%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG248^3 : 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 : 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 07:44:43 AM UTC 2026
% Result : Theorem 0.33s 0.46s
% Output : CNFRefutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 32 ( 9 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 117 ( 7 ~; 3 |; 4 &; 84 @)
% ( 8 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 7 con; 0-4 aty)
% Number of variables : 41 ( 8 ^; 33 !; 0 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
term: $tType ).
thf(decl_sort2,type,
subst: $tType ).
thf(decl_23,type,
one: term ).
thf(decl_26,type,
sub: term > subst > term ).
thf(decl_29,type,
push: term > subst > subst ).
thf(decl_32,type,
pushprop_lem1v2: $o ).
thf(decl_63,type,
pushprop_lem1v2_lthm: $o ).
thf(decl_93,type,
axvarcons: $o ).
thf(decl_142,type,
pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
thf(decl_145,type,
epred1_0: term > $o ).
thf(decl_146,type,
epred2_0: term > $o ).
thf(decl_147,type,
esk1_0: term ).
thf(decl_148,type,
esk2_0: subst ).
thf(pushprop_p_and_p_prime,axiom,
( pushprop_p_and_p_prime
= ( ^ [X1: term,X3: subst,X6: term > $o,X9: term > $o] :
! [X10: term] :
( ( X9 @ X10 )
<=> ( X6 @ ( sub @ X10 @ ( push @ X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.dQV414xd5O/E---3.1_1361509.p',pushprop_p_and_p_prime) ).
thf(pushprop_lem1v2,axiom,
( pushprop_lem1v2
<=> ! [X6: term > $o,X9: term > $o,X1: term,X3: subst] :
( ( X6 @ X1 )
=> ( ( pushprop_p_and_p_prime @ X1 @ X3 @ X6 @ X9 )
=> ( X9 @ one ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.dQV414xd5O/E---3.1_1361509.p',pushprop_lem1v2) ).
thf(thm,conjecture,
pushprop_lem1v2_lthm,
file('/export/starexec/sandbox2/tmp/tmp.dQV414xd5O/E---3.1_1361509.p',thm) ).
thf(pushprop_lem1v2_lthm,axiom,
( pushprop_lem1v2_lthm
<=> ( axvarcons
=> pushprop_lem1v2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.dQV414xd5O/E---3.1_1361509.p',pushprop_lem1v2_lthm) ).
thf(axvarcons,axiom,
( axvarcons
<=> ! [X1: term,X3: subst] :
( ( sub @ one @ ( push @ X1 @ X3 ) )
= X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.dQV414xd5O/E---3.1_1361509.p',axvarcons) ).
thf(c_0_5,plain,
( pushprop_p_and_p_prime
= ( ^ [Z0: term,Z1: subst,Z2: term > $o,Z3: term > $o] :
! [X10: term] :
( ( Z3 @ X10 )
<=> ( Z2 @ ( sub @ X10 @ ( push @ Z0 @ Z1 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[pushprop_p_and_p_prime]) ).
thf(c_0_6,axiom,
( pushprop_lem1v2
= ( ! [X6: term > $o,X9: term > $o,X1: term,X3: subst] :
( ( X6 @ X1 )
=> ( ! [X314: term] :
( ( X9 @ X314 )
<=> ( X6 @ ( sub @ X314 @ ( push @ X1 @ X3 ) ) ) )
=> ( X9 @ one ) ) ) ) ),
inference(apply_def,[status(thm)],[pushprop_lem1v2,c_0_5]) ).
thf(c_0_7,negated_conjecture,
~ pushprop_lem1v2_lthm,
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_8,axiom,
( pushprop_lem1v2_lthm
= ( ! [X1030: term,X1031: subst] :
( ( sub @ one @ ( push @ X1030 @ X1031 ) )
= X1030 )
=> ! [X1032: term > $o,X1033: term > $o,X1034: term,X1035: subst] :
( ( X1032 @ X1034 )
=> ( ! [X1036: term] :
( ( X1033 @ X1036 )
<=> ( X1032 @ ( sub @ X1036 @ ( push @ X1034 @ X1035 ) ) ) )
=> ( X1033 @ one ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[pushprop_lem1v2_lthm,axvarcons]),c_0_6]) ).
