%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : PUZ108^5 : 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 : n017.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 08:20:35 AM UTC 2026
% Result : Theorem 0.07s 0.27s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 2 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 121 ( 13 ~; 10 |; 8 &; 79 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 5 ^; 19 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
s: $i > $i ).
thf(decl_24,type,
cCKB_E2: $i > $i > $o ).
thf(decl_25,type,
esk1_0: $i ).
thf(decl_26,type,
esk2_0: $i ).
thf(decl_27,type,
esk3_1: ( $i > $o ) > $i ).
thf(decl_28,type,
epred1_0: $i > $o ).
thf(cCKB_L35000,conjecture,
! [X1: $i,X2: $i] :
( ( cCKB_E2 @ X1 @ X2 )
=> ( cCKB_E2 @ ( s @ X1 ) @ ( s @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YlTAWUP4qf/E---3.1_317066.p',cCKB_L35000) ).
thf(cCKB_E2_def,axiom,
( cCKB_E2
= ( ^ [X1: $i,X2: $i] :
! [X3: $i > $o] :
( ( ( X3 @ X1 )
& ! [X4: $i] :
( ( X3 @ X4 )
=> ( X3 @ ( s @ ( s @ X4 ) ) ) ) )
=> ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YlTAWUP4qf/E---3.1_317066.p',cCKB_E2_def) ).
thf(c_0_2,negated_conjecture,
~ ! [X1: $i,X2: $i] :
( ( cCKB_E2 @ X1 @ X2 )
=> ( cCKB_E2 @ ( s @ X1 ) @ ( s @ X2 ) ) ),
inference(assume_negation,[status(cth)],[cCKB_L35000]) ).
thf(c_0_3,plain,
( cCKB_E2
= ( ^ [Z0: $i,Z1: $i] :
! [X3: $i > $o] :
( ( ( X3 @ Z0 )
& ! [X4: $i] :
( ( X3 @ X4 )
=> ( X3 @ ( s @ ( s @ X4 ) ) ) ) )
=> ( X3 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[cCKB_E2_def]) ).
thf(c_0_4,negated_conjecture,
~ ! [X1: $i,X2: $i] :
( ! [X7: $i > $o] :
( ( ( X7 @ X1 )
& ! [X8: $i] :
( ( X7 @ X8 )
=> ( X7 @ ( s @ ( s @ X8 ) ) ) ) )
=> ( X7 @ X2 ) )
=> ! [X9: $i > $o] :
( ( ( X9 @ ( s @ X1 ) )
& ! [X10: $i] :
( ( X9 @ X10 )
=> ( X9 @ ( s @ ( s @ X10 ) ) ) ) )
=> ( X9 @ ( s @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_2,c_0_3]) ).
thf(c_0_5,negated_conjecture,
! [X13: $i > $o,X16: $i] :
( ( ( X13 @ ( esk3_1 @ X13 ) )
| ~ ( X13 @ esk1_0 )
| ( X13 @ esk2_0 ) )
& ( ~ ( X13 @ ( s @ ( s @ ( esk3_1 @ X13 ) ) ) )
| ~ ( X13 @ esk1_0 )
| ( X13 @ esk2_0 ) )
& ( epred1_0 @ ( s @ esk1_0 ) )
& ( ~ ( epred1_0 @ X16 )
| ( epred1_0 @ ( s @ ( s @ X16 ) ) ) )
& ~ ( epred1_0 @ ( s @ esk2_0 ) ) ),
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_4])])])])])]) ).
thf(c_0_6,negated_conjecture,
! [X3: $i > $o] :
( ( X3 @ esk2_0 )
| ~ ( X3 @ ( s @ ( s @ ( esk3_1 @ X3 ) ) ) )
| ~ ( X3 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_7,negated_conjecture,
! [X1: $i] :
( ( epred1_0 @ ( s @ ( s @ X1 ) ) )
| ~ ( epred1_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
epred1_0 @ ( s @ esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_9,negated_conjecture,
~ ( epred1_0 @ ( s @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_10,negated_conjecture,
~ ( epred1_0
@ ( s
@ ( esk3_1
@ ^ [Z0: $i] : ( epred1_0 @ ( s @ Z0 ) ) ) ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8])]),c_0_9]) ).
thf(c_0_11,negated_conjecture,
! [X3: $i > $o] :
( ( X3 @ ( esk3_1 @ X3 ) )
| ( X3 @ esk2_0 )
| ~ ( X3 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_12,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_8])]),c_0_9]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ108^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 % Computer : n017.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Sep 29 13:19:22 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.24 Running higher-order theorem proving
% 0.07/0.25 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.YlTAWUP4qf/E---3.1_317066.p
% 0.07/0.27 % Version: 3.5.1-ho
% 0.07/0.27 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.07/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.27 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.07/0.27 % Starting post_as_ho5 with 300s (1) cores
% 0.07/0.27 % Starting sh4l with 300s (1) cores
% 0.07/0.27 % Starting ho_unfolding_2 with 300s (1) cores
% 0.07/0.27 % ho_unfolding_3 with pid 317079 completed with status 0
% 0.07/0.27 % Result found by ho_unfolding_3
% 0.07/0.27 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.07/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.27 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.07/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.27 % No SInE strategy applied
% 0.07/0.27 % Search class: HGUNF-FFSF11-MSFFMSBN
% 0.07/0.27 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.07/0.27 % Starting SubtermCWHack with 136s (1) cores
% 0.07/0.27 % Starting ho_unfolding_3 with 151s (1) cores
% 0.07/0.27 % Starting new_ho_8 with 136s (1) cores
% 0.07/0.27 % Starting new_ho_4 with 136s (1) cores
% 0.07/0.27 % Starting post_as_ho5 with 136s (1) cores
% 0.07/0.27 % SubtermCWHack with pid 317083 completed with status 10
% 0.07/0.27 % Starting lpo8_s with 136s (1) cores
% 0.07/0.27 % lpo8_s with pid 317091 completed with status 10
% 0.07/0.27 % Starting new_ho_10_unif with 669s (1) cores
% 0.07/0.27 % ho_unfolding_3 with pid 317084 completed with status 10
% 0.07/0.27 % new_ho_4 with pid 317086 completed with status 0
% 0.07/0.27 % Result found by new_ho_4
% 0.07/0.27 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.07/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.27 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.07/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.27 % No SInE strategy applied
% 0.07/0.27 % Search class: HGUNF-FFSF11-MSFFMSBN
% 0.07/0.27 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.07/0.27 % Starting SubtermCWHack with 136s (1) cores
% 0.07/0.27 % Starting ho_unfolding_3 with 151s (1) cores
% 0.07/0.27 % Starting new_ho_8 with 136s (1) cores
% 0.07/0.27 % Starting new_ho_4 with 136s (1) cores
% 0.07/0.27 % Preprocessing time : 0.001 s
% 0.07/0.27 % Presaturation interreduction done
% 0.07/0.27
% 0.07/0.27 % Proof found!
