%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ALG273^5 : 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 : n019.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 0.11s 0.23s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 8
% Syntax : Number of formulae : 77 ( 64 unt; 0 typ; 7 def)
% Number of atoms : 394 ( 288 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 1129 ( 156 ~; 78 |; 44 &; 842 @)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 13 con; 0-2 aty)
% Number of variables : 273 ( 13 ^; 244 !; 16 ?; 273 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_g,type,
g: $tType ).
thf(tp_cGROUP2,type,
cGROUP2: ( g > g > g ) > g > $o ).
thf(tp_cGROUP3,type,
cGROUP3: ( g > g > g ) > g > $o ).
thf(tp_cGRP_ASSOC,type,
cGRP_ASSOC: ( g > g > g ) > $o ).
thf(tp_cGRP_LEFT_INVERSE,type,
cGRP_LEFT_INVERSE: ( g > g > g ) > g > $o ).
thf(tp_cGRP_LEFT_UNIT,type,
cGRP_LEFT_UNIT: ( g > g > g ) > g > $o ).
thf(tp_cGRP_RIGHT_INVERSE,type,
cGRP_RIGHT_INVERSE: ( g > g > g ) > g > $o ).
thf(tp_cGRP_RIGHT_UNIT,type,
cGRP_RIGHT_UNIT: ( g > g > g ) > g > $o ).
thf(tp_sK10_SY53,type,
sK10_SY53: g ).
thf(tp_sK11_SY81,type,
sK11_SY81: g ).
thf(tp_sK12_SY83,type,
sK12_SY83: g ).
thf(tp_sK13_SY69,type,
sK13_SY69: g ).
thf(tp_sK14_SY76,type,
sK14_SY76: g > g ).
thf(tp_sK1_SY0,type,
sK1_SY0: g > g > g ).
thf(tp_sK2_SY52,type,
sK2_SY52: g ).
thf(tp_sK3_SY74,type,
sK3_SY74: g ).
thf(tp_sK4_SY59,type,
sK4_SY59: g ).
thf(tp_sK5_SY77,type,
sK5_SY77: g ).
thf(tp_sK6_SY79,type,
sK6_SY79: g ).
thf(tp_sK7_SY75,type,
sK7_SY75: g ).
thf(tp_sK8_SY70,type,
sK8_SY70: g > g ).
thf(tp_sK9_SY68,type,
sK9_SY68: g ).
thf(cGROUP2,definition,
( cGROUP2
= ( ^ [Xf: g > g > g,Xe: g] :
( ( cGRP_ASSOC @ Xf )
& ( cGRP_LEFT_UNIT @ Xf @ Xe )
& ( cGRP_LEFT_INVERSE @ Xf @ Xe ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGROUP2_def) ).
thf(cGROUP3,definition,
( cGROUP3
= ( ^ [Xf: g > g > g,Xe: g] :
( ( cGRP_ASSOC @ Xf )
& ( cGRP_RIGHT_UNIT @ Xf @ Xe )
& ( cGRP_RIGHT_INVERSE @ Xf @ Xe ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGROUP3_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_LEFT_INVERSE,definition,
( cGRP_LEFT_INVERSE
= ( ^ [Xf: g > g > g,Xe: g] :
! [Xa: g] :
? [Xb: g] :
( ( Xf @ Xb @ Xa )
= Xe ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_LEFT_INVERSE_def) ).
thf(cGRP_LEFT_UNIT,definition,
( cGRP_LEFT_UNIT
= ( ^ [Xf: g > g > g,Xe: g] :
! [Xa: g] :
( ( Xf @ Xe @ Xa )
= Xa ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_LEFT_UNIT_def) ).
thf(cGRP_RIGHT_INVERSE,definition,
( cGRP_RIGHT_INVERSE
= ( ^ [Xf: g > g > g,Xe: g] :
! [Xa: g] :
? [Xb: g] :
( ( Xf @ Xa @ Xb )
= Xe ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_RIGHT_INVERSE_def) ).
thf(cGRP_RIGHT_UNIT,definition,
( cGRP_RIGHT_UNIT
= ( ^ [Xf: g > g > g,Xe: g] :
! [Xa: g] :
( ( Xf @ Xa @ Xe )
= Xa ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_RIGHT_UNIT_def) ).
thf(1,conjecture,
! [Xf: g > g > g,Xe: g] :
( ( cGROUP2 @ Xf @ Xe )
<=> ( cGROUP3 @ Xf @ Xe ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEQUIV_02_03) ).
