%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG268^2 : 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 : n020.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 0.22s 0.31s
% Output : CNFRefutation 0.22s
% 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 : 115 ( 30 equ; 0 cnn)
% Maximal formula atoms : 17 ( 2 avg)
% Number of connectives : 1427 ( 46 ~; 78 |; 13 &;1210 @)
% ( 7 <=>; 73 =>; 0 <=; 0 <~>)
% Maximal formula depth : 39 ( 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 : 192 ( 16 ^; 176 !; 0 ?; 192 :)
% 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_58,type,
hoasinduction_lem3: $o ).
thf(decl_76,type,
hoasinduction_lem3aa: $o ).
thf(decl_94,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(decl_100,type,
hoasinduction_lem3_lthm: $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.PTbdsCE50u/E---3.1_1364939.p',hoasinduction_lem3aa) ).
thf(hoasinduction_lem3,axiom,
( hoasinduction_lem3
<=> ! [X24: subst > term > subst > $o] :
( ! [X3: subst,X1: term,X4: subst,X5: subst] :
( ( X24 @ X3 @ X1 @ ( comp @ X5 @ X4 ) )
=> ( X24 @ ( comp @ X3 @ X5 ) @ ( sub @ X1 @ X5 ) @ X4 ) )
=> ( ! [X3: subst,X1: term,X4: subst,X5: subst] :
( ( X24 @ ( comp @ X3 @ X5 ) @ ( sub @ X1 @ X5 ) @ X4 )
=> ( X24 @ X3 @ X1 @ ( comp @ X5 @ X4 ) ) )
=> ( ! [X12: subst > term > term] :
( ! [X3: subst,X1: term,X4: subst] :
( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
= ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
=> ( ! [X1: term] :
( ( X24 @ id @ X1 @ id )
=> ( X24 @ id @ ( X12 @ id @ X1 ) @ id ) )
=> ( X24 @ id
@ ( hoaslam @ id
@ ^ [X3: subst,X1: term] : ( X12 @ X3 @ X1 ) )
@ id ) ) )
=> ! [X1: term] :
( ! [X2: term] :
( ( X24 @ id @ X2 @ id )
=> ( X24 @ id @ ( sub @ X1 @ ( push @ X2 @ id ) ) @ id ) )
=> ( X24 @ id @ ( lam @ X1 ) @ id ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.PTbdsCE50u/E---3.1_1364939.p',hoasinduction_lem3) ).
thf(thm,conjecture,
hoasinduction_lem3_lthm,
file('/export/starexec/sandbox2/tmp/tmp.PTbdsCE50u/E---3.1_1364939.p',thm) ).
thf(hoasinduction_lem3_lthm,axiom,
( hoasinduction_lem3_lthm
<=> ( axvarid
=> ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.PTbdsCE50u/E---3.1_1364939.p',hoasinduction_lem3_lthm) ).
thf(axvarid,axiom,
( axvarid
<=> ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.PTbdsCE50u/E---3.1_1364939.p',axvarid) ).
thf(axvarshift,axiom,
( axvarshift
<=> ( ( push @ one @ sh )
= id ) ),
file('/export/starexec/sandbox2/tmp/tmp.PTbdsCE50u/E---3.1_1364939.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_lem3
<=> ! [X24: subst > term > subst > $o] :
( ! [X3: subst,X1: term,X4: subst,X5: subst] :
( ( X24 @ X3 @ X1 @ ( comp @ X5 @ X4 ) )
=> ( X24 @ ( comp @ X3 @ X5 ) @ ( sub @ X1 @ X5 ) @ X4 ) )
=> ( ! [X3: subst,X1: term,X4: subst,X5: subst] :
( ( X24 @ ( comp @ X3 @ X5 ) @ ( sub @ X1 @ X5 ) @ X4 )
=> ( X24 @ X3 @ X1 @ ( comp @ X5 @ X4 ) ) )
=> ( ! [X12: subst > term > term] :
( ! [X3: subst,X1: term,X4: subst] :
( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
= ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
=> ( ! [X1: term] :
( ( X24 @ id @ X1 @ id )
=> ( X24 @ id @ ( X12 @ id @ X1 ) @ id ) )
=> ( X24 @ id
@ ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X12 @ Z0 @ Z1 ) )
@ id ) ) )
=> ! [X1: term] :
( ! [X2: term] :
( ( X24 @ id @ X2 @ id )
=> ( X24 @ id @ ( sub @ X1 @ ( push @ X2 @ id ) ) @ id ) )
=> ( X24 @ id @ ( lam @ X1 ) @ id ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[hoasinduction_lem3]) ).
