%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : PUZ110^5 : 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 : n016.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 0.10s 0.23s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 2 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 216 ( 18 ~; 14 |; 13 &; 160 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 4 ^; 27 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
c1: $i ).
thf(decl_24,type,
s: $i > $i ).
thf(decl_25,type,
cCKB6_BLACK: $i > $i > $o ).
thf(decl_26,type,
esk1_0: $i ).
thf(decl_27,type,
esk2_0: $i ).
thf(decl_28,type,
esk3_1: ( $i > $i > $o ) > $i ).
thf(decl_29,type,
esk4_1: ( $i > $i > $o ) > $i ).
thf(decl_30,type,
epred1_0: $i > $i > $o ).
thf(cCKB6_L8000,conjecture,
! [X4: $i,X5: $i] :
( ( cCKB6_BLACK @ X4 @ X5 )
=> ( cCKB6_BLACK @ ( s @ ( s @ X4 ) ) @ X5 ) ),
file('/export/starexec/sandbox2/tmp/tmp.Z25tYgBGpp/E---3.1_337473.p',cCKB6_L8000) ).
thf(cCKB6_BLACK_def,axiom,
( cCKB6_BLACK
= ( ^ [X1: $i,X2: $i] :
! [X3: $i > $i > $o] :
( ( ( X3 @ c1 @ c1 )
& ! [X4: $i,X5: $i] :
( ( X3 @ X4 @ X5 )
=> ( ( X3 @ ( s @ ( s @ X4 ) ) @ X5 )
& ( X3 @ ( s @ X4 ) @ ( s @ X5 ) ) ) ) )
=> ( X3 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Z25tYgBGpp/E---3.1_337473.p',cCKB6_BLACK_def) ).
thf(c_0_2,negated_conjecture,
~ ! [X4: $i,X5: $i] :
( ( cCKB6_BLACK @ X4 @ X5 )
=> ( cCKB6_BLACK @ ( s @ ( s @ X4 ) ) @ X5 ) ),
inference(assume_negation,[status(cth)],[cCKB6_L8000]) ).
thf(c_0_3,plain,
( cCKB6_BLACK
= ( ^ [Z0: $i,Z1: $i] :
! [X3: $i > $i > $o] :
( ( ( X3 @ c1 @ c1 )
& ! [X4: $i,X5: $i] :
( ( X3 @ X4 @ X5 )
=> ( ( X3 @ ( s @ ( s @ X4 ) ) @ X5 )
& ( X3 @ ( s @ X4 ) @ ( s @ X5 ) ) ) ) )
=> ( X3 @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[cCKB6_BLACK_def]) ).
thf(c_0_4,negated_conjecture,
~ ! [X4: $i,X5: $i] :
( ! [X8: $i > $i > $o] :
( ( ( X8 @ c1 @ c1 )
& ! [X9: $i,X10: $i] :
( ( X8 @ X9 @ X10 )
=> ( ( X8 @ ( s @ ( s @ X9 ) ) @ X10 )
& ( X8 @ ( s @ X9 ) @ ( s @ X10 ) ) ) ) )
=> ( X8 @ X4 @ X5 ) )
=> ! [X11: $i > $i > $o] :
( ( ( X11 @ c1 @ c1 )
& ! [X12: $i,X13: $i] :
( ( X11 @ X12 @ X13 )
=> ( ( X11 @ ( s @ ( s @ X12 ) ) @ X13 )
& ( X11 @ ( s @ X12 ) @ ( s @ X13 ) ) ) ) )
=> ( X11 @ ( s @ ( s @ X4 ) ) @ X5 ) ) ),
inference(apply_def,[status(thm)],[c_0_2,c_0_3]) ).
