%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM705^1 : 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 : n007.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 08:16:54 AM UTC 2026
% Result : Theorem 0.10s 0.24s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 137 ( 12 equ; 0 cnn)
% Maximal formula atoms : 27 ( 4 avg)
% Number of connectives : 362 ( 89 ~; 28 |; 4 &; 178 @)
% ( 0 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 75 ( 17 ^; 58 !; 0 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_23,type,
p: nat > $o ).
thf(decl_24,type,
some: ( nat > $o ) > $o ).
thf(decl_25,type,
lessis: nat > nat > $o ).
thf(decl_26,type,
more: nat > nat > $o ).
thf(decl_27,type,
esk1_0: nat ).
thf(decl_28,type,
esk2_0: nat ).
thf(satz27a,conjecture,
~ ( ! [X1: nat,X2: nat] :
( ~ ( ! [X5: nat] :
( ( p @ X5 )
=> ( lessis @ X1 @ X5 ) )
=> ~ ( p @ X1 ) )
=> ( ~ ( ! [X5: nat] :
( ( p @ X5 )
=> ( lessis @ X2 @ X5 ) )
=> ~ ( p @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ( some
@ ^ [X1: nat] :
~ ( ! [X5: nat] :
( ( p @ X5 )
=> ( lessis @ X1 @ X5 ) )
=> ~ ( p @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.z7eernOlll/E---3.1_3302001.p',satz27a) ).
thf(satz10d,axiom,
! [X1: nat,X2: nat] :
( ( lessis @ X1 @ X2 )
=> ~ ( more @ X1 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.z7eernOlll/E---3.1_3302001.p',satz10d) ).
thf(satz14,axiom,
! [X1: nat,X2: nat] :
( ( lessis @ X1 @ X2 )
=> ( ~ ( more @ X2 @ X1 )
=> ( X2 = X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.z7eernOlll/E---3.1_3302001.p',satz14) ).
thf(satz27,axiom,
! [X4: nat > $o] :
( ( some @ X4 )
=> ( some
@ ^ [X1: nat] :
~ ( ! [X5: nat] :
( ( X4 @ X5 )
=> ( lessis @ X1 @ X5 ) )
=> ~ ( X4 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.z7eernOlll/E---3.1_3302001.p',satz27) ).
thf(s,axiom,
some @ p,
file('/export/starexec/sandbox2/tmp/tmp.z7eernOlll/E---3.1_3302001.p',s) ).
thf(c_0_5,negated_conjecture,
~ ~ ( ! [X1: nat,X2: nat] :
( ~ ( ! [X5: nat] :
( ( p @ X5 )
=> ( lessis @ X1 @ X5 ) )
=> ~ ( p @ X1 ) )
=> ( ~ ( ! [X5: nat] :
( ( p @ X5 )
=> ( lessis @ X2 @ X5 ) )
=> ~ ( p @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ( some
@ ^ [X1: nat] :
~ ( ! [X5: nat] :
( ( p @ X5 )
=> ( lessis @ X1 @ X5 ) )
=> ~ ( p @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[satz27a]) ).
thf(c_0_6,plain,
! [X1: nat,X2: nat] :
( ( lessis @ X1 @ X2 )
=> ~ ( more @ X1 @ X2 ) ),
inference(fof_simplification,[status(thm)],[satz10d]) ).
thf(c_0_7,plain,
! [X1: nat,X2: nat] :
( ( lessis @ X1 @ X2 )
=> ( ~ ( more @ X2 @ X1 )
=> ( X2 = X1 ) ) ),
inference(fof_simplification,[status(thm)],[satz14]) ).
thf(c_0_8,negated_conjecture,
~ ~ ( ! [X1: nat,X2: nat] :
( ~ ( ! [X5: nat] :
( ( p @ X5 )
=> ( lessis @ X1 @ X5 ) )
=> ~ ( p @ X1 ) )
=> ( ~ ( ! [X5: nat] :
( ( p @ X5 )
=> ( lessis @ X2 @ X5 ) )
=> ~ ( p @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ( some
@ ^ [Z0: nat] :
~ ( ! [X5: nat] :
( ( p @ X5 )
=> ( lessis @ Z0 @ X5 ) )
=> ~ ( p @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_5])]) ).
