%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG257^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 07:44:45 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 43 ( 34 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 166 ( 8 ~; 4 |; 2 &; 140 @)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 9 con; 0-4 aty)
% Number of variables : 66 ( 4 ^; 62 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
term: $tType ).
thf(decl_sort2,type,
subst: $tType ).
thf(decl_24,type,
ap: term > term > term ).
thf(decl_26,type,
sub: term > subst > term ).
thf(decl_27,type,
id: subst ).
thf(decl_39,type,
hoasap: subst > term > subst > term > term ).
thf(decl_43,type,
hoasapinj2: $o ).
thf(decl_87,type,
apinj2: $o ).
thf(decl_89,type,
hoasapinj2_lthm: $o ).
thf(decl_145,type,
esk1_0: term ).
thf(decl_146,type,
esk2_0: term ).
thf(decl_147,type,
esk3_0: term ).
thf(decl_148,type,
esk4_0: term ).
thf(thm,conjecture,
hoasapinj2_lthm,
file('/export/starexec/sandbox/tmp/tmp.Hg49Iv3bvL/E---3.1_922394.p',thm) ).
thf(hoasapinj2_lthm,axiom,
( hoasapinj2_lthm
<=> ( apinj2
=> hoasapinj2 ) ),
file('/export/starexec/sandbox/tmp/tmp.Hg49Iv3bvL/E---3.1_922394.p',hoasapinj2_lthm) ).
thf(apinj2,axiom,
( apinj2
<=> ! [X1: term,X2: term,X7: term,X8: term] :
( ( ( ap @ X1 @ X7 )
= ( ap @ X2 @ X8 ) )
=> ( X7 = X8 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Hg49Iv3bvL/E---3.1_922394.p',apinj2) ).
thf(hoasapinj2,axiom,
( hoasapinj2
<=> ! [X1: term,X2: term,X7: term,X8: term] :
( ( ( hoasap @ id @ X1 @ id @ X7 )
= ( hoasap @ id @ X2 @ id @ X8 ) )
=> ( X7 = X8 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Hg49Iv3bvL/E---3.1_922394.p',hoasapinj2) ).
thf(hoasap,axiom,
( hoasap
= ( ^ [X3: subst,X1: term,X4: subst,X2: term] : ( ap @ ( sub @ X1 @ X4 ) @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Hg49Iv3bvL/E---3.1_922394.p',hoasap) ).
thf(c_0_5,negated_conjecture,
~ hoasapinj2_lthm,
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_6,axiom,
( hoasapinj2_lthm
= ( ! [X1879: term,X1880: term,X1881: term,X1882: term] :
( ( ( ap @ X1879 @ X1881 )
= ( ap @ X1880 @ X1882 ) )
=> ( X1881 = X1882 ) )
=> ! [X1883: term,X1884: term,X1885: term,X1886: term] :
( ( ( hoasap @ id @ X1883 @ id @ X1885 )
= ( hoasap @ id @ X1884 @ id @ X1886 ) )
=> ( X1885 = X1886 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[hoasapinj2_lthm,apinj2]),hoasapinj2]) ).
thf(c_0_7,plain,
! [X3381: subst,X3382: term,X3383: subst,X3384: term] :
( ( hoasap @ X3381 @ X3382 @ X3383 @ X3384 )
= ( ap @ ( sub @ X3382 @ X3383 ) @ X3384 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[hoasap])]) ).
thf(c_0_8,negated_conjecture,
~ ( ! [X3373: term,X3374: term,X3375: term,X3376: term] :
( ( ( ap @ X3373 @ X3375 )
= ( ap @ X3374 @ X3376 ) )
=> ( X3375 = X3376 ) )
=> ! [X3377: term,X3378: term,X3379: term,X3380: term] :
( ( ( hoasap @ id @ X3377 @ id @ X3379 )
= ( hoasap @ id @ X3378 @ id @ X3380 ) )
=> ( X3379 = X3380 ) ) ),
inference(apply_def,[status(thm)],[c_0_5,c_0_6]) ).