thf(c_0_8,negated_conjecture,
~ hoasinduction_lem3_lthm,
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_9,axiom,
( hoasinduction_lem3_lthm
= ( ! [X53: term] :
( ( sub @ X53 @ id )
= X53 )
=> ( ( ( 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 @ ( sub @ X60 @ ( push @ one @ sh ) ) ) @ id ) ) )
=> ! [X62: subst > term > subst > $o] :
( ! [X63: subst,X64: term,X65: subst,X66: subst] :
( ( X62 @ X63 @ X64 @ ( comp @ X66 @ X65 ) )
=> ( X62 @ ( comp @ X63 @ X66 ) @ ( sub @ X64 @ X66 ) @ X65 ) )
=> ( ! [X67: subst,X68: term,X69: subst,X70: subst] :
( ( X62 @ ( comp @ X67 @ X70 ) @ ( sub @ X68 @ X70 ) @ X69 )
=> ( X62 @ X67 @ X68 @ ( comp @ X70 @ X69 ) ) )
=> ( ! [X71: subst > term > term] :
( ! [X72: subst,X73: term,X74: subst] :
( ( sub @ ( X71 @ X72 @ X73 ) @ X74 )
= ( X71 @ ( comp @ X72 @ X74 ) @ ( sub @ X73 @ X74 ) ) )
=> ( ! [X75: term] :
( ( X62 @ id @ X75 @ id )
=> ( X62 @ id @ ( X71 @ id @ X75 ) @ id ) )
=> ( X62 @ id
@ ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X71 @ Z0 @ Z1 ) )
@ id ) ) )
=> ! [X76: term] :
( ! [X77: term] :
( ( X62 @ id @ X77 @ id )
=> ( X62 @ id @ ( sub @ X76 @ ( push @ X77 @ id ) ) @ id ) )
=> ( X62 @ id @ ( lam @ X76 ) @ id ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[hoasinduction_lem3_lthm,axvarid]),axvarshift]),c_0_6]),c_0_7]) ).
thf(c_0_10,negated_conjecture,
~ ( ! [X78: term] :
( ( sub @ X78 @ id )
= X78 )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [X79: subst > term > subst > $o] :
( ! [X80: subst > term > term] :
( ! [X81: subst,X82: term,X83: subst] :
( ( sub @ ( X80 @ X81 @ X82 ) @ X83 )
= ( X80 @ ( comp @ X81 @ X83 ) @ ( sub @ X82 @ X83 ) ) )
=> ( ! [X84: term] :
( ( X79 @ id @ X84 @ id )
=> ( X79 @ id @ ( X80 @ id @ X84 ) @ id ) )
=> ( X79 @ id
@ ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X80 @ Z0 @ Z1 ) )
@ id ) ) )
=> ! [X85: term] :
( ! [X86: term] :
( ( X79 @ id @ X86 @ id )
=> ( X79 @ id @ ( sub @ X85 @ ( push @ X86 @ id ) ) @ id ) )
=> ( X79 @ id @ ( lam @ ( sub @ X85 @ ( push @ one @ sh ) ) ) @ id ) ) )
=> ! [X87: subst > term > subst > $o] :
( ! [X88: subst,X89: term,X90: subst,X91: subst] :
( ( X87 @ X88 @ X89 @ ( comp @ X91 @ X90 ) )
=> ( X87 @ ( comp @ X88 @ X91 ) @ ( sub @ X89 @ X91 ) @ X90 ) )
=> ( ! [X92: subst,X93: term,X94: subst,X95: subst] :
( ( X87 @ ( comp @ X92 @ X95 ) @ ( sub @ X93 @ X95 ) @ X94 )
=> ( X87 @ X92 @ X93 @ ( comp @ X95 @ X94 ) ) )
=> ( ! [X96: subst > term > term] :
( ! [X97: subst,X98: term,X99: subst] :
( ( sub @ ( X96 @ X97 @ X98 ) @ X99 )
= ( X96 @ ( comp @ X97 @ X99 ) @ ( sub @ X98 @ X99 ) ) )
=> ( ! [X100: term] :
( ( X87 @ id @ X100 @ id )
=> ( X87 @ id @ ( X96 @ id @ X100 ) @ id ) )
