%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP069^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 08:04:16 AM UTC 2026
% Result : Theorem 0.21s 0.31s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 28 ( 6 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 160 ( 12 ~; 8 |; 0 &; 137 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 9 ( 0 ^; 9 !; 0 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
tree_a: $tType ).
thf(decl_sort2,type,
a: $tType ).
thf(decl_27,type,
heapIm970322378pify_a: tree_a > tree_a ).
thf(decl_30,type,
heapIm1091024090Down_a: tree_a > tree_a ).
thf(decl_32,type,
t_a: a > tree_a > tree_a > tree_a ).
thf(decl_34,type,
is_heap_a: tree_a > $o ).
thf(decl_59,type,
l: tree_a ).
thf(decl_60,type,
r: tree_a ).
thf(decl_61,type,
v: a ).
thf(conj_0,conjecture,
is_heap_a @ ( heapIm970322378pify_a @ ( t_a @ v @ l @ r ) ),
file('/export/starexec/sandbox/tmp/tmp.AcUqD7cEQS/E---3.1_2121073.p',conj_0) ).
thf(fact_2__092_060open_062_092_060lbrakk_062is__heap_A_Iheapify_Al_J_059_Ais__heap_A_Iheapify_Ar_J_059_AT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_A_061_AT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Ais__heap_A_IsiftDown_A_IT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_J_J_092_060close_062,axiom,
( ( is_heap_a @ ( heapIm970322378pify_a @ l ) )
=> ( ( is_heap_a @ ( heapIm970322378pify_a @ r ) )
=> ( ( ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) )
= ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) )
=> ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AcUqD7cEQS/E---3.1_2121073.p',fact_2__092_060open_062_092_060lbrakk_062is__heap_A_Iheapify_Al_J_059_Ais__heap_A_Iheapify_Ar_J_059_AT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_A_061_AT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Ais__heap_A_IsiftDown_A_IT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_J_J_092_060close_062) ).
thf(fact_3_heapify_Osimps_I2_J,axiom,
! [X1: a,X2: tree_a,X3: tree_a] :
( ( heapIm970322378pify_a @ ( t_a @ X1 @ X2 @ X3 ) )
= ( heapIm1091024090Down_a @ ( t_a @ X1 @ ( heapIm970322378pify_a @ X2 ) @ ( heapIm970322378pify_a @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AcUqD7cEQS/E---3.1_2121073.p',fact_3_heapify_Osimps_I2_J) ).
thf(fact_1_T_Ohyps_I1_J,axiom,
is_heap_a @ ( heapIm970322378pify_a @ l ),
file('/export/starexec/sandbox/tmp/tmp.AcUqD7cEQS/E---3.1_2121073.p',fact_1_T_Ohyps_I1_J) ).
thf(fact_0_T_Ohyps_I2_J,axiom,
is_heap_a @ ( heapIm970322378pify_a @ r ),
file('/export/starexec/sandbox/tmp/tmp.AcUqD7cEQS/E---3.1_2121073.p',fact_0_T_Ohyps_I2_J) ).
thf(c_0_5,negated_conjecture,
~ ( is_heap_a @ ( heapIm970322378pify_a @ ( t_a @ v @ l @ r ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_6,plain,
( ~ ( is_heap_a @ ( heapIm970322378pify_a @ l ) )
| ~ ( is_heap_a @ ( heapIm970322378pify_a @ r ) )
| ( ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) )
!= ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) )
| ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_2__092_060open_062_092_060lbrakk_062is__heap_A_Iheapify_Al_J_059_Ais__heap_A_Iheapify_Ar_J_059_AT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_A_061_AT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Ais__heap_A_IsiftDown_A_IT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_J_J_092_060close_062])]) ).