thf(c_0_9,plain,
! [X3387: subst,X3388: term,X3389: subst,X3390: term] :
( ( hoasap @ X3387 @ X3388 @ X3389 @ X3390 )
= ( ap @ ( sub @ X3388 @ X3389 ) @ X3390 ) ),
inference(variable_rename,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
! [X3393: term,X3394: term,X3395: term,X3396: term] :
( ( ( ( ap @ X3393 @ X3395 )
!= ( ap @ X3394 @ X3396 ) )
| ( X3395 = X3396 ) )
& ( ( hoasap @ id @ esk1_0 @ id @ esk3_0 )
= ( hoasap @ id @ esk2_0 @ id @ esk4_0 ) )
& ( esk3_0 != esk4_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_8])])])])]) ).
thf(c_0_11,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_9]) ).
thf(c_0_12,negated_conjecture,
( ( hoasap @ id @ esk1_0 @ id @ esk3_0 )
= ( hoasap @ id @ esk2_0 @ id @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_13,plain,
! [X1: term,X3: subst,X5: subst,X4: subst,X2: term] :
( ( hoasap @ X3 @ X1 @ X4 @ X2 )
= ( hoasap @ X5 @ X1 @ X4 @ X2 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_11]) ).
thf(c_0_14,negated_conjecture,
! [X3: subst] :
( ( hoasap @ X3 @ esk1_0 @ id @ esk3_0 )
= ( hoasap @ id @ esk2_0 @ id @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_15,negated_conjecture,
! [X1: term,X2: term,X7: term,X8: term] :
( ( X2 = X8 )
| ( ( ap @ X1 @ X2 )
!= ( ap @ X7 @ X8 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_16,negated_conjecture,
! [X3: subst,X4: subst] :
( ( hoasap @ X3 @ esk1_0 @ id @ esk3_0 )
= ( hoasap @ X4 @ esk2_0 @ id @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_17,negated_conjecture,
! [X1: term,X8: term,X7: term,X4: subst,X3: subst,X2: term] :
( ( X1 = X2 )
| ( ( ap @ X7 @ X1 )
!= ( hoasap @ X3 @ X8 @ X4 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_15,c_0_11]) ).
thf(c_0_18,negated_conjecture,
! [X3: subst] :
( ( hoasap @ X3 @ esk1_0 @ id @ esk3_0 )
= ( ap @ ( sub @ esk2_0 @ id ) @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_16]) ).
thf(c_0_19,negated_conjecture,
! [X1: term,X2: term,X3: subst] :
( ( X1 = esk4_0 )
| ( ( ap @ X2 @ X1 )
!= ( hoasap @ X3 @ esk1_0 @ id @ esk3_0 ) ) ),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
thf(c_0_20,negated_conjecture,
( ( ap @ ( sub @ esk1_0 @ id ) @ esk3_0 )
= ( ap @ ( sub @ esk2_0 @ id ) @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_18]) ).
thf(c_0_21,negated_conjecture,
esk3_0 != esk4_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_22,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_18]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG257^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n026.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 17:36:38 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.Hg49Iv3bvL/E---3.1_922394.p
% 0.22/0.30 % Version: 3.5.1-ho
% 0.22/0.30 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.22/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.30 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.22/0.30 % Starting post_as_ho1 with 300s (1) cores
% 0.22/0.30 % Starting post_as_ho5 with 300s (1) cores
% 0.22/0.30 % Starting post_as_ho10 with 300s (1) cores
% 0.22/0.30 % post_as_ho5 with pid 922417 completed with status 9
% 0.22/0.30 % post_as_ho1 with pid 922416 completed with status 0
% 0.22/0.30 % Result found by post_as_ho1
% 0.22/0.30 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.22/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.30 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.22/0.30 % Starting post_as_ho1 with 300s (1) cores
% 0.22/0.30 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.30 % No SInE strategy applied
% 0.22/0.30 % Search class: HHUPS-FFSF32-SHFMMFNN
% 0.22/0.30 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.30 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.30 % SubtermCWHack with pid 922437 completed with status 0
% 0.22/0.30 % Result found by SubtermCWHack
% 0.22/0.30 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.22/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.30 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.22/0.30 % Starting post_as_ho1 with 300s (1) cores
% 0.22/0.30 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.30 % No SInE strategy applied
% 0.22/0.30 % Search class: HHUPS-FFSF32-SHFMMFNN
% 0.22/0.30 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.30 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.30 % Preprocessing time : 0.001 s
% 0.22/0.30
% 0.22/0.30 % Proof found!
