%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG274^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 Sep 30 07:44:49 AM UTC 2026
% Result : Theorem 5.87s 1.16s
% Output : CNFRefutation 5.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 7
% Syntax : Number of formulae : 52 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 156 ( 132 equ; 0 cnn)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 593 ( 35 ~; 47 |; 26 &; 482 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 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 : 190 ( 21 ^; 151 !; 18 ?; 190 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
g: $tType ).
thf(decl_23,type,
cGROUP3: ( 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_RIGHT_INVERSE: ( g > g > g ) > g > $o ).
thf(decl_28,type,
cGRP_RIGHT_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(cGROUP3_def,axiom,
( cGROUP3
= ( ^ [X1: g > g > g,X7: g] :
( ( cGRP_ASSOC @ X1 )
& ( cGRP_RIGHT_UNIT @ X1 @ X7 )
& ( cGRP_RIGHT_INVERSE @ X1 @ X7 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EbQFBpAbDH/E---3.1_2420320.p',cGROUP3_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/sandbox/tmp/tmp.EbQFBpAbDH/E---3.1_2420320.p',cGRP_ASSOC_def) ).
thf(cGRP_RIGHT_INVERSE_def,axiom,
( cGRP_RIGHT_INVERSE
= ( ^ [X1: g > g > g,X7: g] :
! [X2: g] :
? [X3: g] :
( ( X1 @ X2 @ X3 )
= X7 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EbQFBpAbDH/E---3.1_2420320.p',cGRP_RIGHT_INVERSE_def) ).
thf(cGRP_RIGHT_UNIT_def,axiom,
( cGRP_RIGHT_UNIT
= ( ^ [X1: g > g > g,X7: g] :
! [X2: g] :
( ( X1 @ X2 @ X7 )
= X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EbQFBpAbDH/E---3.1_2420320.p',cGRP_RIGHT_UNIT_def) ).
thf(cGROUP4_def,axiom,
( cGROUP4
= ( ^ [X1: g > g > g] :
( ( cGRP_ASSOC @ X1 )
& ( cGRP_DIVISORS @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EbQFBpAbDH/E---3.1_2420320.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/sandbox/tmp/tmp.EbQFBpAbDH/E---3.1_2420320.p',cGRP_DIVISORS_def) ).
thf(cEQUIV_03_04,conjecture,
! [X1: g > g > g] :
( ? [X7: g] : ( cGROUP3 @ X1 @ X7 )
<=> ( cGROUP4 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.EbQFBpAbDH/E---3.1_2420320.p',cEQUIV_03_04) ).
thf(c_0_7,plain,
( cGROUP3
= ( ^ [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 @ X13 @ Z1 )
= X13 )
& ! [X14: g] :
? [X15: g] :
( ( Z0 @ X14 @ X15 )
= Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[cGROUP3_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_RIGHT_INVERSE
= ( ^ [Z0: g > g > g,Z1: g] :
! [X2: g] :
? [X3: g] :
( ( Z0 @ X2 @ X3 )
= Z1 ) ) ),
inference(fof_simplification,[status(thm)],[cGRP_RIGHT_INVERSE_def]) ).
thf(c_0_10,plain,
( cGRP_RIGHT_UNIT
= ( ^ [Z0: g > g > g,Z1: g] :
! [X2: g] :
( ( Z0 @ X2 @ Z1 )
= X2 ) ) ),
inference(fof_simplification,[status(thm)],[cGRP_RIGHT_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] : ( cGROUP3 @ X1 @ X7 )
<=> ( cGROUP4 @ X1 ) ),
inference(assume_negation,[status(cth)],[cEQUIV_03_04]) ).
thf(c_0_14,plain,
( cGROUP3
= ( ^ [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 @ X13 @ Z1 )
= X13 )
& ! [X14: g] :
? [X15: g] :
( ( Z0 @ X14 @ X15 )
= 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 @ X26 @ X7 )
= X26 )
& ! [X27: g] :
? [X28: g] :
( ( X1 @ X27 @ X28 )
= 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 @ ( esk5_1 @ X37 ) @ X37 )
!= ( esk5_1 @ X37 ) )
| ( ( esk1_0 @ ( esk6_1 @ X37 ) @ X43 )
!= 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 @ 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 ) ) ),
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] :
( ( esk1_0 @ ( esk1_0 @ X2 @ X3 ) @ X4 )
= ( esk1_0 @ X2 @ ( esk1_0 @ X3 @ X4 ) ) ),
inference(condense,[status(thm)],[c_0_18]) ).
