%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ALG274^5 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 0.08s 0.24s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 7
% Syntax : Number of formulae : 79 ( 65 unt; 0 typ; 6 def)
% Number of atoms : 405 ( 295 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 1275 ( 159 ~; 82 |; 40 &; 986 @)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 10 con; 0-2 aty)
% Number of variables : 320 ( 9 ^; 282 !; 29 ?; 320 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_g,type,
g: $tType ).
thf(tp_cGROUP3,type,
cGROUP3: ( 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_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_SY66,type,
sK10_SY66: g > g ).
thf(tp_sK11_SY46,type,
sK11_SY46: g > g ).
thf(tp_sK12_SY43,type,
sK12_SY43: g > g ).
thf(tp_sK13_SY71,type,
sK13_SY71: g > g ).
thf(tp_sK14_SY73,type,
sK14_SY73: g > g ).
thf(tp_sK15_SY47,type,
sK15_SY47: g > g ).
thf(tp_sK16_SY55,type,
sK16_SY55: g > g > g ).
thf(tp_sK17_SY54,type,
sK17_SY54: g > g > g ).
thf(tp_sK1_SY0,type,
sK1_SY0: g > g > g ).
thf(tp_sK2_SY52,type,
sK2_SY52: g ).
thf(tp_sK3_SY56,type,
sK3_SY56: g ).
thf(tp_sK4_SY52,type,
sK4_SY52: g ).
thf(tp_sK5_SY59,type,
sK5_SY59: g ).
thf(tp_sK6_SY49,type,
sK6_SY49: g ).
thf(tp_sK7_SY62,type,
sK7_SY62: g ).
thf(tp_sK8_SY64,type,
sK8_SY64: g ).
thf(tp_sK9_SY42,type,
sK9_SY42: g ).
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/sandbox/benchmark/theBenchmark.p',cGROUP3_def) ).
thf(cGROUP4,definition,
( cGROUP4
= ( ^ [Xf: g > g > g] :
( ( cGRP_ASSOC @ Xf )
& ( cGRP_DIVISORS @ Xf ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cGRP_DIVISORS_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cGRP_RIGHT_UNIT_def) ).
thf(1,conjecture,
! [Xf: g > g > g] :
( ? [Xe: g] : ( cGROUP3 @ Xf @ Xe )
<=> ( cGROUP4 @ Xf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEQUIV_03_04) ).
thf(2,negated_conjecture,
( ( ! [Xf: g > g > g] :
( ? [Xe: g] : ( cGROUP3 @ 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 @ SY17 @ SY1 )
= SY17 )
& ! [SY18: g] :
? [SY19: g] :
( ( SY0 @ SY18 @ SY19 )
= 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,cGROUP3,cGROUP4,cGRP_ASSOC,cGRP_DIVISORS,cGRP_RIGHT_INVERSE,cGRP_RIGHT_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 @ SY46 @ SY42 )
= SY46 )
& ! [SY47: g] :
? [SY48: g] :
( ( sK1_SY0 @ SY47 @ SY48 )
= 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 @ SY46 @ SY42 )
= SY46 )
& ! [SY47: g] :
? [SY48: g] :
( ( sK1_SY0 @ SY47 @ SY48 )
= 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 @ SY46 @ SY42 )
= SY46 )
& ! [SY47: g] :
? [SY48: g] :
( ( sK1_SY0 @ SY47 @ SY48 )
= 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 @ SY46 @ SY42 )