=> ( X87 @ id
@ ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X96 @ Z0 @ Z1 ) )
@ id ) ) )
=> ! [X101: term] :
( ! [X102: term] :
( ( X87 @ id @ X102 @ id )
=> ( X87 @ id @ ( sub @ X101 @ ( push @ X102 @ id ) ) @ id ) )
=> ( X87 @ id @ ( lam @ X101 ) @ id ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_11,negated_conjecture,
! [X103: term,X104: subst > term > subst > $o,X106: subst,X107: term,X108: subst,X109: term,X110: term,X113: subst,X114: term,X115: subst,X116: subst,X117: subst,X118: term,X119: subst,X120: subst,X121: subst > term > term,X127: term] :
( ( ( sub @ X103 @ id )
= X103 )
& ( ( push @ one @ sh )
= id )
& ( ( X104 @ id @ ( esk2_2 @ X104 @ X110 ) @ id )
| ( X104 @ id @ ( lam @ ( sub @ X110 @ ( push @ one @ sh ) ) ) @ id )
| ( ( sub @ ( esk1_1 @ X104 @ X106 @ X107 ) @ X108 )
= ( esk1_1 @ X104 @ ( comp @ X106 @ X108 ) @ ( sub @ X107 @ X108 ) ) ) )
& ( ~ ( X104 @ id @ ( sub @ X110 @ ( push @ ( esk2_2 @ X104 @ X110 ) @ id ) ) @ id )
| ( X104 @ id @ ( lam @ ( sub @ X110 @ ( push @ one @ sh ) ) ) @ id )
| ( ( sub @ ( esk1_1 @ X104 @ X106 @ X107 ) @ X108 )
= ( esk1_1 @ X104 @ ( comp @ X106 @ X108 ) @ ( sub @ X107 @ X108 ) ) ) )
& ( ( X104 @ id @ ( esk2_2 @ X104 @ X110 ) @ id )
| ( X104 @ id @ ( lam @ ( sub @ X110 @ ( push @ one @ sh ) ) ) @ id )
| ~ ( X104 @ id @ X109 @ id )
| ( X104 @ id @ ( esk1_1 @ X104 @ id @ X109 ) @ id ) )
& ( ~ ( X104 @ id @ ( sub @ X110 @ ( push @ ( esk2_2 @ X104 @ X110 ) @ id ) ) @ id )
| ( X104 @ id @ ( lam @ ( sub @ X110 @ ( push @ one @ sh ) ) ) @ id )
| ~ ( X104 @ id @ X109 @ id )
| ( X104 @ id @ ( esk1_1 @ X104 @ id @ X109 ) @ id ) )
& ( ( X104 @ id @ ( esk2_2 @ X104 @ X110 ) @ id )
| ( X104 @ id @ ( lam @ ( sub @ X110 @ ( push @ one @ sh ) ) ) @ id )
| ~ ( X104 @ id @ ( hoaslam @ id @ ( esk1_1 @ X104 ) ) @ id ) )
& ( ~ ( X104 @ id @ ( sub @ X110 @ ( push @ ( esk2_2 @ X104 @ X110 ) @ id ) ) @ id )
| ( X104 @ id @ ( lam @ ( sub @ X110 @ ( push @ one @ sh ) ) ) @ id )
| ~ ( X104 @ id @ ( hoaslam @ id @ ( esk1_1 @ X104 ) ) @ id ) )
& ( ~ ( epred1_0 @ X113 @ X114 @ ( comp @ X116 @ X115 ) )
| ( epred1_0 @ ( comp @ X113 @ X116 ) @ ( sub @ X114 @ X116 ) @ X115 ) )
& ( ~ ( epred1_0 @ ( comp @ X117 @ X120 ) @ ( sub @ X118 @ X120 ) @ X119 )
| ( epred1_0 @ X117 @ X118 @ ( comp @ X120 @ X119 ) ) )
& ( ( epred1_0 @ id @ ( esk6_1 @ X121 ) @ id )
| ( epred1_0 @ id @ ( hoaslam @ id @ X121 ) @ id )
| ( ( sub @ ( X121 @ ( esk3_1 @ X121 ) @ ( esk4_1 @ X121 ) ) @ ( esk5_1 @ X121 ) )
!= ( X121 @ ( comp @ ( esk3_1 @ X121 ) @ ( esk5_1 @ X121 ) ) @ ( sub @ ( esk4_1 @ X121 ) @ ( esk5_1 @ X121 ) ) ) ) )
& ( ~ ( epred1_0 @ id @ ( X121 @ id @ ( esk6_1 @ X121 ) ) @ id )
