%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG259^2 : 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 : n007.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 07:44:46 AM UTC 2026
% Result : Theorem 0.22s 0.31s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 26 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 182 ( 12 ~; 0 |; 2 &; 157 @)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 9 con; 0-4 aty)
% Number of variables : 76 ( 12 ^; 64 !; 0 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
term: $tType ).
thf(decl_sort2,type,
subst: $tType ).
thf(decl_23,type,
one: term ).
thf(decl_24,type,
ap: term > term > 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_30,type,
comp: subst > subst > subst ).
thf(decl_39,type,
hoasap: subst > term > subst > term > term ).
thf(decl_62,type,
hoaslamnotap_lthm: $o ).
thf(decl_94,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(decl_109,type,
lamnotap: $o ).
thf(decl_129,type,
hoaslamnotap: $o ).
thf(decl_145,type,
esk1_0: subst > term > term ).
thf(decl_146,type,
esk2_0: term ).
thf(decl_147,type,
esk3_0: term ).
thf(hoaslamnotap,axiom,
( hoaslamnotap
<=> ! [X12: subst > term > term] :
( ! [X3: subst,X1: term,X4: subst] :
( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
= ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
=> ! [X1: term,X2: term] :
( ( hoaslam @ id
@ ^ [X3: subst,X7: term] : ( X12 @ X3 @ X7 ) )
!= ( hoasap @ id @ X1 @ id @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.u7FFqEMYyl/E---3.1_3691218.p',hoaslamnotap) ).
thf(thm,conjecture,
hoaslamnotap_lthm,
file('/export/starexec/sandbox2/tmp/tmp.u7FFqEMYyl/E---3.1_3691218.p',thm) ).
thf(hoaslamnotap_lthm,axiom,
( hoaslamnotap_lthm
<=> ( lamnotap
=> hoaslamnotap ) ),
file('/export/starexec/sandbox2/tmp/tmp.u7FFqEMYyl/E---3.1_3691218.p',hoaslamnotap_lthm) ).
thf(lamnotap,axiom,
( lamnotap
<=> ! [X1: term,X2: term,X7: term] :
( ( lam @ X1 )
!= ( ap @ X2 @ X7 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.u7FFqEMYyl/E---3.1_3691218.p',lamnotap) ).
thf(hoaslam,axiom,
( hoaslam
= ( ^ [X3: subst,X12: subst > term > term] : ( lam @ ( X12 @ sh @ one ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.u7FFqEMYyl/E---3.1_3691218.p',hoaslam) ).
thf(hoasap,axiom,
( hoasap
= ( ^ [X3: subst,X1: term,X4: subst,X2: term] : ( ap @ ( sub @ X1 @ X4 ) @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.u7FFqEMYyl/E---3.1_3691218.p',hoasap) ).
thf(c_0_6,plain,
( hoaslamnotap
<=> ! [X12: subst > term > term] :
( ! [X3: subst,X1: term,X4: subst] :
( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
= ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
=> ! [X1: term,X2: term] :
( ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X12 @ Z0 @ Z1 ) )
!= ( hoasap @ id @ X1 @ id @ X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[hoaslamnotap]) ).
thf(c_0_7,negated_conjecture,
~ hoaslamnotap_lthm,
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_8,axiom,
( hoaslamnotap_lthm
= ( ! [X1021: term,X1022: term,X1023: term] :
( ( lam @ X1021 )
!= ( ap @ X1022 @ X1023 ) )
=> ! [X1024: subst > term > term] :
( ! [X1025: subst,X1026: term,X1027: subst] :
( ( sub @ ( X1024 @ X1025 @ X1026 ) @ X1027 )
= ( X1024 @ ( comp @ X1025 @ X1027 ) @ ( sub @ X1026 @ X1027 ) ) )
=> ! [X1028: term,X1029: term] :
( ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X1024 @ Z0 @ Z1 ) )
!= ( hoasap @ id @ X1028 @ id @ X1029 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[hoaslamnotap_lthm,lamnotap]),c_0_6]) ).
thf(c_0_9,negated_conjecture,
~ ( ! [X3373: term,X3374: term,X3375: term] :
( ( lam @ X3373 )
!= ( ap @ X3374 @ X3375 ) )
=> ! [X3376: subst > term > term] :
( ! [X3377: subst,X3378: term,X3379: subst] :
( ( sub @ ( X3376 @ X3377 @ X3378 ) @ X3379 )
= ( X3376 @ ( comp @ X3377 @ X3379 ) @ ( sub @ X3378 @ X3379 ) ) )
=> ! [X3380: term,X3381: term] :
( ( hoaslam @ id @ X3376 )
!= ( hoasap @ id @ X3380 @ id @ X3381 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[c_0_7,c_0_8])])]) ).
thf(c_0_10,plain,
! [X3386: subst,X3387: subst > term > term] :
( ( hoaslam @ X3386 @ X3387 )
= ( lam @ ( X3387 @ sh @ one ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[hoaslam])]) ).
thf(c_0_11,plain,
! [X3382: subst,X3383: term,X3384: subst,X3385: term] :
( ( hoasap @ X3382 @ X3383 @ X3384 @ X3385 )
= ( ap @ ( sub @ X3383 @ X3384 ) @ X3385 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[hoasap])]) ).
