%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM682^1 : 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 : n002.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 08:16:49 AM UTC 2026
% Result : Theorem 0.06s 0.25s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 53 ( 12 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 171 ( 38 ~; 12 |; 2 &; 104 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 0 ^; 31 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_23,type,
x: nat ).
thf(decl_24,type,
y: nat ).
thf(decl_25,type,
z: nat ).
thf(decl_26,type,
less: nat > nat > $o ).
thf(decl_27,type,
pl: nat > nat > nat ).
thf(decl_28,type,
more: 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/sandbox2/tmp/tmp.U00moxn7BH/E---3.1_1216492.p',satz10b) ).
thf(satz19a,axiom,
! [X2: nat,X3: nat,X4: nat] :
( ( more @ X2 @ X3 )
=> ( more @ ( pl @ X2 @ X4 ) @ ( pl @ X3 @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.U00moxn7BH/E---3.1_1216492.p',satz19a) ).
thf(satz20c,conjecture,
less @ x @ y,
file('/export/starexec/sandbox2/tmp/tmp.U00moxn7BH/E---3.1_1216492.p',satz20c) ).
thf(satz10a,axiom,
! [X2: nat,X3: nat] :
( ( X2 != X3 )
=> ( ~ ( more @ X2 @ X3 )
=> ( less @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.U00moxn7BH/E---3.1_1216492.p',satz10a) ).
thf(l,axiom,
less @ ( pl @ x @ z ) @ ( pl @ y @ z ),
file('/export/starexec/sandbox2/tmp/tmp.U00moxn7BH/E---3.1_1216492.p',l) ).
thf(c_0_5,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_6,plain,
! [X16: nat,X17: nat] :
( ( ( X16 != X17 )
| ~ ( more @ X16 @ X17 ) )
& ( ~ ( more @ X16 @ X17 )
| ~ ( less @ X16 @ X17 ) )
& ( ~ ( less @ X16 @ X17 )
| ( X16 != X17 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
thf(c_0_7,plain,
! [X18: nat,X19: nat,X20: nat] :
( ~ ( more @ X18 @ X19 )
| ( more @ ( pl @ X18 @ X20 ) @ ( pl @ X19 @ X20 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz19a])])]) ).
thf(c_0_8,negated_conjecture,
~ ( less @ x @ y ),
inference(assume_negation,[status(cth)],[satz20c]) ).
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,
! [X2: nat,X4: nat,X3: nat] :
( ( more @ ( pl @ X2 @ X4 ) @ ( pl @ X3 @ X4 ) )
| ~ ( more @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
! [X2: nat,X3: nat] :
( ( X2 != X3 )
=> ( ~ ( more @ X2 @ X3 )
=> ( less @ X2 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[satz10a]) ).
thf(c_0_12,negated_conjecture,
~ ( less @ x @ y ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
thf(c_0_13,plain,
! [X2: nat,X3: nat,X4: nat] :
( ~ ( less @ ( pl @ X2 @ X3 ) @ ( pl @ X4 @ X3 ) )
| ~ ( more @ X2 @ X4 ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_14,plain,
less @ ( pl @ x @ z ) @ ( pl @ y @ z ),
inference(split_conjunct,[status(thm)],[l]) ).
thf(c_0_15,plain,
! [X24: nat,X25: nat] :
( ( X24 = X25 )
| ( more @ X24 @ X25 )
| ( less @ X24 @ X25 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
thf(c_0_16,negated_conjecture,
~ ( less @ x @ y ),
inference(fof_nnf,[status(thm)],[c_0_12]) ).
thf(c_0_17,plain,
~ ( more @ x @ y ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_18,plain,
! [X2: nat,X3: nat] :
( ( X2 = X3 )
| ( more @ X2 @ X3 )
| ( less @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_19,negated_conjecture,
~ ( less @ x @ y ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_20,plain,
! [X2: nat,X3: nat] :
( ~ ( less @ X2 @ X3 )
| ( X2 != X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_21,plain,
x = y,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
thf(c_0_22,plain,
! [X2: nat] :
~ ( less @ X2 @ X2 ),
inference(er,[status(thm)],[c_0_20]) ).
thf(c_0_23,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_21]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM682^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n002.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Sep 29 12:38:52 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running higher-order theorem proving
% 0.06/0.24 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.U00moxn7BH/E---3.1_1216492.p
% 0.06/0.25 % Version: 3.5.1-ho
% 0.06/0.25 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.06/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.06/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.06/0.25 % Starting new_bool_1 with 300s (1) cores
% 0.06/0.25 % Starting full_lambda_5 with 300s (1) cores
% 0.06/0.25 % Starting new_ho_10_unif with 300s (1) cores
% 0.06/0.25 % full_lambda_5 with pid 1216507 completed with status 0
% 0.06/0.25 % Result found by full_lambda_5
% 0.06/0.25 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.06/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.06/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.06/0.25 % Starting new_bool_1 with 300s (1) cores
% 0.06/0.25 % Starting full_lambda_5 with 300s (1) cores
% 0.06/0.25 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.06/0.25 % No SInE strategy applied
% 0.06/0.25 % Search class: HGHSF-FFSF22-SFFFFFNN
% 0.06/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.06/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.06/0.25 % SubtermCWHack with pid 1216509 completed with status 0
% 0.06/0.25 % Result found by SubtermCWHack
% 0.06/0.25 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.06/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.06/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.06/0.25 % Starting new_bool_1 with 300s (1) cores
% 0.06/0.25 % Starting full_lambda_5 with 300s (1) cores
% 0.06/0.25 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.06/0.25 % No SInE strategy applied
% 0.06/0.25 % Search class: HGHSF-FFSF22-SFFFFFNN
% 0.06/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.06/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.06/0.25 % Preprocessing time : 0.001 s
% 0.06/0.25
% 0.06/0.25 % Proof found!