thf(c_0_20,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_21,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 @ ( esk5_1 @ X2 ) @ X2 )
!= ( esk5_1 @ X2 ) )
| ( ( esk1_0 @ ( esk6_1 @ X2 ) @ X3 )
!= 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_22,negated_conjecture,
! [X2: g,X3: g,X4: g,X5: g] :
( ( ( esk1_0 @ ( esk15_2 @ X2 @ X3 ) @ ( esk1_0 @ X2 @ X4 ) )
= ( esk1_0 @ X3 @ X4 ) )
| ( ( esk1_0 @ X5 @ esk12_0 )
= X5 ) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_23,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_24,negated_conjecture,
! [X3: g,X5: g,X4: g,X2: g] :
( ( ( 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 @ ( esk6_1 @ X2 ) @ X5 )
!= X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_19]),c_0_19])]) ).
thf(c_0_25,negated_conjecture,
! [X2: g,X3: g,X4: g,X5: g] :
( ( ( esk1_0 @ ( esk15_2 @ X2 @ X3 ) @ X4 )
= ( esk1_0 @ X3 @ ( esk14_2 @ X2 @ X4 ) ) )
| ( ( esk1_0 @ X5 @ esk12_0 )
= X5 ) ),
inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23])]) ).
thf(c_0_26,negated_conjecture,
! [X2: g,X3: g,X4: g,X5: g] :
( ( ( esk1_0 @ X2 @ esk12_0 )
= X2 )
| ( ( 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_24,c_0_23])]) ).
thf(c_0_27,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( ( esk1_0 @ X2 @ ( esk14_2 @ X3 @ X3 ) )
= X2 )
| ( ( esk1_0 @ X4 @ esk12_0 )
= X4 ) ),
inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_25])]) ).
thf(c_0_28,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( ( esk1_0 @ X2 @ esk12_0 )
= X2 )
| ( ( esk1_0 @ X3 @ esk10_0 )
!= esk11_0 )
| ( ( esk1_0 @ esk10_0 @ X4 )
!= esk11_0 ) ),
inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27])]) ).
thf(c_0_29,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 @ X5 @ esk12_0 )
= X5 ) ),
inference(spm,[status(thm)],[c_0_19,c_0_23]) ).
thf(c_0_30,negated_conjecture,
! [X2: g,X3: g,X4: g,X5: g] :
( ( ( esk1_0 @ X2 @ ( esk1_0 @ ( esk14_2 @ X2 @ X3 ) @ X4 ) )
= ( esk1_0 @ X3 @ X4 ) )
| ( ( esk1_0 @ X5 @ esk12_0 )
= X5 ) ),
inference(spm,[status(thm)],[c_0_19,c_0_23]) ).
thf(c_0_31,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_32,negated_conjecture,
! [X2: g,X3: g] :
( ( ( esk1_0 @ X2 @ esk12_0 )
= X2 )
| ( ( esk1_0 @ esk10_0 @ X3 )
!= esk11_0 ) ),
inference(condense,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_20])])]) ).
thf(c_0_33,negated_conjecture,
! [X2: g,X3: g,X4: g,X5: g] :
( ( ( esk1_0 @ X2 @ ( esk14_2 @ ( esk1_0 @ X3 @ ( esk14_2 @ X3 @ X2 ) ) @ X4 ) )
= X4 )
| ( ( esk1_0 @ X5 @ esk12_0 )
= X5 ) ),
inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30])]) ).
thf(c_0_34,negated_conjecture,
! [X2: g,X3: g,X4: g,X5: g] :
( ( ( esk1_0 @ X2 @ ( esk13_1 @ X2 ) )
= esk12_0 )
| ( ( 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_24,c_0_31])]) ).
thf(c_0_35,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ X2 @ esk12_0 )
= X2 ),
inference(condense,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33])])]) ).
thf(c_0_36,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( ( esk1_0 @ X2 @ ( esk13_1 @ X2 ) )
= esk12_0 )
| ( ( esk1_0 @ X3 @ esk10_0 )
!= esk11_0 )
| ( ( esk1_0 @ esk10_0 @ X4 )
!= esk11_0 ) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
thf(c_0_37,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_38,negated_conjecture,
! [X2: g,X3: g] :
( ( ( esk1_0 @ X2 @ ( esk13_1 @ X2 ) )
= esk12_0 )
| ( ( esk1_0 @ esk10_0 @ X3 )
!= esk11_0 ) ),
inference(condense,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37])])]) ).
