%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG272^5 : 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 : n017.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 0.23s 0.30s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 168 ( 141 equ; 0 cnn)
% Maximal formula atoms : 38 ( 4 avg)
% Number of connectives : 579 ( 38 ~; 50 |; 41 &; 447 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 12 con; 0-2 aty)
% Number of variables : 143 ( 30 ^; 103 !; 10 ?; 143 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
g: $tType ).
thf(decl_23,type,
cGROUP1: ( g > g > g ) > g > $o ).
thf(decl_24,type,
cGROUP2: ( g > g > g ) > g > $o ).
thf(decl_25,type,
cGRP_ASSOC: ( g > g > g ) > $o ).
thf(decl_26,type,
cGRP_INVERSE: ( g > g > g ) > g > $o ).
thf(decl_27,type,
cGRP_LEFT_INVERSE: ( g > g > g ) > g > $o ).
thf(decl_28,type,
cGRP_LEFT_UNIT: ( g > g > g ) > g > $o ).
thf(decl_29,type,
cGRP_UNIT: ( g > g > g ) > g > $o ).
thf(decl_30,type,
esk1_0: g > g > g ).
thf(decl_31,type,
esk2_0: g ).
thf(decl_32,type,
esk3_0: g ).
thf(decl_33,type,
esk4_0: g ).
thf(decl_34,type,
esk5_0: g ).
thf(decl_35,type,
esk6_0: g ).
thf(decl_36,type,
esk7_0: g ).
thf(decl_37,type,
esk8_0: g ).
thf(decl_38,type,
esk9_0: g ).
thf(decl_39,type,
esk10_0: g ).
thf(decl_40,type,
esk11_0: g ).
thf(decl_41,type,
esk12_0: g ).
thf(decl_42,type,
esk13_1: g > g ).
thf(decl_43,type,
esk14_1: g > g ).
thf(cGROUP1_def,axiom,
( cGROUP1
= ( ^ [X1: g > g > g,X5: g] :
( ( cGRP_ASSOC @ X1 )
& ( cGRP_UNIT @ X1 @ X5 )
& ( cGRP_INVERSE @ X1 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.07E9ngqQKM/E---3.1_647125.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.07E9ngqQKM/E---3.1_647125.p',cGRP_ASSOC_def) ).
thf(cGRP_INVERSE_def,axiom,
( cGRP_INVERSE
= ( ^ [X1: g > g > g,X5: g] :
! [X2: g] :
? [X3: g] :
( ( ( X1 @ X2 @ X3 )
= X5 )
& ( ( X1 @ X3 @ X2 )
= X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.07E9ngqQKM/E---3.1_647125.p',cGRP_INVERSE_def) ).
thf(cGRP_UNIT_def,axiom,
( cGRP_UNIT
= ( ^ [X1: g > g > g,X5: g] :
! [X2: g] :
( ( ( X1 @ X5 @ X2 )
= X2 )
& ( ( X1 @ X2 @ X5 )
= X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.07E9ngqQKM/E---3.1_647125.p',cGRP_UNIT_def) ).
thf(cGROUP2_def,axiom,
( cGROUP2
= ( ^ [X1: g > g > g,X5: g] :
( ( cGRP_ASSOC @ X1 )
& ( cGRP_LEFT_UNIT @ X1 @ X5 )
& ( cGRP_LEFT_INVERSE @ X1 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.07E9ngqQKM/E---3.1_647125.p',cGROUP2_def) ).
thf(cGRP_LEFT_INVERSE_def,axiom,
( cGRP_LEFT_INVERSE
= ( ^ [X1: g > g > g,X5: g] :
! [X2: g] :
? [X3: g] :
( ( X1 @ X3 @ X2 )
= X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.07E9ngqQKM/E---3.1_647125.p',cGRP_LEFT_INVERSE_def) ).
thf(cGRP_LEFT_UNIT_def,axiom,
( cGRP_LEFT_UNIT
= ( ^ [X1: g > g > g,X5: g] :
! [X2: g] :
( ( X1 @ X5 @ X2 )
= X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.07E9ngqQKM/E---3.1_647125.p',cGRP_LEFT_UNIT_def) ).