% 0.06/0.25 % SZS status Theorem
% 0.06/0.25 % SZS output start CNFRefutation
% See solution above
% 0.06/0.25 % Parsed axioms : 14
% 0.06/0.25 % Removed by relevancy pruning/SinE : 0
% 0.06/0.25 % Initial clauses : 16
% 0.06/0.25 % Removed in clause preprocessing : 9
% 0.06/0.25 % Initial clauses in saturation : 7
% 0.06/0.25 % Processed clauses : 13
% 0.06/0.25 % ...of these trivial : 0
% 0.06/0.25 % ...subsumed : 1
% 0.06/0.25 % ...remaining for further processing : 12
% 0.06/0.25 % Other redundant clauses eliminated : 2
% 0.06/0.25 % Clauses deleted for lack of memory : 0
% 0.06/0.25 % Backward-subsumed : 0
% 0.06/0.25 % Backward-rewritten : 2
% 0.06/0.25 % Generated clauses : 8
% 0.06/0.25 % ...of the previous two non-redundant : 8
% 0.06/0.25 % ...aggressively subsumed : 0
% 0.06/0.25 % Contextual simplify-reflections : 0
% 0.06/0.25 % Paramodulations : 6
% 0.06/0.25 % Factorizations : 0
% 0.06/0.25 % NegExts : 0
% 0.06/0.25 % Equation resolutions : 2
% 0.06/0.25 % Disequality decompositions : 0
% 0.06/0.25 % Total rewrite steps : 2
% 0.06/0.25 % ...of those cached : 1
% 0.06/0.25 % Propositional unsat checks : 0
% 0.06/0.25 % Propositional check models : 0
% 0.06/0.25 % Propositional check unsatisfiable : 0
% 0.06/0.25 % Propositional clauses : 0
% 0.06/0.25 % Propositional clauses after purity: 0
% 0.06/0.25 % Propositional unsat core size : 0
% 0.06/0.25 % Propositional preprocessing time : 0.000
% 0.06/0.25 % Propositional encoding time : 0.000
% 0.06/0.25 % Propositional solver time : 0.000
% 0.06/0.25 % Success case prop preproc time : 0.000
% 0.06/0.25 % Success case prop encoding time : 0.000
% 0.06/0.25 % Success case prop solver time : 0.000
% 0.06/0.25 % Current number of processed clauses : 8
% 0.06/0.25 % Positive orientable unit clauses : 2
% 0.06/0.25 % Positive unorientable unit clauses: 0
% 0.06/0.25 % Negative unit clauses : 2
% 0.06/0.25 % Non-unit-clauses : 4
% 0.06/0.25 % Current number of unprocessed clauses: 0
% 0.06/0.25 % ...number of literals in the above : 0
% 0.06/0.25 % Current number of archived formulas : 0
% 0.06/0.25 % Current number of archived clauses : 2
% 0.06/0.25 % Clause-clause subsumption calls (NU) : 2
% 0.06/0.25 % Rec. Clause-clause subsumption calls : 1
% 0.06/0.25 % Non-unit clause-clause subsumptions : 0
% 0.06/0.25 % Unit Clause-clause subsumption calls : 1
% 0.06/0.25 % Rewrite failures with RHS unbound : 0
% 0.06/0.25 % BW rewrite match attempts : 1
% 0.06/0.25 % BW rewrite match successes : 1
% 0.06/0.25 % Condensation attempts : 0
% 0.06/0.25 % Condensation successes : 0
% 0.06/0.25 % Termbank termtop insertions : 828
% 0.06/0.25 % Search garbage collected termcells : 154
% 0.06/0.25
% 0.06/0.25 % -------------------------------------------------
% 0.06/0.25 % User time : 0.003 s
% 0.06/0.25 % System time : 0.002 s
% 0.06/0.25 % Total time : 0.005 s
% 0.06/0.25 % Maximum resident set size: 3636 pages
% 0.06/0.25
% 0.06/0.25 % -------------------------------------------------
% 0.06/0.25 % User time : 0.003 s
% 0.06/0.25 % System time : 0.007 s
% 0.06/0.25 % Total time : 0.010 s
% 0.06/0.25 % Maximum resident set size: 4608 pages
% 0.06/0.25 % E exiting
%------------------------------------------------------------------------------