%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG268^3 : 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 : n012.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 0.08s 0.21s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 97 ( 43 equ; 0 cnn)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 646 ( 18 ~; 18 |; 10 &; 537 @)
% ( 13 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 58 ( 58 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 12 con; 0-3 aty)
% Number of variables : 139 ( 16 ^; 120 !; 3 ?; 139 :)
% 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_34,type,
axmap: $o ).
thf(decl_41,type,
hoasinduction_lem3v2_f: $o ).
thf(decl_42,type,
axvarshift: $o ).
thf(decl_83,type,
axclos: $o ).
thf(decl_90,type,
hoasinduction_lem3v2a: $o ).
thf(decl_94,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(decl_104,type,
hoasinduction_lem3v2a_lthm: $o ).
thf(decl_107,type,
hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
thf(decl_143,type,
axvarid: $o ).
thf(decl_145,type,
esk1_1: term > subst > term > term ).
thf(decl_146,type,
epred1_0: subst > term > subst > $o ).
thf(decl_147,type,
epred2_0: term > $o ).
thf(decl_148,type,
esk2_1: ( subst > term > term ) > subst ).
thf(decl_149,type,
esk3_1: ( subst > term > term ) > term ).
thf(decl_150,type,
esk4_1: ( subst > term > term ) > subst ).
thf(decl_151,type,
esk5_1: ( subst > term > term ) > term ).
thf(decl_152,type,
esk6_0: term ).
thf(hoasinduction_lem3v2a,axiom,
( hoasinduction_lem3v2a
<=> ! [X19: subst > term > subst > $o,X9: term > $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] :
( ( X19 @ id @ X1 @ id )
=> ( X19 @ id @ ( X12 @ id @ X1 ) @ id ) )
=> ( X19 @ id
@ ( hoaslam @ id
@ ^ [X3: subst,X1: term] : ( X12 @ X3 @ X1 ) )
@ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ X19 @ X9 )
=> ! [X1: term] :
( ! [X2: term] :
( ( X9 @ X2 )
=> ( X9 @ ( sub @ X1 @ ( push @ X2 @ id ) ) ) )
=> ( X9 @ ( lam @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.SxXfzJmHYL/E---3.1_431005.p',hoasinduction_lem3v2a) ).
thf(hoasinduction_p_and_p_prime,axiom,
( hoasinduction_p_and_p_prime
= ( ^ [X14: subst > term > subst > $o,X9: term > $o] :
! [X10: term] :
( ( X9 @ X10 )
<=> ( X14 @ id @ X10 @ id ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.SxXfzJmHYL/E---3.1_431005.p',hoasinduction_p_and_p_prime) ).
thf(thm,conjecture,
hoasinduction_lem3v2a_lthm,
file('/export/starexec/sandbox2/tmp/tmp.SxXfzJmHYL/E---3.1_431005.p',thm) ).
thf(hoasinduction_lem3v2a_lthm,axiom,
( hoasinduction_lem3v2a_lthm
<=> ( hoasinduction_lem3v2_f
=> ( axvarid
=> ( axvarshift
=> ( axclos
=> ( axmap
=> hoasinduction_lem3v2a ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.SxXfzJmHYL/E---3.1_431005.p',hoasinduction_lem3v2a_lthm) ).
thf(axvarid,axiom,
( axvarid
<=> ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.SxXfzJmHYL/E---3.1_431005.p',axvarid) ).
thf(axclos,axiom,
( axclos
<=> ! [X1: term,X3: subst,X4: subst] :
( ( sub @ ( sub @ X1 @ X3 ) @ X4 )
= ( sub @ X1 @ ( comp @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.SxXfzJmHYL/E---3.1_431005.p',axclos) ).
thf(axmap,axiom,
( axmap
<=> ! [X1: term,X3: subst,X4: subst] :
( ( comp @ ( push @ X1 @ X3 ) @ X4 )
= ( push @ ( sub @ X1 @ X4 ) @ ( comp @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.SxXfzJmHYL/E---3.1_431005.p',axmap) ).