thf(cEQUIV_01_02,conjecture,
! [X1: g > g > g,X5: g] :
( ( cGROUP1 @ X1 @ X5 )
<=> ( cGROUP2 @ X1 @ X5 ) ),
file('/export/starexec/sandbox2/tmp/tmp.07E9ngqQKM/E---3.1_647125.p',cEQUIV_01_02) ).
thf(c_0_8,plain,
( cGROUP1
= ( ^ [Z0: g > g > g,Z1: g] :
( ! [X8: g,X9: g,X10: g] :
( ( Z0 @ ( Z0 @ X8 @ X9 ) @ X10 )
= ( Z0 @ X8 @ ( Z0 @ X9 @ X10 ) ) )
& ! [X11: g] :
( ( ( Z0 @ Z1 @ X11 )
= X11 )
& ( ( Z0 @ X11 @ Z1 )
= X11 ) )
& ! [X12: g] :
? [X13: g] :
( ( ( Z0 @ X12 @ X13 )
= Z1 )
& ( ( Z0 @ X13 @ X12 )
= Z1 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[cGROUP1_def]) ).
thf(c_0_9,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_10,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_11,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_12,plain,
( cGROUP2
= ( ^ [Z0: g > g > g,Z1: g] :
( ! [X14: g,X15: g,X16: g] :
( ( Z0 @ ( Z0 @ X14 @ X15 ) @ X16 )
= ( Z0 @ X14 @ ( Z0 @ X15 @ X16 ) ) )
& ! [X17: g] :
( ( Z0 @ Z1 @ X17 )
= X17 )
& ! [X18: g] :
? [X19: g] :
( ( Z0 @ X19 @ X18 )
= Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[cGROUP2_def]) ).
thf(c_0_13,plain,
( cGRP_LEFT_INVERSE
= ( ^ [Z0: g > g > g,Z1: g] :
! [X2: g] :
? [X3: g] :
( ( Z0 @ X3 @ X2 )
= Z1 ) ) ),
inference(fof_simplification,[status(thm)],[cGRP_LEFT_INVERSE_def]) ).
thf(c_0_14,plain,
( cGRP_LEFT_UNIT
= ( ^ [Z0: g > g > g,Z1: g] :
! [X2: g] :
( ( Z0 @ Z1 @ X2 )
= X2 ) ) ),
inference(fof_simplification,[status(thm)],[cGRP_LEFT_UNIT_def]) ).
thf(c_0_15,negated_conjecture,
~ ! [X1: g > g > g,X5: g] :
( ( cGROUP1 @ X1 @ X5 )
<=> ( cGROUP2 @ X1 @ X5 ) ),
inference(assume_negation,[status(cth)],[cEQUIV_01_02]) ).
thf(c_0_16,plain,
( cGROUP1
= ( ^ [Z0: g > g > g,Z1: g] :
( ! [X8: g,X9: g,X10: g] :
( ( Z0 @ ( Z0 @ X8 @ X9 ) @ X10 )
= ( Z0 @ X8 @ ( Z0 @ X9 @ X10 ) ) )
& ! [X11: g] :
( ( ( Z0 @ Z1 @ X11 )
= X11 )
& ( ( Z0 @ X11 @ Z1 )
= X11 ) )
& ! [X12: g] :
? [X13: g] :
( ( ( Z0 @ X12 @ X13 )
= Z1 )
& ( ( Z0 @ X13 @ X12 )
= Z1 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_8,c_0_9]),c_0_10]),c_0_11]) ).
thf(c_0_17,plain,
( cGROUP2
= ( ^ [Z0: g > g > g,Z1: g] :
( ! [X14: g,X15: g,X16: g] :
( ( Z0 @ ( Z0 @ X14 @ X15 ) @ X16 )
= ( Z0 @ X14 @ ( Z0 @ X15 @ X16 ) ) )
& ! [X17: g] :
( ( Z0 @ Z1 @ X17 )
= X17 )
& ! [X18: g] :
? [X19: g] :
( ( Z0 @ X19 @ X18 )
= Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_12,c_0_9]),c_0_13]),c_0_14]) ).
