%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM693^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 08:16:51 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 19 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 67 ( 15 ~; 4 |; 1 &; 42 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 17 ( 0 ^; 17 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_23,type,
x: nat ).
thf(decl_24,type,
more: nat > nat > $o ).
thf(decl_25,type,
n_1: nat ).
thf(decl_26,type,
suc: nat > nat ).
thf(decl_27,type,
pl: nat > nat > nat ).
thf(decl_28,type,
esk1_1: nat > nat ).
thf(satz3,axiom,
! [X2: nat] :
( ( X2 != n_1 )
=> ~ ! [X3: nat] :
( X2
!= ( suc @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.IjNJ1NmVK9/E---3.1_2597156.p',satz3) ).
thf(satz24,conjecture,
( ~ ( more @ x @ n_1 )
=> ( x = n_1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.IjNJ1NmVK9/E---3.1_2597156.p',satz24) ).
thf(satz4g,axiom,
! [X2: nat] :
( ( suc @ X2 )
= ( pl @ n_1 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.IjNJ1NmVK9/E---3.1_2597156.p',satz4g) ).
thf(satz18,axiom,
! [X2: nat,X4: nat] : ( more @ ( pl @ X2 @ X4 ) @ X2 ),
file('/export/starexec/sandbox2/tmp/tmp.IjNJ1NmVK9/E---3.1_2597156.p',satz18) ).
thf(c_0_4,plain,
! [X2: nat] :
( ( X2 != n_1 )
=> ~ ! [X3: nat] :
( X2
!= ( suc @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[satz3]) ).
thf(c_0_5,negated_conjecture,
~ ( ~ ( more @ x @ n_1 )
=> ( x = n_1 ) ),
inference(assume_negation,[status(cth)],[satz24]) ).
thf(c_0_6,plain,
! [X11: nat] :
( ( X11 = n_1 )
| ( X11
= ( suc @ ( esk1_1 @ X11 ) ) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
thf(c_0_7,plain,
! [X15: nat] :
( ( suc @ X15 )
= ( pl @ n_1 @ X15 ) ),
inference(variable_rename,[status(thm)],[satz4g]) ).
thf(c_0_8,negated_conjecture,
~ ( ~ ( more @ x @ n_1 )
=> ( x = n_1 ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
thf(c_0_9,plain,
! [X13: nat,X14: nat] : ( more @ ( pl @ X13 @ X14 ) @ X13 ),
inference(variable_rename,[status(thm)],[satz18]) ).
thf(c_0_10,plain,
! [X2: nat] :
( ( X2 = n_1 )
| ( X2
= ( suc @ ( esk1_1 @ X2 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_11,plain,
! [X2: nat] :
( ( suc @ X2 )
= ( pl @ n_1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_12,negated_conjecture,
( ~ ( more @ x @ n_1 )
& ( x != n_1 ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])]) ).
thf(c_0_13,plain,
! [X3: nat,X2: nat] : ( more @ ( pl @ X2 @ X3 ) @ X2 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,plain,
! [X2: nat] :
( ( X2 = n_1 )
| ( X2
= ( pl @ n_1 @ ( esk1_1 @ X2 ) ) ) ),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_15,negated_conjecture,
~ ( more @ x @ n_1 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_16,plain,
! [X2: nat] :
( ( X2 = n_1 )
| ( more @ X2 @ n_1 ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_17,negated_conjecture,
x != n_1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_18,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM693^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n014.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 12:40:39 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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.IjNJ1NmVK9/E---3.1_2597156.p
% 0.08/0.25 % Version: 3.5.1-ho
% 0.08/0.25 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.25 % Starting ho_unfolding_6 with 300s (1) cores
% 0.08/0.25 % Starting sh4l with 300s (1) cores
% 0.08/0.25 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.08/0.25 % ho_unfolding_6 with pid 2597170 completed with status 0
% 0.08/0.25 % Result found by ho_unfolding_6
% 0.08/0.25 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.25 % Starting ho_unfolding_6 with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.25 % No SInE strategy applied
% 0.08/0.25 % Search class: HGUSF-FFSF21-SFFFFFNN
% 0.08/0.25 % partial match(1): HHUSF-FFSF21-SFFFFFNN
% 0.08/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.25 % SubtermCWHack with pid 2597174 completed with status 0
% 0.08/0.25 % Result found by SubtermCWHack
% 0.08/0.25 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.25 % Starting ho_unfolding_6 with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.25 % No SInE strategy applied
% 0.08/0.25 % Search class: HGUSF-FFSF21-SFFFFFNN
% 0.08/0.25 % partial match(1): HHUSF-FFSF21-SFFFFFNN
% 0.08/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.25 % Preprocessing time : 0.001 s
% 0.08/0.25
% 0.08/0.25 % Proof found!