thf(axvarshift,axiom,
( axvarshift
<=> ( ( push @ one @ sh )
= id ) ),
file('/export/starexec/sandbox2/tmp/tmp.SxXfzJmHYL/E---3.1_431005.p',axvarshift) ).
thf(hoasinduction_lem3v2_f,axiom,
( hoasinduction_lem3v2_f
<=> ! [X2: term] :
? [X12: subst > term > term] :
! [X1: term,X3: subst] :
( ( X12 @ X3 @ X1 )
= ( sub @ X2 @ ( push @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.SxXfzJmHYL/E---3.1_431005.p',hoasinduction_lem3v2_f) ).
thf(hoaslam,axiom,
( hoaslam
= ( ^ [X3: subst,X12: subst > term > term] : ( lam @ ( X12 @ sh @ one ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.SxXfzJmHYL/E---3.1_431005.p',hoaslam) ).
thf(c_0_10,plain,
( hoasinduction_lem3v2a
<=> ! [X19: subst > term > subst > $o,X9: term > $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] :
( ( X19 @ id @ X1 @ id )
=> ( X19 @ id @ ( X12 @ id @ X1 ) @ id ) )
=> ( X19 @ id
@ ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X12 @ Z0 @ Z1 ) )
@ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ X19 @ X9 )
=> ! [X1: term] :
( ! [X2: term] :
( ( X9 @ X2 )
=> ( X9 @ ( sub @ X1 @ ( push @ X2 @ id ) ) ) )
=> ( X9 @ ( lam @ X1 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[hoasinduction_lem3v2a]) ).
thf(c_0_11,plain,
( hoasinduction_p_and_p_prime
= ( ^ [Z0: subst > term > subst > $o,Z1: term > $o] :
! [X10: term] :
( ( Z1 @ X10 )
<=> ( Z0 @ id @ X10 @ id ) ) ) ),
inference(fof_simplification,[status(thm)],[hoasinduction_p_and_p_prime]) ).
thf(c_0_12,plain,
( hoasinduction_lem3v2a
= ( ! [X19: subst > term > subst > $o,X9: term > $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] :
( ( X19 @ id @ X1 @ id )
=> ( X19 @ id @ ( X12 @ id @ X1 ) @ id ) )
=> ( X19 @ id
@ ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X12 @ Z0 @ Z1 ) )
@ id ) ) )
=> ( ! [X1887: term] :
( ( X9 @ X1887 )
<=> ( X19 @ id @ X1887 @ id ) )
=> ! [X1: term] :
( ! [X2: term] :
( ( X9 @ X2 )
=> ( X9 @ ( sub @ X1 @ ( push @ X2 @ id ) ) ) )
=> ( X9 @ ( lam @ X1 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_13,negated_conjecture,
~ hoasinduction_lem3v2a_lthm,
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_14,axiom,
( hoasinduction_lem3v2a_lthm
= ( ! [X2118: term] :
? [X2119: subst > term > term] :
! [X2120: term,X2121: subst] :
( ( X2119 @ X2121 @ X2120 )
= ( sub @ X2118 @ ( push @ X2120 @ X2121 ) ) )
=> ( ! [X2122: term] :
( ( sub @ X2122 @ id )
= X2122 )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [X2123: term,X2124: subst,X2125: subst] :
( ( sub @ ( sub @ X2123 @ X2124 ) @ X2125 )
= ( sub @ X2123 @ ( comp @ X2124 @ X2125 ) ) )
=> ( ! [X2126: term,X2127: subst,X2128: subst] :
( ( comp @ ( push @ X2126 @ X2127 ) @ X2128 )
= ( push @ ( sub @ X2126 @ X2128 ) @ ( comp @ X2127 @ X2128 ) ) )
=> ! [X2129: subst > term > subst > $o,X2130: term > $o] :
( ! [X2131: subst > term > term] :
( ! [X2132: subst,X2133: term,X2134: subst] :
( ( sub @ ( X2131 @ X2132 @ X2133 ) @ X2134 )
= ( X2131 @ ( comp @ X2132 @ X2134 ) @ ( sub @ X2133 @ X2134 ) ) )
=> ( ! [X2135: term] :
( ( X2129 @ id @ X2135 @ id )
=> ( X2129 @ id @ ( X2131 @ id @ X2135 ) @ id ) )
=> ( X2129 @ id
@ ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X2131 @ Z0 @ Z1 ) )
@ id ) ) )
=> ( ! [X2136: term] :
( ( X2130 @ X2136 )
<=> ( X2129 @ id @ X2136 @ id ) )
=> ! [X2137: term] :
( ! [X2138: term] :
( ( X2130 @ X2138 )
=> ( X2130 @ ( sub @ X2137 @ ( push @ X2138 @ id ) ) ) )
=> ( X2130 @ ( lam @ X2137 ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[hoasinduction_lem3v2a_lthm,axvarid]),axclos]),axmap]),axvarshift]),hoasinduction_lem3v2_f]),c_0_12]) ).