thf(c_0_7,negated_conjecture,
~ ( is_heap_a @ ( heapIm970322378pify_a @ ( t_a @ v @ l @ r ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
thf(c_0_8,plain,
( ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) ) )
| ~ ( is_heap_a @ ( heapIm970322378pify_a @ l ) )
| ~ ( is_heap_a @ ( heapIm970322378pify_a @ r ) )
| ( ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) )
!= ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,plain,
! [X249: a,X250: tree_a,X251: tree_a] :
( ( heapIm970322378pify_a @ ( t_a @ X249 @ X250 @ X251 ) )
= ( heapIm1091024090Down_a @ ( t_a @ X249 @ ( heapIm970322378pify_a @ X250 ) @ ( heapIm970322378pify_a @ X251 ) ) ) ),
inference(variable_rename,[status(thm)],[fact_3_heapify_Osimps_I2_J]) ).
thf(c_0_10,negated_conjecture,
~ ( is_heap_a @ ( heapIm970322378pify_a @ ( t_a @ v @ l @ r ) ) ),
inference(fof_nnf,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
( ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) ) )
| ~ ( is_heap_a @ ( heapIm970322378pify_a @ l ) )
| ~ ( is_heap_a @ ( heapIm970322378pify_a @ r ) ) ),
inference(cn,[status(thm)],[c_0_8]) ).
thf(c_0_12,plain,
! [X1: a,X2: tree_a,X3: tree_a] :
( ( heapIm970322378pify_a @ ( t_a @ X1 @ X2 @ X3 ) )
= ( heapIm1091024090Down_a @ ( t_a @ X1 @ ( heapIm970322378pify_a @ X2 ) @ ( heapIm970322378pify_a @ X3 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,plain,
is_heap_a @ ( heapIm970322378pify_a @ l ),
inference(split_conjunct,[status(thm)],[fact_1_T_Ohyps_I1_J]) ).
thf(c_0_14,plain,
is_heap_a @ ( heapIm970322378pify_a @ r ),
inference(split_conjunct,[status(thm)],[fact_0_T_Ohyps_I2_J]) ).
thf(c_0_15,negated_conjecture,
~ ( is_heap_a @ ( heapIm970322378pify_a @ ( t_a @ v @ l @ r ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_16,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14])]),c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP069^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n005.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 19:46:16 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.24 Running higher-order theorem proving
% 0.21/0.27 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.AcUqD7cEQS/E---3.1_2121073.p
% 0.21/0.31 % Version: 3.5.1-ho
% 0.21/0.31 % Preprocessing class: HSLSSMSSSSSCSFA.
% 0.21/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.31 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.31 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.31 % Starting new_bool_2 with 300s (1) cores
% 0.21/0.31 % Starting new_bool_9 with 300s (1) cores
% 0.21/0.31 % new_bool_9 with pid 2121090 completed with status 0
% 0.21/0.31 % Result found by new_bool_9
% 0.21/0.31 % Preprocessing class: HSLSSMSSSSSCSFA.
% 0.21/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.31 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.31 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.31 % Starting new_bool_2 with 300s (1) cores
% 0.21/0.31 % Starting new_bool_9 with 300s (1) cores
% 0.21/0.31 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1,,2,20000,1.0))
% 0.21/0.31 % SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 0.21/0.31 % Search class: HGUSM-FFMS31-MSFFFSBN
% 0.21/0.31 % partial match(2): HGUSM-FFMS31-DSFFFFBN
% 0.21/0.31 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.31 % Starting SubtermCWHack with 28s (1) cores
% 0.21/0.31 % SubtermCWHack with pid 2121091 completed with status 0
% 0.21/0.31 % Result found by SubtermCWHack
% 0.21/0.31 % Preprocessing class: HSLSSMSSSSSCSFA.
% 0.21/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.31 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.31 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.31 % Starting new_bool_2 with 300s (1) cores
% 0.21/0.31 % Starting new_bool_9 with 300s (1) cores
% 0.21/0.31 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1,,2,20000,1.0))
% 0.21/0.31 % SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 0.21/0.31 % Search class: HGUSM-FFMS31-MSFFFSBN
% 0.21/0.31 % partial match(2): HGUSM-FFMS31-DSFFFFBN
% 0.21/0.31 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.31 % Starting SubtermCWHack with 28s (1) cores
% 0.21/0.31 % Preprocessing time : 0.002 s
% 0.21/0.31
% 0.21/0.31 % Proof found!