% 0.08/0.25 % SZS status Theorem
% 0.08/0.25 % SZS output start CNFRefutation
% See solution above
% 0.08/0.25 % Parsed axioms : 11
% 0.08/0.25 % Removed by relevancy pruning/SinE : 0
% 0.08/0.25 % Initial clauses : 12
% 0.08/0.25 % Removed in clause preprocessing : 8
% 0.08/0.25 % Initial clauses in saturation : 4
% 0.08/0.25 % Processed clauses : 5
% 0.08/0.25 % ...of these trivial : 0
% 0.08/0.25 % ...subsumed : 0
% 0.08/0.25 % ...remaining for further processing : 5
% 0.08/0.25 % Other redundant clauses eliminated : 0
% 0.08/0.25 % Clauses deleted for lack of memory : 0
% 0.08/0.25 % Backward-subsumed : 0
% 0.08/0.25 % Backward-rewritten : 0
% 0.08/0.25 % Generated clauses : 2
% 0.08/0.25 % ...of the previous two non-redundant : 1
% 0.08/0.25 % ...aggressively subsumed : 0
% 0.08/0.25 % Contextual simplify-reflections : 0
% 0.08/0.25 % Paramodulations : 2
% 0.08/0.25 % Factorizations : 0
% 0.08/0.25 % NegExts : 0
% 0.08/0.25 % Equation resolutions : 0
% 0.08/0.25 % Disequality decompositions : 0
% 0.08/0.25 % Total rewrite steps : 0
% 0.08/0.25 % ...of those cached : 0
% 0.08/0.25 % Propositional unsat checks : 0
% 0.08/0.25 % Propositional check models : 0
% 0.08/0.25 % Propositional check unsatisfiable : 0
% 0.08/0.25 % Propositional clauses : 0
% 0.08/0.25 % Propositional clauses after purity: 0
% 0.08/0.25 % Propositional unsat core size : 0
% 0.08/0.25 % Propositional preprocessing time : 0.000
% 0.08/0.25 % Propositional encoding time : 0.000
% 0.08/0.25 % Propositional solver time : 0.000
% 0.08/0.25 % Success case prop preproc time : 0.000
% 0.08/0.25 % Success case prop encoding time : 0.000
% 0.08/0.25 % Success case prop solver time : 0.000
% 0.08/0.25 % Current number of processed clauses : 5
% 0.08/0.25 % Positive orientable unit clauses : 1
% 0.08/0.25 % Positive unorientable unit clauses: 0
% 0.08/0.25 % Negative unit clauses : 2
% 0.08/0.25 % Non-unit-clauses : 2
% 0.08/0.25 % Current number of unprocessed clauses: 0
% 0.08/0.25 % ...number of literals in the above : 0
% 0.08/0.25 % Current number of archived formulas : 0
% 0.08/0.25 % Current number of archived clauses : 1
% 0.08/0.25 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.25 % Rec. Clause-clause subsumption calls : 0
% 0.08/0.25 % Non-unit clause-clause subsumptions : 0
% 0.08/0.25 % Unit Clause-clause subsumption calls : 0
% 0.08/0.25 % Rewrite failures with RHS unbound : 0
% 0.08/0.25 % BW rewrite match attempts : 0
% 0.08/0.25 % BW rewrite match successes : 0
% 0.08/0.25 % Condensation attempts : 0
% 0.08/0.25 % Condensation successes : 0
% 0.08/0.25 % Termbank termtop insertions : 366
% 0.08/0.25 % Search garbage collected termcells : 55
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.003 s
% 0.08/0.25 % System time : 0.003 s
% 0.08/0.25 % Total time : 0.005 s
% 0.08/0.25 % Maximum resident set size: 3632 pages
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.004 s
% 0.08/0.25 % System time : 0.008 s
% 0.08/0.25 % Total time : 0.011 s
% 0.08/0.25 % Maximum resident set size: 4864 pages
% 0.08/0.25 % E exiting
%------------------------------------------------------------------------------