%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG266^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 07:44:48 AM UTC 2026
% Result : Theorem 0.23s 0.30s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 111 ( 30 equ; 0 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 1285 ( 44 ~; 76 |; 11 &;1090 @)
% ( 7 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 10 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 94 ( 94 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 10 con; 0-3 aty)
% Number of variables : 152 ( 16 ^; 136 !; 0 ?; 152 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
term: $tType ).
thf(decl_sort2,type,
subst: $tType ).
thf(decl_23,type,
one: term ).
thf(decl_25,type,
lam: term > term ).
thf(decl_26,type,
sub: term > subst > term ).
thf(decl_27,type,
id: subst ).
thf(decl_28,type,
sh: subst ).
thf(decl_29,type,
push: term > subst > subst ).
thf(decl_30,type,
comp: subst > subst > subst ).
thf(decl_42,type,
axvarshift: $o ).
thf(decl_74,type,
hoasinduction_lem3a_lthm: $o ).
thf(decl_76,type,
hoasinduction_lem3aa: $o ).
thf(decl_94,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(decl_123,type,
hoasinduction_lem3a: $o ).
thf(decl_143,type,
axvarid: $o ).
thf(decl_145,type,
esk1_1: ( subst > term > subst > $o ) > subst > term > term ).
thf(decl_146,type,
esk2_2: ( subst > term > subst > $o ) > term > term ).
thf(decl_147,type,
epred1_0: subst > term > subst > $o ).
thf(decl_148,type,
esk3_1: ( subst > term > term ) > subst ).
thf(decl_149,type,
esk4_1: ( subst > term > term ) > term ).
thf(decl_150,type,
esk5_1: ( subst > term > term ) > subst ).
thf(decl_151,type,
esk6_1: ( subst > term > term ) > term ).
thf(decl_152,type,
esk7_0: term ).
thf(hoasinduction_lem3aa,axiom,
( hoasinduction_lem3aa
<=> ! [X22: subst > term > subst > $o] :
( ! [X12: subst > term > term] :
( ! [X3: subst,X1: term,X4: subst] :
( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
= ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
=> ( ! [X1: term] :
( ( X22 @ id @ X1 @ id )
=> ( X22 @ id @ ( X12 @ id @ X1 ) @ id ) )
=> ( X22 @ id
@ ( hoaslam @ id
@ ^ [X3: subst,X1: term] : ( X12 @ X3 @ X1 ) )
@ id ) ) )
=> ! [X1: term] :
( ! [X2: term] :
( ( X22 @ id @ X2 @ id )
=> ( X22 @ id @ ( sub @ X1 @ ( push @ X2 @ id ) ) @ id ) )
=> ( X22 @ id @ ( lam @ ( sub @ X1 @ ( push @ one @ sh ) ) ) @ id ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.5qnPnc7Agw/E---3.1_2817852.p',hoasinduction_lem3aa) ).
thf(hoasinduction_lem3a,axiom,
( hoasinduction_lem3a
<=> ! [X25: subst > term > subst > $o] :
( ! [X12: subst > term > term] :
( ! [X3: subst,X1: term,X4: subst] :
( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
= ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
=> ( ! [X1: term] :
( ( X25 @ id @ X1 @ id )
=> ( X25 @ id @ ( X12 @ id @ X1 ) @ id ) )
=> ( X25 @ id
@ ( hoaslam @ id
@ ^ [X3: subst,X1: term] : ( X12 @ X3 @ X1 ) )
@ id ) ) )
=> ! [X1: term] :
( ! [X2: term] :
( ( X25 @ id @ X2 @ id )
=> ( X25 @ id @ ( sub @ X1 @ ( push @ X2 @ id ) ) @ id ) )
=> ( X25 @ id @ ( lam @ X1 ) @ id ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.5qnPnc7Agw/E---3.1_2817852.p',hoasinduction_lem3a) ).
thf(thm,conjecture,
hoasinduction_lem3a_lthm,
file('/export/starexec/sandbox2/tmp/tmp.5qnPnc7Agw/E---3.1_2817852.p',thm) ).
