%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM652^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 08:16:42 AM UTC 2026
% Result : Theorem 0.06s 0.23s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 37 ( 12 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 99 ( 30 ~; 7 |; 2 &; 48 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 11 ( 0 ^; 11 !; 0 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_23,type,
x: nat ).
thf(decl_24,type,
y: nat ).
thf(decl_25,type,
more: nat > nat > $o ).
thf(decl_26,type,
less: nat > nat > $o ).
thf(satz10b,axiom,
! [X2: nat,X3: nat] :
~ ( ( ( X2 = X3 )
=> ~ ( more @ X2 @ X3 ) )
=> ~ ~ ( ( ( more @ X2 @ X3 )
=> ~ ( less @ X2 @ X3 ) )
=> ~ ( ( less @ X2 @ X3 )
=> ( X2 != X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lSfC6EQz3N/E---3.1_1174653.p',satz10b) ).
thf(m,axiom,
( ~ ( more @ x @ y )
=> ( x = y ) ),
file('/export/starexec/sandbox/tmp/tmp.lSfC6EQz3N/E---3.1_1174653.p',m) ).
thf(satz10c,conjecture,
~ ( less @ x @ y ),
file('/export/starexec/sandbox/tmp/tmp.lSfC6EQz3N/E---3.1_1174653.p',satz10c) ).
thf(c_0_3,plain,
! [X2: nat,X3: nat] :
~ ( ( ( X2 = X3 )
=> ~ ( more @ X2 @ X3 ) )
=> ~ ~ ( ( ( more @ X2 @ X3 )
=> ~ ( less @ X2 @ X3 ) )
=> ~ ( ( less @ X2 @ X3 )
=> ( X2 != X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[satz10b]) ).
thf(c_0_4,plain,
( ~ ( more @ x @ y )
=> ( x = y ) ),
inference(fof_simplification,[status(thm)],[m]) ).
thf(c_0_5,negated_conjecture,
~ ~ ( less @ x @ y ),
inference(assume_negation,[status(cth)],[satz10c]) ).
thf(c_0_6,plain,
! [X7: nat,X8: nat] :
( ( ( X7 != X8 )
| ~ ( more @ X7 @ X8 ) )
& ( ~ ( more @ X7 @ X8 )
| ~ ( less @ X7 @ X8 ) )
& ( ~ ( less @ X7 @ X8 )
| ( X7 != X8 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
thf(c_0_7,plain,
( ( more @ x @ y )
| ( x = y ) ),
inference(fof_nnf,[status(thm)],[c_0_4]) ).
thf(c_0_8,negated_conjecture,
less @ x @ y,
inference(fof_simplification,[status(thm)],[c_0_5]) ).
thf(c_0_9,plain,
! [X2: nat,X3: nat] :
( ~ ( more @ X2 @ X3 )
| ~ ( less @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,plain,
( ( more @ x @ y )
| ( x = y ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,negated_conjecture,
less @ x @ y,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,plain,
! [X2: nat,X3: nat] :
( ~ ( less @ X2 @ X3 )
| ( X2 != X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_13,plain,
x = y,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11])]) ).
thf(c_0_14,plain,
! [X2: nat] :
~ ( less @ X2 @ X2 ),
inference(er,[status(thm)],[c_0_12]) ).
thf(c_0_15,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_13]),c_0_14]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM652^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.17 % Computer : n001.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 12:38:05 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.21 Running higher-order theorem proving
% 0.06/0.22 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.lSfC6EQz3N/E---3.1_1174653.p
% 0.06/0.23 % Version: 3.5.1-ho
% 0.06/0.23 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.06/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.06/0.23 % Starting new_ho_10 with 1500s (5) cores
% 0.06/0.23 % Starting ho_unfolding_6 with 300s (1) cores
% 0.06/0.23 % Starting sh4l with 300s (1) cores
% 0.06/0.23 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.06/0.23 % ehoh_best_nonlift_rwall with pid 1174669 completed with status 0
% 0.06/0.23 % Result found by ehoh_best_nonlift_rwall
% 0.06/0.23 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.06/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.06/0.23 % Starting new_ho_10 with 1500s (5) cores
% 0.06/0.23 % Starting ho_unfolding_6 with 300s (1) cores
% 0.06/0.23 % Starting sh4l with 300s (1) cores
% 0.06/0.23 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.06/0.23 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = Auto)
% 0.06/0.23 % No SInE strategy applied
% 0.06/0.23 % Search class: HGHSF-FFSF00-SFFFFFNN
% 0.06/0.23 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.06/0.23 % Starting SubtermCWHack with 28s (1) cores
% 0.06/0.23 % SubtermCWHack with pid 1174675 completed with status 0
% 0.06/0.23 % Result found by SubtermCWHack
% 0.06/0.23 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.06/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.06/0.23 % Starting new_ho_10 with 1500s (5) cores
% 0.06/0.23 % Starting ho_unfolding_6 with 300s (1) cores
% 0.06/0.23 % Starting sh4l with 300s (1) cores
% 0.06/0.23 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.06/0.23 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = Auto)
% 0.06/0.23 % No SInE strategy applied
% 0.06/0.23 % Search class: HGHSF-FFSF00-SFFFFFNN
% 0.06/0.23 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.06/0.23 % Starting SubtermCWHack with 28s (1) cores
% 0.06/0.23 % Preprocessing time : 0.001 s
% 0.06/0.23
% 0.06/0.23 % Proof found!