thf(c_0_5,negated_conjecture,
! [X16: $i > $i > $o,X20: $i,X21: $i] :
( ( ( X16 @ ( esk3_1 @ X16 ) @ ( esk4_1 @ X16 ) )
| ~ ( X16 @ c1 @ c1 )
| ( X16 @ esk1_0 @ esk2_0 ) )
& ( ~ ( X16 @ ( s @ ( s @ ( esk3_1 @ X16 ) ) ) @ ( esk4_1 @ X16 ) )
| ~ ( X16 @ ( s @ ( esk3_1 @ X16 ) ) @ ( s @ ( esk4_1 @ X16 ) ) )
| ~ ( X16 @ c1 @ c1 )
| ( X16 @ esk1_0 @ esk2_0 ) )
& ( epred1_0 @ c1 @ c1 )
& ( ( epred1_0 @ ( s @ ( s @ X20 ) ) @ X21 )
| ~ ( epred1_0 @ X20 @ X21 ) )
& ( ( epred1_0 @ ( s @ X20 ) @ ( s @ X21 ) )
| ~ ( epred1_0 @ X20 @ X21 ) )
& ~ ( epred1_0 @ ( s @ ( s @ esk1_0 ) ) @ 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,
~ ( epred1_0 @ ( s @ ( s @ esk1_0 ) ) @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_7,negated_conjecture,
! [X1: $i,X2: $i] :
( ( epred1_0 @ ( s @ ( s @ X1 ) ) @ X2 )
| ~ ( epred1_0 @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
! [X3: $i > $i > $o] :
( ( X3 @ esk1_0 @ esk2_0 )
| ~ ( X3 @ ( s @ ( s @ ( esk3_1 @ X3 ) ) ) @ ( esk4_1 @ X3 ) )
| ~ ( X3 @ ( s @ ( esk3_1 @ X3 ) ) @ ( s @ ( esk4_1 @ X3 ) ) )
| ~ ( X3 @ c1 @ c1 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_9,negated_conjecture,
epred1_0 @ c1 @ c1,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_10,negated_conjecture,
~ ( epred1_0 @ esk1_0 @ esk2_0 ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X2: $i] :
( ( epred1_0 @ ( s @ X1 ) @ ( s @ X2 ) )
| ~ ( epred1_0 @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_12,negated_conjecture,
~ ( epred1_0 @ ( esk3_1 @ epred1_0 ) @ ( esk4_1 @ epred1_0 ) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_7]),c_0_9])]),c_0_10]),c_0_11]) ).
thf(c_0_13,negated_conjecture,
! [X3: $i > $i > $o] :
( ( X3 @ ( esk3_1 @ X3 ) @ ( esk4_1 @ X3 ) )
| ( X3 @ esk1_0 @ esk2_0 )
| ~ ( X3 @ c1 @ c1 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_14,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_9])]),c_0_10]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ110^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.16 % Computer : n016.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Sep 29 13:29:19 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.10/0.21 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.Z25tYgBGpp/E---3.1_337473.p
% 0.10/0.23 % Version: 3.5.1-ho
% 0.10/0.23 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.10/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.23 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.10/0.23 % Starting post_as_ho5 with 300s (1) cores
% 0.10/0.23 % Starting sh4l with 300s (1) cores
% 0.10/0.23 % Starting ho_unfolding_2 with 300s (1) cores
% 0.10/0.23 % sh4l with pid 337488 completed with status 0
% 0.10/0.23 % Result found by sh4l
% 0.10/0.23 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.10/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.23 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.10/0.23 % Starting post_as_ho5 with 300s (1) cores
% 0.10/0.23 % Starting sh4l with 300s (1) cores
% 0.10/0.23 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.23 % No SInE strategy applied
% 0.10/0.23 % Search class: HGUNF-FFSF11-MSFFMSBN
% 0.10/0.23 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.23 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.23 % SubtermCWHack with pid 337493 completed with status 0
% 0.10/0.23 % Result found by SubtermCWHack
% 0.10/0.23 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.10/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.23 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.10/0.23 % Starting post_as_ho5 with 300s (1) cores
% 0.10/0.23 % Starting sh4l with 300s (1) cores
% 0.10/0.23 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.23 % No SInE strategy applied
% 0.10/0.23 % Search class: HGUNF-FFSF11-MSFFMSBN
% 0.10/0.23 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.23 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.23 % Preprocessing time : 0.001 s
% 0.10/0.23
% 0.10/0.23 % Proof found!
