%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG276^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 Sep 30 07:44:49 AM UTC 2026
% Result : Theorem 1.74s 0.54s
% Output : CNFRefutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 7
% Syntax : Number of formulae : 111 ( 67 unt; 0 typ; 0 def)
% Number of atoms : 283 ( 259 equ; 0 cnn)
% Maximal formula atoms : 38 ( 2 avg)
% Number of connectives : 1245 ( 81 ~; 99 |; 42 &;1020 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 7 con; 0-2 aty)
% Number of variables : 341 ( 21 ^; 302 !; 18 ?; 341 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
g: $tType ).
thf(decl_23,type,
cGROUP1: ( g > g > g ) > g > $o ).
thf(decl_24,type,
cGROUP4: ( g > g > g ) > $o ).
thf(decl_25,type,
cGRP_ASSOC: ( g > g > g ) > $o ).
thf(decl_26,type,
cGRP_DIVISORS: ( g > g > g ) > $o ).
thf(decl_27,type,
cGRP_INVERSE: ( g > g > g ) > g > $o ).
thf(decl_28,type,
cGRP_UNIT: ( g > g > g ) > g > $o ).
thf(decl_29,type,
esk1_0: g > g > g ).
thf(decl_30,type,
esk2_1: g > g ).
thf(decl_31,type,
esk3_1: g > g ).
thf(decl_32,type,
esk4_1: g > g ).
thf(decl_33,type,
esk5_1: g > g ).
thf(decl_34,type,
esk6_1: g > g ).
thf(decl_35,type,
esk7_0: g ).
thf(decl_36,type,
esk8_0: g ).
thf(decl_37,type,
esk9_0: g ).
thf(decl_38,type,
esk10_0: g ).
thf(decl_39,type,
esk11_0: g ).
thf(decl_40,type,
esk12_0: g ).
thf(decl_41,type,
esk13_1: g > g ).
thf(decl_42,type,
esk14_2: g > g > g ).
thf(decl_43,type,
esk15_2: g > g > g ).
thf(cGROUP1_def,axiom,
( cGROUP1
= ( ^ [X1: g > g > g,X7: g] :
( ( cGRP_ASSOC @ X1 )
& ( cGRP_UNIT @ X1 @ X7 )
& ( cGRP_INVERSE @ X1 @ X7 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.agV68Aifv5/E---3.1_3694695.p',cGROUP1_def) ).
thf(cGRP_ASSOC_def,axiom,
( cGRP_ASSOC
= ( ^ [X1: g > g > g] :
! [X2: g,X3: g,X4: g] :
( ( X1 @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ X2 @ ( X1 @ X3 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.agV68Aifv5/E---3.1_3694695.p',cGRP_ASSOC_def) ).
thf(cGRP_INVERSE_def,axiom,
( cGRP_INVERSE
= ( ^ [X1: g > g > g,X7: g] :
! [X2: g] :
? [X3: g] :
( ( ( X1 @ X2 @ X3 )
= X7 )
& ( ( X1 @ X3 @ X2 )
= X7 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.agV68Aifv5/E---3.1_3694695.p',cGRP_INVERSE_def) ).
thf(cGRP_UNIT_def,axiom,
( cGRP_UNIT
= ( ^ [X1: g > g > g,X7: g] :
! [X2: g] :
( ( ( X1 @ X7 @ X2 )
= X2 )
& ( ( X1 @ X2 @ X7 )
= X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.agV68Aifv5/E---3.1_3694695.p',cGRP_UNIT_def) ).
thf(cGROUP4_def,axiom,
( cGROUP4
= ( ^ [X1: g > g > g] :
( ( cGRP_ASSOC @ X1 )
& ( cGRP_DIVISORS @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.agV68Aifv5/E---3.1_3694695.p',cGROUP4_def) ).
thf(cGRP_DIVISORS_def,axiom,
( cGRP_DIVISORS
= ( ^ [X1: g > g > g] :
! [X2: g,X3: g] :
( ? [X5: g] :
( ( X1 @ X2 @ X5 )
= X3 )
& ? [X6: g] :
( ( X1 @ X6 @ X2 )
= X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.agV68Aifv5/E---3.1_3694695.p',cGRP_DIVISORS_def) ).
thf(cEQUIV_01_04,conjecture,
! [X1: g > g > g] :
( ? [X7: g] : ( cGROUP1 @ X1 @ X7 )
<=> ( cGROUP4 @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.agV68Aifv5/E---3.1_3694695.p',cEQUIV_01_04) ).
thf(c_0_7,plain,
( cGROUP1
= ( ^ [Z0: g > g > g,Z1: g] :
( ! [X10: g,X11: g,X12: g] :
( ( Z0 @ ( Z0 @ X10 @ X11 ) @ X12 )
= ( Z0 @ X10 @ ( Z0 @ X11 @ X12 ) ) )
& ! [X13: g] :
( ( ( Z0 @ Z1 @ X13 )
= X13 )
& ( ( Z0 @ X13 @ Z1 )
= X13 ) )
& ! [X14: g] :
? [X15: g] :
( ( ( Z0 @ X14 @ X15 )
= Z1 )
& ( ( Z0 @ X15 @ X14 )
= Z1 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[cGROUP1_def]) ).
thf(c_0_8,plain,
( cGRP_ASSOC
= ( ^ [Z0: g > g > g] :
! [X2: g,X3: g,X4: g] :
( ( Z0 @ ( Z0 @ X2 @ X3 ) @ X4 )
= ( Z0 @ X2 @ ( Z0 @ X3 @ X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[cGRP_ASSOC_def]) ).
thf(c_0_9,plain,
( cGRP_INVERSE
= ( ^ [Z0: g > g > g,Z1: g] :
! [X2: g] :
? [X3: g] :
( ( ( Z0 @ X2 @ X3 )
= Z1 )
& ( ( Z0 @ X3 @ X2 )
= Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[cGRP_INVERSE_def]) ).
thf(c_0_10,plain,
( cGRP_UNIT
= ( ^ [Z0: g > g > g,Z1: g] :
! [X2: g] :
( ( ( Z0 @ Z1 @ X2 )
= X2 )
& ( ( Z0 @ X2 @ Z1 )
= X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[cGRP_UNIT_def]) ).
thf(c_0_11,plain,
( cGROUP4
= ( ^ [Z0: g > g > g] :
( ! [X16: g,X17: g,X18: g] :
( ( Z0 @ ( Z0 @ X16 @ X17 ) @ X18 )
= ( Z0 @ X16 @ ( Z0 @ X17 @ X18 ) ) )
& ! [X19: g,X20: g] :
( ? [X21: g] :
( ( Z0 @ X19 @ X21 )
= X20 )
& ? [X22: g] :
( ( Z0 @ X22 @ X19 )
= X20 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[cGROUP4_def]) ).