= SY46 )
& ! [SY47: g] :
? [SY48: g] :
( ( sK1_SY0 @ SY47 @ SY48 )
= 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 @ SY46 @ SY42 )
= SY46 )
& ! [SY47: g] :
? [SY48: g] :
( ( sK1_SY0 @ SY47 @ SY48 )
= SY42 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(9,plain,
( ( ! [SY65: g] :
( ( sK1_SY0 @ SY65 @ ( sK10_SY66 @ SY65 ) )
= sK9_SY42 )
& ! [SY43: g,SY44: g,SY45: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY43 @ SY44 ) @ SY45 )
= ( sK1_SY0 @ SY43 @ ( sK1_SY0 @ SY44 @ SY45 ) ) )
& ! [SY70: g] :
( ( sK1_SY0 @ SY70 @ sK9_SY42 )
= SY70 )
& ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK6_SY49 @ sK7_SY62 ) @ sK8_SY64 )
!= ( sK1_SY0 @ sK6_SY49 @ ( sK1_SY0 @ sK7_SY62 @ sK8_SY64 ) ) )
| ! [SY61: g] :
( ( sK1_SY0 @ sK4_SY52 @ SY61 )
!= sK5_SY59 )
| ! [SY58: g] :
( ( sK1_SY0 @ SY58 @ sK2_SY52 )
!= sK3_SY56 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(10,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] :
( ( sK1_SY0 @ SY52 @ ( sK17_SY54 @ SY53 @ SY52 ) )
= SY53 )
& ! [SY52: g,SY53: g] :
( ( sK1_SY0 @ ( sK16_SY55 @ SY53 @ SY52 ) @ SY52 )
= SY53 )
& ! [SY42: g] :
( ! [SY74: g] :
( ( sK1_SY0 @ ( sK15_SY47 @ SY42 ) @ SY74 )
!= SY42 )
| ( ( sK1_SY0 @ ( sK1_SY0 @ ( sK12_SY43 @ SY42 ) @ ( sK13_SY71 @ SY42 ) ) @ ( sK14_SY73 @ SY42 ) )
!= ( sK1_SY0 @ ( sK12_SY43 @ SY42 ) @ ( sK1_SY0 @ ( sK13_SY71 @ SY42 ) @ ( sK14_SY73 @ SY42 ) ) ) )
| ( ( sK1_SY0 @ ( sK11_SY46 @ SY42 ) @ SY42 )
!= ( sK11_SY46 @ SY42 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(11,plain,
( ( ! [SY65: g] :
( ( sK1_SY0 @ SY65 @ ( sK10_SY66 @ SY65 ) )
= sK9_SY42 )
& ! [SY43: g,SY44: g,SY45: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY43 @ SY44 ) @ SY45 )
= ( sK1_SY0 @ SY43 @ ( sK1_SY0 @ SY44 @ SY45 ) ) )
& ! [SY70: g] :
( ( sK1_SY0 @ SY70 @ sK9_SY42 )
= SY70 )
& ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK6_SY49 @ sK7_SY62 ) @ sK8_SY64 )
!= ( sK1_SY0 @ sK6_SY49 @ ( sK1_SY0 @ sK7_SY62 @ sK8_SY64 ) ) )
| ! [SY61: g] :
( ( sK1_SY0 @ sK4_SY52 @ SY61 )
!= sK5_SY59 )
| ! [SY58: g] :
( ( sK1_SY0 @ SY58 @ sK2_SY52 )
!= sK3_SY56 ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ ( sK10_SY66 @ SX0 ) )
= sK9_SY42 )
| ~ ~ ( ~ ! [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 @ sK9_SY42 )
= SX0 ) ) )
| ~ ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK6_SY49 @ sK7_SY62 ) @ sK8_SY64 )
!= ( sK1_SY0 @ sK6_SY49 @ ( sK1_SY0 @ sK7_SY62 @ sK8_SY64 ) ) )
| ! [SX0: g] :
( ( sK1_SY0 @ sK4_SY52 @ SX0 )
!= sK5_SY59 )
| ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ sK2_SY52 )
!= sK3_SY56 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,cGROUP3,cGROUP4,cGRP_ASSOC,cGRP_DIVISORS,cGRP_RIGHT_INVERSE,cGRP_RIGHT_UNIT]) ).