thf(c_0_15,plain,
! [X3398: subst,X3399: subst > term > term] :
( ( hoaslam @ X3398 @ X3399 )
= ( lam @ ( X3399 @ sh @ one ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[hoaslam])]) ).
thf(c_0_16,negated_conjecture,
~ ( ! [X3373: term] :
? [X3374: subst > term > term] :
! [X3375: term,X3376: subst] :
( ( X3374 @ X3376 @ X3375 )
= ( sub @ X3373 @ ( push @ X3375 @ X3376 ) ) )
=> ( ! [X3377: term] :
( ( sub @ X3377 @ id )
= X3377 )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [X3378: term,X3379: subst,X3380: subst] :
( ( sub @ ( sub @ X3378 @ X3379 ) @ X3380 )
= ( sub @ X3378 @ ( comp @ X3379 @ X3380 ) ) )
=> ( ! [X3381: term,X3382: subst,X3383: subst] :
( ( comp @ ( push @ X3381 @ X3382 ) @ X3383 )
= ( push @ ( sub @ X3381 @ X3383 ) @ ( comp @ X3382 @ X3383 ) ) )
=> ! [X3384: subst > term > subst > $o,X3385: term > $o] :
( ! [X3386: subst > term > term] :
( ! [X3387: subst,X3388: term,X3389: subst] :
( ( sub @ ( X3386 @ X3387 @ X3388 ) @ X3389 )
= ( X3386 @ ( comp @ X3387 @ X3389 ) @ ( sub @ X3388 @ X3389 ) ) )
=> ( ! [X3390: term] :
( ( X3384 @ id @ X3390 @ id )
=> ( X3384 @ id @ ( X3386 @ id @ X3390 ) @ id ) )
=> ( X3384 @ id
@ ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X3386 @ Z0 @ Z1 ) )
@ id ) ) )
=> ( ! [X3391: term] :
( ( X3385 @ X3391 )
<=> ( X3384 @ id @ X3391 @ id ) )
=> ! [X3392: term] :
( ! [X3393: term] :
( ( X3385 @ X3393 )
=> ( X3385 @ ( sub @ X3392 @ ( push @ X3393 @ id ) ) ) )
=> ( X3385 @ ( lam @ X3392 ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_17,plain,
! [X3404: subst,X3405: subst > term > term] :
( ( hoaslam @ X3404 @ X3405 )
= ( lam @ ( X3405 @ sh @ one ) ) ),
inference(variable_rename,[status(thm)],[c_0_15]) ).