thf(c_0_9,negated_conjecture,
~ ( ! [X3373: term,X3374: subst] :
( ( sub @ one @ ( push @ X3373 @ X3374 ) )
= X3373 )
=> ! [X3375: term > $o,X3376: term > $o,X3377: term,X3378: subst] :
( ( X3375 @ X3377 )
=> ( ! [X3379: term] :
( ( X3376 @ X3379 )
<=> ( X3375 @ ( sub @ X3379 @ ( push @ X3377 @ X3378 ) ) ) )
=> ( X3376 @ one ) ) ) ),
inference(apply_def,[status(thm)],[c_0_7,c_0_8]) ).
thf(c_0_10,negated_conjecture,
! [X3392: term,X3393: subst,X3398: term] :
( ( ( sub @ one @ ( push @ X3392 @ X3393 ) )
= X3392 )
& ( epred1_0 @ esk1_0 )
& ( ~ ( epred2_0 @ X3398 )
| ( epred1_0 @ ( sub @ X3398 @ ( push @ esk1_0 @ esk2_0 ) ) ) )
& ( ~ ( epred1_0 @ ( sub @ X3398 @ ( push @ esk1_0 @ esk2_0 ) ) )
| ( epred2_0 @ X3398 ) )
& ~ ( epred2_0 @ one ) ),
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_11,negated_conjecture,
! [X1: term] :
( ( epred2_0 @ X1 )
| ~ ( epred1_0 @ ( sub @ X1 @ ( push @ esk1_0 @ esk2_0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_12,negated_conjecture,
! [X3: subst,X1: term] :
( ( sub @ one @ ( push @ X1 @ X3 ) )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_13,negated_conjecture,
epred1_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_14,negated_conjecture,
~ ( epred2_0 @ one ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_15,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]),c_0_14]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG248^3 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.25 % Computer : n020.cluster.edu
% 0.10/0.25 % Model : x86_64 x86_64
% 0.10/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.25 % Memory : 8046.5625MB
% 0.10/0.25 % OS : Linux 6.8.0-71-generic
% 0.10/0.25 % CPULimit : 300
% 0.10/0.25 % WCLimit : 300
% 0.10/0.25 % DateTime : Tue Sep 29 17:33:04 UTC 2026
% 0.10/0.26 % CPUTime :
% 0.10/0.26 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.32 Running higher-order theorem proving
% 0.33/0.38 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.dQV414xd5O/E---3.1_1361509.p
% 0.33/0.46 % Version: 3.5.1-ho
% 0.33/0.46 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.33/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.33/0.46 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.33/0.46 % Starting post_as_ho1 with 300s (1) cores
% 0.33/0.46 % Starting post_as_ho5 with 300s (1) cores
% 0.33/0.46 % Starting post_as_ho10 with 300s (1) cores
% 0.33/0.46 % post_as_ho5 with pid 1361524 completed with status 9
% 0.33/0.46 % new_ho_10_cnf2 with pid 1361522 completed with status 0
% 0.33/0.46 % Result found by new_ho_10_cnf2
% 0.33/0.46 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.33/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.33/0.46 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.33/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.33/0.46 % No SInE strategy applied
% 0.33/0.46 % Search class: HHUSS-FFSF32-SHFMMFNN
% 0.33/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.33/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.33/0.46 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.33/0.46 % Starting sh5l with 136s (1) cores
% 0.33/0.46 % Starting new_bool_1 with 136s (1) cores
% 0.33/0.46 % Starting new_bool_2 with 136s (1) cores
% 0.33/0.46 % new_ho_10_cnf2 with pid 1361538 completed with status 0
% 0.33/0.46 % Result found by new_ho_10_cnf2
% 0.33/0.46 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.33/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.33/0.46 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.33/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.33/0.46 % No SInE strategy applied
% 0.33/0.46 % Search class: HHUSS-FFSF32-SHFMMFNN
% 0.33/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.33/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.33/0.46 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.33/0.46 % Preprocessing time : 0.001 s
% 0.33/0.46 % Presaturation interreduction done
% 0.33/0.46
% 0.33/0.46 % Proof found!