thf(13,plain,
( ( ~ ~ ( ~ ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ ( sK10_SY66 @ SX0 ) )
= sK9_SY42 )
| ~ ~ ( ~ ! [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 @ sK9_SY42 )
= SX0 ) ) )
| ~ ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK6_SY49 @ sK7_SY62 ) @ sK8_SY64 )
!= ( sK1_SY0 @ sK6_SY49 @ ( sK1_SY0 @ sK7_SY62 @ sK8_SY64 ) ) )
| ! [SX0: g] :
( ( sK1_SY0 @ sK4_SY52 @ SX0 )
!= sK5_SY59 )
| ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ sK2_SY52 )
!= sK3_SY56 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(14,plain,
( ( ~ ~ ( ~ ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ ( sK10_SY66 @ SX0 ) )
= sK9_SY42 )
| ~ ~ ( ~ ! [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 @ sK9_SY42 )
= SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(15,plain,
( ( ~ ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK6_SY49 @ sK7_SY62 ) @ sK8_SY64 )
!= ( sK1_SY0 @ sK6_SY49 @ ( sK1_SY0 @ sK7_SY62 @ sK8_SY64 ) ) )
| ! [SX0: g] :
( ( sK1_SY0 @ sK4_SY52 @ SX0 )
!= sK5_SY59 )
| ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ sK2_SY52 )
!= sK3_SY56 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( ~ ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ ( sK10_SY66 @ SX0 ) )
= sK9_SY42 )
| ~ ~ ( ~ ! [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 @ sK9_SY42 )
= SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK6_SY49 @ sK7_SY62 ) @ sK8_SY64 )
!= ( sK1_SY0 @ sK6_SY49 @ ( sK1_SY0 @ sK7_SY62 @ sK8_SY64 ) ) )
| ! [SX0: g] :
( ( sK1_SY0 @ sK4_SY52 @ SX0 )
!= sK5_SY59 )
| ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ sK2_SY52 )
!= sK3_SY56 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ ( sK10_SY66 @ SX0 ) )
= sK9_SY42 )
| ~ ~ ( ~ ! [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 @ sK9_SY42 )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK6_SY49 @ sK7_SY62 ) @ sK8_SY64 )
!= ( sK1_SY0 @ sK6_SY49 @ ( sK1_SY0 @ sK7_SY62 @ sK8_SY64 ) ) )
= $true )
| ( ( ! [SX0: g] :
( ( sK1_SY0 @ sK4_SY52 @ SX0 )
!= sK5_SY59 )
| ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ sK2_SY52 )
!= sK3_SY56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ ( sK10_SY66 @ SX0 ) )
= sK9_SY42 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(21,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 @ sK9_SY42 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(22,plain,
( ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK6_SY49 @ sK7_SY62 ) @ sK8_SY64 )
= ( sK1_SY0 @ sK6_SY49 @ ( sK1_SY0 @ sK7_SY62 @ sK8_SY64 ) ) )
= $false )
| ( ( ! [SX0: g] :
( ( sK1_SY0 @ sK4_SY52 @ SX0 )
!= sK5_SY59 )
| ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ sK2_SY52 )
!= sK3_SY56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(23,plain,
( ( ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ ( sK10_SY66 @ SX0 ) )
= sK9_SY42 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(24,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 @ sK9_SY42 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(25,plain,
( ( ( ! [SX0: g] :
( ( sK1_SY0 @ sK4_SY52 @ SX0 )
!= sK5_SY59 ) )
= $true )
| ( ( ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ sK2_SY52 )
!= sK3_SY56 ) )
= $true )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK6_SY49 @ sK7_SY62 ) @ sK8_SY64 )
= ( sK1_SY0 @ sK6_SY49 @ ( sK1_SY0 @ sK7_SY62 @ sK8_SY64 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(26,plain,
! [SV1: g] :
( ( ( sK1_SY0 @ SV1 @ ( sK10_SY66 @ SV1 ) )
= sK9_SY42 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(27,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 @ sK9_SY42 )
= SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(28,plain,
! [SV2: g] :
( ( ( ( sK1_SY0 @ sK4_SY52 @ SV2 )
!= sK5_SY59 )
= $true )
| ( ( ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ sK2_SY52 )
!= sK3_SY56 ) )
= $true )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK6_SY49 @ sK7_SY62 ) @ sK8_SY64 )
= ( sK1_SY0 @ sK6_SY49 @ ( sK1_SY0 @ sK7_SY62 @ sK8_SY64 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(29,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)],[27]) ).