thf(c_0_12,negated_conjecture,
! [X3394: term,X3395: term,X3396: term,X3398: subst,X3399: term,X3400: subst] :
( ( ( lam @ X3394 )
!= ( ap @ X3395 @ X3396 ) )
& ( ( sub @ ( esk1_0 @ X3398 @ X3399 ) @ X3400 )
= ( esk1_0 @ ( comp @ X3398 @ X3400 ) @ ( sub @ X3399 @ X3400 ) ) )
& ( ( hoaslam @ id @ esk1_0 )
= ( hoasap @ id @ esk2_0 @ id @ esk3_0 ) ) ),
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_9])])])])]) ).
thf(c_0_13,plain,
! [X3392: subst,X3393: subst > term > term] :
( ( hoaslam @ X3392 @ X3393 )
= ( lam @ ( X3393 @ sh @ one ) ) ),
inference(variable_rename,[status(thm)],[c_0_10]) ).
thf(c_0_14,plain,
! [X3388: subst,X3389: term,X3390: subst,X3391: term] :
( ( hoasap @ X3388 @ X3389 @ X3390 @ X3391 )
= ( ap @ ( sub @ X3389 @ X3390 ) @ X3391 ) ),
inference(variable_rename,[status(thm)],[c_0_11]) ).
thf(c_0_15,negated_conjecture,
! [X1: term,X2: term,X7: term] :
( ( lam @ X1 )
!= ( ap @ X2 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_16,plain,
! [X3: subst,X12: subst > term > term] :
( ( hoaslam @ X3 @ X12 )
= ( lam @ ( X12 @ sh @ one ) ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_17,negated_conjecture,
( ( hoaslam @ id @ esk1_0 )
= ( hoasap @ id @ esk2_0 @ id @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_18,plain,
! [X1: term,X3: subst,X4: subst,X2: term] :
( ( hoasap @ X3 @ X1 @ X4 @ X2 )
= ( ap @ ( sub @ X1 @ X4 ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_19,negated_conjecture,
! [X1: term,X12: subst > term > term,X3: subst,X2: term] :
( ( hoaslam @ X3 @ X12 )
!= ( ap @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_20,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG259^2 : 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 : n007.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
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 17:32:46 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
% 0.22/0.26 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.u7FFqEMYyl/E---3.1_3691218.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_ho10 with pid 3691269 completed with status 0
% 0.22/0.31 % Result found by post_as_ho10
% 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 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.31 % No SInE strategy applied
% 0.22/0.31 % Search class: HUUPS-FFSF32-SHFMMFNN
% 0.22/0.31 % partial match(1): HHUPS-FFSF32-SHFMMFNN
% 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 3691281 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 % Starting post_as_ho10 with 300s (1) cores
% 0.22/0.31 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.31 % No SInE strategy applied
% 0.22/0.31 % Search class: HUUPS-FFSF32-SHFMMFNN
% 0.22/0.31 % partial match(1): HHUPS-FFSF32-SHFMMFNN
% 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 : 0
% 0.22/0.31 % Initial clauses : 129
% 0.22/0.31 % Removed in clause preprocessing : 124
% 0.22/0.31 % Initial clauses in saturation : 5
% 0.22/0.31 % Processed clauses : 16
% 0.22/0.31 % ...of these trivial : 0
% 0.22/0.31 % ...subsumed : 9
% 0.22/0.31 % ...remaining for further processing : 7
% 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 : 0
% 0.22/0.31 % Backward-rewritten : 1
% 0.22/0.31 % Generated clauses : 12
% 0.22/0.31 % ...of the previous two non-redundant : 11
% 0.22/0.31 % ...aggressively subsumed : 0
% 0.22/0.31 % Contextual simplify-reflections : 0
% 0.22/0.31 % Paramodulations : 12
% 0.22/0.31 % Factorizations : 0
% 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 : 1
% 0.22/0.31 % ...of those cached : 0
% 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 : 6
% 0.22/0.31 % Positive orientable unit clauses : 2
% 0.22/0.31 % Positive unorientable unit clauses: 2
% 0.22/0.31 % Negative unit clauses : 2
% 0.22/0.31 % Non-unit-clauses : 0
% 0.22/0.31 % Current number of unprocessed clauses: 0
% 0.22/0.31 % ...number of literals in the above : 0
% 0.22/0.31 % Current number of archived formulas : 0
% 0.22/0.31 % Current number of archived clauses : 1
% 0.22/0.31 % Clause-clause subsumption calls (NU) : 0
% 0.22/0.31 % Rec. Clause-clause subsumption calls : 0
% 0.22/0.31 % Non-unit clause-clause subsumptions : 0
% 0.22/0.31 % Unit Clause-clause subsumption calls : 1
% 0.22/0.31 % Rewrite failures with RHS unbound : 20
% 0.22/0.31 % BW rewrite match attempts : 4
% 0.22/0.31 % BW rewrite match successes : 3
% 0.22/0.31 % Condensation attempts : 0
% 0.22/0.31 % Condensation successes : 0
% 0.22/0.31 % Termbank termtop insertions : 26514
% 0.22/0.31 % Search garbage collected termcells : 1720
% 0.22/0.31
% 0.22/0.31 % -------------------------------------------------
% 0.22/0.31 % User time : 0.014 s
% 0.22/0.31 % System time : 0.010 s
% 0.22/0.31 % Total time : 0.024 s
% 0.22/0.31 % Maximum resident set size: 7820 pages
% 0.22/0.31
% 0.22/0.31 % -------------------------------------------------
% 0.22/0.31 % User time : 0.024 s
% 0.22/0.31 % System time : 0.013 s
% 0.22/0.31 % Total time : 0.037 s
% 0.22/0.31 % Maximum resident set size: 5120 pages
% 0.22/0.31 % E exiting
%------------------------------------------------------------------------------