thf(2,negated_conjecture,
( ( ! [Xf: g > g > g,Xe: g] :
( ( cGROUP2 @ Xf @ Xe )
<=> ( cGROUP3 @ Xf @ Xe ) ) )
= $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 )
& ! [SY18: g] :
? [SY19: g] :
( ( SY0 @ SY19 @ SY18 )
= SY1 ) )
<=> ( ! [SY21: g,SY22: g,SY23: g] :
( ( SY0 @ ( SY0 @ SY21 @ SY22 ) @ SY23 )
= ( SY0 @ SY21 @ ( SY0 @ SY22 @ SY23 ) ) )
& ! [SY35: g] :
( ( SY0 @ SY35 @ SY1 )
= SY35 )
& ! [SY36: g] :
? [SY37: g] :
( ( SY0 @ SY36 @ SY37 )
= SY1 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,cGROUP2,cGROUP3,cGRP_ASSOC,cGRP_LEFT_INVERSE,cGRP_LEFT_UNIT,cGRP_RIGHT_INVERSE,cGRP_RIGHT_UNIT]) ).
thf(4,plain,
( ( ! [SY52: g] :
( ( ! [SY53: g,SY54: g,SY55: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY53 @ SY54 ) @ SY55 )
= ( sK1_SY0 @ SY53 @ ( sK1_SY0 @ SY54 @ SY55 ) ) )
& ! [SY56: g] :
( ( sK1_SY0 @ SY52 @ SY56 )
= SY56 )
& ! [SY57: g] :
? [SY58: g] :
( ( sK1_SY0 @ SY58 @ SY57 )
= SY52 ) )
<=> ( ! [SY59: g,SY60: g,SY61: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY59 @ SY60 ) @ SY61 )
= ( sK1_SY0 @ SY59 @ ( sK1_SY0 @ SY60 @ SY61 ) ) )
& ! [SY62: g] :
( ( sK1_SY0 @ SY62 @ SY52 )
= SY62 )
& ! [SY63: g] :
? [SY64: g] :
( ( sK1_SY0 @ SY63 @ SY64 )
= SY52 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ( ! [SY53: g,SY54: g,SY55: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY53 @ SY54 ) @ SY55 )
= ( sK1_SY0 @ SY53 @ ( sK1_SY0 @ SY54 @ SY55 ) ) )
& ! [SY68: g] :
( ( sK1_SY0 @ sK2_SY52 @ SY68 )
= SY68 )
& ! [SY69: g] :
? [SY70: g] :
( ( sK1_SY0 @ SY70 @ SY69 )
= sK2_SY52 ) )
<=> ( ! [SY59: g,SY60: g,SY61: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY59 @ SY60 ) @ SY61 )
= ( sK1_SY0 @ SY59 @ ( sK1_SY0 @ SY60 @ SY61 ) ) )
& ! [SY74: g] :
( ( sK1_SY0 @ SY74 @ sK2_SY52 )
= SY74 )
& ! [SY75: g] :
? [SY76: g] :
( ( sK1_SY0 @ SY75 @ SY76 )
= sK2_SY52 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ( ! [SY53: g,SY54: g,SY55: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY53 @ SY54 ) @ SY55 )
= ( sK1_SY0 @ SY53 @ ( sK1_SY0 @ SY54 @ SY55 ) ) )
& ! [SY68: g] :
( ( sK1_SY0 @ sK2_SY52 @ SY68 )
= SY68 )
& ! [SY69: g] :
? [SY70: g] :
( ( sK1_SY0 @ SY70 @ SY69 )
= sK2_SY52 ) )
=> ( ! [SY59: g,SY60: g,SY61: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY59 @ SY60 ) @ SY61 )
= ( sK1_SY0 @ SY59 @ ( sK1_SY0 @ SY60 @ SY61 ) ) )
& ! [SY74: g] :
( ( sK1_SY0 @ SY74 @ sK2_SY52 )
= SY74 )
& ! [SY75: g] :
? [SY76: g] :
( ( sK1_SY0 @ SY75 @ SY76 )
= sK2_SY52 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[5]) ).