thf(30,plain,
( ( ~ ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ sK9_SY42 )
= SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(31,plain,
! [SV2: g] :
( ( ( ( sK1_SY0 @ sK4_SY52 @ SV2 )
= sK5_SY59 )
= $false )
| ( ( ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ sK2_SY52 )
!= sK3_SY56 ) )
= $true )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK6_SY49 @ sK7_SY62 ) @ sK8_SY64 )
= ( sK1_SY0 @ sK6_SY49 @ ( sK1_SY0 @ sK7_SY62 @ sK8_SY64 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(32,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)],[29]) ).
thf(33,plain,
( ( ! [SX0: g] :
( ( sK1_SY0 @ SX0 @ sK9_SY42 )
= SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(34,plain,
! [SV2: g,SV3: g] :
( ( ( ( sK1_SY0 @ SV3 @ sK2_SY52 )
!= sK3_SY56 )
= $true )
| ( ( ( sK1_SY0 @ sK4_SY52 @ SV2 )
= sK5_SY59 )
= $false )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK6_SY49 @ sK7_SY62 ) @ sK8_SY64 )
= ( sK1_SY0 @ sK6_SY49 @ ( sK1_SY0 @ sK7_SY62 @ sK8_SY64 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV4: g] :
( ( ! [SY75: g,SY76: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SV4 @ SY75 ) @ SY76 )
= ( sK1_SY0 @ SV4 @ ( sK1_SY0 @ SY75 @ SY76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(36,plain,
! [SV5: g] :
( ( ( sK1_SY0 @ SV5 @ sK9_SY42 )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV2: g,SV3: g] :
( ( ( ( sK1_SY0 @ SV3 @ sK2_SY52 )
= sK3_SY56 )
= $false )
| ( ( ( sK1_SY0 @ sK4_SY52 @ SV2 )
= sK5_SY59 )
= $false )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ sK6_SY49 @ sK7_SY62 ) @ sK8_SY64 )
= ( sK1_SY0 @ sK6_SY49 @ ( sK1_SY0 @ sK7_SY62 @ sK8_SY64 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV6: g,SV4: g] :
( ( ! [SY77: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SV4 @ SV6 ) @ SY77 )
= ( sK1_SY0 @ SV4 @ ( sK1_SY0 @ SV6 @ SY77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV7: g,SV6: g,SV4: g] :
( ( ( sK1_SY0 @ ( sK1_SY0 @ SV4 @ SV6 ) @ SV7 )
= ( sK1_SY0 @ SV4 @ ( sK1_SY0 @ SV6 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(40,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[26,39,37,36]) ).