thf(hoasinduction_lem3a_lthm,axiom,
( hoasinduction_lem3a_lthm
<=> ( axvarid
=> ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3a ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.5qnPnc7Agw/E---3.1_2817852.p',hoasinduction_lem3a_lthm) ).
thf(axvarid,axiom,
( axvarid
<=> ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.5qnPnc7Agw/E---3.1_2817852.p',axvarid) ).
thf(axvarshift,axiom,
( axvarshift
<=> ( ( push @ one @ sh )
= id ) ),
file('/export/starexec/sandbox2/tmp/tmp.5qnPnc7Agw/E---3.1_2817852.p',axvarshift) ).
thf(c_0_6,plain,
( hoasinduction_lem3aa
<=> ! [X22: subst > term > subst > $o] :
( ! [X12: subst > term > term] :
( ! [X3: subst,X1: term,X4: subst] :
( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
= ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
=> ( ! [X1: term] :
( ( X22 @ id @ X1 @ id )
=> ( X22 @ id @ ( X12 @ id @ X1 ) @ id ) )
=> ( X22 @ id
@ ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X12 @ Z0 @ Z1 ) )
@ id ) ) )
=> ! [X1: term] :
( ! [X2: term] :
( ( X22 @ id @ X2 @ id )
=> ( X22 @ id @ ( sub @ X1 @ ( push @ X2 @ id ) ) @ id ) )
=> ( X22 @ id @ ( lam @ ( sub @ X1 @ ( push @ one @ sh ) ) ) @ id ) ) ) ),
inference(fof_simplification,[status(thm)],[hoasinduction_lem3aa]) ).
thf(c_0_7,plain,
( hoasinduction_lem3a
<=> ! [X25: subst > term > subst > $o] :
( ! [X12: subst > term > term] :
( ! [X3: subst,X1: term,X4: subst] :
( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
= ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
=> ( ! [X1: term] :
( ( X25 @ id @ X1 @ id )
=> ( X25 @ id @ ( X12 @ id @ X1 ) @ id ) )
=> ( X25 @ id
@ ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X12 @ Z0 @ Z1 ) )
@ id ) ) )
=> ! [X1: term] :
( ! [X2: term] :
( ( X25 @ id @ X2 @ id )
=> ( X25 @ id @ ( sub @ X1 @ ( push @ X2 @ id ) ) @ id ) )
=> ( X25 @ id @ ( lam @ X1 ) @ id ) ) ) ),
inference(fof_simplification,[status(thm)],[hoasinduction_lem3a]) ).
thf(c_0_8,negated_conjecture,
~ hoasinduction_lem3a_lthm,
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_9,axiom,
( hoasinduction_lem3a_lthm
= ( ! [X45: term] :
( ( sub @ X45 @ id )
= X45 )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [X46: subst > term > subst > $o] :
( ! [X47: subst > term > term] :
( ! [X48: subst,X49: term,X50: subst] :
( ( sub @ ( X47 @ X48 @ X49 ) @ X50 )
= ( X47 @ ( comp @ X48 @ X50 ) @ ( sub @ X49 @ X50 ) ) )
=> ( ! [X51: term] :
( ( X46 @ id @ X51 @ id )
=> ( X46 @ id @ ( X47 @ id @ X51 ) @ id ) )
=> ( X46 @ id
@ ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X47 @ Z0 @ Z1 ) )
@ id ) ) )
=> ! [X52: term] :
( ! [X53: term] :
( ( X46 @ id @ X53 @ id )
=> ( X46 @ id @ ( sub @ X52 @ ( push @ X53 @ id ) ) @ id ) )
=> ( X46 @ id @ ( lam @ ( sub @ X52 @ ( push @ one @ sh ) ) ) @ id ) ) )
=> ! [X54: subst > term > subst > $o] :
( ! [X55: subst > term > term] :
( ! [X56: subst,X57: term,X58: subst] :
( ( sub @ ( X55 @ X56 @ X57 ) @ X58 )
= ( X55 @ ( comp @ X56 @ X58 ) @ ( sub @ X57 @ X58 ) ) )
=> ( ! [X59: term] :
( ( X54 @ id @ X59 @ id )
=> ( X54 @ id @ ( X55 @ id @ X59 ) @ id ) )
=> ( X54 @ id
@ ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X55 @ Z0 @ Z1 ) )
@ id ) ) )
=> ! [X60: term] :
( ! [X61: term] :
( ( X54 @ id @ X61 @ id )
=> ( X54 @ id @ ( sub @ X60 @ ( push @ X61 @ id ) ) @ id ) )
=> ( X54 @ id @ ( lam @ X60 ) @ id ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[hoasinduction_lem3a_lthm,axvarid]),axvarshift]),c_0_6]),c_0_7]) ).
