TSTP Solution File: ALG271^5 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : ALG271^5 : TPTP v8.1.0. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 17:25:39 EDT 2022
% Result : Theorem 0.21s 0.46s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 30
% Syntax : Number of formulae : 144 ( 83 unt; 22 typ; 7 def)
% Number of atoms : 762 ( 524 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 1961 ( 561 ~; 212 |; 10 &;1170 @)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 49 ( 49 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 13 con; 0-2 aty)
% Number of variables : 367 ( 13 ^ 352 !; 2 ?; 367 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_g,type,
g: $tType ).
thf(tp_cGROUP1,type,
cGROUP1: ( 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_INVERSE,type,
cGRP_INVERSE: ( 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_cGRP_UNIT,type,
cGRP_UNIT: ( g > g > g ) > g > $o ).
thf(tp_sK10_SX0,type,
sK10_SX0: g ).
thf(tp_sK11_SY13,type,
sK11_SY13: g ).
thf(tp_sK12_SY15,type,
sK12_SY15: g ).
thf(tp_sK13_SX0,type,
sK13_SX0: g ).
thf(tp_sK14_SX0,type,
sK14_SX0: g ).
thf(tp_sK1_Xf,type,
sK1_Xf: g > g > g ).
thf(tp_sK2_SY0,type,
sK2_SY0: g ).
thf(tp_sK3_SY1,type,
sK3_SY1: g > g ).
thf(tp_sK4_SX0,type,
sK4_SX0: g ).
thf(tp_sK5_SY5,type,
sK5_SY5: g ).
thf(tp_sK6_SY7,type,
sK6_SY7: g ).
thf(tp_sK7_SX0,type,
sK7_SX0: g ).
thf(tp_sK8_SX0,type,
sK8_SX0: g ).
thf(tp_sK9_SY9,type,
sK9_SY9: 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/sandbox/benchmark/theBenchmark.p',cGROUP1) ).
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) ).
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) ).
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/sandbox/benchmark/theBenchmark.p',cGRP_INVERSE) ).
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) ).
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) ).
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/sandbox/benchmark/theBenchmark.p',cGRP_UNIT) ).
thf(1,conjecture,
! [Xf: g > g > g,Xe: g] :
( ( cGROUP1 @ Xf @ Xe )
<=> ( cGROUP3 @ Xf @ Xe ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEQUIV_01_03) ).
thf(2,negated_conjecture,
( ( ! [Xf: g > g > g,Xe: g] :
( ( cGROUP1 @ Xf @ Xe )
<=> ( cGROUP3 @ Xf @ Xe ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: g] :
( ( cGROUP1 @ sK1_Xf @ SY0 )
<=> ( cGROUP3 @ sK1_Xf @ SY0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[2]) ).
thf(4,plain,
( ( ( cGROUP1 @ sK1_Xf @ sK2_SY0 )
<=> ( cGROUP3 @ sK1_Xf @ sK2_SY0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ( cGROUP1 @ sK1_Xf @ sK2_SY0 )
=> ( cGROUP3 @ sK1_Xf @ sK2_SY0 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[4]) ).
thf(6,plain,
( ( ( cGROUP3 @ sK1_Xf @ sK2_SY0 )
=> ( cGROUP1 @ sK1_Xf @ sK2_SY0 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[4]) ).
thf(7,plain,
( ( ~ ( ( cGROUP1 @ sK1_Xf @ sK2_SY0 )
=> ( cGROUP3 @ sK1_Xf @ sK2_SY0 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ( ( cGROUP3 @ sK1_Xf @ sK2_SY0 )
=> ( cGROUP1 @ sK1_Xf @ sK2_SY0 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(9,plain,
( ( ( cGROUP1 @ sK1_Xf @ sK2_SY0 )
& ~ ( cGROUP3 @ sK1_Xf @ sK2_SY0 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(10,plain,
( ( ( cGROUP3 @ sK1_Xf @ sK2_SY0 )
& ~ ( cGROUP1 @ sK1_Xf @ sK2_SY0 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(11,plain,
( ( ( cGROUP1 @ sK1_Xf @ sK2_SY0 )
& ~ ( cGROUP3 @ sK1_Xf @ sK2_SY0 ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
~ ( ( ( sK1_Xf @ sK2_SY0 @ SX0 )
!= SX0 )
| ( ( sK1_Xf @ SX0 @ sK2_SY0 )
!= SX0 ) ) )
| ~ ! [SX0: g] :
~ ! [SX1: g] :
~ ~ ( ( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SX1 @ SX0 )
!= sK2_SY0 ) ) )
| ~ ~ ~ ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_Xf @ SX0 @ sK2_SY0 )
= SX0 ) )
| ~ ! [SX0: g] :
~ ! [SX1: g] :
( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,cGROUP1,cGROUP3,cGRP_ASSOC,cGRP_INVERSE,cGRP_RIGHT_INVERSE,cGRP_RIGHT_UNIT,cGRP_UNIT]) ).