% 0.22/0.30 % SZS status Theorem
% 0.22/0.30 % SZS output start CNFRefutation
% See solution above
% 0.22/0.30 % Parsed axioms : 238
% 0.22/0.30 % Removed by relevancy pruning/SinE : 0
% 0.22/0.30 % Initial clauses : 129
% 0.22/0.30 % Removed in clause preprocessing : 124
% 0.22/0.30 % Initial clauses in saturation : 5
% 0.22/0.30 % Processed clauses : 54
% 0.22/0.30 % ...of these trivial : 0
% 0.22/0.30 % ...subsumed : 37
% 0.22/0.30 % ...remaining for further processing : 17
% 0.22/0.30 % Other redundant clauses eliminated : 0
% 0.22/0.30 % Clauses deleted for lack of memory : 0
% 0.22/0.30 % Backward-subsumed : 1
% 0.22/0.30 % Backward-rewritten : 2
% 0.22/0.30 % Generated clauses : 102
% 0.22/0.30 % ...of the previous two non-redundant : 100
% 0.22/0.30 % ...aggressively subsumed : 0
% 0.22/0.30 % Contextual simplify-reflections : 0
% 0.22/0.30 % Paramodulations : 101
% 0.22/0.30 % Factorizations : 0
% 0.22/0.30 % NegExts : 0
% 0.22/0.30 % Equation resolutions : 1
% 0.22/0.30 % Disequality decompositions : 0
% 0.22/0.30 % Total rewrite steps : 3
% 0.22/0.30 % ...of those cached : 1
% 0.22/0.30 % Propositional unsat checks : 0
% 0.22/0.30 % Propositional check models : 0
% 0.22/0.30 % Propositional check unsatisfiable : 0
% 0.22/0.30 % Propositional clauses : 0
% 0.22/0.30 % Propositional clauses after purity: 0
% 0.22/0.30 % Propositional unsat core size : 0
% 0.22/0.30 % Propositional preprocessing time : 0.000
% 0.22/0.30 % Propositional encoding time : 0.000
% 0.22/0.30 % Propositional solver time : 0.000
% 0.22/0.30 % Success case prop preproc time : 0.000
% 0.22/0.30 % Success case prop encoding time : 0.000
% 0.22/0.30 % Success case prop solver time : 0.000
% 0.22/0.30 % Current number of processed clauses : 14
% 0.22/0.30 % Positive orientable unit clauses : 1
% 0.22/0.30 % Positive unorientable unit clauses: 9
% 0.22/0.30 % Negative unit clauses : 1
% 0.22/0.30 % Non-unit-clauses : 3
% 0.22/0.30 % Current number of unprocessed clauses: 34
% 0.22/0.30 % ...number of literals in the above : 50
% 0.22/0.30 % Current number of archived formulas : 0
% 0.22/0.30 % Current number of archived clauses : 3
% 0.22/0.30 % Clause-clause subsumption calls (NU) : 3
% 0.22/0.30 % Rec. Clause-clause subsumption calls : 2
% 0.22/0.30 % Non-unit clause-clause subsumptions : 1
% 0.22/0.30 % Unit Clause-clause subsumption calls : 3
% 0.22/0.30 % Rewrite failures with RHS unbound : 163
% 0.22/0.30 % BW rewrite match attempts : 19
% 0.22/0.30 % BW rewrite match successes : 19
% 0.22/0.30 % Condensation attempts : 0
% 0.22/0.30 % Condensation successes : 0
% 0.22/0.30 % Termbank termtop insertions : 27227
% 0.22/0.30 % Search garbage collected termcells : 1693
% 0.22/0.30
% 0.22/0.30 % -------------------------------------------------
% 0.22/0.30 % User time : 0.028 s
% 0.22/0.30 % System time : 0.013 s
% 0.22/0.30 % Total time : 0.041 s
% 0.22/0.30 % Maximum resident set size: 7564 pages
% 0.22/0.30
% 0.22/0.30 % -------------------------------------------------
% 0.22/0.30 % User time : 0.043 s
% 0.22/0.30 % System time : 0.046 s
% 0.22/0.30 % Total time : 0.089 s
% 0.22/0.30 % Maximum resident set size: 5120 pages
% 0.22/0.30 % E exiting
%------------------------------------------------------------------------------