thf(c_0_12,plain,
( cGRP_DIVISORS
= ( ^ [Z0: g > g > g] :
! [X2: g,X3: g] :
( ? [X5: g] :
( ( Z0 @ X2 @ X5 )
= X3 )
& ? [X6: g] :
( ( Z0 @ X6 @ X2 )
= X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[cGRP_DIVISORS_def]) ).
thf(c_0_13,negated_conjecture,
~ ! [X1: g > g > g] :
( ? [X7: g] : ( cGROUP1 @ X1 @ X7 )
<=> ( cGROUP4 @ X1 ) ),
inference(assume_negation,[status(cth)],[cEQUIV_01_04]) ).
thf(c_0_14,plain,
( cGROUP1
= ( ^ [Z0: g > g > g,Z1: g] :
( ! [X10: g,X11: g,X12: g] :
( ( Z0 @ ( Z0 @ X10 @ X11 ) @ X12 )
= ( Z0 @ X10 @ ( Z0 @ X11 @ X12 ) ) )
& ! [X13: g] :
( ( ( Z0 @ Z1 @ X13 )
= X13 )
& ( ( Z0 @ X13 @ Z1 )
= X13 ) )
& ! [X14: g] :
? [X15: g] :
( ( ( Z0 @ X14 @ X15 )
= Z1 )
& ( ( Z0 @ X15 @ X14 )
= Z1 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_7,c_0_8]),c_0_9]),c_0_10]) ).
thf(c_0_15,plain,
( cGROUP4
= ( ^ [Z0: g > g > g] :
( ! [X16: g,X17: g,X18: g] :
( ( Z0 @ ( Z0 @ X16 @ X17 ) @ X18 )
= ( Z0 @ X16 @ ( Z0 @ X17 @ X18 ) ) )
& ! [X19: g,X20: g] :
( ? [X21: g] :
( ( Z0 @ X19 @ X21 )
= X20 )
& ? [X22: g] :
( ( Z0 @ X22 @ X19 )
= X20 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_11,c_0_8]),c_0_12]) ).
thf(c_0_16,negated_conjecture,
~ ! [X1: g > g > g] :
( ? [X7: g] :
( ! [X23: g,X24: g,X25: g] :
( ( X1 @ ( X1 @ X23 @ X24 ) @ X25 )
= ( X1 @ X23 @ ( X1 @ X24 @ X25 ) ) )
& ! [X26: g] :
( ( ( X1 @ X7 @ X26 )
= X26 )
& ( ( X1 @ X26 @ X7 )
= X26 ) )
& ! [X27: g] :
? [X28: g] :
( ( ( X1 @ X27 @ X28 )
= X7 )
& ( ( X1 @ X28 @ X27 )
= X7 ) ) )
<=> ( ! [X29: g,X30: g,X31: g] :
( ( X1 @ ( X1 @ X29 @ X30 ) @ X31 )
= ( X1 @ X29 @ ( X1 @ X30 @ X31 ) ) )
& ! [X32: g,X33: g] :
( ? [X34: g] :
( ( X1 @ X32 @ X34 )
= X33 )
& ? [X35: g] :
( ( X1 @ X35 @ X32 )
= X33 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
thf(c_0_17,negated_conjecture,
! [X37: g,X43: g,X49: g,X50: g,X52: g,X53: g,X54: g,X55: g,X56: g,X58: g,X59: g,X60: g,X61: g,X62: g] :
( ( ( ( esk1_0 @ ( esk1_0 @ ( esk2_1 @ X37 ) @ ( esk3_1 @ X37 ) ) @ ( esk4_1 @ X37 ) )
!= ( esk1_0 @ ( esk2_1 @ X37 ) @ ( esk1_0 @ ( esk3_1 @ X37 ) @ ( esk4_1 @ X37 ) ) ) )
| ( ( esk1_0 @ X37 @ ( esk5_1 @ X37 ) )
!= ( esk5_1 @ X37 ) )
| ( ( esk1_0 @ ( esk5_1 @ X37 ) @ X37 )
!= ( esk5_1 @ X37 ) )
| ( ( esk1_0 @ ( esk6_1 @ X37 ) @ X43 )
!= X37 )
| ( ( esk1_0 @ X43 @ ( esk6_1 @ X37 ) )
!= X37 )
| ( ( esk1_0 @ ( esk1_0 @ esk7_0 @ esk8_0 ) @ esk9_0 )
!= ( esk1_0 @ esk7_0 @ ( esk1_0 @ esk8_0 @ esk9_0 ) ) )
| ( ( esk1_0 @ esk10_0 @ X49 )
!= esk11_0 )
| ( ( esk1_0 @ X50 @ esk10_0 )
!= esk11_0 ) )
& ( ( ( esk1_0 @ ( esk1_0 @ X58 @ X59 ) @ X60 )
= ( esk1_0 @ X58 @ ( esk1_0 @ X59 @ X60 ) ) )
| ( ( esk1_0 @ ( esk1_0 @ X52 @ X53 ) @ X54 )
= ( esk1_0 @ X52 @ ( esk1_0 @ X53 @ X54 ) ) ) )
& ( ( ( esk1_0 @ X61 @ ( esk14_2 @ X61 @ X62 ) )
= X62 )
| ( ( esk1_0 @ ( esk1_0 @ X52 @ X53 ) @ X54 )
= ( esk1_0 @ X52 @ ( esk1_0 @ X53 @ X54 ) ) ) )
& ( ( ( esk1_0 @ ( esk15_2 @ X61 @ X62 ) @ X61 )
= X62 )
| ( ( esk1_0 @ ( esk1_0 @ X52 @ X53 ) @ X54 )
= ( esk1_0 @ X52 @ ( esk1_0 @ X53 @ X54 ) ) ) )
& ( ( ( esk1_0 @ ( esk1_0 @ X58 @ X59 ) @ X60 )
= ( esk1_0 @ X58 @ ( esk1_0 @ X59 @ X60 ) ) )
| ( ( esk1_0 @ esk12_0 @ X55 )
= X55 ) )
& ( ( ( esk1_0 @ X61 @ ( esk14_2 @ X61 @ X62 ) )
= X62 )
| ( ( esk1_0 @ esk12_0 @ X55 )
= X55 ) )
& ( ( ( esk1_0 @ ( esk15_2 @ X61 @ X62 ) @ X61 )
= X62 )
| ( ( esk1_0 @ esk12_0 @ X55 )
= X55 ) )
& ( ( ( esk1_0 @ ( esk1_0 @ X58 @ X59 ) @ X60 )
= ( esk1_0 @ X58 @ ( esk1_0 @ X59 @ X60 ) ) )
| ( ( esk1_0 @ X55 @ esk12_0 )
= X55 ) )
& ( ( ( esk1_0 @ X61 @ ( esk14_2 @ X61 @ X62 ) )
= X62 )
| ( ( esk1_0 @ X55 @ esk12_0 )
