%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM817^5 : 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 : 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 08:17:10 AM UTC 2026
% Result : Theorem 0.24s 0.29s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 29 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 137 ( 21 ~; 11 |; 11 &; 78 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 7 ^; 33 !; 3 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
c0: $i ).
thf(decl_24,type,
cS: $i > $i ).
thf(decl_25,type,
cEVEN1: $i > $o ).
thf(decl_26,type,
cODD1: $i > $o ).
thf(decl_27,type,
esk1_2: $i > ( $i > $o ) > $i ).
thf(decl_28,type,
esk1_1: $i > $i ).
thf(cODD1_def,axiom,
( cODD1
= ( ^ [X1: $i] :
~ ( cEVEN1 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.dwlwjhVEuN/E---3.1_1626001.p',cODD1_def) ).
thf(cEVEN1_def,axiom,
( cEVEN1
= ( ^ [X1: $i] :
! [X2: $i > $o] :
( ( ( X2 @ c0 )
& ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( cS @ ( cS @ X3 ) ) ) ) )
=> ( X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.dwlwjhVEuN/E---3.1_1626001.p',cEVEN1_def) ).
thf(cTHM405,conjecture,
( ( ! [X4: $i] :
( ( cS @ X4 )
!= c0 )
& ! [X5: $i,X6: $i] :
( ( ( cS @ X5 )
= ( cS @ X6 ) )
=> ( X5 = X6 ) ) )
=> ? [X1: $i] : ( cODD1 @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.dwlwjhVEuN/E---3.1_1626001.p',cTHM405) ).
thf(c_0_3,plain,
( cODD1
= ( ^ [Z0: $i] :
~ ! [X11: $i > $o] :
( ( ( X11 @ c0 )
& ! [X12: $i] :
( ( X11 @ X12 )
=> ( X11 @ ( cS @ ( cS @ X12 ) ) ) ) )
=> ( X11 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[cODD1_def]) ).
thf(c_0_4,plain,
( cEVEN1
= ( ^ [Z0: $i] :
! [X2: $i > $o] :
( ( ( X2 @ c0 )
& ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( cS @ ( cS @ X3 ) ) ) ) )
=> ( X2 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[cEVEN1_def]) ).
thf(c_0_5,negated_conjecture,
~ ( ( ! [X4: $i] :
( ( cS @ X4 )
!= c0 )
& ! [X5: $i,X6: $i] :
( ( ( cS @ X5 )
= ( cS @ X6 ) )
=> ( X5 = X6 ) ) )
=> ? [X1: $i] : ( cODD1 @ X1 ) ),
inference(assume_negation,[status(cth)],[cTHM405]) ).
thf(c_0_6,plain,
( cODD1
= ( ^ [Z0: $i] :
~ ! [X11: $i > $o] :
( ( ( X11 @ c0 )
& ! [X12: $i] :
( ( X11 @ X12 )
=> ( X11 @ ( cS @ ( cS @ X12 ) ) ) ) )
=> ( X11 @ Z0 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_3,c_0_4]) ).
thf(c_0_7,negated_conjecture,
~ ( ( ! [X4: $i] :
( ( cS @ X4 )
!= c0 )
& ! [X5: $i,X6: $i] :
( ( ( cS @ X5 )
= ( cS @ X6 ) )
=> ( X5 = X6 ) ) )
=> ? [X1: $i] :
~ ! [X13: $i > $o] :
( ( ( X13 @ c0 )
& ! [X14: $i] :
( ( X13 @ X14 )
=> ( X13 @ ( cS @ ( cS @ X14 ) ) ) ) )
=> ( X13 @ X1 ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[c_0_5,c_0_6])]) ).