thf(c_0_18,negated_conjecture,
~ ! [X1: g > g > g,X5: g] :
( ( ! [X20: g,X21: g,X22: g] :
( ( X1 @ ( X1 @ X20 @ X21 ) @ X22 )
= ( X1 @ X20 @ ( X1 @ X21 @ X22 ) ) )
& ! [X23: g] :
( ( ( X1 @ X5 @ X23 )
= X23 )
& ( ( X1 @ X23 @ X5 )
= X23 ) )
& ! [X24: g] :
? [X25: g] :
( ( ( X1 @ X24 @ X25 )
= X5 )
& ( ( X1 @ X25 @ X24 )
= X5 ) ) )
<=> ( ! [X26: g,X27: g,X28: g] :
( ( X1 @ ( X1 @ X26 @ X27 ) @ X28 )
= ( X1 @ X26 @ ( X1 @ X27 @ X28 ) ) )
& ! [X29: g] :
( ( X1 @ X5 @ X29 )
= X29 )
& ! [X30: g] :
? [X31: g] :
( ( X1 @ X31 @ X30 )
= X5 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
thf(c_0_19,negated_conjecture,
! [X39: g,X45: g,X46: g,X47: g,X48: g,X49: g,X50: g,X52: g,X53: g,X54: g,X55: g,X56: g] :
( ( ( ( esk1_0 @ ( esk1_0 @ esk3_0 @ esk4_0 ) @ esk5_0 )
!= ( esk1_0 @ esk3_0 @ ( esk1_0 @ esk4_0 @ esk5_0 ) ) )
| ( ( esk1_0 @ esk2_0 @ esk6_0 )
!= esk6_0 )
| ( ( esk1_0 @ esk6_0 @ esk2_0 )
!= esk6_0 )
| ( ( esk1_0 @ esk7_0 @ X39 )
!= esk2_0 )
| ( ( esk1_0 @ X39 @ esk7_0 )
!= esk2_0 )
| ( ( esk1_0 @ ( esk1_0 @ esk8_0 @ esk9_0 ) @ esk10_0 )
!= ( esk1_0 @ esk8_0 @ ( esk1_0 @ esk9_0 @ esk10_0 ) ) )
| ( ( esk1_0 @ esk2_0 @ esk11_0 )
!= esk11_0 )
| ( ( esk1_0 @ X45 @ esk12_0 )
!= esk2_0 ) )
& ( ( ( esk1_0 @ ( esk1_0 @ X52 @ X53 ) @ X54 )
= ( esk1_0 @ X52 @ ( esk1_0 @ X53 @ X54 ) ) )
| ( ( esk1_0 @ ( esk1_0 @ X46 @ X47 ) @ X48 )
= ( esk1_0 @ X46 @ ( esk1_0 @ X47 @ X48 ) ) ) )
& ( ( ( esk1_0 @ esk2_0 @ X55 )
= X55 )
| ( ( esk1_0 @ ( esk1_0 @ X46 @ X47 ) @ X48 )
= ( esk1_0 @ X46 @ ( esk1_0 @ X47 @ X48 ) ) ) )
& ( ( ( esk1_0 @ ( esk14_1 @ X56 ) @ X56 )
= esk2_0 )
| ( ( esk1_0 @ ( esk1_0 @ X46 @ X47 ) @ X48 )
= ( esk1_0 @ X46 @ ( esk1_0 @ X47 @ X48 ) ) ) )
& ( ( ( esk1_0 @ ( esk1_0 @ X52 @ X53 ) @ X54 )
= ( esk1_0 @ X52 @ ( esk1_0 @ X53 @ X54 ) ) )
| ( ( esk1_0 @ esk2_0 @ X49 )
= X49 ) )
& ( ( ( esk1_0 @ esk2_0 @ X55 )
= X55 )
| ( ( esk1_0 @ esk2_0 @ X49 )
= X49 ) )
& ( ( ( esk1_0 @ ( esk14_1 @ X56 ) @ X56 )
= esk2_0 )
| ( ( esk1_0 @ esk2_0 @ X49 )