= X55 ) )
& ( ( ( esk1_0 @ ( esk15_2 @ X61 @ X62 ) @ X61 )
= X62 )
| ( ( esk1_0 @ X55 @ esk12_0 )
= X55 ) )
& ( ( ( esk1_0 @ ( esk1_0 @ X58 @ X59 ) @ X60 )
= ( esk1_0 @ X58 @ ( esk1_0 @ X59 @ X60 ) ) )
| ( ( esk1_0 @ X56 @ ( esk13_1 @ X56 ) )
= esk12_0 ) )
& ( ( ( esk1_0 @ X61 @ ( esk14_2 @ X61 @ X62 ) )
= X62 )
| ( ( esk1_0 @ X56 @ ( esk13_1 @ X56 ) )
= esk12_0 ) )
& ( ( ( esk1_0 @ ( esk15_2 @ X61 @ X62 ) @ X61 )
= X62 )
| ( ( esk1_0 @ X56 @ ( esk13_1 @ X56 ) )
= esk12_0 ) )
& ( ( ( esk1_0 @ ( esk1_0 @ X58 @ X59 ) @ X60 )
= ( esk1_0 @ X58 @ ( esk1_0 @ X59 @ X60 ) ) )
| ( ( esk1_0 @ ( esk13_1 @ X56 ) @ X56 )
= esk12_0 ) )
& ( ( ( esk1_0 @ X61 @ ( esk14_2 @ X61 @ X62 ) )
= X62 )
| ( ( esk1_0 @ ( esk13_1 @ X56 ) @ X56 )
= esk12_0 ) )
& ( ( ( esk1_0 @ ( esk15_2 @ X61 @ X62 ) @ X61 )
= X62 )
| ( ( esk1_0 @ ( esk13_1 @ X56 ) @ X56 )
= esk12_0 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])])])]) ).
thf(c_0_18,negated_conjecture,
! [X2: g,X3: g,X4: g,X5: g,X6: g,X7: g] :
( ( ( esk1_0 @ ( esk1_0 @ X2 @ X3 ) @ X4 )
= ( esk1_0 @ X2 @ ( esk1_0 @ X3 @ X4 ) ) )
| ( ( esk1_0 @ ( esk1_0 @ X5 @ X6 ) @ X7 )
= ( esk1_0 @ X5 @ ( esk1_0 @ X6 @ X7 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_19,negated_conjecture,
! [X2: g,X3: g,X4: g,X5: g] :
( ( ( esk1_0 @ ( esk1_0 @ ( esk2_1 @ X2 ) @ ( esk3_1 @ X2 ) ) @ ( esk4_1 @ X2 ) )
!= ( esk1_0 @ ( esk2_1 @ X2 ) @ ( esk1_0 @ ( esk3_1 @ X2 ) @ ( esk4_1 @ X2 ) ) ) )
| ( ( esk1_0 @ X2 @ ( esk5_1 @ X2 ) )
!= ( esk5_1 @ X2 ) )
| ( ( esk1_0 @ ( esk5_1 @ X2 ) @ X2 )
!= ( esk5_1 @ X2 ) )
| ( ( esk1_0 @ ( esk6_1 @ X2 ) @ X3 )
!= X2 )
| ( ( esk1_0 @ X3 @ ( esk6_1 @ X2 ) )
!= X2 )
| ( ( esk1_0 @ ( esk1_0 @ esk7_0 @ esk8_0 ) @ esk9_0 )
!= ( esk1_0 @ esk7_0 @ ( esk1_0 @ esk8_0 @ esk9_0 ) ) )
| ( ( esk1_0 @ esk10_0 @ X4 )
!= esk11_0 )
| ( ( esk1_0 @ X5 @ esk10_0 )
!= esk11_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( esk1_0 @ ( esk1_0 @ X2 @ X3 ) @ X4 )
= ( esk1_0 @ X2 @ ( esk1_0 @ X3 @ X4 ) ) ),
inference(condense,[status(thm)],[c_0_18]) ).
thf(c_0_21,negated_conjecture,
! [X3: g,X5: g,X4: g,X2: g] :
( ( ( esk1_0 @ X2 @ ( esk5_1 @ X2 ) )
!= ( esk5_1 @ X2 ) )
| ( ( esk1_0 @ ( esk5_1 @ X2 ) @ X2 )
!= ( esk5_1 @ X2 ) )
| ( ( esk1_0 @ X3 @ esk10_0 )
!= esk11_0 )
| ( ( esk1_0 @ esk10_0 @ X4 )
!= esk11_0 )
| ( ( esk1_0 @ X5 @ ( esk6_1 @ X2 ) )
!= X2 )
| ( ( esk1_0 @ ( esk6_1 @ X2 ) @ X5 )
!= X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_20])]) ).
thf(c_0_22,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( ( esk1_0 @ ( esk15_2 @ X2 @ X3 ) @ X2 )
= X3 )
| ( ( esk1_0 @ ( esk13_1 @ X4 ) @ X4 )
= esk12_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_23,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( ( esk1_0 @ ( esk15_2 @ X2 @ X3 ) @ X2 )
= X3 )
| ( ( esk1_0 @ X4 @ esk12_0 )
= X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_24,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( ( esk1_0 @ ( esk15_2 @ X2 @ X3 ) @ X2 )
= X3 )
| ( ( esk1_0 @ esk12_0 @ X4 )
= X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_25,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( ( esk1_0 @ ( esk15_2 @ X2 @ X3 ) @ X2 )
= X3 )
| ( ( esk1_0 @ X4 @ ( esk13_1 @ X4 ) )
= esk12_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_26,negated_conjecture,
! [X2: g,X3: g,X4: g,X5: g] :
( ( ( esk1_0 @ ( esk15_2 @ X2 @ X3 ) @ X2 )
= X3 )
| ( ( esk1_0 @ X4 @ esk10_0 )
!= esk11_0 )
| ( ( esk1_0 @ esk10_0 @ X5 )
!= esk11_0 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22])]),c_0_23]),c_0_24]),c_0_25]) ).