thf(c_0_10,negated_conjecture,
~ ( ! [X62: term] :
( ( sub @ X62 @ id )
= X62 )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [X63: subst > term > subst > $o] :
( ! [X64: subst > term > term] :
( ! [X65: subst,X66: term,X67: subst] :
( ( sub @ ( X64 @ X65 @ X66 ) @ X67 )
= ( X64 @ ( comp @ X65 @ X67 ) @ ( sub @ X66 @ X67 ) ) )
=> ( ! [X68: term] :
( ( X63 @ id @ X68 @ id )
=> ( X63 @ id @ ( X64 @ id @ X68 ) @ id ) )
=> ( X63 @ id
@ ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X64 @ Z0 @ Z1 ) )
@ id ) ) )
=> ! [X69: term] :
( ! [X70: term] :
( ( X63 @ id @ X70 @ id )
=> ( X63 @ id @ ( sub @ X69 @ ( push @ X70 @ id ) ) @ id ) )
=> ( X63 @ id @ ( lam @ ( sub @ X69 @ ( push @ one @ sh ) ) ) @ id ) ) )
=> ! [X71: subst > term > subst > $o] :
( ! [X72: subst > term > term] :
( ! [X73: subst,X74: term,X75: subst] :
( ( sub @ ( X72 @ X73 @ X74 ) @ X75 )
= ( X72 @ ( comp @ X73 @ X75 ) @ ( sub @ X74 @ X75 ) ) )
=> ( ! [X76: term] :
( ( X71 @ id @ X76 @ id )
=> ( X71 @ id @ ( X72 @ id @ X76 ) @ id ) )
=> ( X71 @ id
@ ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X72 @ Z0 @ Z1 ) )
@ id ) ) )
=> ! [X77: term] :
( ! [X78: term] :
( ( X71 @ id @ X78 @ id )
=> ( X71 @ id @ ( sub @ X77 @ ( push @ X78 @ id ) ) @ id ) )
=> ( X71 @ id @ ( lam @ X77 ) @ id ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_11,negated_conjecture,
! [X79: term,X80: subst > term > subst > $o,X82: subst,X83: term,X84: subst,X85: term,X86: term,X89: subst > term > term,X95: term] :
( ( ( sub @ X79 @ id )
= X79 )
& ( ( push @ one @ sh )
= id )
& ( ( X80 @ id @ ( esk2_2 @ X80 @ X86 ) @ id )
| ( X80 @ id @ ( lam @ ( sub @ X86 @ ( push @ one @ sh ) ) ) @ id )
| ( ( sub @ ( esk1_1 @ X80 @ X82 @ X83 ) @ X84 )
= ( esk1_1 @ X80 @ ( comp @ X82 @ X84 ) @ ( sub @ X83 @ X84 ) ) ) )
& ( ~ ( X80 @ id @ ( sub @ X86 @ ( push @ ( esk2_2 @ X80 @ X86 ) @ id ) ) @ id )