= X49 ) )
& ( ( ( esk1_0 @ ( esk1_0 @ X52 @ X53 ) @ X54 )
= ( esk1_0 @ X52 @ ( esk1_0 @ X53 @ X54 ) ) )
| ( ( esk1_0 @ X49 @ esk2_0 )
= X49 ) )
& ( ( ( esk1_0 @ esk2_0 @ X55 )
= X55 )
| ( ( esk1_0 @ X49 @ esk2_0 )
= X49 ) )
& ( ( ( esk1_0 @ ( esk14_1 @ X56 ) @ X56 )
= esk2_0 )
| ( ( esk1_0 @ X49 @ esk2_0 )
= X49 ) )
& ( ( ( esk1_0 @ ( esk1_0 @ X52 @ X53 ) @ X54 )
= ( esk1_0 @ X52 @ ( esk1_0 @ X53 @ X54 ) ) )
| ( ( esk1_0 @ X50 @ ( esk13_1 @ X50 ) )
= esk2_0 ) )
& ( ( ( esk1_0 @ esk2_0 @ X55 )
= X55 )
| ( ( esk1_0 @ X50 @ ( esk13_1 @ X50 ) )
= esk2_0 ) )
& ( ( ( esk1_0 @ ( esk14_1 @ X56 ) @ X56 )
= esk2_0 )
| ( ( esk1_0 @ X50 @ ( esk13_1 @ X50 ) )
= esk2_0 ) )
& ( ( ( esk1_0 @ ( esk1_0 @ X52 @ X53 ) @ X54 )
= ( esk1_0 @ X52 @ ( esk1_0 @ X53 @ X54 ) ) )
| ( ( esk1_0 @ ( esk13_1 @ X50 ) @ X50 )
= esk2_0 ) )
& ( ( ( esk1_0 @ esk2_0 @ X55 )
= X55 )
| ( ( esk1_0 @ ( esk13_1 @ X50 ) @ X50 )
= esk2_0 ) )
& ( ( ( esk1_0 @ ( esk14_1 @ X56 ) @ X56 )
= esk2_0 )
| ( ( esk1_0 @ ( esk13_1 @ X50 ) @ X50 )
= esk2_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_18])])])])])]) ).
thf(c_0_20,negated_conjecture,
! [X2: g,X3: g] :
( ( ( esk1_0 @ esk2_0 @ X2 )
= X2 )
| ( ( esk1_0 @ esk2_0 @ X3 )
= X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_21,negated_conjecture,
! [X2: g,X3: g] :
( ( ( esk1_0 @ ( esk1_0 @ esk3_0 @ esk4_0 ) @ esk5_0 )
!= ( esk1_0 @ esk3_0 @ ( esk1_0 @ esk4_0 @ esk5_0 ) ) )
| ( ( esk1_0 @ esk2_0 @ esk6_0 )
!= esk6_0 )
| ( ( esk1_0 @ esk6_0 @ esk2_0 )
!= esk6_0 )
| ( ( esk1_0 @ esk7_0 @ X2 )
!= esk2_0 )
| ( ( esk1_0 @ X2 @ esk7_0 )
!= esk2_0 )
| ( ( esk1_0 @ ( esk1_0 @ esk8_0 @ esk9_0 ) @ esk10_0 )
!= ( esk1_0 @ esk8_0 @ ( esk1_0 @ esk9_0 @ esk10_0 ) ) )
| ( ( esk1_0 @ esk2_0 @ esk11_0 )
!= esk11_0 )
| ( ( esk1_0 @ X3 @ esk12_0 )
!= esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_22,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ esk2_0 @ X2 )
= X2 ),
inference(condense,[status(thm)],[c_0_20]) ).