thf(c_0_27,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( ( esk1_0 @ X2 @ ( esk14_2 @ X2 @ X3 ) )
= X3 )
| ( ( esk1_0 @ ( esk13_1 @ X4 ) @ X4 )
= esk12_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_28,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( ( esk1_0 @ X2 @ ( esk14_2 @ X2 @ X3 ) )
= X3 )
| ( ( esk1_0 @ X4 @ esk12_0 )
= X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_29,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( ( esk1_0 @ X2 @ ( esk14_2 @ X2 @ X3 ) )
= X3 )
| ( ( esk1_0 @ esk12_0 @ X4 )
= X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_30,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( ( esk1_0 @ X2 @ ( esk14_2 @ X2 @ X3 ) )
= X3 )
| ( ( esk1_0 @ X4 @ ( esk13_1 @ X4 ) )
= esk12_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_31,negated_conjecture,
! [X2: g,X3: g,X4: g,X5: g,X6: g] :
( ( ( esk1_0 @ ( esk15_2 @ X2 @ X3 ) @ X2 )
= X3 )
| ( ( esk1_0 @ X4 @ ( esk1_0 @ X5 @ esk10_0 ) )
!= esk11_0 )
| ( ( esk1_0 @ esk10_0 @ X6 )
!= esk11_0 ) ),
inference(spm,[status(thm)],[c_0_26,c_0_20]) ).
thf(c_0_32,negated_conjecture,
! [X2: g,X3: g,X4: g,X5: g] :
( ( ( esk1_0 @ X2 @ ( esk14_2 @ X2 @ X3 ) )
= X3 )
| ( ( esk1_0 @ X4 @ esk10_0 )
!= esk11_0 )
| ( ( esk1_0 @ esk10_0 @ X5 )
!= esk11_0 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_27])]),c_0_28]),c_0_29]),c_0_30]) ).
thf(c_0_33,negated_conjecture,
! [X2: g,X3: g,X4: g,X5: g] :
( ( ( esk1_0 @ ( esk15_2 @ X2 @ X3 ) @ X2 )
= X3 )
| ( ( esk1_0 @ X4 @ esk12_0 )
!= esk11_0 )
| ( ( esk1_0 @ esk10_0 @ X5 )
!= esk11_0 ) ),
inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_22])]) ).
thf(c_0_34,negated_conjecture,
! [X2: g,X3: g,X4: g,X5: g,X6: g] :
( ( ( esk1_0 @ X2 @ ( esk14_2 @ X2 @ X3 ) )
= X3 )
| ( ( esk1_0 @ X4 @ ( esk1_0 @ X5 @ esk10_0 ) )
!= esk11_0 )
| ( ( esk1_0 @ esk10_0 @ X6 )
!= esk11_0 ) ),
inference(spm,[status(thm)],[c_0_32,c_0_20]) ).
thf(c_0_35,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( ( esk1_0 @ ( esk15_2 @ X2 @ X3 ) @ X2 )
= X3 )
| ( ( esk1_0 @ esk10_0 @ X4 )
!= esk11_0 ) ),
inference(condense,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_23])])]) ).
thf(c_0_36,negated_conjecture,
! [X2: g,X3: g,X4: g,X5: g] :
( ( ( esk1_0 @ X2 @ ( esk1_0 @ ( esk13_1 @ X2 ) @ X3 ) )
= ( esk1_0 @ esk12_0 @ X3 ) )
| ( ( esk1_0 @ ( esk15_2 @ X4 @ X5 ) @ X4 )
= X5 ) ),
inference(spm,[status(thm)],[c_0_20,c_0_25]) ).
thf(c_0_37,negated_conjecture,
! [X2: g,X3: g,X4: g,X5: g] :
( ( ( esk1_0 @ X2 @ ( esk1_0 @ X3 @ ( esk14_2 @ ( esk1_0 @ X2 @ X3 ) @ X4 ) ) )
= X4 )
| ( ( esk1_0 @ esk12_0 @ X5 )
= X5 ) ),
inference(spm,[status(thm)],[c_0_20,c_0_29]) ).
thf(c_0_38,negated_conjecture,
! [X2: g,X3: g,X4: g,X5: g] :
( ( ( esk1_0 @ X2 @ ( esk14_2 @ X2 @ X3 ) )
= X3 )
| ( ( esk1_0 @ X4 @ esk12_0 )
!= esk11_0 )
| ( ( esk1_0 @ esk10_0 @ X5 )
!= esk11_0 ) ),
inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_27])]) ).
thf(c_0_39,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( ( esk1_0 @ ( esk15_2 @ X2 @ X3 ) @ X2 )
= X3 )
| ( ( esk1_0 @ esk12_0 @ X4 )
!= esk11_0 ) ),
inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36])]) ).
thf(c_0_40,negated_conjecture,
! [X2: g,X3: g] :
( ( ( esk1_0 @ esk12_0 @ ( esk1_0 @ X2 @ ( esk14_2 @ ( esk1_0 @ esk12_0 @ X2 ) @ X3 ) ) )
= X3 )
| ( ( esk1_0 @ X2 @ ( esk14_2 @ ( esk1_0 @ esk12_0 @ X2 ) @ X3 ) )
!= X3 ) ),
inference(ef,[status(thm)],[c_0_37]) ).
thf(c_0_41,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( ( esk1_0 @ X2 @ ( esk14_2 @ X2 @ X3 ) )
= X3 )
| ( ( esk1_0 @ esk10_0 @ X4 )
!= esk11_0 ) ),
inference(condense,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_28])])]) ).
thf(c_0_42,negated_conjecture,
! [X2: g,X3: g,X4: g,X5: g] :
( ( ( esk1_0 @ X2 @ ( esk1_0 @ ( esk13_1 @ X2 ) @ X3 ) )
= ( esk1_0 @ esk12_0 @ X3 ) )
| ( ( esk1_0 @ X4 @ ( esk14_2 @ X4 @ X5 ) )
= X5 ) ),
inference(spm,[status(thm)],[c_0_20,c_0_30]) ).
thf(c_0_43,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( ( esk1_0 @ ( esk15_2 @ X2 @ X3 ) @ X2 )
= X3 )
| ( ( esk1_0 @ X4 @ ( esk14_2 @ ( esk1_0 @ esk12_0 @ X4 ) @ esk11_0 ) )
!= esk11_0 ) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40])]) ).
thf(c_0_44,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( ( esk1_0 @ X2 @ ( esk14_2 @ X2 @ X3 ) )
= X3 )
| ( ( esk1_0 @ esk12_0 @ X4 )
!= esk11_0 ) ),
inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42])]) ).
thf(c_0_45,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( ( esk1_0 @ ( esk15_2 @ X2 @ X3 ) @ X2 )
= X3 )
| ( ( esk1_0 @ X4 @ ( esk14_2 @ X4 @ esk11_0 ) )
!= esk11_0 ) ),
inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_24])]) ).
thf(c_0_46,negated_conjecture,
! [X2: g,X3: g] :
( ( esk1_0 @ X2 @ ( esk14_2 @ X2 @ X3 ) )
= X3 ),
inference(condense,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_29])])]) ).