thf(c_0_8,negated_conjecture,
! [X15: $i,X16: $i,X17: $i,X18: $i,X19: $i > $o] :
( ( ( cS @ X15 )
!= c0 )
& ( ( ( cS @ X16 )
!= ( cS @ X17 ) )
| ( X16 = X17 ) )
& ( ( X19 @ ( esk1_2 @ X18 @ X19 ) )
| ~ ( X19 @ c0 )
| ( X19 @ X18 ) )
& ( ~ ( X19 @ ( cS @ ( cS @ ( esk1_2 @ X18 @ X19 ) ) ) )
| ~ ( X19 @ c0 )
| ( X19 @ X18 ) ) ),
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_7])])])])])]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i,X3: $i] :
( ( X1 = X3 )
| ( ( cS @ X1 )
!= ( cS @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i,X2: $i > $o] :
( ( X2 @ X1 )
| ~ ( X2 @ ( cS @ ( cS @ ( esk1_2 @ X1 @ X2 ) ) ) )
| ~ ( X2 @ c0 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i] :
( ( esk1_1 @ ( cS @ X1 ) )
= X1 ),
inference(recognize_injectivity,[status(thm)],[c_0_9]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i] :
( ( ( cS
@ ( cS
@ ( esk1_2 @ X1
@ ^ [Z0: $i] : ( Z0 != X1 ) ) ) )
= X1 )
| ( c0 = X1 ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_10]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i] :
( ( cS @ X1 )
!= c0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i] :
( ( ( cS
@ ( esk1_2 @ X1
@ ^ [Z0: $i] : ( Z0 != X1 ) ) )
= ( esk1_1 @ X1 ) )
| ( c0 = X1 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i] :
( ( c0 = X1 )
| ( ( esk1_1 @ X1 )
!= c0 ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_16,negated_conjecture,
$false,
inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_11]),c_0_13])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM817^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n005.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 13:02:31 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.25 Running higher-order theorem proving
% 0.08/0.26 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.dwlwjhVEuN/E---3.1_1626001.p
% 0.24/0.29 % Version: 3.5.1-ho
% 0.24/0.29 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.24/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.29 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.24/0.29 % Starting post_as_ho5 with 300s (1) cores
% 0.24/0.29 % Starting sh4l with 300s (1) cores
% 0.24/0.29 % Starting ho_unfolding_2 with 300s (1) cores
% 0.24/0.29 % ho_unfolding_3 with pid 1626014 completed with status 0
% 0.24/0.29 % Result found by ho_unfolding_3
% 0.24/0.29 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.24/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.29 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.24/0.29 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.29 % No SInE strategy applied
% 0.24/0.29 % Search class: HGUSF-FFSF21-MSFFMMBN
% 0.24/0.29 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.29 % Starting SubtermCWHack with 151s (1) cores
% 0.24/0.29 % Starting ho_unfolding_3 with 901s (1) cores
% 0.24/0.29 % Starting ehoh_best_sine_rwall with 151s (1) cores
% 0.24/0.29 % Starting sh5l with 151s (1) cores
% 0.24/0.29 % Starting new_bool_3 with 146s (1) cores
% 0.24/0.29 % SubtermCWHack with pid 1626018 completed with status 10
% 0.24/0.29 % ho_unfolding_3 with pid 1626020 completed with status 0
% 0.24/0.29 % Result found by ho_unfolding_3
% 0.24/0.29 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.24/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.29 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.24/0.29 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.29 % No SInE strategy applied
% 0.24/0.29 % Search class: HGUSF-FFSF21-MSFFMMBN
% 0.24/0.29 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.29 % Starting SubtermCWHack with 151s (1) cores
% 0.24/0.29 % Starting ho_unfolding_3 with 901s (1) cores
% 0.24/0.29 % Preprocessing time : 0.001 s
% 0.24/0.29 % Presaturation interreduction done
% 0.24/0.29
% 0.24/0.29 % Proof found!