thf(c_0_23,negated_conjecture,
! [X2: g,X3: g,X4: g,X5: g,X7: g,X8: g] :
( ( ( esk1_0 @ ( esk1_0 @ X2 @ X3 ) @ X4 )
= ( esk1_0 @ X2 @ ( esk1_0 @ X3 @ X4 ) ) )
| ( ( esk1_0 @ ( esk1_0 @ X5 @ X7 ) @ X8 )
= ( esk1_0 @ X5 @ ( esk1_0 @ X7 @ X8 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_24,negated_conjecture,
! [X2: g,X3: g] :
( ( ( esk1_0 @ ( esk1_0 @ esk3_0 @ esk4_0 ) @ esk5_0 )
!= ( esk1_0 @ esk3_0 @ ( esk1_0 @ esk4_0 @ esk5_0 ) ) )
| ( ( esk1_0 @ ( esk1_0 @ esk8_0 @ esk9_0 ) @ esk10_0 )
!= ( esk1_0 @ esk8_0 @ ( esk1_0 @ esk9_0 @ esk10_0 ) ) )
| ( ( esk1_0 @ esk6_0 @ esk2_0 )
!= esk6_0 )
| ( ( esk1_0 @ X2 @ esk12_0 )
!= esk2_0 )
| ( ( esk1_0 @ X3 @ esk7_0 )
!= esk2_0 )
| ( ( esk1_0 @ esk7_0 @ X3 )
!= esk2_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_22])]) ).
thf(c_0_25,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_23]) ).
thf(c_0_26,negated_conjecture,
! [X2: g,X3: g] :
( ( ( esk1_0 @ esk6_0 @ esk2_0 )
!= esk6_0 )
| ( ( esk1_0 @ X2 @ esk12_0 )
!= esk2_0 )
| ( ( esk1_0 @ X3 @ esk7_0 )
!= esk2_0 )
| ( ( esk1_0 @ esk7_0 @ X3 )
!= esk2_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_25])]) ).
thf(c_0_27,negated_conjecture,
! [X2: g,X3: g] :
( ( ( esk1_0 @ ( esk14_1 @ X2 ) @ X2 )
= esk2_0 )
| ( ( esk1_0 @ X3 @ esk2_0 )
= X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_28,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( ( esk1_0 @ ( esk14_1 @ X2 ) @ X2 )
= esk2_0 )
| ( ( esk1_0 @ X3 @ esk12_0 )
!= esk2_0 )
| ( ( esk1_0 @ X4 @ esk7_0 )
!= esk2_0 )
| ( ( esk1_0 @ esk7_0 @ X4 )
!= esk2_0 ) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
thf(c_0_29,negated_conjecture,
! [X2: g,X3: g] :
( ( ( esk1_0 @ ( esk14_1 @ X2 ) @ X2 )
= esk2_0 )
| ( ( esk1_0 @ ( esk13_1 @ X3 ) @ X3 )
= esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_30,negated_conjecture,
! [X2: g,X3: g] :
( ( ( esk1_0 @ ( esk14_1 @ X2 ) @ X2 )
= esk2_0 )
| ( ( esk1_0 @ X3 @ esk7_0 )
!= esk2_0 )
| ( ( esk1_0 @ esk7_0 @ X3 )
!= esk2_0 ) ),
inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29])]) ).
thf(c_0_31,negated_conjecture,
! [X2: g,X3: g] :
( ( ( esk1_0 @ ( esk14_1 @ X2 ) @ X2 )
= esk2_0 )
| ( ( esk1_0 @ X3 @ ( esk13_1 @ X3 ) )
= esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_32,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ ( esk14_1 @ X2 ) @ X2 )
= esk2_0 ),
inference(csr,[status(thm)],[inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_29])]),c_0_31]) ).
thf(c_0_33,negated_conjecture,
! [X2: g,X3: g] :
( ( esk1_0 @ ( esk14_1 @ X2 ) @ ( esk1_0 @ X2 @ X3 ) )
= X3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_32]),c_0_22]) ).