thf(c_0_47,negated_conjecture,
! [X2: g,X3: g] :
( ( esk1_0 @ ( esk15_2 @ X2 @ X3 ) @ X2 )
= X3 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]) ).
thf(c_0_48,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( esk1_0 @ ( esk15_2 @ X2 @ X3 ) @ ( esk1_0 @ X2 @ X4 ) )
= ( esk1_0 @ X3 @ X4 ) ),
inference(spm,[status(thm)],[c_0_20,c_0_47]) ).
thf(c_0_49,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( esk1_0 @ ( esk15_2 @ X2 @ X3 ) @ X4 )
= ( esk1_0 @ X3 @ ( esk14_2 @ X2 @ X4 ) ) ),
inference(spm,[status(thm)],[c_0_48,c_0_46]) ).
thf(c_0_50,negated_conjecture,
! [X2: g,X3: g] :
( ( esk1_0 @ ( esk15_2 @ X2 @ X2 ) @ X3 )
= X3 ),
inference(spm,[status(thm)],[c_0_46,c_0_49]) ).
thf(c_0_51,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( esk1_0 @ X2 @ ( esk14_2 @ X3 @ ( esk1_0 @ X3 @ X4 ) ) )
= ( esk1_0 @ X2 @ X4 ) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
thf(c_0_52,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( esk1_0 @ X2 @ ( esk1_0 @ ( esk14_2 @ X2 @ X3 ) @ X4 ) )
= ( esk1_0 @ X3 @ X4 ) ),
inference(spm,[status(thm)],[c_0_20,c_0_46]) ).
thf(c_0_53,negated_conjecture,
! [X3: g,X2: g] :
( ( esk1_0 @ X2 @ ( esk14_2 @ X3 @ X3 ) )
= X2 ),
inference(rw,[status(thm)],[c_0_47,c_0_49]) ).
thf(c_0_54,negated_conjecture,
! [X2: g,X3: g] :
( ( esk14_2 @ X2 @ ( esk1_0 @ X2 @ X3 ) )
= X3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_50]) ).
thf(c_0_55,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( esk1_0 @ X2 @ ( esk14_2 @ ( esk14_2 @ X3 @ X2 ) @ X4 ) )
= ( esk1_0 @ X3 @ X4 ) ),
inference(spm,[status(thm)],[c_0_52,c_0_46]) ).
thf(c_0_56,negated_conjecture,
! [X2: g,X3: g,X4: g,X5: g] :
( ( ( esk1_0 @ ( esk13_1 @ X2 ) @ X2 )
= esk12_0 )
| ( ( esk1_0 @ ( esk6_1 @ X3 ) @ ( esk15_2 @ ( esk6_1 @ X3 ) @ X3 ) )
!= X3 )
| ( ( esk1_0 @ X3 @ ( esk5_1 @ X3 ) )
!= ( esk5_1 @ X3 ) )
| ( ( esk1_0 @ ( esk5_1 @ X3 ) @ X3 )
!= ( esk5_1 @ X3 ) )
| ( ( esk1_0 @ X4 @ esk10_0 )
!= esk11_0 )
| ( ( esk1_0 @ esk10_0 @ X5 )
!= esk11_0 ) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22])]) ).
thf(c_0_57,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( esk15_2 @ X2 @ X3 )
= ( esk1_0 @ X3 @ ( esk14_2 @ X2 @ ( esk14_2 @ X4 @ X4 ) ) ) ),
inference(spm,[status(thm)],[c_0_49,c_0_53]) ).
thf(c_0_58,negated_conjecture,
! [X2: g,X3: g] :
( ( esk14_2 @ ( esk15_2 @ X2 @ X2 ) @ X3 )
= X3 ),
inference(spm,[status(thm)],[c_0_46,c_0_50]) ).
thf(c_0_59,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( esk14_2 @ ( esk14_2 @ X2 @ X3 ) @ X4 )
= ( esk14_2 @ X3 @ ( esk1_0 @ X2 @ X4 ) ) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
thf(c_0_60,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( esk14_2 @ X2 @ ( esk1_0 @ X3 @ X4 ) )
= ( esk1_0 @ ( esk14_2 @ X2 @ X3 ) @ X4 ) ),
inference(spm,[status(thm)],[c_0_54,c_0_52]) ).
thf(c_0_61,negated_conjecture,
! [X4: g,X3: g,X2: g] :
( ( esk1_0 @ ( esk15_2 @ ( esk15_2 @ X2 @ X3 ) @ X4 ) @ X3 )
= ( esk1_0 @ X4 @ X2 ) ),
inference(spm,[status(thm)],[c_0_48,c_0_47]) ).
thf(c_0_62,negated_conjecture,
! [X2: g,X3: g,X4: g,X5: g] :
( ( ( esk1_0 @ ( esk13_1 @ X2 ) @ X2 )
= esk12_0 )
| ( ( esk1_0 @ ( esk6_1 @ X3 ) @ ( esk1_0 @ X3 @ ( esk14_2 @ ( esk6_1 @ X3 ) @ ( esk14_2 @ esk7_0 @ esk7_0 ) ) ) )
!= X3 )
| ( ( esk1_0 @ X3 @ ( esk5_1 @ X3 ) )
!= ( esk5_1 @ X3 ) )
| ( ( esk1_0 @ ( esk5_1 @ X3 ) @ X3 )
!= ( esk5_1 @ X3 ) )
| ( ( esk1_0 @ X4 @ esk10_0 )
!= esk11_0 )
| ( ( esk1_0 @ esk10_0 @ X5 )
!= esk11_0 ) ),
inference(rw,[status(thm)],[c_0_56,c_0_57]) ).
thf(c_0_63,negated_conjecture,
! [X3: g,X2: g] :
( ( esk1_0 @ X2 @ ( esk15_2 @ X3 @ X3 ) )
= X2 ),
inference(spm,[status(thm)],[c_0_53,c_0_58]) ).
thf(c_0_64,negated_conjecture,
! [X2: g,X3: g] :
( ( esk14_2 @ X2 @ X2 )
= ( esk15_2 @ X3 @ X3 ) ),
inference(spm,[status(thm)],[c_0_53,c_0_50]) ).
thf(c_0_65,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( esk1_0 @ X2 @ ( esk1_0 @ X3 @ ( esk14_2 @ ( esk1_0 @ X2 @ X3 ) @ X4 ) ) )
= X4 ),
inference(spm,[status(thm)],[c_0_20,c_0_46]) ).
thf(c_0_66,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( esk14_2 @ ( esk14_2 @ X2 @ X3 ) @ X4 )
= ( esk1_0 @ ( esk14_2 @ X3 @ X2 ) @ X4 ) ),
inference(rw,[status(thm)],[c_0_59,c_0_60]) ).