% 0.33/0.46 % SZS status Theorem
% 0.33/0.46 % SZS output start CNFRefutation
% See solution above
% 0.33/0.46 % Parsed axioms : 238
% 0.33/0.46 % Removed by relevancy pruning/SinE : 0
% 0.33/0.46 % Initial clauses : 131
% 0.33/0.46 % Removed in clause preprocessing : 124
% 0.33/0.46 % Initial clauses in saturation : 7
% 0.33/0.46 % Processed clauses : 11
% 0.33/0.46 % ...of these trivial : 0
% 0.33/0.46 % ...subsumed : 0
% 0.33/0.46 % ...remaining for further processing : 11
% 0.33/0.46 % Other redundant clauses eliminated : 0
% 0.33/0.46 % Clauses deleted for lack of memory : 0
% 0.33/0.46 % Backward-subsumed : 0
% 0.33/0.46 % Backward-rewritten : 0
% 0.33/0.46 % Generated clauses : 1
% 0.33/0.46 % ...of the previous two non-redundant : 0
% 0.33/0.46 % ...aggressively subsumed : 0
% 0.33/0.46 % Contextual simplify-reflections : 0
% 0.33/0.46 % Paramodulations : 1
% 0.33/0.46 % Factorizations : 0
% 0.33/0.46 % NegExts : 0
% 0.33/0.46 % Equation resolutions : 0
% 0.33/0.46 % Disequality decompositions : 0
% 0.33/0.46 % Total rewrite steps : 1
% 0.33/0.46 % ...of those cached : 0
% 0.33/0.46 % Propositional unsat checks : 0
% 0.33/0.46 % Propositional check models : 0
% 0.33/0.46 % Propositional check unsatisfiable : 0
% 0.33/0.46 % Propositional clauses : 0
% 0.33/0.46 % Propositional clauses after purity: 0
% 0.33/0.46 % Propositional unsat core size : 0
% 0.33/0.46 % Propositional preprocessing time : 0.000
% 0.33/0.46 % Propositional encoding time : 0.000
% 0.33/0.46 % Propositional solver time : 0.000
% 0.33/0.46 % Success case prop preproc time : 0.000
% 0.33/0.46 % Success case prop encoding time : 0.000
% 0.33/0.46 % Success case prop solver time : 0.000
% 0.33/0.46 % Current number of processed clauses : 4
% 0.33/0.46 % Positive orientable unit clauses : 2
% 0.33/0.46 % Positive unorientable unit clauses: 0
% 0.33/0.46 % Negative unit clauses : 1
% 0.33/0.46 % Non-unit-clauses : 1
% 0.33/0.46 % Current number of unprocessed clauses: 3
% 0.33/0.46 % ...number of literals in the above : 4
% 0.33/0.46 % Current number of archived formulas : 0
% 0.33/0.46 % Current number of archived clauses : 7
% 0.33/0.46 % Clause-clause subsumption calls (NU) : 0
% 0.33/0.46 % Rec. Clause-clause subsumption calls : 0
% 0.33/0.46 % Non-unit clause-clause subsumptions : 0
% 0.33/0.46 % Unit Clause-clause subsumption calls : 0
% 0.33/0.46 % Rewrite failures with RHS unbound : 0
% 0.33/0.46 % BW rewrite match attempts : 0
% 0.33/0.46 % BW rewrite match successes : 0
% 0.33/0.46 % Condensation attempts : 11
% 0.33/0.46 % Condensation successes : 0
% 0.33/0.46 % Termbank termtop insertions : 26557
% 0.33/0.46 % Search garbage collected termcells : 1756
% 0.33/0.46
% 0.33/0.46 % -------------------------------------------------
% 0.33/0.46 % User time : 0.036 s
% 0.33/0.46 % System time : 0.012 s
% 0.33/0.46 % Total time : 0.049 s
% 0.33/0.46 % Maximum resident set size: 7256 pages
% 0.33/0.46
% 0.33/0.46 % -------------------------------------------------
% 0.33/0.46 % User time : 0.088 s
% 0.33/0.46 % System time : 0.065 s
% 0.33/0.46 % Total time : 0.153 s
% 0.33/0.46 % Maximum resident set size: 5120 pages
% 0.33/0.46 % E exiting
%------------------------------------------------------------------------------