thf(41,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] :
( ( sK1_SY0 @ SY52 @ ( sK17_SY54 @ SY53 @ SY52 ) )
= SY53 )
& ! [SY52: g,SY53: g] :
( ( sK1_SY0 @ ( sK16_SY55 @ SY53 @ SY52 ) @ SY52 )
= SY53 )
& ! [SY42: g] :
( ! [SY74: g] :
( ( sK1_SY0 @ ( sK15_SY47 @ SY42 ) @ SY74 )
!= SY42 )
| ( ( sK1_SY0 @ ( sK1_SY0 @ ( sK12_SY43 @ SY42 ) @ ( sK13_SY71 @ SY42 ) ) @ ( sK14_SY73 @ SY42 ) )
!= ( sK1_SY0 @ ( sK12_SY43 @ SY42 ) @ ( sK1_SY0 @ ( sK13_SY71 @ SY42 ) @ ( sK14_SY73 @ SY42 ) ) ) )
| ( ( sK1_SY0 @ ( sK11_SY46 @ SY42 ) @ SY42 )
!= ( sK11_SY46 @ SY42 ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(42,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] :
( ( sK1_SY0 @ SX0 @ ( sK17_SY54 @ SX1 @ SX0 ) )
= SX1 )
| ~ ! [SX0: g,SX1: g] :
( ( sK1_SY0 @ ( sK16_SY55 @ SX1 @ SX0 ) @ SX0 )
= SX1 ) ) )
| ~ ! [SX0: g] :
( ! [SX1: g] :
( ( sK1_SY0 @ ( sK15_SY47 @ SX0 ) @ SX1 )
!= SX0 )
| ( ( sK1_SY0 @ ( sK1_SY0 @ ( sK12_SY43 @ SX0 ) @ ( sK13_SY71 @ SX0 ) ) @ ( sK14_SY73 @ SX0 ) )
!= ( sK1_SY0 @ ( sK12_SY43 @ SX0 ) @ ( sK1_SY0 @ ( sK13_SY71 @ SX0 ) @ ( sK14_SY73 @ SX0 ) ) ) )
| ( ( sK1_SY0 @ ( sK11_SY46 @ SX0 ) @ SX0 )
!= ( sK11_SY46 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41,cGROUP3,cGROUP4,cGRP_ASSOC,cGRP_DIVISORS,cGRP_RIGHT_INVERSE,cGRP_RIGHT_UNIT]) ).
thf(43,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] :
( ( sK1_SY0 @ SX0 @ ( sK17_SY54 @ SX1 @ SX0 ) )
= SX1 )
| ~ ! [SX0: g,SX1: g] :
( ( sK1_SY0 @ ( sK16_SY55 @ SX1 @ SX0 ) @ SX0 )
= SX1 ) ) )
| ~ ! [SX0: g] :
( ! [SX1: g] :
( ( sK1_SY0 @ ( sK15_SY47 @ SX0 ) @ SX1 )
!= SX0 )
| ( ( sK1_SY0 @ ( sK1_SY0 @ ( sK12_SY43 @ SX0 ) @ ( sK13_SY71 @ SX0 ) ) @ ( sK14_SY73 @ SX0 ) )
!= ( sK1_SY0 @ ( sK12_SY43 @ SX0 ) @ ( sK1_SY0 @ ( sK13_SY71 @ SX0 ) @ ( sK14_SY73 @ SX0 ) ) ) )
| ( ( sK1_SY0 @ ( sK11_SY46 @ SX0 ) @ SX0 )
!= ( sK11_SY46 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(44,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] :
( ( sK1_SY0 @ SX0 @ ( sK17_SY54 @ SX1 @ SX0 ) )
= SX1 )
| ~ ! [SX0: g,SX1: g] :
( ( sK1_SY0 @ ( sK16_SY55 @ SX1 @ SX0 ) @ SX0 )
= SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(45,plain,
( ( ~ ! [SX0: g] :
( ! [SX1: g] :
( ( sK1_SY0 @ ( sK15_SY47 @ SX0 ) @ SX1 )
!= SX0 )
| ( ( sK1_SY0 @ ( sK1_SY0 @ ( sK12_SY43 @ SX0 ) @ ( sK13_SY71 @ SX0 ) ) @ ( sK14_SY73 @ SX0 ) )