thf(7,plain,
( ( ( ! [SY59: g,SY60: g,SY61: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY59 @ SY60 ) @ SY61 )
= ( sK1_SY0 @ SY59 @ ( sK1_SY0 @ SY60 @ SY61 ) ) )
& ! [SY74: g] :
( ( sK1_SY0 @ SY74 @ sK2_SY52 )
= SY74 )
& ! [SY75: g] :
? [SY76: g] :
( ( sK1_SY0 @ SY75 @ SY76 )
= sK2_SY52 ) )
=> ( ! [SY53: g,SY54: g,SY55: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY53 @ SY54 ) @ SY55 )
= ( sK1_SY0 @ SY53 @ ( sK1_SY0 @ SY54 @ SY55 ) ) )
& ! [SY68: g] :
( ( sK1_SY0 @ sK2_SY52 @ SY68 )
= SY68 )
& ! [SY69: g] :
? [SY70: g] :
( ( sK1_SY0 @ SY70 @ SY69 )
= sK2_SY52 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[5]) ).
thf(8,plain,
( ( ~ ( ( ! [SY53: g,SY54: g,SY55: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY53 @ SY54 ) @ SY55 )
= ( sK1_SY0 @ SY53 @ ( sK1_SY0 @ SY54 @ SY55 ) ) )
& ! [SY68: g] :
( ( sK1_SY0 @ sK2_SY52 @ SY68 )
= SY68 )
& ! [SY69: g] :
? [SY70: g] :
( ( sK1_SY0 @ SY70 @ SY69 )
= sK2_SY52 ) )
=> ( ! [SY59: g,SY60: g,SY61: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY59 @ SY60 ) @ SY61 )
= ( sK1_SY0 @ SY59 @ ( sK1_SY0 @ SY60 @ SY61 ) ) )
& ! [SY74: g] :
( ( sK1_SY0 @ SY74 @ sK2_SY52 )
= SY74 )
& ! [SY75: g] :
? [SY76: g] :
( ( sK1_SY0 @ SY75 @ SY76 )
= sK2_SY52 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ( ( ! [SY59: g,SY60: g,SY61: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY59 @ SY60 ) @ SY61 )
= ( sK1_SY0 @ SY59 @ ( sK1_SY0 @ SY60 @ SY61 ) ) )
& ! [SY74: g] :
( ( sK1_SY0 @ SY74 @ sK2_SY52 )
= SY74 )
& ! [SY75: g] :
? [SY76: g] :
( ( sK1_SY0 @ SY75 @ SY76 )
= sK2_SY52 ) )
=> ( ! [SY53: g,SY54: g,SY55: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY53 @ SY54 ) @ SY55 )
= ( sK1_SY0 @ SY53 @ ( sK1_SY0 @ SY54 @ SY55 ) ) )
& ! [SY68: g] :
( ( sK1_SY0 @ sK2_SY52 @ SY68 )
= SY68 )
& ! [SY69: g] :
? [SY70: g] :
( ( sK1_SY0 @ SY70 @ SY69 )
= sK2_SY52 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [SY69: g] :
( ( sK1_SY0 @ ( sK8_SY70 @ SY69 ) @ SY69 )
= sK2_SY52 )
& ! [SY53: g,SY54: g,SY55: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY53 @ SY54 ) @ SY55 )
= ( sK1_SY0 @ SY53 @ ( sK1_SY0 @ SY54 @ SY55 ) ) )
& ! [SY68: g] :
( ( sK1_SY0 @ sK2_SY52 @ SY68 )
= SY68 )
& ( ! [SY80: g] :
( ( sK1_SY0 @ sK7_SY75 @ SY80 )
!= sK2_SY52 )
| ( ( sK1_SY0 @ ( sK1_SY0 @ sK4_SY59 @ sK5_SY77 ) @ sK6_SY79 )
!= ( sK1_SY0 @ sK4_SY59 @ ( sK1_SY0 @ sK5_SY77 @ sK6_SY79 ) ) )
| ( ( sK1_SY0 @ sK3_SY74 @ sK2_SY52 )
!= sK3_SY74 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(11,plain,
( ( ! [SY75: g] :
( ( sK1_SY0 @ SY75 @ ( sK14_SY76 @ SY75 ) )
= sK2_SY52 )
& ! [SY59: g,SY60: g,SY61: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY59 @ SY60 ) @ SY61 )
= ( sK1_SY0 @ SY59 @ ( sK1_SY0 @ SY60 @ SY61 ) ) )
& ! [SY74: g] :
( ( sK1_SY0 @ SY74 @ sK2_SY52 )
= SY74 )
& ( ! [SY84: g] :
( ( sK1_SY0 @ SY84 @ sK13_SY69 )
!= sK2_SY52 )
| ( ( sK1_SY0 @ ( sK1_SY0 @ sK10_SY53 @ sK11_SY81 ) @ sK12_SY83 )
!= ( sK1_SY0 @ sK10_SY53 @ ( sK1_SY0 @ sK11_SY81 @ sK12_SY83 ) ) )
| ( ( sK1_SY0 @ sK2_SY52 @ sK9_SY68 )