thf(c_0_34,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ ( esk14_1 @ ( esk14_1 @ X2 ) ) @ esk2_0 )
= X2 ),
inference(spm,[status(thm)],[c_0_33,c_0_32]) ).
thf(c_0_35,negated_conjecture,
! [X2: g,X3: g] :
( ( esk1_0 @ ( esk14_1 @ ( esk14_1 @ X2 ) ) @ X3 )
= ( esk1_0 @ X2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_33,c_0_33]) ).
thf(c_0_36,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ X2 @ esk2_0 )
= X2 ),
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
thf(c_0_37,negated_conjecture,
! [X2: g,X3: g] :
( ( ( esk1_0 @ X2 @ esk12_0 )
!= esk2_0 )
| ( ( esk1_0 @ X3 @ esk7_0 )
!= esk2_0 )
| ( ( esk1_0 @ esk7_0 @ X3 )
!= esk2_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_36])]) ).
thf(c_0_38,negated_conjecture,
! [X2: g] :
( ( esk14_1 @ ( esk14_1 @ X2 ) )
= X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_36]) ).
thf(c_0_39,negated_conjecture,
! [X2: g] :
( ( ( esk1_0 @ X2 @ esk7_0 )
!= esk2_0 )
| ( ( esk1_0 @ esk7_0 @ X2 )
!= esk2_0 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_32]) ).
thf(c_0_40,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ X2 @ ( esk14_1 @ X2 ) )
= esk2_0 ),
inference(spm,[status(thm)],[c_0_32,c_0_38]) ).
thf(c_0_41,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_32]),c_0_40])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG272^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.19 % Computer : n017.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Tue Sep 29 17:31:22 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.23 Running higher-order theorem proving
% 0.11/0.25 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.07E9ngqQKM/E---3.1_647125.p
% 0.23/0.30 % Version: 3.5.1-ho
% 0.23/0.30 % Preprocessing class: HSSSSMSSSLSNHSN.
% 0.23/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.30 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.23/0.30 % Starting lpo8_lambda_fix with 300s (1) cores
% 0.23/0.30 % Starting lpo8_s with 300s (1) cores
% 0.23/0.30 % Starting new_bool_11 with 300s (1) cores
% 0.23/0.30 % ho_unfolding_3 with pid 647157 completed with status 0
% 0.23/0.30 % Result found by ho_unfolding_3
% 0.23/0.30 % Preprocessing class: HSSSSMSSSLSNHSN.
% 0.23/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.30 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.23/0.30 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.30 % No SInE strategy applied
% 0.23/0.30 % Search class: HGHPF-FFMF11-SHSFMFNN
% 0.23/0.30 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.30 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.30 % Starting ho_unfolding_3 with 151s (1) cores
% 0.23/0.30 % Starting sh5l with 136s (1) cores
% 0.23/0.30 % Starting new_bool_1 with 136s (1) cores
% 0.23/0.30 % Starting lpo1_def_fix with 136s (1) cores
% 0.23/0.30 % ho_unfolding_3 with pid 647167 completed with status 0
% 0.23/0.30 % Result found by ho_unfolding_3
% 0.23/0.30 % Preprocessing class: HSSSSMSSSLSNHSN.
% 0.23/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.30 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.23/0.30 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.30 % No SInE strategy applied
% 0.23/0.30 % Search class: HGHPF-FFMF11-SHSFMFNN
% 0.23/0.30 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.30 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.30 % Starting ho_unfolding_3 with 151s (1) cores
% 0.23/0.30 % Preprocessing time : 0.002 s
% 0.23/0.30 % Presaturation interreduction done
% 0.23/0.30
% 0.23/0.30 % Proof found!