% 0.24/0.29 % SZS status Theorem
% 0.24/0.29 % SZS output start CNFRefutation
% See solution above
% 0.24/0.29 % Parsed axioms : 7
% 0.24/0.29 % Removed by relevancy pruning/SinE : 0
% 0.24/0.29 % Initial clauses : 8
% 0.24/0.29 % Removed in clause preprocessing : 4
% 0.24/0.29 % Initial clauses in saturation : 4
% 0.24/0.29 % Processed clauses : 18
% 0.24/0.29 % ...of these trivial : 0
% 0.24/0.29 % ...subsumed : 2
% 0.24/0.29 % ...remaining for further processing : 16
% 0.24/0.29 % Other redundant clauses eliminated : 4
% 0.24/0.29 % Clauses deleted for lack of memory : 0
% 0.24/0.29 % Backward-subsumed : 0
% 0.24/0.29 % Backward-rewritten : 0
% 0.24/0.29 % Generated clauses : 29
% 0.24/0.29 % ...of the previous two non-redundant : 19
% 0.24/0.29 % ...aggressively subsumed : 0
% 0.24/0.29 % Contextual simplify-reflections : 0
% 0.24/0.29 % Paramodulations : 13
% 0.24/0.29 % Factorizations : 0
% 0.24/0.29 % NegExts : 1
% 0.24/0.29 % Equation resolutions : 5
% 0.24/0.29 % Disequality decompositions : 0
% 0.24/0.29 % Total rewrite steps : 0
% 0.24/0.29 % ...of those cached : 0
% 0.24/0.29 % Propositional unsat checks : 0
% 0.24/0.29 % Propositional check models : 0
% 0.24/0.29 % Propositional check unsatisfiable : 0
% 0.24/0.29 % Propositional clauses : 0
% 0.24/0.29 % Propositional clauses after purity: 0
% 0.24/0.29 % Propositional unsat core size : 0
% 0.24/0.29 % Propositional preprocessing time : 0.000
% 0.24/0.29 % Propositional encoding time : 0.000
% 0.24/0.29 % Propositional solver time : 0.000
% 0.24/0.29 % Success case prop preproc time : 0.000
% 0.24/0.29 % Success case prop encoding time : 0.000
% 0.24/0.29 % Success case prop solver time : 0.000
% 0.24/0.29 % Current number of processed clauses : 11
% 0.24/0.29 % Positive orientable unit clauses : 1
% 0.24/0.29 % Positive unorientable unit clauses: 0
% 0.24/0.29 % Negative unit clauses : 1
% 0.24/0.29 % Non-unit-clauses : 9
% 0.24/0.29 % Current number of unprocessed clauses: 9
% 0.24/0.29 % ...number of literals in the above : 22
% 0.24/0.29 % Current number of archived formulas : 0
% 0.24/0.29 % Current number of archived clauses : 5
% 0.24/0.29 % Clause-clause subsumption calls (NU) : 13
% 0.24/0.29 % Rec. Clause-clause subsumption calls : 13
% 0.24/0.29 % Non-unit clause-clause subsumptions : 0
% 0.24/0.29 % Unit Clause-clause subsumption calls : 0
% 0.24/0.29 % Rewrite failures with RHS unbound : 0
% 0.24/0.29 % BW rewrite match attempts : 0
% 0.24/0.29 % BW rewrite match successes : 0
% 0.24/0.29 % Condensation attempts : 18
% 0.24/0.29 % Condensation successes : 0
% 0.24/0.29 % Termbank termtop insertions : 1083
% 0.24/0.29 % Search garbage collected termcells : 212
% 0.24/0.29
% 0.24/0.29 % -------------------------------------------------
% 0.24/0.29 % User time : 0.006 s
% 0.24/0.29 % System time : 0.004 s
% 0.24/0.29 % Total time : 0.010 s
% 0.24/0.29 % Maximum resident set size: 3580 pages
% 0.24/0.29
% 0.24/0.29 % -------------------------------------------------
% 0.24/0.29 % User time : 0.010 s
% 0.24/0.29 % System time : 0.012 s
% 0.24/0.29 % Total time : 0.022 s
% 0.24/0.29 % Maximum resident set size: 4608 pages
% 0.24/0.29 % E exiting
%------------------------------------------------------------------------------