thf(c_0_67,negated_conjecture,
! [X2: g,X4: g,X3: g] :
( ( esk1_0 @ X2 @ ( esk14_2 @ ( esk15_2 @ X3 @ X4 ) @ X4 ) )
= ( esk1_0 @ X2 @ X3 ) ),
inference(rw,[status(thm)],[c_0_61,c_0_49]) ).
thf(c_0_68,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( esk1_0 @ ( esk15_2 @ ( esk14_2 @ X2 @ X3 ) @ X3 ) @ X4 )
= ( esk1_0 @ X2 @ X4 ) ),
inference(spm,[status(thm)],[c_0_55,c_0_49]) ).
thf(c_0_69,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( ( esk1_0 @ ( esk13_1 @ X2 ) @ X2 )
= esk12_0 )
| ( ( esk1_0 @ X3 @ esk10_0 )
!= esk11_0 )
| ( ( esk1_0 @ esk10_0 @ X4 )
!= esk11_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_50]),c_0_46]),c_0_50]),c_0_63])]),c_0_64]) ).
thf(c_0_70,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( esk1_0 @ X2 @ ( esk1_0 @ ( esk15_2 @ ( esk1_0 @ X2 @ X3 ) @ X3 ) @ X4 ) )
= X4 ),
inference(spm,[status(thm)],[c_0_65,c_0_49]) ).
thf(c_0_71,negated_conjecture,
! [X3: g,X2: g] :
( ( esk14_2 @ ( esk14_2 @ X2 @ X3 ) )
= ( esk1_0 @ ( esk14_2 @ X3 @ X2 ) ) ),
inference(pos_ext,[status(thm)],[c_0_66]) ).
thf(c_0_72,negated_conjecture,
! [X3: g,X2: g] :
( ( esk14_2 @ ( esk15_2 @ X2 @ X3 ) @ X3 )
= X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_67]),c_0_50]) ).
thf(c_0_73,negated_conjecture,
! [X3: g,X2: g] :
( ( esk15_2 @ ( esk14_2 @ X2 @ X3 ) @ X3 )
= X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_68]),c_0_63]) ).
thf(c_0_74,negated_conjecture,
! [X2: g,X3: g,X4: g,X5: g] :
( ( ( esk1_0 @ ( esk13_1 @ X2 ) @ X2 )
= esk12_0 )
| ( ( esk1_0 @ X3 @ ( esk14_2 @ X4 @ esk10_0 ) )
!= esk11_0 )
| ( ( esk1_0 @ esk10_0 @ X5 )
!= esk11_0 ) ),
inference(spm,[status(thm)],[c_0_69,c_0_49]) ).
thf(c_0_75,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( esk14_2 @ ( esk15_2 @ ( esk1_0 @ X2 @ X3 ) @ X3 ) @ X4 )
= ( esk1_0 @ X2 @ X4 ) ),
inference(spm,[status(thm)],[c_0_70,c_0_46]) ).
thf(c_0_76,negated_conjecture,
! [X2: g,X3: g] :
( ( esk1_0 @ ( esk14_2 @ X2 @ ( esk15_2 @ X3 @ X2 ) ) )
= ( esk14_2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
thf(c_0_77,negated_conjecture,
! [X2: g,X3: g] :
( ( esk15_2 @ X2 @ ( esk1_0 @ X3 @ X2 ) )
= X3 ),
inference(spm,[status(thm)],[c_0_73,c_0_54]) ).
thf(c_0_78,negated_conjecture,
! [X2: g,X3: g] :
( ( ( esk1_0 @ ( esk13_1 @ X2 ) @ X2 )
= esk12_0 )
| ( ( esk1_0 @ esk10_0 @ X3 )
!= esk11_0 ) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_64]),c_0_63])]) ).
thf(c_0_79,negated_conjecture,
! [X3: g,X2: g] :
( ( esk14_2 @ ( esk15_2 @ ( esk1_0 @ X2 @ X3 ) @ X3 ) )
= ( esk1_0 @ X2 ) ),
inference(pos_ext,[status(thm)],[c_0_75]) ).
thf(c_0_80,negated_conjecture,
! [X2: g,X3: g] :
( ( esk1_0 @ ( esk14_2 @ ( esk1_0 @ X2 @ X3 ) @ X2 ) )
= ( esk14_2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
thf(c_0_81,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ ( esk13_1 @ X2 ) @ X2 )
= esk12_0 ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_46])]) ).
thf(c_0_82,negated_conjecture,
! [X2: g,X3: g] :
( ( esk14_2 @ ( esk15_2 @ X2 @ ( esk14_2 @ X3 @ X2 ) ) )
= ( esk1_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_79,c_0_46]) ).
thf(c_0_83,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ ( esk14_2 @ esk12_0 @ ( esk13_1 @ X2 ) ) )
= ( esk14_2 @ X2 ) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
thf(c_0_84,negated_conjecture,
! [X2: g,X3: g] :
( ( esk14_2 @ ( esk15_2 @ esk12_0 @ X2 ) @ X3 )
= ( esk1_0 @ ( esk13_1 @ X2 ) @ X3 ) ),
inference(spm,[status(thm)],[c_0_75,c_0_81]) ).
thf(c_0_85,negated_conjecture,
! [X2: g,X3: g] :
( ( esk1_0 @ ( esk14_2 @ esk12_0 @ ( esk13_1 @ ( esk15_2 @ X2 @ ( esk14_2 @ X3 @ X2 ) ) ) ) )
= ( esk1_0 @ X3 ) ),
inference(rw,[status(thm)],[c_0_82,c_0_83]) ).
thf(c_0_86,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ ( esk14_2 @ esk12_0 @ ( esk13_1 @ ( esk15_2 @ esk12_0 @ X2 ) ) ) )
= ( esk1_0 @ ( esk13_1 @ X2 ) ) ),
inference(rw,[status(thm)],[inference(pos_ext,[status(thm)],[c_0_84]),c_0_83]) ).
thf(c_0_87,negated_conjecture,
! [X2: g,X3: g,X4: g,X5: g] :
( ( ( esk1_0 @ esk12_0 @ X2 )
= X2 )
| ( ( esk1_0 @ ( esk6_1 @ X3 ) @ ( esk15_2 @ ( esk6_1 @ X3 ) @ X3 ) )
!= X3 )
| ( ( esk1_0 @ X3 @ ( esk5_1 @ X3 ) )
!= ( esk5_1 @ X3 ) )
| ( ( esk1_0 @ ( esk5_1 @ X3 ) @ X3 )
!= ( esk5_1 @ X3 ) )
| ( ( esk1_0 @ X4 @ esk10_0 )
!= esk11_0 )
| ( ( esk1_0 @ esk10_0 @ X5 )
!= esk11_0 ) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_24])]) ).