!= sK9_SY68 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(12,plain,
( ( ! [SY69: g] :
( ( sK1_SY0 @ ( sK8_SY70 @ SY69 ) @ SY69 )
= sK2_SY52 )
& ! [SY53: g,SY54: g,SY55: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY53 @ SY54 ) @ SY55 )
= ( sK1_SY0 @ SY53 @ ( sK1_SY0 @ SY54 @ SY55 ) ) )
& ! [SY68: g] :
( ( sK1_SY0 @ sK2_SY52 @ SY68 )
= SY68 )
& ( ! [SY80: g] :
( ( sK1_SY0 @ sK7_SY75 @ SY80 )
!= sK2_SY52 )
| ( ( sK1_SY0 @ ( sK1_SY0 @ sK4_SY59 @ sK5_SY77 ) @ sK6_SY79 )
!= ( sK1_SY0 @ sK4_SY59 @ ( sK1_SY0 @ sK5_SY77 @ sK6_SY79 ) ) )
| ( ( sK1_SY0 @ sK3_SY74 @ sK2_SY52 )
!= sK3_SY74 ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: g] :
( ( sK1_SY0 @ ( sK8_SY70 @ SX0 ) @ SX0 )
= sK2_SY52 )
| ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX0 @ SX1 ) @ SX2 )
= ( sK1_SY0 @ SX0 @ ( sK1_SY0 @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_SY0 @ sK2_SY52 @ SX0 )
= SX0 ) ) )
| ~ ( ! [SX0: g] :
( ( sK1_SY0 @ sK7_SY75 @ SX0 )
!= sK2_SY52 )
| ( ( sK1_SY0 @ ( sK1_SY0 @ sK4_SY59 @ sK5_SY77 ) @ sK6_SY79 )
!= ( sK1_SY0 @ sK4_SY59 @ ( sK1_SY0 @ sK5_SY77 @ sK6_SY79 ) ) )
| ( ( sK1_SY0 @ sK3_SY74 @ sK2_SY52 )
!= sK3_SY74 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,cGROUP2,cGROUP3,cGRP_ASSOC,cGRP_LEFT_INVERSE,cGRP_LEFT_UNIT,cGRP_RIGHT_INVERSE,cGRP_RIGHT_UNIT]) ).
thf(14,plain,
( ( ~ ~ ( ~ ! [SX0: g] :
( ( sK1_SY0 @ ( sK8_SY70 @ SX0 ) @ SX0 )
= sK2_SY52 )
| ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX0 @ SX1 ) @ SX2 )
= ( sK1_SY0 @ SX0 @ ( sK1_SY0 @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_SY0 @ sK2_SY52 @ SX0 )
= SX0 ) ) )
| ~ ( ! [SX0: g] :
( ( sK1_SY0 @ sK7_SY75 @ SX0 )
!= sK2_SY52 )
| ( ( sK1_SY0 @ ( sK1_SY0 @ sK4_SY59 @ sK5_SY77 ) @ sK6_SY79 )
!= ( sK1_SY0 @ sK4_SY59 @ ( sK1_SY0 @ sK5_SY77 @ sK6_SY79 ) ) )
| ( ( sK1_SY0 @ sK3_SY74 @ sK2_SY52 )
!= sK3_SY74 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(15,plain,
( ( ~ ~ ( ~ ! [SX0: g] :
( ( sK1_SY0 @ ( sK8_SY70 @ SX0 ) @ SX0 )
= sK2_SY52 )
| ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX0 @ SX1 ) @ SX2 )
= ( sK1_SY0 @ SX0 @ ( sK1_SY0 @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_SY0 @ sK2_SY52 @ SX0 )
= SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(16,plain,
( ( ~ ( ! [SX0: g] :
( ( sK1_SY0 @ sK7_SY75 @ SX0 )
!= sK2_SY52 )
| ( ( sK1_SY0 @ ( sK1_SY0 @ sK4_SY59 @ sK5_SY77 ) @ sK6_SY79 )
!= ( sK1_SY0 @ sK4_SY59 @ ( sK1_SY0 @ sK5_SY77 @ sK6_SY79 ) ) )
| ( ( sK1_SY0 @ sK3_SY74 @ sK2_SY52 )
!= sK3_SY74 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ( ~ ! [SX0: g] :
( ( sK1_SY0 @ ( sK8_SY70 @ SX0 ) @ SX0 )
= sK2_SY52 )
| ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX0 @ SX1 ) @ SX2 )
= ( sK1_SY0 @ SX0 @ ( sK1_SY0 @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_SY0 @ sK2_SY52 @ SX0 )
= SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(18,plain,
( ( ! [SX0: g] :
( ( sK1_SY0 @ sK7_SY75 @ SX0 )
!= sK2_SY52 )
| ( ( sK1_SY0 @ ( sK1_SY0 @ sK4_SY59 @ sK5_SY77 ) @ sK6_SY79 )
!= ( sK1_SY0 @ sK4_SY59 @ ( sK1_SY0 @ sK5_SY77 @ sK6_SY79 ) ) )