thf(c_0_18,negated_conjecture,
! [X3406: term,X3408: term,X3409: subst,X3410: term,X3411: term,X3412: subst,X3413: subst,X3414: term,X3415: subst,X3416: subst,X3419: subst > term > term,X3424: term,X3426: term] :
( ( ( esk1_1 @ X3406 @ X3409 @ X3408 )
= ( sub @ X3406 @ ( push @ X3408 @ X3409 ) ) )
& ( ( sub @ X3410 @ id )
= X3410 )
& ( ( push @ one @ sh )
= id )
& ( ( sub @ ( sub @ X3411 @ X3412 ) @ X3413 )
= ( sub @ X3411 @ ( comp @ X3412 @ X3413 ) ) )
& ( ( comp @ ( push @ X3414 @ X3415 ) @ X3416 )
= ( push @ ( sub @ X3414 @ X3416 ) @ ( comp @ X3415 @ X3416 ) ) )
& ( ( epred1_0 @ id @ ( esk5_1 @ X3419 ) @ id )
| ( epred1_0 @ id @ ( hoaslam @ id @ X3419 ) @ id )
| ( ( sub @ ( X3419 @ ( esk2_1 @ X3419 ) @ ( esk3_1 @ X3419 ) ) @ ( esk4_1 @ X3419 ) )
!= ( X3419 @ ( comp @ ( esk2_1 @ X3419 ) @ ( esk4_1 @ X3419 ) ) @ ( sub @ ( esk3_1 @ X3419 ) @ ( esk4_1 @ X3419 ) ) ) ) )
& ( ~ ( epred1_0 @ id @ ( X3419 @ id @ ( esk5_1 @ X3419 ) ) @ id )
| ( epred1_0 @ id @ ( hoaslam @ id @ X3419 ) @ id )
| ( ( sub @ ( X3419 @ ( esk2_1 @ X3419 ) @ ( esk3_1 @ X3419 ) ) @ ( esk4_1 @ X3419 ) )
!= ( X3419 @ ( comp @ ( esk2_1 @ X3419 ) @ ( esk4_1 @ X3419 ) ) @ ( sub @ ( esk3_1 @ X3419 ) @ ( esk4_1 @ X3419 ) ) ) ) )
& ( ~ ( epred2_0 @ X3424 )
| ( epred1_0 @ id @ X3424 @ id ) )
& ( ~ ( epred1_0 @ id @ X3424 @ id )
| ( epred2_0 @ X3424 ) )
& ( ~ ( epred2_0 @ X3426 )
| ( epred2_0 @ ( sub @ esk6_0 @ ( push @ X3426 @ id ) ) ) )
& ~ ( epred2_0 @ ( lam @ esk6_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_19,plain,
! [X3: subst,X12: subst > term > term] :
( ( hoaslam @ X3 @ X12 )
= ( lam @ ( X12 @ sh @ one ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,negated_conjecture,
! [X1: term,X2: term,X3: subst] :
( ( esk1_1 @ X1 @ X3 @ X2 )
= ( sub @ X1 @ ( push @ X2 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_21,negated_conjecture,
( ( push @ one @ sh )
= id ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_22,negated_conjecture,
! [X1: term] :
( ( sub @ X1 @ id )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_23,negated_conjecture,
! [X12: subst > term > term] :
( ( epred1_0 @ id @ ( hoaslam @ id @ X12 ) @ id )
| ~ ( epred1_0 @ id @ ( X12 @ id @ ( esk5_1 @ X12 ) ) @ id )
| ( ( sub @ ( X12 @ ( esk2_1 @ X12 ) @ ( esk3_1 @ X12 ) ) @ ( esk4_1 @ X12 ) )
!= ( X12 @ ( comp @ ( esk2_1 @ X12 ) @ ( esk4_1 @ X12 ) ) @ ( sub @ ( esk3_1 @ X12 ) @ ( esk4_1 @ X12 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_24,negated_conjecture,
! [X3: subst,X1: term] :
( ( hoaslam @ X3 @ ( esk1_1 @ X1 ) )
= ( lam @ X1 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22]) ).
thf(c_0_25,negated_conjecture,
! [X1: term,X3: subst,X4: subst] :
( ( comp @ ( push @ X1 @ X3 ) @ X4 )
= ( push @ ( sub @ X1 @ X4 ) @ ( comp @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_26,negated_conjecture,
! [X1: term,X3: subst,X4: subst] :
( ( sub @ ( sub @ X1 @ X3 ) @ X4 )
= ( sub @ X1 @ ( comp @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_27,negated_conjecture,
! [X12: subst > term > term] :
( ( epred1_0 @ id @ ( esk5_1 @ X12 ) @ id )
| ( epred1_0 @ id @ ( hoaslam @ id @ X12 ) @ id )
| ( ( sub @ ( X12 @ ( esk2_1 @ X12 ) @ ( esk3_1 @ X12 ) ) @ ( esk4_1 @ X12 ) )
!= ( X12 @ ( comp @ ( esk2_1 @ X12 ) @ ( esk4_1 @ X12 ) ) @ ( sub @ ( esk3_1 @ X12 ) @ ( esk4_1 @ X12 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_28,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ id @ ( lam @ X1 ) @ id )
| ~ ( epred1_0 @ id @ ( sub @ X1 @ ( push @ ( esk5_1 @ ( esk1_1 @ X1 ) ) @ id ) ) @ id ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_20]),c_0_24]),c_0_25]),c_0_26]),c_0_20]),c_0_20])]) ).