% 0.06/0.23 % SZS status Theorem
% 0.06/0.23 % SZS output start CNFRefutation
% See solution above
% 0.06/0.23 % Parsed axioms : 9
% 0.06/0.23 % Removed by relevancy pruning/SinE : 0
% 0.06/0.23 % Initial clauses : 11
% 0.06/0.23 % Removed in clause preprocessing : 6
% 0.06/0.23 % Initial clauses in saturation : 5
% 0.06/0.23 % Processed clauses : 8
% 0.06/0.23 % ...of these trivial : 0
% 0.06/0.23 % ...subsumed : 0
% 0.06/0.23 % ...remaining for further processing : 8
% 0.06/0.23 % Other redundant clauses eliminated : 2
% 0.06/0.23 % Clauses deleted for lack of memory : 0
% 0.06/0.23 % Backward-subsumed : 0
% 0.06/0.23 % Backward-rewritten : 2
% 0.06/0.23 % Generated clauses : 3
% 0.06/0.23 % ...of the previous two non-redundant : 3
% 0.06/0.23 % ...aggressively subsumed : 0
% 0.06/0.23 % Contextual simplify-reflections : 0
% 0.06/0.23 % Paramodulations : 1
% 0.06/0.23 % Factorizations : 0
% 0.06/0.23 % NegExts : 0
% 0.06/0.23 % Equation resolutions : 2
% 0.06/0.23 % Disequality decompositions : 0
% 0.06/0.23 % Total rewrite steps : 4
% 0.06/0.23 % ...of those cached : 2
% 0.06/0.23 % Propositional unsat checks : 0
% 0.06/0.23 % Propositional check models : 0
% 0.06/0.23 % Propositional check unsatisfiable : 0
% 0.06/0.23 % Propositional clauses : 0
% 0.06/0.23 % Propositional clauses after purity: 0
% 0.06/0.23 % Propositional unsat core size : 0
% 0.06/0.23 % Propositional preprocessing time : 0.000
% 0.06/0.23 % Propositional encoding time : 0.000
% 0.06/0.23 % Propositional solver time : 0.000
% 0.06/0.23 % Success case prop preproc time : 0.000
% 0.06/0.23 % Success case prop encoding time : 0.000
% 0.06/0.23 % Success case prop solver time : 0.000
% 0.06/0.23 % Current number of processed clauses : 4
% 0.06/0.23 % Positive orientable unit clauses : 1
% 0.06/0.23 % Positive unorientable unit clauses: 0
% 0.06/0.23 % Negative unit clauses : 2
% 0.06/0.23 % Non-unit-clauses : 1
% 0.06/0.23 % Current number of unprocessed clauses: 0
% 0.06/0.23 % ...number of literals in the above : 0
% 0.06/0.23 % Current number of archived formulas : 0
% 0.06/0.23 % Current number of archived clauses : 2
% 0.06/0.23 % Clause-clause subsumption calls (NU) : 0
% 0.06/0.23 % Rec. Clause-clause subsumption calls : 0
% 0.06/0.23 % Non-unit clause-clause subsumptions : 0
% 0.06/0.23 % Unit Clause-clause subsumption calls : 0
% 0.06/0.23 % Rewrite failures with RHS unbound : 0
% 0.06/0.23 % BW rewrite match attempts : 1
% 0.06/0.23 % BW rewrite match successes : 1
% 0.06/0.23 % Condensation attempts : 0
% 0.06/0.23 % Condensation successes : 0
% 0.06/0.23 % Termbank termtop insertions : 489
% 0.06/0.23 % Search garbage collected termcells : 95
% 0.06/0.23
% 0.06/0.23 % -------------------------------------------------
% 0.06/0.23 % User time : 0.002 s
% 0.06/0.23 % System time : 0.001 s
% 0.06/0.23 % Total time : 0.004 s
% 0.06/0.23 % Maximum resident set size: 3632 pages
% 0.06/0.23
% 0.06/0.23 % -------------------------------------------------
% 0.06/0.23 % User time : 0.004 s
% 0.06/0.23 % System time : 0.005 s
% 0.06/0.23 % Total time : 0.009 s
% 0.06/0.23 % Maximum resident set size: 4864 pages
% 0.06/0.23 % E exiting
%------------------------------------------------------------------------------