| ( ( sK1_SY0 @ sK3_SY74 @ sK2_SY52 )
!= sK3_SY74 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ! [SX0: g] :
( ( sK1_SY0 @ ( sK8_SY70 @ SX0 ) @ SX0 )
= sK2_SY52 )
| ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX0 @ SX1 ) @ SX2 )
= ( sK1_SY0 @ SX0 @ ( sK1_SY0 @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_SY0 @ sK2_SY52 @ SX0 )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(20,plain,
( ( ( ! [SX0: g] :
( ( sK1_SY0 @ sK7_SY75 @ SX0 )
!= sK2_SY52 ) )
= $true )
| ( ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK4_SY59 @ sK5_SY77 ) @ sK6_SY79 )
!= ( sK1_SY0 @ sK4_SY59 @ ( sK1_SY0 @ sK5_SY77 @ sK6_SY79 ) ) )
| ( ( sK1_SY0 @ sK3_SY74 @ sK2_SY52 )
!= sK3_SY74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(21,plain,
( ( ~ ! [SX0: g] :
( ( sK1_SY0 @ ( sK8_SY70 @ SX0 ) @ SX0 )
= sK2_SY52 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(22,plain,
( ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX0 @ SX1 ) @ SX2 )
= ( sK1_SY0 @ SX0 @ ( sK1_SY0 @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_SY0 @ sK2_SY52 @ SX0 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(23,plain,
! [SV1: g] :
( ( ( ( sK1_SY0 @ sK7_SY75 @ SV1 )
!= sK2_SY52 )
= $true )
| ( ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK4_SY59 @ sK5_SY77 ) @ sK6_SY79 )
!= ( sK1_SY0 @ sK4_SY59 @ ( sK1_SY0 @ sK5_SY77 @ sK6_SY79 ) ) )
| ( ( sK1_SY0 @ sK3_SY74 @ sK2_SY52 )
!= sK3_SY74 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(24,plain,
( ( ! [SX0: g] :
( ( sK1_SY0 @ ( sK8_SY70 @ SX0 ) @ SX0 )
= sK2_SY52 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(25,plain,
( ( ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX0 @ SX1 ) @ SX2 )
= ( sK1_SY0 @ SX0 @ ( sK1_SY0 @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_SY0 @ sK2_SY52 @ SX0 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(26,plain,
! [SV1: g] :
( ( ( ( sK1_SY0 @ sK7_SY75 @ SV1 )
= sK2_SY52 )
= $false )
| ( ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK4_SY59 @ sK5_SY77 ) @ sK6_SY79 )
!= ( sK1_SY0 @ sK4_SY59 @ ( sK1_SY0 @ sK5_SY77 @ sK6_SY79 ) ) )
| ( ( sK1_SY0 @ sK3_SY74 @ sK2_SY52 )
!= sK3_SY74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(27,plain,
! [SV2: g] :
( ( ( sK1_SY0 @ ( sK8_SY70 @ SV2 ) @ SV2 )
= sK2_SY52 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(28,plain,
( ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX0 @ SX1 ) @ SX2 )
= ( sK1_SY0 @ SX0 @ ( sK1_SY0 @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_SY0 @ sK2_SY52 @ SX0 )
= SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV1: g] :
( ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK4_SY59 @ sK5_SY77 ) @ sK6_SY79 )
!= ( sK1_SY0 @ sK4_SY59 @ ( sK1_SY0 @ sK5_SY77 @ sK6_SY79 ) ) )
= $true )
| ( ( ( sK1_SY0 @ sK3_SY74 @ sK2_SY52 )
!= sK3_SY74 )
= $true )
| ( ( ( sK1_SY0 @ sK7_SY75 @ SV1 )
= sK2_SY52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(30,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)],[28]) ).