thf(c_0_29,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ id @ X1 @ id )
| ~ ( epred2_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_30,negated_conjecture,
! [X1: term] :
( ( epred2_0 @ X1 )
| ~ ( epred1_0 @ id @ X1 @ id ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_31,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ id @ ( esk5_1 @ ( esk1_1 @ X1 ) ) @ id )
| ( epred1_0 @ id @ ( lam @ X1 ) @ id ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_20]),c_0_24]),c_0_25]),c_0_26]),c_0_20])]) ).
thf(c_0_32,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ id @ ( lam @ X1 ) @ id )
| ~ ( epred2_0 @ ( sub @ X1 @ ( push @ ( esk5_1 @ ( esk1_1 @ X1 ) ) @ id ) ) ) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_33,negated_conjecture,
! [X1: term] :
( ( epred2_0 @ ( sub @ esk6_0 @ ( push @ X1 @ id ) ) )
| ~ ( epred2_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_34,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ id @ ( lam @ X1 ) @ id )
| ( epred2_0 @ ( esk5_1 @ ( esk1_1 @ X1 ) ) ) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
thf(c_0_35,negated_conjecture,
epred1_0 @ id @ ( lam @ esk6_0 ) @ id,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
thf(c_0_36,negated_conjecture,
~ ( epred2_0 @ ( lam @ esk6_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_37,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_35]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ALG268^3 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 17:34:33 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.13 Running higher-order theorem proving
% 0.08/0.15 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.SxXfzJmHYL/E---3.1_431005.p
% 0.08/0.21 % Version: 3.5.1-ho
% 0.08/0.21 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.08/0.21 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.21 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.08/0.21 % Starting post_as_ho1 with 300s (1) cores
% 0.08/0.21 % Starting post_as_ho5 with 300s (1) cores
% 0.08/0.21 % Starting post_as_ho10 with 300s (1) cores
% 0.08/0.21 % post_as_ho10 with pid 431028 completed with status 0
% 0.08/0.21 % Result found by post_as_ho10
% 0.08/0.21 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.08/0.21 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.21 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.08/0.21 % Starting post_as_ho1 with 300s (1) cores
% 0.08/0.21 % Starting post_as_ho5 with 300s (1) cores
% 0.08/0.21 % Starting post_as_ho10 with 300s (1) cores
% 0.08/0.21 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.21 % No SInE strategy applied
% 0.08/0.21 % Search class: HGUSM-FFSF31-MHFMMSNN
% 0.08/0.21 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.21 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.21 % SubtermCWHack with pid 431033 completed with status 0
% 0.08/0.21 % Result found by SubtermCWHack
% 0.08/0.21 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.08/0.21 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.21 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.08/0.21 % Starting post_as_ho1 with 300s (1) cores
% 0.08/0.21 % Starting post_as_ho5 with 300s (1) cores
% 0.08/0.21 % Starting post_as_ho10 with 300s (1) cores
% 0.08/0.21 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.21 % No SInE strategy applied
% 0.08/0.21 % Search class: HGUSM-FFSF31-MHFMMSNN
% 0.08/0.21 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.21 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.21 % Preprocessing time : 0.001 s
% 0.08/0.21
% 0.08/0.21 % Proof found!