thf(13,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
~ ( ( ( sK1_Xf @ sK2_SY0 @ SX0 )
!= SX0 )
| ( ( sK1_Xf @ SX0 @ sK2_SY0 )
!= SX0 ) ) )
| ~ ! [SX0: g] :
~ ! [SX1: g] :
~ ~ ( ( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SX1 @ SX0 )
!= sK2_SY0 ) ) )
| ~ ~ ~ ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_Xf @ SX0 @ sK2_SY0 )
= SX0 ) )
| ~ ! [SX0: g] :
~ ! [SX1: g] :
( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(14,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
~ ( ( ( sK1_Xf @ sK2_SY0 @ SX0 )
!= SX0 )
| ( ( sK1_Xf @ SX0 @ sK2_SY0 )
!= SX0 ) ) )
| ~ ! [SX0: g] :
~ ! [SX1: g] :
~ ~ ( ( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SX1 @ SX0 )
!= sK2_SY0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(15,plain,
( ( ~ ~ ~ ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_Xf @ SX0 @ sK2_SY0 )
= SX0 ) )
| ~ ! [SX0: g] :
~ ! [SX1: g] :
( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
~ ( ( ( sK1_Xf @ sK2_SY0 @ SX0 )
!= SX0 )
| ( ( sK1_Xf @ SX0 @ sK2_SY0 )
!= SX0 ) ) )
| ~ ! [SX0: g] :
~ ! [SX1: g] :
~ ~ ( ( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SX1 @ SX0 )
!= sK2_SY0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_Xf @ SX0 @ sK2_SY0 )
= SX0 ) )
| ~ ! [SX0: g] :
~ ! [SX1: g] :
( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
~ ( ( ( sK1_Xf @ sK2_SY0 @ SX0 )
!= SX0 )
| ( ( sK1_Xf @ SX0 @ sK2_SY0 )
!= SX0 ) ) )
| ~ ! [SX0: g] :
~ ! [SX1: g] :
~ ~ ( ( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SX1 @ SX0 )
!= sK2_SY0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_Xf @ SX0 @ sK2_SY0 )
= SX0 ) )
| ~ ! [SX0: g] :
~ ! [SX1: g] :
( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
~ ( ( ( sK1_Xf @ sK2_SY0 @ SX0 )
!= SX0 )
| ( ( sK1_Xf @ SX0 @ sK2_SY0 )
!= SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(21,plain,
( ( ~ ! [SX0: g] :
~ ! [SX1: g] :
~ ~ ( ( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SX1 @ SX0 )
!= sK2_SY0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_Xf @ SX0 @ sK2_SY0 )
= SX0 ) )
| ~ ! [SX0: g] :
~ ! [SX1: g] :
( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(23,plain,
( ( ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
~ ( ( ( sK1_Xf @ sK2_SY0 @ SX0 )
!= SX0 )
| ( ( sK1_Xf @ SX0 @ sK2_SY0 )
!= SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(24,plain,
( ( ! [SX0: g] :
~ ! [SX1: g] :
~ ~ ( ( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SX1 @ SX0 )
!= sK2_SY0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(25,plain,
( ( ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_Xf @ SX0 @ sK2_SY0 )
= SX0 ) ) )
= $true )
| ( ( ~ ! [SX0: g] :
~ ! [SX1: g] :
( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(26,plain,
( ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
~ ( ( ( sK1_Xf @ sK2_SY0 @ SX0 )
!= SX0 )
| ( ( sK1_Xf @ SX0 @ sK2_SY0 )
!= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(27,plain,
! [SV1: g] :
( ( ~ ! [SY1: g] :
~ ~ ( ( ( sK1_Xf @ SV1 @ SY1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SY1 @ SV1 )
!= sK2_SY0 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(28,plain,
( ( ( ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_Xf @ SX0 @ sK2_SY0 )
= SX0 ) ) )
= $false )
| ( ( ~ ! [SX0: g] :
~ ! [SX1: g] :
( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(29,plain,
( ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(30,plain,
( ( ~ ! [SX0: g] :
~ ( ( ( sK1_Xf @ sK2_SY0 @ SX0 )
!= SX0 )
| ( ( sK1_Xf @ SX0 @ sK2_SY0 )
!= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(31,plain,
! [SV1: g] :
( ( ! [SY1: g] :
~ ~ ( ( ( sK1_Xf @ SV1 @ SY1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SY1 @ SV1 )
!= sK2_SY0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(32,plain,
( ( ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_Xf @ SX0 @ sK2_SY0 )
= SX0 ) )
= $true )
| ( ( ~ ! [SX0: g] :
~ ! [SX1: g] :
( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(33,plain,
( ( ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(34,plain,
( ( ! [SX0: g] :
~ ( ( ( sK1_Xf @ sK2_SY0 @ SX0 )
!= SX0 )
| ( ( sK1_Xf @ SX0 @ sK2_SY0 )
!= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(35,plain,
! [SV1: g] :
( ( ~ ~ ( ( ( sK1_Xf @ SV1 @ ( sK3_SY1 @ SV1 ) )
!= sK2_SY0 )
| ( ( sK1_Xf @ ( sK3_SY1 @ SV1 ) @ SV1 )
!= sK2_SY0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[31]) ).