!= ( sK1_SY0 @ ( sK12_SY43 @ SX0 ) @ ( sK1_SY0 @ ( sK13_SY71 @ SX0 ) @ ( sK14_SY73 @ SX0 ) ) ) )
| ( ( sK1_SY0 @ ( sK11_SY46 @ SX0 ) @ SX0 )
!= ( sK11_SY46 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(46,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] :
( ( sK1_SY0 @ SX0 @ ( sK17_SY54 @ SX1 @ SX0 ) )
= SX1 )
| ~ ! [SX0: g,SX1: g] :
( ( sK1_SY0 @ ( sK16_SY55 @ SX1 @ SX0 ) @ SX0 )
= SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(47,plain,
( ( ! [SX0: g] :
( ! [SX1: g] :
( ( sK1_SY0 @ ( sK15_SY47 @ SX0 ) @ SX1 )
!= SX0 )
| ( ( sK1_SY0 @ ( sK1_SY0 @ ( sK12_SY43 @ SX0 ) @ ( sK13_SY71 @ SX0 ) ) @ ( sK14_SY73 @ SX0 ) )
!= ( sK1_SY0 @ ( sK12_SY43 @ SX0 ) @ ( sK1_SY0 @ ( sK13_SY71 @ SX0 ) @ ( sK14_SY73 @ SX0 ) ) ) )
| ( ( sK1_SY0 @ ( sK11_SY46 @ SX0 ) @ SX0 )
!= ( sK11_SY46 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(48,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] :
( ( sK1_SY0 @ SX0 @ ( sK17_SY54 @ SX1 @ SX0 ) )
= SX1 )
| ~ ! [SX0: g,SX1: g] :
( ( sK1_SY0 @ ( sK16_SY55 @ SX1 @ SX0 ) @ SX0 )
= SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(49,plain,
! [SV8: g] :
( ( ! [SY78: g] :
( ( sK1_SY0 @ ( sK15_SY47 @ SV8 ) @ SY78 )
!= SV8 )
| ( ( sK1_SY0 @ ( sK1_SY0 @ ( sK12_SY43 @ SV8 ) @ ( sK13_SY71 @ SV8 ) ) @ ( sK14_SY73 @ SV8 ) )
!= ( sK1_SY0 @ ( sK12_SY43 @ SV8 ) @ ( sK1_SY0 @ ( sK13_SY71 @ SV8 ) @ ( sK14_SY73 @ SV8 ) ) ) )
| ( ( sK1_SY0 @ ( sK11_SY46 @ SV8 ) @ SV8 )
!= ( sK11_SY46 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(50,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)],[48]) ).
thf(51,plain,
( ( ~ ~ ( ~ ! [SX0: g,SX1: g] :
( ( sK1_SY0 @ SX0 @ ( sK17_SY54 @ SX1 @ SX0 ) )
= SX1 )
| ~ ! [SX0: g,SX1: g] :
( ( sK1_SY0 @ ( sK16_SY55 @ SX1 @ SX0 ) @ SX0 )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(52,plain,
! [SV8: g] :
( ( ( ! [SY78: g] :
( ( sK1_SY0 @ ( sK15_SY47 @ SV8 ) @ SY78 )
!= SV8 ) )
= $true )
| ( ( ( ( sK1_SY0 @ ( sK1_SY0 @ ( sK12_SY43 @ SV8 ) @ ( sK13_SY71 @ SV8 ) ) @ ( sK14_SY73 @ SV8 ) )
!= ( sK1_SY0 @ ( sK12_SY43 @ SV8 ) @ ( sK1_SY0 @ ( sK13_SY71 @ SV8 ) @ ( sK14_SY73 @ SV8 ) ) ) )
| ( ( sK1_SY0 @ ( sK11_SY46 @ SV8 ) @ SV8 )
!= ( sK11_SY46 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(53,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)],[50]) ).