% 0.21/0.31 % SZS status Theorem
% 0.21/0.31 % SZS output start CNFRefutation
% See solution above
% 0.21/0.31 % Parsed axioms : 192
% 0.21/0.31 % Removed by relevancy pruning/SinE : 174
% 0.21/0.31 % Initial clauses : 24
% 0.21/0.31 % Removed in clause preprocessing : 1
% 0.21/0.31 % Initial clauses in saturation : 23
% 0.21/0.31 % Processed clauses : 55
% 0.21/0.31 % ...of these trivial : 0
% 0.21/0.31 % ...subsumed : 15
% 0.21/0.31 % ...remaining for further processing : 39
% 0.21/0.31 % Other redundant clauses eliminated : 3
% 0.21/0.31 % Clauses deleted for lack of memory : 0
% 0.21/0.31 % Backward-subsumed : 2
% 0.21/0.31 % Backward-rewritten : 0
% 0.21/0.31 % Generated clauses : 67
% 0.21/0.31 % ...of the previous two non-redundant : 58
% 0.21/0.31 % ...aggressively subsumed : 0
% 0.21/0.31 % Contextual simplify-reflections : 0
% 0.21/0.31 % Paramodulations : 60
% 0.21/0.31 % Factorizations : 4
% 0.21/0.31 % NegExts : 0
% 0.21/0.31 % Equation resolutions : 3
% 0.21/0.31 % Disequality decompositions : 0
% 0.21/0.31 % Total rewrite steps : 11
% 0.21/0.31 % ...of those cached : 0
% 0.21/0.31 % Propositional unsat checks : 0
% 0.21/0.31 % Propositional check models : 0
% 0.21/0.31 % Propositional check unsatisfiable : 0
% 0.21/0.31 % Propositional clauses : 0
% 0.21/0.31 % Propositional clauses after purity: 0
% 0.21/0.31 % Propositional unsat core size : 0
% 0.21/0.31 % Propositional preprocessing time : 0.000
% 0.21/0.31 % Propositional encoding time : 0.000
% 0.21/0.31 % Propositional solver time : 0.000
% 0.21/0.31 % Success case prop preproc time : 0.000
% 0.21/0.31 % Success case prop encoding time : 0.000
% 0.21/0.31 % Success case prop solver time : 0.000
% 0.21/0.31 % Current number of processed clauses : 34
% 0.21/0.31 % Positive orientable unit clauses : 14
% 0.21/0.31 % Positive unorientable unit clauses: 0
% 0.21/0.31 % Negative unit clauses : 2
% 0.21/0.31 % Non-unit-clauses : 18
% 0.21/0.31 % Current number of unprocessed clauses: 24
% 0.21/0.31 % ...number of literals in the above : 57
% 0.21/0.31 % Current number of archived formulas : 0
% 0.21/0.31 % Current number of archived clauses : 5
% 0.21/0.31 % Clause-clause subsumption calls (NU) : 65
% 0.21/0.31 % Rec. Clause-clause subsumption calls : 59
% 0.21/0.31 % Non-unit clause-clause subsumptions : 15
% 0.21/0.31 % Unit Clause-clause subsumption calls : 2
% 0.21/0.31 % Rewrite failures with RHS unbound : 0
% 0.21/0.31 % BW rewrite match attempts : 2
% 0.21/0.31 % BW rewrite match successes : 2
% 0.21/0.31 % Condensation attempts : 0
% 0.21/0.31 % Condensation successes : 0
% 0.21/0.31 % Termbank termtop insertions : 5560
% 0.21/0.31 % Search garbage collected termcells : 1966
% 0.21/0.31
% 0.21/0.31 % -------------------------------------------------
% 0.21/0.31 % User time : 0.010 s
% 0.21/0.31 % System time : 0.002 s
% 0.21/0.31 % Total time : 0.012 s
% 0.21/0.31 % Maximum resident set size: 3996 pages
% 0.21/0.31
% 0.21/0.31 % -------------------------------------------------
% 0.21/0.31 % User time : 0.020 s
% 0.21/0.31 % System time : 0.006 s
% 0.21/0.31 % Total time : 0.025 s
% 0.21/0.31 % Maximum resident set size: 5120 pages
% 0.21/0.31 % E exiting
%------------------------------------------------------------------------------