thf(36,plain,
( ( ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) ) )
= $true )
| ( ( ~ ! [SX0: g] :
( ( sK1_Xf @ SX0 @ sK2_SY0 )
= SX0 ) )
= $true )
| ( ( ~ ! [SX0: g] :
~ ! [SX1: g] :
( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV2: g] :
( ( ! [SY2: g,SY3: g] :
( ( sK1_Xf @ ( sK1_Xf @ SV2 @ SY2 ) @ SY3 )
= ( sK1_Xf @ SV2 @ ( sK1_Xf @ SY2 @ SY3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV3: g] :
( ( ~ ( ( ( sK1_Xf @ sK2_SY0 @ SV3 )
!= SV3 )
| ( ( sK1_Xf @ SV3 @ sK2_SY0 )
!= SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(39,plain,
! [SV1: g] :
( ( ~ ( ( ( sK1_Xf @ SV1 @ ( sK3_SY1 @ SV1 ) )
!= sK2_SY0 )
| ( ( sK1_Xf @ ( sK3_SY1 @ SV1 ) @ SV1 )
!= sK2_SY0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(40,plain,
( ( ( ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) ) )
= $false )
| ( ( ~ ! [SX0: g] :
( ( sK1_Xf @ SX0 @ sK2_SY0 )
= SX0 ) )
= $true )
| ( ( ~ ! [SX0: g] :
~ ! [SX1: g] :
( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(41,plain,
! [SV4: g,SV2: g] :
( ( ! [SY4: g] :
( ( sK1_Xf @ ( sK1_Xf @ SV2 @ SV4 ) @ SY4 )
= ( sK1_Xf @ SV2 @ ( sK1_Xf @ SV4 @ SY4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV3: g] :
( ( ( ( sK1_Xf @ sK2_SY0 @ SV3 )
!= SV3 )
| ( ( sK1_Xf @ SV3 @ sK2_SY0 )
!= SV3 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV1: g] :
( ( ( ( sK1_Xf @ SV1 @ ( sK3_SY1 @ SV1 ) )
!= sK2_SY0 )
| ( ( sK1_Xf @ ( sK3_SY1 @ SV1 ) @ SV1 )
!= sK2_SY0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(44,plain,
( ( ( ! [SY5: g,SY6: g] :
( ( sK1_Xf @ ( sK1_Xf @ sK4_SX0 @ SY5 ) @ SY6 )
= ( sK1_Xf @ sK4_SX0 @ ( sK1_Xf @ SY5 @ SY6 ) ) ) )
= $false )
| ( ( ~ ! [SX0: g] :
( ( sK1_Xf @ SX0 @ sK2_SY0 )
= SX0 ) )
= $true )
| ( ( ~ ! [SX0: g] :
~ ! [SX1: g] :
( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[40]) ).
thf(45,plain,
! [SV5: g,SV4: g,SV2: g] :
( ( ( sK1_Xf @ ( sK1_Xf @ SV2 @ SV4 ) @ SV5 )
= ( sK1_Xf @ SV2 @ ( sK1_Xf @ SV4 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(46,plain,
! [SV3: g] :
( ( ( ( sK1_Xf @ sK2_SY0 @ SV3 )
!= SV3 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(47,plain,
! [SV3: g] :
( ( ( ( sK1_Xf @ SV3 @ sK2_SY0 )
!= SV3 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(48,plain,
! [SV1: g] :
( ( ( ( sK1_Xf @ SV1 @ ( sK3_SY1 @ SV1 ) )
!= sK2_SY0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(49,plain,
! [SV1: g] :
( ( ( ( sK1_Xf @ ( sK3_SY1 @ SV1 ) @ SV1 )
!= sK2_SY0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(50,plain,
( ( ( ! [SY7: g] :
( ( sK1_Xf @ ( sK1_Xf @ sK4_SX0 @ sK5_SY5 ) @ SY7 )
= ( sK1_Xf @ sK4_SX0 @ ( sK1_Xf @ sK5_SY5 @ SY7 ) ) ) )
= $false )
| ( ( ~ ! [SX0: g] :
( ( sK1_Xf @ SX0 @ sK2_SY0 )
= SX0 ) )
= $true )
| ( ( ~ ! [SX0: g] :
~ ! [SX1: g] :
( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[44]) ).
thf(51,plain,
! [SV3: g] :
( ( ( sK1_Xf @ sK2_SY0 @ SV3 )
= SV3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(52,plain,
! [SV3: g] :
( ( ( sK1_Xf @ SV3 @ sK2_SY0 )
= SV3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(53,plain,
! [SV1: g] :
( ( ( sK1_Xf @ SV1 @ ( sK3_SY1 @ SV1 ) )
= sK2_SY0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(54,plain,
! [SV1: g] :
( ( ( sK1_Xf @ ( sK3_SY1 @ SV1 ) @ SV1 )
= sK2_SY0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(55,plain,
( ( ( ( sK1_Xf @ ( sK1_Xf @ sK4_SX0 @ sK5_SY5 ) @ sK6_SY7 )
= ( sK1_Xf @ sK4_SX0 @ ( sK1_Xf @ sK5_SY5 @ sK6_SY7 ) ) )
= $false )
| ( ( ~ ! [SX0: g] :
( ( sK1_Xf @ SX0 @ sK2_SY0 )
= SX0 ) )
= $true )
| ( ( ~ ! [SX0: g] :
~ ! [SX1: g] :
( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[50]) ).
thf(56,plain,
( ( ( ! [SX0: g] :
( ( sK1_Xf @ SX0 @ sK2_SY0 )
= SX0 ) )
= $false )
| ( ( ( sK1_Xf @ ( sK1_Xf @ sK4_SX0 @ sK5_SY5 ) @ sK6_SY7 )
= ( sK1_Xf @ sK4_SX0 @ ( sK1_Xf @ sK5_SY5 @ sK6_SY7 ) ) )
= $false )
| ( ( ~ ! [SX0: g] :
~ ! [SX1: g] :
( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(57,plain,
( ( ( ( sK1_Xf @ sK7_SX0 @ sK2_SY0 )
= sK7_SX0 )
= $false )
| ( ( ( sK1_Xf @ ( sK1_Xf @ sK4_SX0 @ sK5_SY5 ) @ sK6_SY7 )
= ( sK1_Xf @ sK4_SX0 @ ( sK1_Xf @ sK5_SY5 @ sK6_SY7 ) ) )
= $false )
| ( ( ~ ! [SX0: g] :
~ ! [SX1: g] :
( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[56]) ).