thf(54,plain,
( ( ~ ( ~ ! [SX0: g,SX1: g] :
( ( sK1_SY0 @ SX0 @ ( sK17_SY54 @ SX1 @ SX0 ) )
= SX1 )
| ~ ! [SX0: g,SX1: g] :
( ( sK1_SY0 @ ( sK16_SY55 @ SX1 @ SX0 ) @ SX0 )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(55,plain,
! [SV9: g,SV8: g] :
( ( ( ( sK1_SY0 @ ( sK15_SY47 @ SV8 ) @ SV9 )
!= SV8 )
= $true )
| ( ( ( ( sK1_SY0 @ ( sK1_SY0 @ ( sK12_SY43 @ SV8 ) @ ( sK13_SY71 @ SV8 ) ) @ ( sK14_SY73 @ SV8 ) )
!= ( sK1_SY0 @ ( sK12_SY43 @ SV8 ) @ ( sK1_SY0 @ ( sK13_SY71 @ SV8 ) @ ( sK14_SY73 @ SV8 ) ) ) )
| ( ( sK1_SY0 @ ( sK11_SY46 @ SV8 ) @ SV8 )
!= ( sK11_SY46 @ SV8 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(56,plain,
! [SV10: g] :
( ( ! [SY79: g,SY80: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SV10 @ SY79 ) @ SY80 )
= ( sK1_SY0 @ SV10 @ ( sK1_SY0 @ SY79 @ SY80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(57,plain,
( ( ~ ! [SX0: g,SX1: g] :
( ( sK1_SY0 @ SX0 @ ( sK17_SY54 @ SX1 @ SX0 ) )
= SX1 )
| ~ ! [SX0: g,SX1: g] :
( ( sK1_SY0 @ ( sK16_SY55 @ SX1 @ SX0 ) @ SX0 )
= SX1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(58,plain,
! [SV9: g,SV8: g] :
( ( ( ( sK1_SY0 @ ( sK15_SY47 @ SV8 ) @ SV9 )
= SV8 )
= $false )
| ( ( ( ( sK1_SY0 @ ( sK1_SY0 @ ( sK12_SY43 @ SV8 ) @ ( sK13_SY71 @ SV8 ) ) @ ( sK14_SY73 @ SV8 ) )
!= ( sK1_SY0 @ ( sK12_SY43 @ SV8 ) @ ( sK1_SY0 @ ( sK13_SY71 @ SV8 ) @ ( sK14_SY73 @ SV8 ) ) ) )
| ( ( sK1_SY0 @ ( sK11_SY46 @ SV8 ) @ SV8 )
!= ( sK11_SY46 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(59,plain,
! [SV11: g,SV10: g] :
( ( ! [SY81: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SV10 @ SV11 ) @ SY81 )
= ( sK1_SY0 @ SV10 @ ( sK1_SY0 @ SV11 @ SY81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(60,plain,
( ( ~ ! [SX0: g,SX1: g] :
( ( sK1_SY0 @ SX0 @ ( sK17_SY54 @ SX1 @ SX0 ) )
= SX1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(61,plain,
( ( ~ ! [SX0: g,SX1: g] :
( ( sK1_SY0 @ ( sK16_SY55 @ SX1 @ SX0 ) @ SX0 )
= SX1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(62,plain,
! [SV9: g,SV8: g] :
( ( ( ( sK1_SY0 @ ( sK1_SY0 @ ( sK12_SY43 @ SV8 ) @ ( sK13_SY71 @ SV8 ) ) @ ( sK14_SY73 @ SV8 ) )
!= ( sK1_SY0 @ ( sK12_SY43 @ SV8 ) @ ( sK1_SY0 @ ( sK13_SY71 @ SV8 ) @ ( sK14_SY73 @ SV8 ) ) ) )
= $true )
| ( ( ( sK1_SY0 @ ( sK11_SY46 @ SV8 ) @ SV8 )
!= ( sK11_SY46 @ SV8 ) )
= $true )
| ( ( ( sK1_SY0 @ ( sK15_SY47 @ SV8 ) @ SV9 )
= SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(63,plain,
! [SV12: g,SV11: g,SV10: g] :
( ( ( sK1_SY0 @ ( sK1_SY0 @ SV10 @ SV11 ) @ SV12 )
= ( sK1_SY0 @ SV10 @ ( sK1_SY0 @ SV11 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(64,plain,
( ( ! [SX0: g,SX1: g] :
( ( sK1_SY0 @ SX0 @ ( sK17_SY54 @ SX1 @ SX0 ) )
= SX1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(65,plain,
( ( ! [SX0: g,SX1: g] :
( ( sK1_SY0 @ ( sK16_SY55 @ SX1 @ SX0 ) @ SX0 )