thf(c_0_88,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ ( esk13_1 @ esk12_0 ) @ X2 )
= X2 ),
inference(spm,[status(thm)],[c_0_58,c_0_84]) ).
thf(c_0_89,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ ( esk13_1 @ ( esk14_2 @ X2 @ esk12_0 ) ) )
= ( esk1_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
thf(c_0_90,negated_conjecture,
! [X3: g,X2: g] :
( ( esk14_2 @ ( esk15_2 @ X2 @ X3 ) )
= ( esk1_0 @ ( esk15_2 @ X3 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_82,c_0_72]) ).
thf(c_0_91,negated_conjecture,
! [X2: g,X3: g,X4: g,X5: g] :
( ( ( esk1_0 @ esk12_0 @ X2 )
= X2 )
| ( ( esk1_0 @ ( esk6_1 @ X3 ) @ ( esk1_0 @ X3 @ ( esk14_2 @ ( esk6_1 @ X3 ) @ ( esk14_2 @ esk7_0 @ esk7_0 ) ) ) )
!= X3 )
| ( ( esk1_0 @ X3 @ ( esk5_1 @ X3 ) )
!= ( esk5_1 @ X3 ) )
| ( ( esk1_0 @ ( esk5_1 @ X3 ) @ X3 )
!= ( esk5_1 @ X3 ) )
| ( ( esk1_0 @ X4 @ esk10_0 )
!= esk11_0 )
| ( ( esk1_0 @ esk10_0 @ X5 )
!= esk11_0 ) ),
inference(rw,[status(thm)],[c_0_87,c_0_57]) ).
thf(c_0_92,negated_conjecture,
! [X2: g] :
( ( esk15_2 @ X2 @ X2 )
= ( esk13_1 @ esk12_0 ) ),
inference(spm,[status(thm)],[c_0_63,c_0_88]) ).
thf(c_0_93,negated_conjecture,
! [X2: g] :
( ( esk14_2 @ X2 )
= ( esk1_0 @ ( esk13_1 @ ( esk1_0 @ X2 @ esk12_0 ) ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_75]),c_0_90]),c_0_77]) ).
thf(c_0_94,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( ( esk1_0 @ esk12_0 @ X2 )
= X2 )
| ( ( esk1_0 @ X3 @ esk10_0 )
!= esk11_0 )
| ( ( esk1_0 @ esk10_0 @ X4 )
!= esk11_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_50]),c_0_46]),c_0_50]),c_0_63])]),c_0_64]) ).
thf(c_0_95,negated_conjecture,
! [X2: g] :
( ( esk14_2 @ X2 @ X2 )
= ( esk13_1 @ esk12_0 ) ),
inference(rw,[status(thm)],[c_0_64,c_0_92]) ).
thf(c_0_96,negated_conjecture,
! [X2: g,X3: g] :
( ( esk14_2 @ X2 @ X3 )
= ( esk1_0 @ ( esk13_1 @ ( esk1_0 @ X2 @ esk12_0 ) ) @ X3 ) ),
inference(arg_cong,[status(thm)],[c_0_93]) ).
thf(c_0_97,negated_conjecture,
! [X2: g,X3: g,X4: g,X5: g] :
( ( ( esk1_0 @ esk12_0 @ X2 )
= X2 )
| ( ( esk1_0 @ X3 @ ( esk1_0 @ X4 @ esk10_0 ) )
!= esk11_0 )
| ( ( esk1_0 @ esk10_0 @ X5 )
!= esk11_0 ) ),
inference(spm,[status(thm)],[c_0_94,c_0_20]) ).
thf(c_0_98,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ ( esk13_1 @ ( esk1_0 @ X2 @ esk12_0 ) ) @ X2 )
= ( esk13_1 @ esk12_0 ) ),
inference(rw,[status(thm)],[c_0_95,c_0_96]) ).
thf(c_0_99,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ X2 @ ( esk13_1 @ esk12_0 ) )
= X2 ),
inference(rw,[status(thm)],[c_0_63,c_0_92]) ).
thf(c_0_100,negated_conjecture,
! [X2: g,X3: g] :
( ( ( esk1_0 @ esk12_0 @ X2 )
= X2 )
| ( ( esk1_0 @ esk10_0 @ X3 )
!= esk11_0 ) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_99])]) ).
thf(c_0_101,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ esk12_0 @ X2 )
= X2 ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_70])]) ).
thf(c_0_102,negated_conjecture,
( ( esk13_1 @ esk12_0 )
= esk12_0 ),
inference(spm,[status(thm)],[c_0_99,c_0_101]) ).
thf(c_0_103,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ X2 @ esk12_0 )
= X2 ),
inference(rw,[status(thm)],[c_0_99,c_0_102]) ).
thf(c_0_104,negated_conjecture,
! [X2: g,X3: g] :
( ( esk1_0 @ X2 @ ( esk1_0 @ ( esk13_1 @ X2 ) @ X3 ) )
= X3 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_103]),c_0_96]),c_0_103]),c_0_103]) ).
thf(c_0_105,negated_conjecture,
! [X2: g,X3: g] :
( ( ( esk1_0 @ ( esk6_1 @ ( esk13_1 @ esk12_0 ) ) @ ( esk13_1 @ ( esk1_0 @ ( esk6_1 @ ( esk13_1 @ esk12_0 ) ) @ esk12_0 ) ) )
!= ( esk13_1 @ esk12_0 ) )
| ( ( esk1_0 @ X2 @ esk10_0 )
!= esk11_0 )
| ( ( esk1_0 @ esk10_0 @ X3 )
!= esk11_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_98])]),c_0_88]),c_0_99])]) ).
thf(c_0_106,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ X2 @ ( esk13_1 @ X2 ) )
= esk12_0 ),
inference(spm,[status(thm)],[c_0_104,c_0_103]) ).
thf(c_0_107,negated_conjecture,
! [X2: g,X3: g] :
( ( ( esk1_0 @ X2 @ esk10_0 )
!= esk11_0 )
| ( ( esk1_0 @ esk10_0 @ X3 )
!= esk11_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_102]),c_0_102]),c_0_102]),c_0_103]),c_0_106])]) ).
thf(c_0_108,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( ( esk1_0 @ X2 @ ( esk1_0 @ X3 @ esk10_0 ) )
!= esk11_0 )
| ( ( esk1_0 @ esk10_0 @ X4 )
!= esk11_0 ) ),
inference(spm,[status(thm)],[c_0_107,c_0_20]) ).
thf(c_0_109,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ esk10_0 @ X2 )
!= esk11_0 ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_81]),c_0_103])]) ).
thf(c_0_110,negated_conjecture,
$false,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_70])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG276^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n007.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 17:34:11 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.25 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.agV68Aifv5/E---3.1_3694695.p
% 1.74/0.54 % Version: 3.5.1-ho
% 1.74/0.54 % Preprocessing class: HSSSSMSSSLSNHSN.