thf(c_0_39,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ X2 @ ( esk13_1 @ X2 ) )
= esk12_0 ),
inference(condense,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_31])])]) ).
thf(c_0_40,negated_conjecture,
! [X2: g,X3: g] :
( ( esk1_0 @ X2 @ ( esk1_0 @ ( esk13_1 @ X2 ) @ X3 ) )
= ( esk1_0 @ esk12_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_19,c_0_39]) ).
thf(c_0_41,negated_conjecture,
! [X2: g,X3: g] :
( ( esk1_0 @ X2 @ ( esk1_0 @ esk12_0 @ X3 ) )
= ( esk1_0 @ X2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_19,c_0_35]) ).
thf(c_0_42,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ esk12_0 @ ( esk13_1 @ ( esk13_1 @ X2 ) ) )
= X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_39]),c_0_35]) ).
thf(c_0_43,negated_conjecture,
! [X2: g,X3: g] :
( ( esk1_0 @ X2 @ ( esk13_1 @ ( esk13_1 @ X3 ) ) )
= ( esk1_0 @ X2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
thf(c_0_44,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ esk12_0 @ X2 )
= X2 ),
inference(rw,[status(thm)],[c_0_42,c_0_43]) ).
thf(c_0_45,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(er,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_39])]),c_0_35])]) ).
thf(c_0_46,negated_conjecture,
! [X2: g] :
( ( esk13_1 @ ( esk13_1 @ X2 ) )
= X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_44]) ).
thf(c_0_47,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_45,c_0_19]) ).
thf(c_0_48,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ ( esk13_1 @ X2 ) @ X2 )
= esk12_0 ),
inference(spm,[status(thm)],[c_0_39,c_0_46]) ).
thf(c_0_49,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_47,c_0_48]),c_0_35])]) ).
thf(c_0_50,negated_conjecture,
! [X2: g,X3: g] :
( ( esk1_0 @ X2 @ ( esk1_0 @ ( esk13_1 @ X2 ) @ X3 ) )
= X3 ),
inference(rw,[status(thm)],[c_0_40,c_0_44]) ).
thf(c_0_51,negated_conjecture,
$false,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG274^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n013.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 17:35:51 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.23 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.EbQFBpAbDH/E---3.1_2420320.p
% 5.87/1.16 % Version: 3.5.1-ho
% 5.87/1.16 % Preprocessing class: HSSSSMSSSLSNHSN.
% 5.87/1.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.87/1.16 % Starting ho_unfolding_3 with 1500s (5) cores
% 5.87/1.16 % Starting lpo8_lambda_fix with 300s (1) cores
% 5.87/1.16 % Starting lpo8_s with 300s (1) cores
% 5.87/1.16 % Starting new_bool_11 with 300s (1) cores
% 5.87/1.16 % ho_unfolding_3 with pid 2420333 completed with status 0
% 5.87/1.16 % Result found by ho_unfolding_3
% 5.87/1.16 % Preprocessing class: HSSSSMSSSLSNHSN.
% 5.87/1.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.87/1.16 % Starting ho_unfolding_3 with 1500s (5) cores
% 5.87/1.16 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.87/1.16 % No SInE strategy applied
% 5.87/1.16 % Search class: HGHPF-FFSF21-MHSFMFNN
% 5.87/1.16 % partial match(3): HGHPF-FFMF11-SHSFMFNN
% 5.87/1.16 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.87/1.16 % Starting SubtermCWHack with 136s (1) cores
% 5.87/1.16 % Starting ho_unfolding_3 with 151s (1) cores
% 5.87/1.16 % Starting sh5l with 136s (1) cores
% 5.87/1.16 % Starting new_bool_1 with 136s (1) cores
% 5.87/1.16 % Starting lpo1_def_fix with 136s (1) cores
% 5.87/1.16 % ho_unfolding_3 with pid 2420340 completed with status 0
% 5.87/1.16 % Result found by ho_unfolding_3
% 5.87/1.16 % Preprocessing class: HSSSSMSSSLSNHSN.
% 5.87/1.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.87/1.16 % Starting ho_unfolding_3 with 1500s (5) cores
% 5.87/1.16 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.87/1.16 % No SInE strategy applied
% 5.87/1.16 % Search class: HGHPF-FFSF21-MHSFMFNN
% 5.87/1.16 % partial match(3): HGHPF-FFMF11-SHSFMFNN
% 5.87/1.16 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.87/1.16 % Starting SubtermCWHack with 136s (1) cores
% 5.87/1.16 % Starting ho_unfolding_3 with 151s (1) cores
% 5.87/1.16 % Preprocessing time : 0.002 s
% 5.87/1.16 % Presaturation interreduction done
% 5.87/1.16
% 5.87/1.16 % Proof found!