% 0.10/0.23 % SZS status Theorem
% 0.10/0.23 % SZS output start CNFRefutation
% See solution above
% 0.10/0.23 % Parsed axioms : 5
% 0.10/0.23 % Removed by relevancy pruning/SinE : 0
% 0.10/0.23 % Initial clauses : 9
% 0.10/0.23 % Removed in clause preprocessing : 3
% 0.10/0.23 % Initial clauses in saturation : 6
% 0.10/0.23 % Processed clauses : 8
% 0.10/0.23 % ...of these trivial : 0
% 0.10/0.23 % ...subsumed : 0
% 0.10/0.23 % ...remaining for further processing : 8
% 0.10/0.23 % Other redundant clauses eliminated : 0
% 0.10/0.23 % Clauses deleted for lack of memory : 0
% 0.10/0.23 % Backward-subsumed : 0
% 0.10/0.23 % Backward-rewritten : 0
% 0.10/0.23 % Generated clauses : 3
% 0.10/0.23 % ...of the previous two non-redundant : 2
% 0.10/0.23 % ...aggressively subsumed : 0
% 0.10/0.23 % Contextual simplify-reflections : 1
% 0.10/0.23 % Paramodulations : 3
% 0.10/0.23 % Factorizations : 0
% 0.10/0.23 % NegExts : 0
% 0.10/0.23 % Equation resolutions : 0
% 0.10/0.23 % Disequality decompositions : 0
% 0.10/0.23 % Total rewrite steps : 2
% 0.10/0.23 % ...of those cached : 1
% 0.10/0.23 % Propositional unsat checks : 0
% 0.10/0.23 % Propositional check models : 0
% 0.10/0.23 % Propositional check unsatisfiable : 0
% 0.10/0.23 % Propositional clauses : 0
% 0.10/0.23 % Propositional clauses after purity: 0
% 0.10/0.23 % Propositional unsat core size : 0
% 0.10/0.23 % Propositional preprocessing time : 0.000
% 0.10/0.23 % Propositional encoding time : 0.000
% 0.10/0.23 % Propositional solver time : 0.000
% 0.10/0.23 % Success case prop preproc time : 0.000
% 0.10/0.23 % Success case prop encoding time : 0.000
% 0.10/0.23 % Success case prop solver time : 0.000
% 0.10/0.23 % Current number of processed clauses : 8
% 0.10/0.23 % Positive orientable unit clauses : 1
% 0.10/0.23 % Positive unorientable unit clauses: 0
% 0.10/0.23 % Negative unit clauses : 3
% 0.10/0.23 % Non-unit-clauses : 4
% 0.10/0.23 % Current number of unprocessed clauses: 0
% 0.10/0.23 % ...number of literals in the above : 0
% 0.10/0.23 % Current number of archived formulas : 0
% 0.10/0.23 % Current number of archived clauses : 0
% 0.10/0.23 % Clause-clause subsumption calls (NU) : 6
% 0.10/0.23 % Rec. Clause-clause subsumption calls : 6
% 0.10/0.23 % Non-unit clause-clause subsumptions : 1
% 0.10/0.23 % Unit Clause-clause subsumption calls : 1
% 0.10/0.23 % Rewrite failures with RHS unbound : 0
% 0.10/0.23 % BW rewrite match attempts : 0
% 0.10/0.23 % BW rewrite match successes : 0
% 0.10/0.23 % Condensation attempts : 0
% 0.10/0.23 % Condensation successes : 0
% 0.10/0.23 % Termbank termtop insertions : 930
% 0.10/0.23 % Search garbage collected termcells : 290
% 0.10/0.23
% 0.10/0.23 % -------------------------------------------------
% 0.10/0.23 % User time : 0.003 s
% 0.10/0.23 % System time : 0.002 s
% 0.10/0.23 % Total time : 0.005 s
% 0.10/0.23 % Maximum resident set size: 3580 pages
% 0.10/0.23
% 0.10/0.23 % -------------------------------------------------
% 0.10/0.23 % User time : 0.004 s
% 0.10/0.23 % System time : 0.005 s
% 0.10/0.23 % Total time : 0.009 s
% 0.10/0.23 % Maximum resident set size: 4864 pages
% 0.10/0.23 % E exiting
%------------------------------------------------------------------------------