% 1.74/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.74/0.54 % Starting ho_unfolding_3 with 1500s (5) cores
% 1.74/0.54 % Starting lpo8_lambda_fix with 300s (1) cores
% 1.74/0.54 % Starting lpo8_s with 300s (1) cores
% 1.74/0.54 % Starting new_bool_11 with 300s (1) cores
% 1.74/0.54 % ho_unfolding_3 with pid 3694729 completed with status 0
% 1.74/0.54 % Result found by ho_unfolding_3
% 1.74/0.54 % Preprocessing class: HSSSSMSSSLSNHSN.
% 1.74/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.74/0.54 % Starting ho_unfolding_3 with 1500s (5) cores
% 1.74/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.74/0.54 % No SInE strategy applied
% 1.74/0.54 % Search class: HGHPF-FFMF21-MHSFMFNN
% 1.74/0.54 % partial match(2): HGHPF-FFMF11-SHSFMFNN
% 1.74/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.74/0.54 % Starting SubtermCWHack with 136s (1) cores
% 1.74/0.54 % Starting ho_unfolding_3 with 151s (1) cores
% 1.74/0.54 % Starting sh5l with 136s (1) cores
% 1.74/0.54 % Starting new_bool_1 with 136s (1) cores
% 1.74/0.54 % Starting lpo1_def_fix with 136s (1) cores
% 1.74/0.54 % ho_unfolding_3 with pid 3694738 completed with status 0
% 1.74/0.54 % Result found by ho_unfolding_3
% 1.74/0.54 % Preprocessing class: HSSSSMSSSLSNHSN.
% 1.74/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.74/0.54 % Starting ho_unfolding_3 with 1500s (5) cores
% 1.74/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.74/0.54 % No SInE strategy applied
% 1.74/0.54 % Search class: HGHPF-FFMF21-MHSFMFNN
% 1.74/0.54 % partial match(2): HGHPF-FFMF11-SHSFMFNN
% 1.74/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.74/0.54 % Starting SubtermCWHack with 136s (1) cores
% 1.74/0.54 % Starting ho_unfolding_3 with 151s (1) cores
% 1.74/0.54 % Preprocessing time : 0.002 s
% 1.74/0.54 % Presaturation interreduction done
% 1.74/0.54
% 1.74/0.54 % Proof found!
% 1.74/0.54 % SZS status Theorem
% 1.74/0.54 % SZS output start CNFRefutation
% See solution above
% 1.74/0.54 % Parsed axioms : 14
% 1.74/0.54 % Removed by relevancy pruning/SinE : 0
% 1.74/0.54 % Initial clauses : 23
% 1.74/0.54 % Removed in clause preprocessing : 7
% 1.74/0.54 % Initial clauses in saturation : 16
% 1.74/0.54 % Processed clauses : 1284
% 1.74/0.54 % ...of these trivial : 89
% 1.74/0.54 % ...subsumed : 826
% 1.74/0.54 % ...remaining for further processing : 369
% 1.74/0.54 % Other redundant clauses eliminated : 403
% 1.74/0.54 % Clauses deleted for lack of memory : 0
% 1.74/0.54 % Backward-subsumed : 105
% 1.74/0.54 % Backward-rewritten : 227
% 1.74/0.54 % Generated clauses : 8878
% 1.74/0.54 % ...of the previous two non-redundant : 7516
% 1.74/0.54 % ...aggressively subsumed : 0
% 1.74/0.54 % Contextual simplify-reflections : 6
% 1.74/0.54 % Paramodulations : 8417
% 1.74/0.54 % Factorizations : 6
% 1.74/0.54 % NegExts : 0
% 1.74/0.54 % Equation resolutions : 403
% 1.74/0.54 % Disequality decompositions : 0
% 1.74/0.54 % Total rewrite steps : 6455
% 1.74/0.54 % ...of those cached : 4285
% 1.74/0.54 % Propositional unsat checks : 0
% 1.74/0.54 % Propositional check models : 0
% 1.74/0.54 % Propositional check unsatisfiable : 0
% 1.74/0.54 % Propositional clauses : 0
% 1.74/0.54 % Propositional clauses after purity: 0
% 1.74/0.54 % Propositional unsat core size : 0
% 1.74/0.54 % Propositional preprocessing time : 0.000
% 1.74/0.54 % Propositional encoding time : 0.000
% 1.74/0.54 % Propositional solver time : 0.000
% 1.74/0.54 % Success case prop preproc time : 0.000
% 1.74/0.54 % Success case prop encoding time : 0.000
% 1.74/0.54 % Success case prop solver time : 0.000
% 1.74/0.54 % Current number of processed clauses : 27
% 1.74/0.54 % Positive orientable unit clauses : 25
% 1.74/0.54 % Positive unorientable unit clauses: 0
% 1.74/0.54 % Negative unit clauses : 2
% 1.74/0.54 % Non-unit-clauses : 0
% 1.74/0.54 % Current number of unprocessed clauses: 2691
% 1.74/0.54 % ...number of literals in the above : 6393
% 1.74/0.54 % Current number of archived formulas : 0
% 1.74/0.54 % Current number of archived clauses : 342
% 1.74/0.54 % Clause-clause subsumption calls (NU) : 6170
% 1.74/0.54 % Rec. Clause-clause subsumption calls : 4852
% 1.74/0.54 % Non-unit clause-clause subsumptions : 475
% 1.74/0.54 % Unit Clause-clause subsumption calls : 1149
% 1.74/0.54 % Rewrite failures with RHS unbound : 0
% 1.74/0.54 % BW rewrite match attempts : 416
% 1.74/0.54 % BW rewrite match successes : 197
% 1.74/0.54 % Condensation attempts : 1285
% 1.74/0.54 % Condensation successes : 62
% 1.74/0.54 % Termbank termtop insertions : 126372
% 1.74/0.54 % Search garbage collected termcells : 481
% 1.74/0.54
% 1.74/0.54 % -------------------------------------------------
% 1.74/0.54 % User time : 0.241 s
% 1.74/0.54 % System time : 0.009 s
% 1.74/0.54 % Total time : 0.250 s
% 1.74/0.54 % Maximum resident set size: 3640 pages
% 1.74/0.54
% 1.74/0.54 % -------------------------------------------------
% 1.74/0.54 % User time : 1.142 s
% 1.74/0.54 % System time : 0.047 s
% 1.74/0.54 % Total time : 1.188 s
% 1.74/0.54 % Maximum resident set size: 4864 pages
% 1.74/0.54 % E exiting
%------------------------------------------------------------------------------