thf(58,plain,
( ( ( ! [SX0: g] :
~ ! [SX1: g] :
( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 ) )
= $false )
| ( ( ( sK1_Xf @ ( sK1_Xf @ sK4_SX0 @ sK5_SY5 ) @ sK6_SY7 )
= ( sK1_Xf @ sK4_SX0 @ ( sK1_Xf @ sK5_SY5 @ sK6_SY7 ) ) )
= $false )
| ( ( ( sK1_Xf @ sK7_SX0 @ sK2_SY0 )
= sK7_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(59,plain,
( ( ( ~ ! [SY8: g] :
( ( sK1_Xf @ sK8_SX0 @ SY8 )
!= sK2_SY0 ) )
= $false )
| ( ( ( sK1_Xf @ ( sK1_Xf @ sK4_SX0 @ sK5_SY5 ) @ sK6_SY7 )
= ( sK1_Xf @ sK4_SX0 @ ( sK1_Xf @ sK5_SY5 @ sK6_SY7 ) ) )
= $false )
| ( ( ( sK1_Xf @ sK7_SX0 @ sK2_SY0 )
= sK7_SX0 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[58]) ).
thf(60,plain,
( ( ( ! [SY8: g] :
( ( sK1_Xf @ sK8_SX0 @ SY8 )
!= sK2_SY0 ) )
= $true )
| ( ( ( sK1_Xf @ ( sK1_Xf @ sK4_SX0 @ sK5_SY5 ) @ sK6_SY7 )
= ( sK1_Xf @ sK4_SX0 @ ( sK1_Xf @ sK5_SY5 @ sK6_SY7 ) ) )
= $false )
| ( ( ( sK1_Xf @ sK7_SX0 @ sK2_SY0 )
= sK7_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(61,plain,
! [SV6: g] :
( ( ( ( ( sK1_Xf @ sK8_SX0 @ SV6 )
!= sK2_SY0 ) )
= $true )
| ( ( ( sK1_Xf @ ( sK1_Xf @ sK4_SX0 @ sK5_SY5 ) @ sK6_SY7 )
= ( sK1_Xf @ sK4_SX0 @ ( sK1_Xf @ sK5_SY5 @ sK6_SY7 ) ) )
= $false )
| ( ( ( sK1_Xf @ sK7_SX0 @ sK2_SY0 )
= sK7_SX0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(62,plain,
! [SV6: g] :
( ( ( ( sK1_Xf @ sK8_SX0 @ SV6 )
= sK2_SY0 )
= $false )
| ( ( ( sK1_Xf @ ( sK1_Xf @ sK4_SX0 @ sK5_SY5 ) @ sK6_SY7 )
= ( sK1_Xf @ sK4_SX0 @ ( sK1_Xf @ sK5_SY5 @ sK6_SY7 ) ) )
= $false )
| ( ( ( sK1_Xf @ sK7_SX0 @ sK2_SY0 )
= sK7_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(63,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[45,62,54,53,52,51]) ).
thf(64,plain,
( ( ( cGROUP3 @ sK1_Xf @ sK2_SY0 )
& ~ ( cGROUP1 @ sK1_Xf @ sK2_SY0 ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(65,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_Xf @ SX0 @ sK2_SY0 )
= SX0 ) )
| ~ ! [SX0: g] :
~ ! [SX1: g] :
( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 ) )
| ~ ~ ~ ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
~ ( ( ( sK1_Xf @ sK2_SY0 @ SX0 )
!= SX0 )
| ( ( sK1_Xf @ SX0 @ sK2_SY0 )
!= SX0 ) ) )
| ~ ! [SX0: g] :
~ ! [SX1: g] :
~ ~ ( ( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SX1 @ SX0 )
!= sK2_SY0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64,cGROUP1,cGROUP3,cGRP_ASSOC,cGRP_INVERSE,cGRP_RIGHT_INVERSE,cGRP_RIGHT_UNIT,cGRP_UNIT]) ).