| ( X80 @ id @ ( lam @ ( sub @ X86 @ ( push @ one @ sh ) ) ) @ id )
| ( ( sub @ ( esk1_1 @ X80 @ X82 @ X83 ) @ X84 )
= ( esk1_1 @ X80 @ ( comp @ X82 @ X84 ) @ ( sub @ X83 @ X84 ) ) ) )
& ( ( X80 @ id @ ( esk2_2 @ X80 @ X86 ) @ id )
| ( X80 @ id @ ( lam @ ( sub @ X86 @ ( push @ one @ sh ) ) ) @ id )
| ~ ( X80 @ id @ X85 @ id )
| ( X80 @ id @ ( esk1_1 @ X80 @ id @ X85 ) @ id ) )
& ( ~ ( X80 @ id @ ( sub @ X86 @ ( push @ ( esk2_2 @ X80 @ X86 ) @ id ) ) @ id )
| ( X80 @ id @ ( lam @ ( sub @ X86 @ ( push @ one @ sh ) ) ) @ id )
| ~ ( X80 @ id @ X85 @ id )
| ( X80 @ id @ ( esk1_1 @ X80 @ id @ X85 ) @ id ) )
& ( ( X80 @ id @ ( esk2_2 @ X80 @ X86 ) @ id )
| ( X80 @ id @ ( lam @ ( sub @ X86 @ ( push @ one @ sh ) ) ) @ id )
| ~ ( X80 @ id @ ( hoaslam @ id @ ( esk1_1 @ X80 ) ) @ id ) )
& ( ~ ( X80 @ id @ ( sub @ X86 @ ( push @ ( esk2_2 @ X80 @ X86 ) @ id ) ) @ id )
| ( X80 @ id @ ( lam @ ( sub @ X86 @ ( push @ one @ sh ) ) ) @ id )
| ~ ( X80 @ id @ ( hoaslam @ id @ ( esk1_1 @ X80 ) ) @ id ) )
& ( ( epred1_0 @ id @ ( esk6_1 @ X89 ) @ id )
| ( epred1_0 @ id @ ( hoaslam @ id @ X89 ) @ id )
| ( ( sub @ ( X89 @ ( esk3_1 @ X89 ) @ ( esk4_1 @ X89 ) ) @ ( esk5_1 @ X89 ) )
!= ( X89 @ ( comp @ ( esk3_1 @ X89 ) @ ( esk5_1 @ X89 ) ) @ ( sub @ ( esk4_1 @ X89 ) @ ( esk5_1 @ X89 ) ) ) ) )
& ( ~ ( epred1_0 @ id @ ( X89 @ id @ ( esk6_1 @ X89 ) ) @ id )
| ( epred1_0 @ id @ ( hoaslam @ id @ X89 ) @ id )
| ( ( sub @ ( X89 @ ( esk3_1 @ X89 ) @ ( esk4_1 @ X89 ) ) @ ( esk5_1 @ X89 ) )
!= ( X89 @ ( comp @ ( esk3_1 @ X89 ) @ ( esk5_1 @ X89 ) ) @ ( sub @ ( esk4_1 @ X89 ) @ ( esk5_1 @ X89 ) ) ) ) )
& ( ~ ( epred1_0 @ id @ X95 @ id )
| ( epred1_0 @ id @ ( sub @ esk7_0 @ ( push @ X95 @ id ) ) @ id ) )
& ~ ( epred1_0 @ id @ ( lam @ esk7_0 ) @ id ) ),
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_10])])])])])]) ).
