88 %**** Beginning of derivation protocol ****
% 141.38/23.88 % SZS output start CNFRefutation
% See solution above
% 141.38/23.88
% 141.38/23.88 %**** End of derivation protocol ****
% 141.38/23.88 %**** no. of clauses in derivation: 121 ****
% 141.38/23.88 %**** clause counter: 120 ****
% 141.38/23.88
% 141.38/23.88 % 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:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:120,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------