thf(31,plain,
( ( ~ ! [SX0: g] :
( ( sK1_SY0 @ sK2_SY52 @ SX0 )
= SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(32,plain,
! [SV1: g] :
( ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK4_SY59 @ sK5_SY77 ) @ sK6_SY79 )
= ( sK1_SY0 @ sK4_SY59 @ ( sK1_SY0 @ sK5_SY77 @ sK6_SY79 ) ) )
= $false )
| ( ( ( sK1_SY0 @ sK3_SY74 @ sK2_SY52 )
!= sK3_SY74 )
= $true )
| ( ( ( sK1_SY0 @ sK7_SY75 @ SV1 )
= sK2_SY52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(33,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)],[30]) ).
thf(34,plain,
( ( ! [SX0: g] :
( ( sK1_SY0 @ sK2_SY52 @ SX0 )
= SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(35,plain,
! [SV1: g] :
( ( ( ( sK1_SY0 @ sK3_SY74 @ sK2_SY52 )
= sK3_SY74 )
= $false )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK4_SY59 @ sK5_SY77 ) @ sK6_SY79 )
= ( sK1_SY0 @ sK4_SY59 @ ( sK1_SY0 @ sK5_SY77 @ sK6_SY79 ) ) )
= $false )
| ( ( ( sK1_SY0 @ sK7_SY75 @ SV1 )
= sK2_SY52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(36,plain,
! [SV3: g] :
( ( ! [SY85: g,SY86: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SV3 @ SY85 ) @ SY86 )
= ( sK1_SY0 @ SV3 @ ( sK1_SY0 @ SY85 @ SY86 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV4: g] :
( ( ( sK1_SY0 @ sK2_SY52 @ SV4 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV5: g,SV3: g] :
( ( ! [SY87: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SV3 @ SV5 ) @ SY87 )
= ( sK1_SY0 @ SV3 @ ( sK1_SY0 @ SV5 @ SY87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV6: g,SV5: g,SV3: g] :
( ( ( sK1_SY0 @ ( sK1_SY0 @ SV3 @ SV5 ) @ SV6 )
= ( sK1_SY0 @ SV3 @ ( sK1_SY0 @ SV5 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(40,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[27,39,37,35]) ).
thf(41,plain,
( ( ! [SY75: g] :
( ( sK1_SY0 @ SY75 @ ( sK14_SY76 @ SY75 ) )
= sK2_SY52 )
& ! [SY59: g,SY60: g,SY61: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY59 @ SY60 ) @ SY61 )
= ( sK1_SY0 @ SY59 @ ( sK1_SY0 @ SY60 @ SY61 ) ) )
& ! [SY74: g] :
( ( sK1_SY0 @ SY74 @ sK2_SY52 )
= SY74 )
& ( ! [SY84: g] :
( ( sK1_SY0 @ SY84 @ sK13_SY69 )
!= sK2_SY52 )
| ( ( sK1_SY0 @ ( sK1_SY0 @ sK10_SY53 @ sK11_SY81 ) @ sK12_SY83 )
!= ( sK1_SY0 @ sK10_SY53 @ ( sK1_SY0 @ sK11_SY81 @ sK12_SY83 ) ) )
| ( ( sK1_SY0 @ sK2_SY52 @ sK9_SY68 )
!= sK9_SY68 ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(42,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ ( sK14_SY76 @ SX0 ) )
= sK2_SY52 )
| ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX0 @ SX1 ) @ SX2 )
= ( sK1_SY0 @ SX0 @ ( sK1_SY0 @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ sK2_SY52 )
= SX0 ) ) )
| ~ ( ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ sK13_SY69 )
!= sK2_SY52 )
| ( ( sK1_SY0 @ ( sK1_SY0 @ sK10_SY53 @ sK11_SY81 ) @ sK12_SY83 )
!= ( sK1_SY0 @ sK10_SY53 @ ( sK1_SY0 @ sK11_SY81 @ sK12_SY83 ) ) )
| ( ( sK1_SY0 @ sK2_SY52 @ sK9_SY68 )
!= sK9_SY68 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41,cGROUP2,cGROUP3,cGRP_ASSOC,cGRP_LEFT_INVERSE,cGRP_LEFT_UNIT,cGRP_RIGHT_INVERSE,cGRP_RIGHT_UNIT]) ).