thf(c_0_12,negated_conjecture,
! [X1: term,X2: term,X3: subst,X14: subst > term > subst > $o,X4: subst] :
( ( X14 @ id @ ( esk2_2 @ X14 @ X1 ) @ id )
| ( X14 @ id @ ( lam @ ( sub @ X1 @ ( push @ one @ sh ) ) ) @ id )
| ( ( sub @ ( esk1_1 @ X14 @ X3 @ X2 ) @ X4 )
= ( esk1_1 @ X14 @ ( comp @ X3 @ X4 ) @ ( sub @ X2 @ X4 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_13,negated_conjecture,
( ( push @ one @ sh )
= id ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_14,negated_conjecture,
! [X1: term] :
( ( sub @ X1 @ id )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_15,negated_conjecture,
! [X1: term,X14: subst > term > subst > $o,X2: term] :
( ( X14 @ id @ ( esk2_2 @ X14 @ X1 ) @ id )
| ( X14 @ id @ ( lam @ ( sub @ X1 @ ( push @ one @ sh ) ) ) @ id )
| ( X14 @ id @ ( esk1_1 @ X14 @ id @ X2 ) @ id )
| ~ ( X14 @ id @ X2 @ id ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_16,negated_conjecture,
! [X12: subst > term > term] :
( ( epred1_0 @ id @ ( esk6_1 @ X12 ) @ id )
| ( epred1_0 @ id @ ( hoaslam @ id @ X12 ) @ id )
| ( ( sub @ ( X12 @ ( esk3_1 @ X12 ) @ ( esk4_1 @ X12 ) ) @ ( esk5_1 @ X12 ) )
!= ( X12 @ ( comp @ ( esk3_1 @ X12 ) @ ( esk5_1 @ X12 ) ) @ ( sub @ ( esk4_1 @ X12 ) @ ( esk5_1 @ X12 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_17,negated_conjecture,
! [X1: term,X3: subst,X14: subst > term > subst > $o,X4: subst,X2: term] :
( ( ( esk1_1 @ X14 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) )
= ( sub @ ( esk1_1 @ X14 @ X3 @ X1 ) @ X4 ) )
| ( X14 @ id @ ( esk2_2 @ X14 @ X2 ) @ id )
| ( X14 @ id @ ( lam @ X2 ) @ id ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
thf(c_0_18,negated_conjecture,
! [X14: subst > term > subst > $o,X2: term,X1: term] :
( ( X14 @ id @ ( esk1_1 @ X14 @ id @ X1 ) @ id )
| ( X14 @ id @ ( esk2_2 @ X14 @ X2 ) @ id )
| ( X14 @ id @ ( lam @ X2 ) @ id )
| ~ ( X14 @ id @ X1 @ id ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_13]),c_0_14]) ).
thf(c_0_19,negated_conjecture,
! [X14: subst > term > subst > $o,X1: term] :
( ( epred1_0 @ id @ ( hoaslam @ id @ ( esk1_1 @ X14 ) ) @ id )
| ( epred1_0 @ id @ ( esk6_1 @ ( esk1_1 @ X14 ) ) @ id )
| ( X14 @ id @ ( esk2_2 @ X14 @ X1 ) @ id )
| ( X14 @ id @ ( lam @ X1 ) @ id ) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_20,negated_conjecture,
! [X1: term,X14: subst > term > subst > $o] :
( ( X14 @ id @ ( esk2_2 @ X14 @ X1 ) @ id )
| ( X14 @ id @ ( lam @ ( sub @ X1 @ ( push @ one @ sh ) ) ) @ id )
| ~ ( X14 @ id @ ( hoaslam @ id @ ( esk1_1 @ X14 ) ) @ id ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_21,negated_conjecture,
! [X12: subst > term > term] :
( ( epred1_0 @ id @ ( hoaslam @ id @ X12 ) @ id )
| ~ ( epred1_0 @ id @ ( X12 @ id @ ( esk6_1 @ X12 ) ) @ id )
| ( ( sub @ ( X12 @ ( esk3_1 @ X12 ) @ ( esk4_1 @ X12 ) ) @ ( esk5_1 @ X12 ) )
!= ( X12 @ ( comp @ ( esk3_1 @ X12 ) @ ( esk5_1 @ X12 ) ) @ ( sub @ ( esk4_1 @ X12 ) @ ( esk5_1 @ X12 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_22,negated_conjecture,
! [X1: term,X14: subst > term > subst > $o,X2: term] :
( ( epred1_0 @ id @ ( esk1_1 @ epred1_0 @ id @ ( esk6_1 @ ( esk1_1 @ X14 ) ) ) @ id )
| ( epred1_0 @ id @ ( hoaslam @ id @ ( esk1_1 @ X14 ) ) @ id )
| ( epred1_0 @ id @ ( esk2_2 @ epred1_0 @ X1 ) @ id )
| ( X14 @ id @ ( esk2_2 @ X14 @ X2 ) @ id )
| ( epred1_0 @ id @ ( lam @ X1 ) @ id )
| ( X14 @ id @ ( lam @ X2 ) @ id ) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_23,negated_conjecture,
! [X1: term,X14: subst > term > subst > $o] :
( ( X14 @ id @ ( esk2_2 @ X14 @ X1 ) @ id )
| ( X14 @ id @ ( lam @ X1 ) @ id )
| ~ ( X14 @ id @ ( hoaslam @ id @ ( esk1_1 @ X14 ) ) @ id ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_13]),c_0_14]) ).