thf(66,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_Xf @ SX0 @ sK2_SY0 )
= SX0 ) )
| ~ ! [SX0: g] :
~ ! [SX1: g] :
( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 ) )
| ~ ~ ~ ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
~ ( ( ( sK1_Xf @ sK2_SY0 @ SX0 )
!= SX0 )
| ( ( sK1_Xf @ SX0 @ sK2_SY0 )
!= SX0 ) ) )
| ~ ! [SX0: g] :
~ ! [SX1: g] :
~ ~ ( ( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SX1 @ SX0 )
!= sK2_SY0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(67,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_Xf @ SX0 @ sK2_SY0 )
= SX0 ) )
| ~ ! [SX0: g] :
~ ! [SX1: g] :
( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(68,plain,
( ( ~ ~ ~ ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
~ ( ( ( sK1_Xf @ sK2_SY0 @ SX0 )
!= SX0 )
| ( ( sK1_Xf @ SX0 @ sK2_SY0 )
!= SX0 ) ) )
| ~ ! [SX0: g] :
~ ! [SX1: g] :
~ ~ ( ( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SX1 @ SX0 )
!= sK2_SY0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(69,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_Xf @ SX0 @ sK2_SY0 )
= SX0 ) )
| ~ ! [SX0: g] :
~ ! [SX1: g] :
( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(70,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
~ ( ( ( sK1_Xf @ sK2_SY0 @ SX0 )
!= SX0 )
| ( ( sK1_Xf @ SX0 @ sK2_SY0 )
!= SX0 ) ) )
| ~ ! [SX0: g] :
~ ! [SX1: g] :
~ ~ ( ( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SX1 @ SX0 )
!= sK2_SY0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(71,plain,
( ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_Xf @ SX0 @ sK2_SY0 )
= SX0 ) )
| ~ ! [SX0: g] :
~ ! [SX1: g] :
( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(72,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
~ ( ( ( sK1_Xf @ sK2_SY0 @ SX0 )
!= SX0 )
| ( ( sK1_Xf @ SX0 @ sK2_SY0 )
!= SX0 ) ) )
| ~ ! [SX0: g] :
~ ! [SX1: g] :
~ ~ ( ( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SX1 @ SX0 )
!= sK2_SY0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(73,plain,
( ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_Xf @ SX0 @ sK2_SY0 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(74,plain,
( ( ~ ! [SX0: g] :
~ ! [SX1: g] :
( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(75,plain,
( ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
~ ( ( ( sK1_Xf @ sK2_SY0 @ SX0 )
!= SX0 )
| ( ( sK1_Xf @ SX0 @ sK2_SY0 )
!= SX0 ) ) )
| ~ ! [SX0: g] :
~ ! [SX1: g] :
~ ~ ( ( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SX1 @ SX0 )
!= sK2_SY0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(76,plain,
( ( ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_Xf @ SX0 @ sK2_SY0 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(77,plain,
( ( ! [SX0: g] :
~ ! [SX1: g] :
( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(78,plain,
( ( ( ~ ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
~ ( ( ( sK1_Xf @ sK2_SY0 @ SX0 )
!= SX0 )
| ( ( sK1_Xf @ SX0 @ sK2_SY0 )
!= SX0 ) ) ) )
= $true )
| ( ( ~ ! [SX0: g] :
~ ! [SX1: g] :
~ ~ ( ( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SX1 @ SX0 )
!= sK2_SY0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(79,plain,
( ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
( ( sK1_Xf @ SX0 @ sK2_SY0 )
= SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(80,plain,
! [SV7: g] :
( ( ~ ! [SY9: g] :
( ( sK1_Xf @ SV7 @ SY9 )
!= sK2_SY0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(81,plain,
( ( ( ~ ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
~ ( ( ( sK1_Xf @ sK2_SY0 @ SX0 )
!= SX0 )
| ( ( sK1_Xf @ SX0 @ sK2_SY0 )
!= SX0 ) ) ) )
= $false )
| ( ( ~ ! [SX0: g] :
~ ! [SX1: g] :
~ ~ ( ( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SX1 @ SX0 )
!= sK2_SY0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(82,plain,
( ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(83,plain,
( ( ~ ! [SX0: g] :
( ( sK1_Xf @ SX0 @ sK2_SY0 )
= SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(84,plain,
! [SV7: g] :
( ( ! [SY9: g] :
( ( sK1_Xf @ SV7 @ SY9 )
!= sK2_SY0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(85,plain,
( ( ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) )
| ~ ! [SX0: g] :
~ ( ( ( sK1_Xf @ sK2_SY0 @ SX0 )
!= SX0 )
| ( ( sK1_Xf @ SX0 @ sK2_SY0 )
!= SX0 ) ) )
= $true )
| ( ( ~ ! [SX0: g] :
~ ! [SX1: g] :
~ ~ ( ( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SX1 @ SX0 )
!= sK2_SY0 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(86,plain,
( ( ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(87,plain,
( ( ! [SX0: g] :
( ( sK1_Xf @ SX0 @ sK2_SY0 )
= SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(88,plain,
! [SV7: g] :
( ( ( ( sK1_Xf @ SV7 @ ( sK9_SY9 @ SV7 ) )
!= sK2_SY0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[84]) ).