% 0.08/0.21 % SZS status Theorem
% 0.08/0.21 % SZS output start CNFRefutation
% See solution above
% 0.08/0.21 % Parsed axioms : 238
% 0.08/0.21 % Removed by relevancy pruning/SinE : 0
% 0.08/0.21 % Initial clauses : 137
% 0.08/0.21 % Removed in clause preprocessing : 124
% 0.08/0.21 % Initial clauses in saturation : 13
% 0.08/0.21 % Processed clauses : 72
% 0.08/0.21 % ...of these trivial : 0
% 0.08/0.21 % ...subsumed : 41
% 0.08/0.21 % ...remaining for further processing : 31
% 0.08/0.21 % Other redundant clauses eliminated : 0
% 0.08/0.21 % Clauses deleted for lack of memory : 0
% 0.08/0.21 % Backward-subsumed : 0
% 0.08/0.21 % Backward-rewritten : 0
% 0.08/0.21 % Generated clauses : 96
% 0.08/0.21 % ...of the previous two non-redundant : 81
% 0.08/0.21 % ...aggressively subsumed : 0
% 0.08/0.21 % Contextual simplify-reflections : 1
% 0.08/0.21 % Paramodulations : 96
% 0.08/0.21 % Factorizations : 0
% 0.08/0.21 % NegExts : 0
% 0.08/0.21 % Equation resolutions : 0
% 0.08/0.21 % Disequality decompositions : 0
% 0.08/0.21 % Total rewrite steps : 51
% 0.08/0.21 % ...of those cached : 26
% 0.08/0.21 % Propositional unsat checks : 0
% 0.08/0.21 % Propositional check models : 0
% 0.08/0.21 % Propositional check unsatisfiable : 0
% 0.08/0.21 % Propositional clauses : 0
% 0.08/0.21 % Propositional clauses after purity: 0
% 0.08/0.21 % Propositional unsat core size : 0
% 0.08/0.21 % Propositional preprocessing time : 0.000
% 0.08/0.21 % Propositional encoding time : 0.000
% 0.08/0.21 % Propositional solver time : 0.000
% 0.08/0.21 % Success case prop preproc time : 0.000
% 0.08/0.21 % Success case prop encoding time : 0.000
% 0.08/0.21 % Success case prop solver time : 0.000
% 0.08/0.21 % Current number of processed clauses : 31
% 0.08/0.21 % Positive orientable unit clauses : 14
% 0.08/0.21 % Positive unorientable unit clauses: 7
% 0.08/0.21 % Negative unit clauses : 1
% 0.08/0.21 % Non-unit-clauses : 9
% 0.08/0.21 % Current number of unprocessed clauses: 22
% 0.08/0.21 % ...number of literals in the above : 38
% 0.08/0.21 % Current number of archived formulas : 0
% 0.08/0.21 % Current number of archived clauses : 0
% 0.08/0.21 % Clause-clause subsumption calls (NU) : 11
% 0.08/0.21 % Rec. Clause-clause subsumption calls : 11
% 0.08/0.21 % Non-unit clause-clause subsumptions : 1
% 0.08/0.21 % Unit Clause-clause subsumption calls : 7
% 0.08/0.21 % Rewrite failures with RHS unbound : 136
% 0.08/0.21 % BW rewrite match attempts : 18
% 0.08/0.21 % BW rewrite match successes : 10
% 0.08/0.21 % Condensation attempts : 0
% 0.08/0.21 % Condensation successes : 0
% 0.08/0.21 % Termbank termtop insertions : 28744
% 0.08/0.21 % Search garbage collected termcells : 2060
% 0.08/0.21
% 0.08/0.21 % -------------------------------------------------
% 0.08/0.21 % User time : 0.025 s
% 0.08/0.21 % System time : 0.012 s
% 0.08/0.21 % Total time : 0.037 s
% 0.08/0.21 % Maximum resident set size: 7820 pages
% 0.08/0.21
% 0.08/0.21 % -------------------------------------------------
% 0.08/0.21 % User time : 0.035 s
% 0.08/0.21 % System time : 0.015 s
% 0.08/0.21 % Total time : 0.050 s
% 0.08/0.21 % Maximum resident set size: 5376 pages
% 0.08/0.21 % E exiting
%------------------------------------------------------------------------------