thf(c_0_24,negated_conjecture,
! [X3: subst,X2: term,X14: subst > term > subst > $o,X4: subst,X1: term] :
( ( X14 @ id @ ( lam @ ( sub @ X1 @ ( push @ one @ sh ) ) ) @ id )
| ( ( sub @ ( esk1_1 @ X14 @ X3 @ X2 ) @ X4 )
= ( esk1_1 @ X14 @ ( comp @ X3 @ X4 ) @ ( sub @ X2 @ X4 ) ) )
| ~ ( X14 @ id @ ( sub @ X1 @ ( push @ ( esk2_2 @ X14 @ X1 ) @ id ) ) @ id ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_25,negated_conjecture,
! [X1: term,X14: subst > term > subst > $o] :
( ( X14 @ id @ ( lam @ ( sub @ X1 @ ( push @ one @ sh ) ) ) @ id )
| ~ ( X14 @ id @ ( sub @ X1 @ ( push @ ( esk2_2 @ X14 @ X1 ) @ id ) ) @ id )
| ~ ( X14 @ id @ ( hoaslam @ id @ ( esk1_1 @ X14 ) ) @ id ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_26,negated_conjecture,
! [X1: term,X14: subst > term > subst > $o,X2: term] :
( ( X14 @ id @ ( lam @ ( sub @ X1 @ ( push @ one @ sh ) ) ) @ id )
| ( X14 @ id @ ( esk1_1 @ X14 @ id @ X2 ) @ id )
| ~ ( X14 @ id @ ( sub @ X1 @ ( push @ ( esk2_2 @ X14 @ X1 ) @ id ) ) @ id )
| ~ ( X14 @ id @ X2 @ id ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_27,negated_conjecture,
! [X1: term,X14: subst > term > subst > $o] :
( ( epred1_0 @ id @ ( hoaslam @ id @ ( esk1_1 @ X14 ) ) @ id )
| ( X14 @ id @ ( esk2_2 @ X14 @ X1 ) @ id )
| ( X14 @ id @ ( lam @ X1 ) @ id )
| ~ ( epred1_0 @ id @ ( esk1_1 @ X14 @ id @ ( esk6_1 @ ( esk1_1 @ X14 ) ) ) @ id ) ),
inference(spm,[status(thm)],[c_0_21,c_0_17]) ).
thf(c_0_28,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ id @ ( esk1_1 @ epred1_0 @ id @ ( esk6_1 @ ( esk1_1 @ epred1_0 ) ) ) @ id )
| ( epred1_0 @ id @ ( esk2_2 @ epred1_0 @ X1 ) @ id )
| ( epred1_0 @ id @ ( lam @ X1 ) @ id ) ),
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_22]),c_0_23]) ).
thf(c_0_29,negated_conjecture,
! [X1: term,X3: subst,X14: subst > term > subst > $o,X4: subst,X2: term] :
( ( ( esk1_1 @ X14 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) )
= ( sub @ ( esk1_1 @ X14 @ X3 @ X1 ) @ X4 ) )
| ( X14 @ id @ ( lam @ X2 ) @ id )
| ~ ( X14 @ id @ ( sub @ X2 @ ( push @ ( esk2_2 @ X14 @ X2 ) @ id ) ) @ id ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_13]),c_0_14]) ).
thf(c_0_30,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ id @ ( sub @ esk7_0 @ ( push @ X1 @ id ) ) @ id )
| ~ ( epred1_0 @ id @ X1 @ id ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_31,negated_conjecture,
~ ( epred1_0 @ id @ ( lam @ esk7_0 ) @ id ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_32,negated_conjecture,
! [X1: term,X14: subst > term > subst > $o] :
( ( X14 @ id @ ( lam @ X1 ) @ id )
| ~ ( X14 @ id @ ( sub @ X1 @ ( push @ ( esk2_2 @ X14 @ X1 ) @ id ) ) @ id )
| ~ ( X14 @ id @ ( hoaslam @ id @ ( esk1_1 @ X14 ) ) @ id ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_13]),c_0_14]) ).