thf(89,plain,
( ( ( ~ ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) ) )
= $true )
| ( ( ~ ! [SX0: g] :
~ ( ( ( sK1_Xf @ sK2_SY0 @ SX0 )
!= SX0 )
| ( ( sK1_Xf @ SX0 @ sK2_SY0 )
!= SX0 ) ) )
= $true )
| ( ( ~ ! [SX0: g] :
~ ! [SX1: g] :
~ ~ ( ( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SX1 @ SX0 )
!= sK2_SY0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(90,plain,
! [SV8: g] :
( ( ! [SY10: g,SY11: g] :
( ( sK1_Xf @ ( sK1_Xf @ SV8 @ SY10 ) @ SY11 )
= ( sK1_Xf @ SV8 @ ( sK1_Xf @ SY10 @ SY11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(91,plain,
! [SV9: g] :
( ( ( sK1_Xf @ SV9 @ sK2_SY0 )
= SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(92,plain,
! [SV7: g] :
( ( ( sK1_Xf @ SV7 @ ( sK9_SY9 @ SV7 ) )
= sK2_SY0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(93,plain,
( ( ( ! [SX0: g,SX1: g,SX2: g] :
( ( sK1_Xf @ ( sK1_Xf @ SX0 @ SX1 ) @ SX2 )
= ( sK1_Xf @ SX0 @ ( sK1_Xf @ SX1 @ SX2 ) ) ) )
= $false )
| ( ( ~ ! [SX0: g] :
~ ( ( ( sK1_Xf @ sK2_SY0 @ SX0 )
!= SX0 )
| ( ( sK1_Xf @ SX0 @ sK2_SY0 )
!= SX0 ) ) )
= $true )
| ( ( ~ ! [SX0: g] :
~ ! [SX1: g] :
~ ~ ( ( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SX1 @ SX0 )
!= sK2_SY0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(94,plain,
! [SV10: g,SV8: g] :
( ( ! [SY12: g] :
( ( sK1_Xf @ ( sK1_Xf @ SV8 @ SV10 ) @ SY12 )
= ( sK1_Xf @ SV8 @ ( sK1_Xf @ SV10 @ SY12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(95,plain,
( ( ( ! [SY13: g,SY14: g] :
( ( sK1_Xf @ ( sK1_Xf @ sK10_SX0 @ SY13 ) @ SY14 )
= ( sK1_Xf @ sK10_SX0 @ ( sK1_Xf @ SY13 @ SY14 ) ) ) )
= $false )
| ( ( ~ ! [SX0: g] :
~ ( ( ( sK1_Xf @ sK2_SY0 @ SX0 )
!= SX0 )
| ( ( sK1_Xf @ SX0 @ sK2_SY0 )
!= SX0 ) ) )
= $true )
| ( ( ~ ! [SX0: g] :
~ ! [SX1: g] :
~ ~ ( ( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SX1 @ SX0 )
!= sK2_SY0 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[93]) ).
thf(96,plain,
! [SV11: g,SV10: g,SV8: g] :
( ( ( sK1_Xf @ ( sK1_Xf @ SV8 @ SV10 ) @ SV11 )
= ( sK1_Xf @ SV8 @ ( sK1_Xf @ SV10 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(97,plain,
( ( ( ! [SY15: g] :
( ( sK1_Xf @ ( sK1_Xf @ sK10_SX0 @ sK11_SY13 ) @ SY15 )
= ( sK1_Xf @ sK10_SX0 @ ( sK1_Xf @ sK11_SY13 @ SY15 ) ) ) )
= $false )
| ( ( ~ ! [SX0: g] :
~ ( ( ( sK1_Xf @ sK2_SY0 @ SX0 )
!= SX0 )
| ( ( sK1_Xf @ SX0 @ sK2_SY0 )
!= SX0 ) ) )
= $true )
| ( ( ~ ! [SX0: g] :
~ ! [SX1: g] :
~ ~ ( ( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SX1 @ SX0 )
!= sK2_SY0 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[95]) ).
thf(98,plain,
( ( ( ( sK1_Xf @ ( sK1_Xf @ sK10_SX0 @ sK11_SY13 ) @ sK12_SY15 )
= ( sK1_Xf @ sK10_SX0 @ ( sK1_Xf @ sK11_SY13 @ sK12_SY15 ) ) )
= $false )
| ( ( ~ ! [SX0: g] :
~ ( ( ( sK1_Xf @ sK2_SY0 @ SX0 )
!= SX0 )
| ( ( sK1_Xf @ SX0 @ sK2_SY0 )
!= SX0 ) ) )
= $true )
| ( ( ~ ! [SX0: g] :
~ ! [SX1: g] :
~ ~ ( ( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SX1 @ SX0 )
!= sK2_SY0 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[97]) ).
thf(99,plain,
( ( ( ! [SX0: g] :
~ ( ( ( sK1_Xf @ sK2_SY0 @ SX0 )
!= SX0 )
| ( ( sK1_Xf @ SX0 @ sK2_SY0 )
!= SX0 ) ) )
= $false )
| ( ( ( sK1_Xf @ ( sK1_Xf @ sK10_SX0 @ sK11_SY13 ) @ sK12_SY15 )
= ( sK1_Xf @ sK10_SX0 @ ( sK1_Xf @ sK11_SY13 @ sK12_SY15 ) ) )
= $false )
| ( ( ~ ! [SX0: g] :
~ ! [SX1: g] :
~ ~ ( ( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SX1 @ SX0 )
!= sK2_SY0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(100,plain,
( ( ( ~ ( ( ( sK1_Xf @ sK2_SY0 @ sK13_SX0 )
!= sK13_SX0 )
| ( ( sK1_Xf @ sK13_SX0 @ sK2_SY0 )
!= sK13_SX0 ) ) )
= $false )
| ( ( ( sK1_Xf @ ( sK1_Xf @ sK10_SX0 @ sK11_SY13 ) @ sK12_SY15 )
= ( sK1_Xf @ sK10_SX0 @ ( sK1_Xf @ sK11_SY13 @ sK12_SY15 ) ) )
= $false )
| ( ( ~ ! [SX0: g] :
~ ! [SX1: g] :
~ ~ ( ( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SX1 @ SX0 )
!= sK2_SY0 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[99]) ).