% 0.23/0.30 % SZS status Theorem
% 0.23/0.30 % SZS output start CNFRefutation
% See solution above
% 0.23/0.30 % Parsed axioms : 16
% 0.23/0.30 % Removed by relevancy pruning/SinE : 0
% 0.23/0.30 % Initial clauses : 24
% 0.23/0.30 % Removed in clause preprocessing : 8
% 0.23/0.30 % Initial clauses in saturation : 16
% 0.23/0.30 % Processed clauses : 162
% 0.23/0.30 % ...of these trivial : 12
% 0.23/0.30 % ...subsumed : 67
% 0.23/0.30 % ...remaining for further processing : 83
% 0.23/0.30 % Other redundant clauses eliminated : 0
% 0.23/0.30 % Clauses deleted for lack of memory : 0
% 0.23/0.30 % Backward-subsumed : 26
% 0.23/0.30 % Backward-rewritten : 39
% 0.23/0.30 % Generated clauses : 671
% 0.23/0.30 % ...of the previous two non-redundant : 592
% 0.23/0.30 % ...aggressively subsumed : 0
% 0.23/0.30 % Contextual simplify-reflections : 3
% 0.23/0.30 % Paramodulations : 665
% 0.23/0.30 % Factorizations : 5
% 0.23/0.30 % NegExts : 0
% 0.23/0.30 % Equation resolutions : 0
% 0.23/0.30 % Disequality decompositions : 0
% 0.23/0.30 % Total rewrite steps : 193
% 0.23/0.30 % ...of those cached : 127
% 0.23/0.30 % Propositional unsat checks : 0
% 0.23/0.30 % Propositional check models : 0
% 0.23/0.30 % Propositional check unsatisfiable : 0
% 0.23/0.30 % Propositional clauses : 0
% 0.23/0.30 % Propositional clauses after purity: 0
% 0.23/0.30 % Propositional unsat core size : 0
% 0.23/0.30 % Propositional preprocessing time : 0.000
% 0.23/0.30 % Propositional encoding time : 0.000
% 0.23/0.30 % Propositional solver time : 0.000
% 0.23/0.30 % Success case prop preproc time : 0.000
% 0.23/0.30 % Success case prop encoding time : 0.000
% 0.23/0.30 % Success case prop solver time : 0.000
% 0.23/0.30 % Current number of processed clauses : 12
% 0.23/0.30 % Positive orientable unit clauses : 8
% 0.23/0.30 % Positive unorientable unit clauses: 0
% 0.23/0.30 % Negative unit clauses : 0
% 0.23/0.30 % Non-unit-clauses : 4
% 0.23/0.30 % Current number of unprocessed clauses: 384
% 0.23/0.30 % ...number of literals in the above : 1231
% 0.23/0.30 % Current number of archived formulas : 0
% 0.23/0.30 % Current number of archived clauses : 71
% 0.23/0.30 % Clause-clause subsumption calls (NU) : 765
% 0.23/0.30 % Rec. Clause-clause subsumption calls : 520
% 0.23/0.30 % Non-unit clause-clause subsumptions : 80
% 0.23/0.30 % Unit Clause-clause subsumption calls : 64
% 0.23/0.30 % Rewrite failures with RHS unbound : 0
% 0.23/0.30 % BW rewrite match attempts : 34
% 0.23/0.30 % BW rewrite match successes : 24
% 0.23/0.30 % Condensation attempts : 162
% 0.23/0.30 % Condensation successes : 4
% 0.23/0.30 % Termbank termtop insertions : 10674
% 0.23/0.30 % Search garbage collected termcells : 469
% 0.23/0.30
% 0.23/0.30 % -------------------------------------------------
% 0.23/0.30 % User time : 0.025 s
% 0.23/0.30 % System time : 0.004 s
% 0.23/0.30 % Total time : 0.029 s
% 0.23/0.30 % Maximum resident set size: 3640 pages
% 0.23/0.30
% 0.23/0.30 % -------------------------------------------------
% 0.23/0.30 % User time : 0.098 s
% 0.23/0.30 % System time : 0.017 s
% 0.23/0.30 % Total time : 0.115 s
% 0.23/0.30 % Maximum resident set size: 4864 pages
% 0.23/0.30 % E exiting
%------------------------------------------------------------------------------