thf(43,plain,
( ( ~ ~ ( ~ ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ ( sK14_SY76 @ SX0 ) )
= sK2_SY52 )
| ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX0 @ SX1 ) @ SX2 )
= ( sK1_SY0 @ SX0 @ ( sK1_SY0 @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ sK2_SY52 )
= SX0 ) ) )
| ~ ( ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ sK13_SY69 )
!= sK2_SY52 )
| ( ( sK1_SY0 @ ( sK1_SY0 @ sK10_SY53 @ sK11_SY81 ) @ sK12_SY83 )
!= ( sK1_SY0 @ sK10_SY53 @ ( sK1_SY0 @ sK11_SY81 @ sK12_SY83 ) ) )
| ( ( sK1_SY0 @ sK2_SY52 @ sK9_SY68 )
!= sK9_SY68 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(44,plain,
( ( ~ ~ ( ~ ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ ( sK14_SY76 @ SX0 ) )
= sK2_SY52 )
| ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX0 @ SX1 ) @ SX2 )
= ( sK1_SY0 @ SX0 @ ( sK1_SY0 @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ sK2_SY52 )
= SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(45,plain,
( ( ~ ( ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ sK13_SY69 )
!= sK2_SY52 )
| ( ( sK1_SY0 @ ( sK1_SY0 @ sK10_SY53 @ sK11_SY81 ) @ sK12_SY83 )
!= ( sK1_SY0 @ sK10_SY53 @ ( sK1_SY0 @ sK11_SY81 @ sK12_SY83 ) ) )
| ( ( sK1_SY0 @ sK2_SY52 @ sK9_SY68 )
!= sK9_SY68 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(46,plain,
( ( ~ ( ~ ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ ( sK14_SY76 @ SX0 ) )
= sK2_SY52 )
| ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX0 @ SX1 ) @ SX2 )
= ( sK1_SY0 @ SX0 @ ( sK1_SY0 @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ sK2_SY52 )
= SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(47,plain,
( ( ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ sK13_SY69 )
!= sK2_SY52 )
| ( ( sK1_SY0 @ ( sK1_SY0 @ sK10_SY53 @ sK11_SY81 ) @ sK12_SY83 )
!= ( sK1_SY0 @ sK10_SY53 @ ( sK1_SY0 @ sK11_SY81 @ sK12_SY83 ) ) )
| ( ( sK1_SY0 @ sK2_SY52 @ sK9_SY68 )
!= sK9_SY68 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(48,plain,
( ( ~ ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ ( sK14_SY76 @ SX0 ) )
= sK2_SY52 )
| ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX0 @ SX1 ) @ SX2 )
= ( sK1_SY0 @ SX0 @ ( sK1_SY0 @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ sK2_SY52 )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(49,plain,
( ( ( ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ sK13_SY69 )
!= sK2_SY52 ) )
= $true )
| ( ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK10_SY53 @ sK11_SY81 ) @ sK12_SY83 )
!= ( sK1_SY0 @ sK10_SY53 @ ( sK1_SY0 @ sK11_SY81 @ sK12_SY83 ) ) )
| ( ( sK1_SY0 @ sK2_SY52 @ sK9_SY68 )
!= sK9_SY68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(50,plain,
( ( ~ ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ ( sK14_SY76 @ SX0 ) )
= sK2_SY52 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(51,plain,
( ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX0 @ SX1 ) @ SX2 )
= ( sK1_SY0 @ SX0 @ ( sK1_SY0 @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ sK2_SY52 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(52,plain,
! [SV7: g] :
( ( ( ( sK1_SY0 @ SV7 @ sK13_SY69 )
!= sK2_SY52 )
= $true )
| ( ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK10_SY53 @ sK11_SY81 ) @ sK12_SY83 )
!= ( sK1_SY0 @ sK10_SY53 @ ( sK1_SY0 @ sK11_SY81 @ sK12_SY83 ) ) )
| ( ( sK1_SY0 @ sK2_SY52 @ sK9_SY68 )
!= sK9_SY68 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(53,plain,
( ( ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ ( sK14_SY76 @ SX0 ) )
= sK2_SY52 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(54,plain,
( ( ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX0 @ SX1 ) @ SX2 )
= ( sK1_SY0 @ SX0 @ ( sK1_SY0 @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ sK2_SY52 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(55,plain,
! [SV7: g] :
( ( ( ( sK1_SY0 @ SV7 @ sK13_SY69 )
= sK2_SY52 )
= $false )
| ( ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK10_SY53 @ sK11_SY81 ) @ sK12_SY83 )
!= ( sK1_SY0 @ sK10_SY53 @ ( sK1_SY0 @ sK11_SY81 @ sK12_SY83 ) ) )
| ( ( sK1_SY0 @ sK2_SY52 @ sK9_SY68 )
!= sK9_SY68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(56,plain,
! [SV8: g] :
( ( ( sK1_SY0 @ SV8 @ ( sK14_SY76 @ SV8 ) )
= sK2_SY52 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(57,plain,
( ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SX0 @ SX1 ) @ SX2 )
= ( sK1_SY0 @ SX0 @ ( sK1_SY0 @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ sK2_SY52 )
= SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(58,plain,
! [SV7: g] :
( ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK10_SY53 @ sK11_SY81 ) @ sK12_SY83 )
!= ( sK1_SY0 @ sK10_SY53 @ ( sK1_SY0 @ sK11_SY81 @ sK12_SY83 ) ) )
= $true )
| ( ( ( sK1_SY0 @ sK2_SY52 @ sK9_SY68 )
!= sK9_SY68 )
= $true )
| ( ( ( sK1_SY0 @ SV7 @ sK13_SY69 )
= sK2_SY52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(59,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)],[57]) ).