thf(c_0_33,negated_conjecture,
! [X14: subst > term > subst > $o,X2: term,X1: term] :
( ( X14 @ id @ ( esk1_1 @ X14 @ id @ X1 ) @ id )
| ( X14 @ id @ ( lam @ X2 ) @ id )
| ~ ( X14 @ id @ ( sub @ X2 @ ( push @ ( esk2_2 @ X14 @ X2 ) @ id ) ) @ id )
| ~ ( X14 @ id @ X1 @ id ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_13]),c_0_14]) ).
thf(c_0_34,negated_conjecture,
! [X1: term,X2: term] :
( ( epred1_0 @ id @ ( esk2_2 @ epred1_0 @ X1 ) @ id )
| ( epred1_0 @ id @ ( esk2_2 @ epred1_0 @ X2 ) @ id )
| ( epred1_0 @ id @ ( lam @ X1 ) @ id )
| ( epred1_0 @ id @ ( lam @ X2 ) @ id ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_23]) ).
thf(c_0_35,negated_conjecture,
! [X1: term,X3: subst,X4: subst] :
( ( ( esk1_1 @ epred1_0 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) )
= ( sub @ ( esk1_1 @ epred1_0 @ X3 @ X1 ) @ X4 ) )
| ~ ( epred1_0 @ id @ ( esk2_2 @ epred1_0 @ esk7_0 ) @ id ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
thf(c_0_36,negated_conjecture,
( ~ ( epred1_0 @ id @ ( hoaslam @ id @ ( esk1_1 @ epred1_0 ) ) @ id )
| ~ ( epred1_0 @ id @ ( esk2_2 @ epred1_0 @ esk7_0 ) @ id ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_30]),c_0_31]) ).
thf(c_0_37,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ id @ ( esk1_1 @ epred1_0 @ id @ X1 ) @ id )
| ~ ( epred1_0 @ id @ ( esk2_2 @ epred1_0 @ esk7_0 ) @ id )
| ~ ( epred1_0 @ id @ X1 @ id ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_30]),c_0_31]) ).
thf(c_0_38,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ id @ ( esk2_2 @ epred1_0 @ X1 ) @ id )
| ( epred1_0 @ id @ ( lam @ X1 ) @ id ) ),
inference(ef,[status(thm)],[c_0_34]) ).
thf(c_0_39,negated_conjecture,
( ~ ( epred1_0 @ id @ ( esk1_1 @ epred1_0 @ id @ ( esk6_1 @ ( esk1_1 @ epred1_0 ) ) ) @ id )
| ~ ( epred1_0 @ id @ ( esk2_2 @ epred1_0 @ esk7_0 ) @ id ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_35]),c_0_36]) ).
thf(c_0_40,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ id @ ( esk1_1 @ epred1_0 @ id @ X1 ) @ id )
| ~ ( epred1_0 @ id @ X1 @ id ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_31]) ).
thf(c_0_41,negated_conjecture,
( ( epred1_0 @ id @ ( esk6_1 @ ( esk1_1 @ epred1_0 ) ) @ id )
| ~ ( epred1_0 @ id @ ( esk2_2 @ epred1_0 @ esk7_0 ) @ id ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_35]),c_0_36]) ).