= SX1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(66,plain,
! [SV9: g,SV8: g] :
( ( ( ( sK1_SY0 @ ( sK1_SY0 @ ( sK12_SY43 @ SV8 ) @ ( sK13_SY71 @ SV8 ) ) @ ( sK14_SY73 @ SV8 ) )
= ( sK1_SY0 @ ( sK12_SY43 @ SV8 ) @ ( sK1_SY0 @ ( sK13_SY71 @ SV8 ) @ ( sK14_SY73 @ SV8 ) ) ) )
= $false )
| ( ( ( sK1_SY0 @ ( sK11_SY46 @ SV8 ) @ SV8 )
!= ( sK11_SY46 @ SV8 ) )
= $true )
| ( ( ( sK1_SY0 @ ( sK15_SY47 @ SV8 ) @ SV9 )
= SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(67,plain,
! [SV13: g] :
( ( ! [SY82: g] :
( ( sK1_SY0 @ SV13 @ ( sK17_SY54 @ SY82 @ SV13 ) )
= SY82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(68,plain,
! [SV14: g] :
( ( ! [SY83: g] :
( ( sK1_SY0 @ ( sK16_SY55 @ SY83 @ SV14 ) @ SV14 )
= SY83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(69,plain,
! [SV9: g,SV8: g] :
( ( ( ( sK1_SY0 @ ( sK11_SY46 @ SV8 ) @ SV8 )
= ( sK11_SY46 @ SV8 ) )
= $false )
| ( ( ( sK1_SY0 @ ( sK1_SY0 @ ( sK12_SY43 @ SV8 ) @ ( sK13_SY71 @ SV8 ) ) @ ( sK14_SY73 @ SV8 ) )
= ( sK1_SY0 @ ( sK12_SY43 @ SV8 ) @ ( sK1_SY0 @ ( sK13_SY71 @ SV8 ) @ ( sK14_SY73 @ SV8 ) ) ) )
= $false )
| ( ( ( sK1_SY0 @ ( sK15_SY47 @ SV8 ) @ SV9 )
= SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(70,plain,
! [SV15: g,SV13: g] :
( ( ( sK1_SY0 @ SV13 @ ( sK17_SY54 @ SV15 @ SV13 ) )
= SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(71,plain,
! [SV14: g,SV16: g] :
( ( ( sK1_SY0 @ ( sK16_SY55 @ SV16 @ SV14 ) @ SV14 )
= SV16 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(72,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[63,71,70,69]) ).
thf(73,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[72,40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG274^5 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.16 % Computer : n013.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Oct 6 18:09:21 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.24
% 0.08/0.24 No.of.Axioms: 0
% 0.08/0.24
% 0.08/0.24 Length.of.Defs: 1205
% 0.08/0.24
% 0.08/0.24 Contains.Choice.Funs: false
% 0.08/0.24 ....
% 0.08/0.24
% 0.08/0.24 ********************************
% 0.08/0.24 * All subproblems solved! *
% 0.08/0.24 ********************************
% 0.08/0.24 % SZS status Theorem for /export/starexec/sandbox/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:72,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.24
% 0.08/0.24 %**** Beginning of derivation protocol ****
% 0.08/0.24 % SZS output start CNFRefutation
% See solution above
% 0.08/0.24
% 0.08/0.24 %**** End of derivation protocol ****
% 0.08/0.24 %**** no. of clauses in derivation: 73 ****
% 0.08/0.24 %**** clause counter: 72 ****
% 0.08/0.24
% 0.08/0.24 % SZS status Theorem for /export/starexec/sandbox/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:72,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------