thf(60,plain,
( ( ~ ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ sK2_SY52 )
= SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(61,plain,
! [SV7: g] :
( ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK10_SY53 @ sK11_SY81 ) @ sK12_SY83 )
= ( sK1_SY0 @ sK10_SY53 @ ( sK1_SY0 @ sK11_SY81 @ sK12_SY83 ) ) )
= $false )
| ( ( ( sK1_SY0 @ sK2_SY52 @ sK9_SY68 )
!= sK9_SY68 )
= $true )
| ( ( ( sK1_SY0 @ SV7 @ sK13_SY69 )
= sK2_SY52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(62,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)],[59]) ).
thf(63,plain,
( ( ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ sK2_SY52 )
= SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(64,plain,
! [SV7: g] :
( ( ( ( sK1_SY0 @ sK2_SY52 @ sK9_SY68 )
= sK9_SY68 )
= $false )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK10_SY53 @ sK11_SY81 ) @ sK12_SY83 )
= ( sK1_SY0 @ sK10_SY53 @ ( sK1_SY0 @ sK11_SY81 @ sK12_SY83 ) ) )
= $false )
| ( ( ( sK1_SY0 @ SV7 @ sK13_SY69 )
= sK2_SY52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(65,plain,
! [SV9: g] :
( ( ! [SY88: g,SY89: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SV9 @ SY88 ) @ SY89 )
= ( sK1_SY0 @ SV9 @ ( sK1_SY0 @ SY88 @ SY89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(66,plain,
! [SV10: g] :
( ( ( sK1_SY0 @ SV10 @ sK2_SY52 )
= SV10 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(67,plain,
! [SV11: g,SV9: g] :
( ( ! [SY90: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SV9 @ SV11 ) @ SY90 )
= ( sK1_SY0 @ SV9 @ ( sK1_SY0 @ SV11 @ SY90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(68,plain,
! [SV12: g,SV11: g,SV9: g] :
( ( ( sK1_SY0 @ ( sK1_SY0 @ SV9 @ SV11 ) @ SV12 )
= ( sK1_SY0 @ SV9 @ ( sK1_SY0 @ SV11 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(69,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[56,68,66,64]) ).
thf(70,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[69,40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG273^5 : 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
% 0.11/0.16 % Computer : n019.cluster.edu
% 0.11/0.16 % Model : x86_64 x86_64
% 0.11/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.16 % Memory : 8046.5625MB
% 0.11/0.16 % OS : Linux 6.8.0-71-generic
% 0.11/0.16 % CPULimit : 300
% 0.11/0.16 % WCLimit : 300
% 0.11/0.16 % DateTime : Tue Oct 6 18:10:01 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
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% 0.11/0.23 No.of.Axioms: 0
% 0.11/0.23
% 0.11/0.23 Length.of.Defs: 1416
% 0.11/0.23
% 0.11/0.23 Contains.Choice.Funs: false
% 0.11/0.23 ...
% 0.11/0.23
% 0.11/0.23 ********************************
% 0.11/0.23 * All subproblems solved! *
% 0.11/0.23 ********************************
% 0.11/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:69,loop_count:0,foatp_calls:1,translation:fof_full)
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% 0.11/0.23 %**** Beginning of derivation protocol ****
% 0.11/0.23 % SZS output start CNFRefutation
% See solution above
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% 0.11/0.23 %**** End of derivation protocol ****
% 0.11/0.23 %**** no. of clauses in derivation: 70 ****
% 0.11/0.23 %**** clause counter: 69 ****
% 0.11/0.23
% 0.11/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:69,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------