thf(101,plain,
( ( ( ( ( sK1_Xf @ sK2_SY0 @ sK13_SX0 )
!= sK13_SX0 )
| ( ( sK1_Xf @ sK13_SX0 @ sK2_SY0 )
!= sK13_SX0 ) )
= $true )
| ( ( ( sK1_Xf @ ( sK1_Xf @ sK10_SX0 @ sK11_SY13 ) @ sK12_SY15 )
= ( sK1_Xf @ sK10_SX0 @ ( sK1_Xf @ sK11_SY13 @ sK12_SY15 ) ) )
= $false )
| ( ( ~ ! [SX0: g] :
~ ! [SX1: g] :
~ ~ ( ( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SX1 @ SX0 )
!= sK2_SY0 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(102,plain,
( ( ( ( ( sK1_Xf @ sK2_SY0 @ sK13_SX0 )
!= sK13_SX0 ) )
= $true )
| ( ( ( ( sK1_Xf @ sK13_SX0 @ sK2_SY0 )
!= sK13_SX0 ) )
= $true )
| ( ( ( sK1_Xf @ ( sK1_Xf @ sK10_SX0 @ sK11_SY13 ) @ sK12_SY15 )
= ( sK1_Xf @ sK10_SX0 @ ( sK1_Xf @ sK11_SY13 @ sK12_SY15 ) ) )
= $false )
| ( ( ~ ! [SX0: g] :
~ ! [SX1: g] :
~ ~ ( ( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SX1 @ SX0 )
!= sK2_SY0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(103,plain,
( ( ( ( sK1_Xf @ sK2_SY0 @ sK13_SX0 )
= sK13_SX0 )
= $false )
| ( ( ( ( sK1_Xf @ sK13_SX0 @ sK2_SY0 )
!= sK13_SX0 ) )
= $true )
| ( ( ( sK1_Xf @ ( sK1_Xf @ sK10_SX0 @ sK11_SY13 ) @ sK12_SY15 )
= ( sK1_Xf @ sK10_SX0 @ ( sK1_Xf @ sK11_SY13 @ sK12_SY15 ) ) )
= $false )
| ( ( ~ ! [SX0: g] :
~ ! [SX1: g] :
~ ~ ( ( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SX1 @ SX0 )
!= sK2_SY0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(104,plain,
( ( ( ( sK1_Xf @ sK13_SX0 @ sK2_SY0 )
= sK13_SX0 )
= $false )
| ( ( ( sK1_Xf @ sK2_SY0 @ sK13_SX0 )
= sK13_SX0 )
= $false )
| ( ( ( sK1_Xf @ ( sK1_Xf @ sK10_SX0 @ sK11_SY13 ) @ sK12_SY15 )
= ( sK1_Xf @ sK10_SX0 @ ( sK1_Xf @ sK11_SY13 @ sK12_SY15 ) ) )
= $false )
| ( ( ~ ! [SX0: g] :
~ ! [SX1: g] :
~ ~ ( ( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SX1 @ SX0 )
!= sK2_SY0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(105,plain,
( ( ( ! [SX0: g] :
~ ! [SX1: g] :
~ ~ ( ( ( sK1_Xf @ SX0 @ SX1 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SX1 @ SX0 )
!= sK2_SY0 ) ) )
= $false )
| ( ( ( sK1_Xf @ ( sK1_Xf @ sK10_SX0 @ sK11_SY13 ) @ sK12_SY15 )
= ( sK1_Xf @ sK10_SX0 @ ( sK1_Xf @ sK11_SY13 @ sK12_SY15 ) ) )
= $false )
| ( ( ( sK1_Xf @ sK2_SY0 @ sK13_SX0 )
= sK13_SX0 )
= $false )
| ( ( ( sK1_Xf @ sK13_SX0 @ sK2_SY0 )
= sK13_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(106,plain,
( ( ( ~ ! [SY16: g] :
~ ~ ( ( ( sK1_Xf @ sK14_SX0 @ SY16 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SY16 @ sK14_SX0 )
!= sK2_SY0 ) ) )
= $false )
| ( ( ( sK1_Xf @ ( sK1_Xf @ sK10_SX0 @ sK11_SY13 ) @ sK12_SY15 )
= ( sK1_Xf @ sK10_SX0 @ ( sK1_Xf @ sK11_SY13 @ sK12_SY15 ) ) )
= $false )
| ( ( ( sK1_Xf @ sK2_SY0 @ sK13_SX0 )
= sK13_SX0 )
= $false )
| ( ( ( sK1_Xf @ sK13_SX0 @ sK2_SY0 )
= sK13_SX0 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[105]) ).