thf(c_0_42,negated_conjecture,
~ ( epred1_0 @ id @ ( esk2_2 @ epred1_0 @ esk7_0 ) @ id ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
thf(c_0_43,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_38]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG266^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n003.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 17:36:44 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.23/0.26 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.5qnPnc7Agw/E---3.1_2817852.p
% 0.23/0.30 % Version: 3.5.1-ho
% 0.23/0.30 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.23/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.30 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.23/0.30 % Starting post_as_ho1 with 300s (1) cores
% 0.23/0.30 % Starting post_as_ho5 with 300s (1) cores
% 0.23/0.30 % Starting post_as_ho10 with 300s (1) cores
% 0.23/0.30 % post_as_ho5 with pid 2817884 completed with status 0
% 0.23/0.30 % Result found by post_as_ho5
% 0.23/0.30 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.23/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.30 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.23/0.30 % Starting post_as_ho1 with 300s (1) cores
% 0.23/0.30 % Starting post_as_ho5 with 300s (1) cores
% 0.23/0.30 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.23/0.30 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.23/0.30 % Search class: HGUSF-FFMF21-MHFMMMBN
% 0.23/0.30 % partial match(2): HGUSS-FFMF31-MHFMMMBN
% 0.23/0.30 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.30 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.30 % SubtermCWHack with pid 2817888 completed with status 0
% 0.23/0.30 % Result found by SubtermCWHack
% 0.23/0.30 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.23/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.30 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.23/0.30 % Starting post_as_ho1 with 300s (1) cores
% 0.23/0.30 % Starting post_as_ho5 with 300s (1) cores
% 0.23/0.30 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.23/0.30 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.23/0.30 % Search class: HGUSF-FFMF21-MHFMMMBN
% 0.23/0.30 % partial match(2): HGUSS-FFMF31-MHFMMMBN
% 0.23/0.30 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.30 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.30 % Preprocessing time : 0.002 s
% 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 : 238
% 0.23/0.30 % Removed by relevancy pruning/SinE : 232
% 0.23/0.30 % Initial clauses : 12
% 0.23/0.30 % Removed in clause preprocessing : 0
% 0.23/0.30 % Initial clauses in saturation : 12
% 0.23/0.30 % Processed clauses : 39
% 0.23/0.30 % ...of these trivial : 0
% 0.23/0.30 % ...subsumed : 8
% 0.23/0.30 % ...remaining for further processing : 31
% 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 : 13
% 0.23/0.30 % Backward-rewritten : 0
% 0.23/0.30 % Generated clauses : 83
% 0.23/0.30 % ...of the previous two non-redundant : 78
% 0.23/0.30 % ...aggressively subsumed : 0
% 0.23/0.30 % Contextual simplify-reflections : 6
% 0.23/0.30 % Paramodulations : 79
% 0.23/0.30 % Factorizations : 4
% 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 : 22
% 0.23/0.30 % ...of those cached : 18
% 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 : 18
% 0.23/0.30 % Positive orientable unit clauses : 2
% 0.23/0.30 % Positive unorientable unit clauses: 0
% 0.23/0.30 % Negative unit clauses : 2
% 0.23/0.30 % Non-unit-clauses : 14
% 0.23/0.30 % Current number of unprocessed clauses: 50
% 0.23/0.30 % ...number of literals in the above : 294
% 0.23/0.30 % Current number of archived formulas : 0
% 0.23/0.30 % Current number of archived clauses : 13
% 0.23/0.30 % Clause-clause subsumption calls (NU) : 132
% 0.23/0.30 % Rec. Clause-clause subsumption calls : 78
% 0.23/0.30 % Non-unit clause-clause subsumptions : 22
% 0.23/0.30 % Unit Clause-clause subsumption calls : 5
% 0.23/0.30 % Rewrite failures with RHS unbound : 0
% 0.23/0.30 % BW rewrite match attempts : 0
% 0.23/0.30 % BW rewrite match successes : 0
% 0.23/0.30 % Condensation attempts : 0
% 0.23/0.30 % Condensation successes : 0
% 0.23/0.30 % Termbank termtop insertions : 10425
% 0.23/0.30 % Search garbage collected termcells : 2329
% 0.23/0.30
% 0.23/0.30 % -------------------------------------------------
% 0.23/0.30 % User time : 0.011 s
% 0.23/0.30 % System time : 0.005 s
% 0.23/0.30 % Total time : 0.016 s
% 0.23/0.30 % Maximum resident set size: 4492 pages
% 0.23/0.30
% 0.23/0.30 % -------------------------------------------------
% 0.23/0.30 % User time : 0.018 s
% 0.23/0.30 % System time : 0.011 s
% 0.23/0.30 % Total time : 0.029 s
% 0.23/0.30 % Maximum resident set size: 5120 pages
% 0.23/0.30 % E exiting
%------------------------------------------------------------------------------