| ( epred1_0 @ id @ ( hoaslam @ id @ X121 ) @ id )
| ( ( sub @ ( X121 @ ( esk3_1 @ X121 ) @ ( esk4_1 @ X121 ) ) @ ( esk5_1 @ X121 ) )
!= ( X121 @ ( comp @ ( esk3_1 @ X121 ) @ ( esk5_1 @ X121 ) ) @ ( sub @ ( esk4_1 @ X121 ) @ ( esk5_1 @ X121 ) ) ) ) )
& ( ~ ( epred1_0 @ id @ X127 @ id )
| ( epred1_0 @ id @ ( sub @ esk7_0 @ ( push @ X127 @ 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
% 0.00/0.02 % Problem : ALG268^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n020.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 17:35:49 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.22/0.27 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.PTbdsCE50u/E---3.1_1364939.p
% 0.22/0.31 % Version: 3.5.1-ho
% 0.22/0.31 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.22/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.31 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.22/0.31 % Starting post_as_ho1 with 300s (1) cores
% 0.22/0.31 % Starting post_as_ho5 with 300s (1) cores
% 0.22/0.31 % Starting post_as_ho10 with 300s (1) cores
% 0.22/0.31 % post_as_ho5 with pid 1364954 completed with status 0
% 0.22/0.31 % Result found by post_as_ho5
% 0.22/0.31 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.22/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.31 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.22/0.31 % Starting post_as_ho1 with 300s (1) cores
% 0.22/0.31 % Starting post_as_ho5 with 300s (1) cores
% 0.22/0.31 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.22/0.31 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.22/0.31 % Search class: HGUSF-FFMF21-MHFMMMBN
% 0.22/0.31 % partial match(2): HGUSS-FFMF31-MHFMMMBN
% 0.22/0.31 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.31 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.31 % SubtermCWHack with pid 1364956 completed with status 0
% 0.22/0.31 % Result found by SubtermCWHack
% 0.22/0.31 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.22/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.31 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.22/0.31 % Starting post_as_ho1 with 300s (1) cores
% 0.22/0.31 % Starting post_as_ho5 with 300s (1) cores
% 0.22/0.31 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.22/0.31 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.22/0.31 % Search class: HGUSF-FFMF21-MHFMMMBN
% 0.22/0.31 % partial match(2): HGUSS-FFMF31-MHFMMMBN
% 0.22/0.31 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.31 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.31 % Preprocessing time : 0.002 s
% 0.22/0.31
% 0.22/0.31 % Proof found!