% 0.07/0.27 % SZS status Theorem
% 0.07/0.27 % SZS output start CNFRefutation
% See solution above
% 0.07/0.27 % Parsed axioms : 4
% 0.07/0.27 % Removed by relevancy pruning/SinE : 0
% 0.07/0.27 % Initial clauses : 7
% 0.07/0.27 % Removed in clause preprocessing : 2
% 0.07/0.27 % Initial clauses in saturation : 5
% 0.07/0.27 % Processed clauses : 11
% 0.07/0.27 % ...of these trivial : 0
% 0.07/0.27 % ...subsumed : 0
% 0.07/0.27 % ...remaining for further processing : 11
% 0.07/0.27 % Other redundant clauses eliminated : 0
% 0.07/0.27 % Clauses deleted for lack of memory : 0
% 0.07/0.27 % Backward-subsumed : 0
% 0.07/0.27 % Backward-rewritten : 0
% 0.07/0.27 % Generated clauses : 11
% 0.07/0.27 % ...of the previous two non-redundant : 3
% 0.07/0.27 % ...aggressively subsumed : 0
% 0.07/0.27 % Contextual simplify-reflections : 0
% 0.07/0.27 % Paramodulations : 8
% 0.07/0.27 % Factorizations : 0
% 0.07/0.27 % NegExts : 0
% 0.07/0.27 % Equation resolutions : 3
% 0.07/0.27 % Disequality decompositions : 0
% 0.07/0.27 % Total rewrite steps : 6
% 0.07/0.27 % ...of those cached : 5
% 0.07/0.27 % Propositional unsat checks : 0
% 0.07/0.27 % Propositional check models : 0
% 0.07/0.27 % Propositional check unsatisfiable : 0
% 0.07/0.27 % Propositional clauses : 0
% 0.07/0.27 % Propositional clauses after purity: 0
% 0.07/0.27 % Propositional unsat core size : 0
% 0.07/0.27 % Propositional preprocessing time : 0.000
% 0.07/0.27 % Propositional encoding time : 0.000
% 0.07/0.27 % Propositional solver time : 0.000
% 0.07/0.27 % Success case prop preproc time : 0.000
% 0.07/0.27 % Success case prop encoding time : 0.000
% 0.07/0.27 % Success case prop solver time : 0.000
% 0.07/0.27 % Current number of processed clauses : 6
% 0.07/0.27 % Positive orientable unit clauses : 1
% 0.07/0.27 % Positive unorientable unit clauses: 0
% 0.07/0.27 % Negative unit clauses : 2
% 0.07/0.27 % Non-unit-clauses : 3
% 0.07/0.27 % Current number of unprocessed clauses: 2
% 0.07/0.27 % ...number of literals in the above : 6
% 0.07/0.27 % Current number of archived formulas : 0
% 0.07/0.27 % Current number of archived clauses : 5
% 0.07/0.27 % Clause-clause subsumption calls (NU) : 0
% 0.07/0.27 % Rec. Clause-clause subsumption calls : 0
% 0.07/0.27 % Non-unit clause-clause subsumptions : 0
% 0.07/0.27 % Unit Clause-clause subsumption calls : 0
% 0.07/0.27 % Rewrite failures with RHS unbound : 0
% 0.07/0.27 % BW rewrite match attempts : 0
% 0.07/0.27 % BW rewrite match successes : 0
% 0.07/0.27 % Condensation attempts : 0
% 0.07/0.27 % Condensation successes : 0
% 0.07/0.27 % Termbank termtop insertions : 1772
% 0.07/0.27 % Search garbage collected termcells : 240
% 0.07/0.27
% 0.07/0.27 % -------------------------------------------------
% 0.07/0.27 % User time : 0.010 s
% 0.07/0.27 % System time : 0.005 s
% 0.07/0.27 % Total time : 0.015 s
% 0.07/0.27 % Maximum resident set size: 3632 pages
% 0.07/0.27
% 0.07/0.27 % -------------------------------------------------
% 0.07/0.27 % User time : 0.017 s
% 0.07/0.27 % System time : 0.011 s
% 0.07/0.27 % Total time : 0.028 s
% 0.07/0.27 % Maximum resident set size: 4864 pages
% 0.07/0.27 % E exiting
%------------------------------------------------------------------------------