% 5.87/1.16 % SZS status Theorem
% 5.87/1.16 % SZS output start CNFRefutation
% See solution above
% 5.87/1.16 % Parsed axioms : 14
% 5.87/1.16 % Removed by relevancy pruning/SinE : 0
% 5.87/1.16 % Initial clauses : 17
% 5.87/1.16 % Removed in clause preprocessing : 7
% 5.87/1.16 % Initial clauses in saturation : 10
% 5.87/1.16 % Processed clauses : 2959
% 5.87/1.16 % ...of these trivial : 118
% 5.87/1.16 % ...subsumed : 2375
% 5.87/1.16 % ...remaining for further processing : 466
% 5.87/1.16 % Other redundant clauses eliminated : 1013
% 5.87/1.16 % Clauses deleted for lack of memory : 0
% 5.87/1.16 % Backward-subsumed : 220
% 5.87/1.16 % Backward-rewritten : 214
% 5.87/1.16 % Generated clauses : 27696
% 5.87/1.16 % ...of the previous two non-redundant : 26042
% 5.87/1.16 % ...aggressively subsumed : 0
% 5.87/1.16 % Contextual simplify-reflections : 13
% 5.87/1.16 % Paramodulations : 26633
% 5.87/1.16 % Factorizations : 50
% 5.87/1.16 % NegExts : 0
% 5.87/1.16 % Equation resolutions : 1013
% 5.87/1.16 % Disequality decompositions : 0
% 5.87/1.16 % Total rewrite steps : 4161
% 5.87/1.16 % ...of those cached : 3275
% 5.87/1.16 % Propositional unsat checks : 0
% 5.87/1.16 % Propositional check models : 0
% 5.87/1.16 % Propositional check unsatisfiable : 0
% 5.87/1.16 % Propositional clauses : 0
% 5.87/1.16 % Propositional clauses after purity: 0
% 5.87/1.16 % Propositional unsat core size : 0
% 5.87/1.16 % Propositional preprocessing time : 0.000
% 5.87/1.16 % Propositional encoding time : 0.000
% 5.87/1.16 % Propositional solver time : 0.000
% 5.87/1.16 % Success case prop preproc time : 0.000
% 5.87/1.16 % Success case prop encoding time : 0.000
% 5.87/1.16 % Success case prop solver time : 0.000
% 5.87/1.16 % Current number of processed clauses : 26
% 5.87/1.16 % Positive orientable unit clauses : 9
% 5.87/1.16 % Positive unorientable unit clauses: 0
% 5.87/1.16 % Negative unit clauses : 1
% 5.87/1.16 % Non-unit-clauses : 16
% 5.87/1.16 % Current number of unprocessed clauses: 22946
% 5.87/1.16 % ...number of literals in the above : 85267
% 5.87/1.16 % Current number of archived formulas : 0
% 5.87/1.16 % Current number of archived clauses : 440
% 5.87/1.16 % Clause-clause subsumption calls (NU) : 35696
% 5.87/1.16 % Rec. Clause-clause subsumption calls : 22217
% 5.87/1.16 % Non-unit clause-clause subsumptions : 2762
% 5.87/1.16 % Unit Clause-clause subsumption calls : 361
% 5.87/1.16 % Rewrite failures with RHS unbound : 0
% 5.87/1.16 % BW rewrite match attempts : 96
% 5.87/1.16 % BW rewrite match successes : 71
% 5.87/1.16 % Condensation attempts : 2960
% 5.87/1.16 % Condensation successes : 245
% 5.87/1.16 % Termbank termtop insertions : 453550
% 5.87/1.16 % Search garbage collected termcells : 419
% 5.87/1.16
% 5.87/1.16 % -------------------------------------------------
% 5.87/1.16 % User time : 0.872 s
% 5.87/1.16 % System time : 0.021 s
% 5.87/1.16 % Total time : 0.894 s
% 5.87/1.16 % Maximum resident set size: 3640 pages
% 5.87/1.16
% 5.87/1.16 % -------------------------------------------------
% 5.87/1.16 % User time : 3.954 s
% 5.87/1.16 % System time : 0.096 s
% 5.87/1.16 % Total time : 4.051 s
% 5.87/1.16 % Maximum resident set size: 4864 pages
% 5.87/1.16 % E exiting
%------------------------------------------------------------------------------