thf(107,plain,
( ( ( ! [SY16: g] :
~ ~ ( ( ( sK1_Xf @ sK14_SX0 @ SY16 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SY16 @ sK14_SX0 )
!= sK2_SY0 ) ) )
= $true )
| ( ( ( sK1_Xf @ ( sK1_Xf @ sK10_SX0 @ sK11_SY13 ) @ sK12_SY15 )
= ( sK1_Xf @ sK10_SX0 @ ( sK1_Xf @ sK11_SY13 @ sK12_SY15 ) ) )
= $false )
| ( ( ( sK1_Xf @ sK2_SY0 @ sK13_SX0 )
= sK13_SX0 )
= $false )
| ( ( ( sK1_Xf @ sK13_SX0 @ sK2_SY0 )
= sK13_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(108,plain,
! [SV12: g] :
( ( ( ~ ~ ( ( ( sK1_Xf @ sK14_SX0 @ SV12 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SV12 @ sK14_SX0 )
!= sK2_SY0 ) ) )
= $true )
| ( ( ( sK1_Xf @ ( sK1_Xf @ sK10_SX0 @ sK11_SY13 ) @ sK12_SY15 )
= ( sK1_Xf @ sK10_SX0 @ ( sK1_Xf @ sK11_SY13 @ sK12_SY15 ) ) )
= $false )
| ( ( ( sK1_Xf @ sK2_SY0 @ sK13_SX0 )
= sK13_SX0 )
= $false )
| ( ( ( sK1_Xf @ sK13_SX0 @ sK2_SY0 )
= sK13_SX0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(109,plain,
! [SV12: g] :
( ( ( ~ ( ( ( sK1_Xf @ sK14_SX0 @ SV12 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SV12 @ sK14_SX0 )
!= sK2_SY0 ) ) )
= $false )
| ( ( ( sK1_Xf @ ( sK1_Xf @ sK10_SX0 @ sK11_SY13 ) @ sK12_SY15 )
= ( sK1_Xf @ sK10_SX0 @ ( sK1_Xf @ sK11_SY13 @ sK12_SY15 ) ) )
= $false )
| ( ( ( sK1_Xf @ sK2_SY0 @ sK13_SX0 )
= sK13_SX0 )
= $false )
| ( ( ( sK1_Xf @ sK13_SX0 @ sK2_SY0 )
= sK13_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(110,plain,
! [SV12: g] :
( ( ( ( ( sK1_Xf @ sK14_SX0 @ SV12 )
!= sK2_SY0 )
| ( ( sK1_Xf @ SV12 @ sK14_SX0 )
!= sK2_SY0 ) )
= $true )
| ( ( ( sK1_Xf @ ( sK1_Xf @ sK10_SX0 @ sK11_SY13 ) @ sK12_SY15 )
= ( sK1_Xf @ sK10_SX0 @ ( sK1_Xf @ sK11_SY13 @ sK12_SY15 ) ) )
= $false )
| ( ( ( sK1_Xf @ sK2_SY0 @ sK13_SX0 )
= sK13_SX0 )
= $false )
| ( ( ( sK1_Xf @ sK13_SX0 @ sK2_SY0 )
= sK13_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(111,plain,
! [SV12: g] :
( ( ( ( ( sK1_Xf @ sK14_SX0 @ SV12 )
!= sK2_SY0 ) )
= $true )
| ( ( ( ( sK1_Xf @ SV12 @ sK14_SX0 )
!= sK2_SY0 ) )
= $true )
| ( ( ( sK1_Xf @ ( sK1_Xf @ sK10_SX0 @ sK11_SY13 ) @ sK12_SY15 )
= ( sK1_Xf @ sK10_SX0 @ ( sK1_Xf @ sK11_SY13 @ sK12_SY15 ) ) )
= $false )
| ( ( ( sK1_Xf @ sK2_SY0 @ sK13_SX0 )
= sK13_SX0 )
= $false )
| ( ( ( sK1_Xf @ sK13_SX0 @ sK2_SY0 )
= sK13_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(112,plain,
! [SV12: g] :
( ( ( ( sK1_Xf @ sK14_SX0 @ SV12 )
= sK2_SY0 )
= $false )
| ( ( ( ( sK1_Xf @ SV12 @ sK14_SX0 )
!= sK2_SY0 ) )
= $true )
| ( ( ( sK1_Xf @ ( sK1_Xf @ sK10_SX0 @ sK11_SY13 ) @ sK12_SY15 )
= ( sK1_Xf @ sK10_SX0 @ ( sK1_Xf @ sK11_SY13 @ sK12_SY15 ) ) )
= $false )
| ( ( ( sK1_Xf @ sK2_SY0 @ sK13_SX0 )
= sK13_SX0 )
= $false )
| ( ( ( sK1_Xf @ sK13_SX0 @ sK2_SY0 )
= sK13_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(113,plain,
! [SV12: g] :
( ( ( ( sK1_Xf @ SV12 @ sK14_SX0 )
= sK2_SY0 )
= $false )
| ( ( ( sK1_Xf @ sK14_SX0 @ SV12 )
= sK2_SY0 )
= $false )
| ( ( ( sK1_Xf @ ( sK1_Xf @ sK10_SX0 @ sK11_SY13 ) @ sK12_SY15 )
= ( sK1_Xf @ sK10_SX0 @ ( sK1_Xf @ sK11_SY13 @ sK12_SY15 ) ) )
= $false )
| ( ( ( sK1_Xf @ sK2_SY0 @ sK13_SX0 )
= sK13_SX0 )
= $false )
| ( ( ( sK1_Xf @ sK13_SX0 @ sK2_SY0 )
= sK13_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(114,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[91,113,96,92]) ).
thf(115,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[114,63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG271^5 : TPTP v8.1.0. Bugfixed v5.3.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Wed Jun 8 03:15:18 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35
% 0.14/0.35 No.of.Axioms: 0
% 0.14/0.35
% 0.14/0.35 Length.of.Defs: 1389
% 0.14/0.35
% 0.14/0.35 Contains.Choice.Funs: false
% 0.14/0.35 (rf:0,axioms:0,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)........
% 0.21/0.46
% 0.21/0.46 ********************************
% 0.21/0.46 * All subproblems solved! *
% 0.21/0.46 ********************************
% 0.21/0.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:114,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.21/0.46
% 0.21/0.46 %**** Beginning of derivation protocol ****
% 0.21/0.46 % SZS output start CNFRefutation
% See solution above
% 0.21/0.46
% 0.21/0.46 %**** End of derivation protocol ****
% 0.21/0.46 %**** no. of clauses in derivation: 115 ****
% 0.21/0.46 %**** clause counter: 114 ****
% 0.21/0.46
% 0.21/0.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:114,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------