% 0.22/0.31 % SZS status Theorem
% 0.22/0.31 % SZS output start CNFRefutation
% See solution above
% 0.22/0.31 % Parsed axioms : 238
% 0.22/0.31 % Removed by relevancy pruning/SinE : 232
% 0.22/0.31 % Initial clauses : 14
% 0.22/0.31 % Removed in clause preprocessing : 0
% 0.22/0.31 % Initial clauses in saturation : 14
% 0.22/0.31 % Processed clauses : 42
% 0.22/0.31 % ...of these trivial : 0
% 0.22/0.31 % ...subsumed : 7
% 0.22/0.31 % ...remaining for further processing : 35
% 0.22/0.31 % Other redundant clauses eliminated : 0
% 0.22/0.31 % Clauses deleted for lack of memory : 0
% 0.22/0.31 % Backward-subsumed : 13
% 0.22/0.31 % Backward-rewritten : 0
% 0.22/0.31 % Generated clauses : 89
% 0.22/0.31 % ...of the previous two non-redundant : 80
% 0.22/0.31 % ...aggressively subsumed : 0
% 0.22/0.31 % Contextual simplify-reflections : 6
% 0.22/0.31 % Paramodulations : 85
% 0.22/0.31 % Factorizations : 4
% 0.22/0.31 % NegExts : 0
% 0.22/0.31 % Equation resolutions : 0
% 0.22/0.31 % Disequality decompositions : 0
% 0.22/0.31 % Total rewrite steps : 24
% 0.22/0.31 % ...of those cached : 20
% 0.22/0.31 % Propositional unsat checks : 0
% 0.22/0.31 % Propositional check models : 0
% 0.22/0.31 % Propositional check unsatisfiable : 0
% 0.22/0.31 % Propositional clauses : 0
% 0.22/0.31 % Propositional clauses after purity: 0
% 0.22/0.31 % Propositional unsat core size : 0
% 0.22/0.31 % Propositional preprocessing time : 0.000
% 0.22/0.31 % Propositional encoding time : 0.000
% 0.22/0.31 % Propositional solver time : 0.000
% 0.22/0.31 % Success case prop preproc time : 0.000
% 0.22/0.31 % Success case prop encoding time : 0.000
% 0.22/0.31 % Success case prop solver time : 0.000
% 0.22/0.31 % Current number of processed clauses : 22
% 0.22/0.31 % Positive orientable unit clauses : 2
% 0.22/0.31 % Positive unorientable unit clauses: 0
% 0.22/0.31 % Negative unit clauses : 2
% 0.22/0.31 % Non-unit-clauses : 18
% 0.22/0.31 % Current number of unprocessed clauses: 51
% 0.22/0.31 % ...number of literals in the above : 299
% 0.22/0.31 % Current number of archived formulas : 0
% 0.22/0.31 % Current number of archived clauses : 13
% 0.22/0.31 % Clause-clause subsumption calls (NU) : 132
% 0.22/0.31 % Rec. Clause-clause subsumption calls : 79
% 0.22/0.31 % Non-unit clause-clause subsumptions : 21
% 0.22/0.31 % Unit Clause-clause subsumption calls : 5
% 0.22/0.31 % Rewrite failures with RHS unbound : 0
% 0.22/0.31 % BW rewrite match attempts : 0
% 0.22/0.31 % BW rewrite match successes : 0
% 0.22/0.31 % Condensation attempts : 0
% 0.22/0.31 % Condensation successes : 0
% 0.22/0.31 % Termbank termtop insertions : 10922
% 0.22/0.31 % Search garbage collected termcells : 2497
% 0.22/0.31
% 0.22/0.31 % -------------------------------------------------
% 0.22/0.31 % User time : 0.006 s
% 0.22/0.31 % System time : 0.008 s
% 0.22/0.31 % Total time : 0.014 s
% 0.22/0.31 % Maximum resident set size: 4748 pages
% 0.22/0.31
% 0.22/0.31 % -------------------------------------------------
% 0.22/0.31 % User time : 0.014 s
% 0.22/0.31 % System time : 0.014 s
% 0.22/0.31 % Total time : 0.028 s
% 0.22/0.31 % Maximum resident set size: 5120 pages
% 0.22/0.31 % E exiting
%------------------------------------------------------------------------------