thf(c_0_9,plain,
! [X4: nat > $o] :
( ( some @ X4 )
=> ( some
@ ^ [Z0: nat] :
~ ( ! [X5: nat] :
( ( X4 @ X5 )
=> ( lessis @ Z0 @ X5 ) )
=> ~ ( X4 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[satz27]) ).
thf(c_0_10,plain,
! [X22: nat,X23: nat] :
( ~ ( lessis @ X22 @ X23 )
| ~ ( more @ X22 @ X23 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
thf(c_0_11,plain,
! [X20: nat,X21: nat] :
( ~ ( lessis @ X20 @ X21 )
| ( more @ X21 @ X20 )
| ( X21 = X20 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
thf(c_0_12,negated_conjecture,
! [X17: nat,X18: nat] :
( ( ~ ( p @ X17 )
| ( lessis @ esk1_0 @ X17 )
| ~ ( some
@ ^ [Z0: nat] :
~ ( ! [X5: nat] :
( ( p @ X5 )
=> ( lessis @ Z0 @ X5 ) )
=> ~ ( p @ Z0 ) ) ) )
& ( ( p @ esk1_0 )
| ~ ( some
@ ^ [Z0: nat] :
~ ( ! [X5: nat] :
( ( p @ X5 )
=> ( lessis @ Z0 @ X5 ) )
=> ~ ( p @ Z0 ) ) ) )
& ( ~ ( p @ X18 )
| ( lessis @ esk2_0 @ X18 )
| ~ ( some
@ ^ [Z0: nat] :
~ ( ! [X5: nat] :
( ( p @ X5 )
=> ( lessis @ Z0 @ X5 ) )
=> ~ ( p @ Z0 ) ) ) )
& ( ( p @ esk2_0 )
| ~ ( some
@ ^ [Z0: nat] :
~ ( ! [X5: nat] :
( ( p @ X5 )
=> ( lessis @ Z0 @ X5 ) )
=> ~ ( p @ Z0 ) ) ) )
& ( ( esk1_0 != esk2_0 )
| ~ ( some
@ ^ [Z0: nat] :
~ ( ! [X5: nat] :
( ( p @ X5 )
=> ( lessis @ Z0 @ X5 ) )
=> ~ ( p @ Z0 ) ) ) ) ),
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_8])])])])])]) ).
thf(c_0_13,plain,
! [X19: nat > $o] :
( ~ ( some @ X19 )
| ( some
@ ^ [Z0: nat] :
~ ( ! [X5: nat] :
( ( X19 @ X5 )
=> ( lessis @ Z0 @ X5 ) )
=> ~ ( X19 @ Z0 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
thf(c_0_14,plain,
! [X1: nat,X2: nat] :
( ~ ( lessis @ X1 @ X2 )
| ~ ( more @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_15,plain,
! [X1: nat,X2: nat] :
( ( more @ X2 @ X1 )
| ( X2 = X1 )
| ~ ( lessis @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_16,negated_conjecture,
! [X1: nat] :
( ( lessis @ esk1_0 @ X1 )
| ~ ( p @ X1 )
| ~ ( some
@ ^ [Z0: nat] :
~ ( ! [X24: nat] :
( ( p @ X24 )
=> ( lessis @ Z0 @ X24 ) )
=> ~ ( p @ Z0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_17,plain,
! [X4: nat > $o] :
( ( some
@ ^ [Z0: nat] :
~ ( ! [X25: nat] :
( ( X4 @ X25 )
=> ( lessis @ Z0 @ X25 ) )
=> ~ ( X4 @ Z0 ) ) )
| ~ ( some @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_18,plain,
some @ p,
inference(split_conjunct,[status(thm)],[s]) ).
thf(c_0_19,plain,
! [X1: nat,X2: nat] :
( ( X1 = X2 )
| ~ ( lessis @ X2 @ X1 )
| ~ ( lessis @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_20,negated_conjecture,
! [X1: nat] :
( ( lessis @ esk1_0 @ X1 )
| ~ ( p @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
thf(c_0_21,negated_conjecture,
! [X1: nat] :
( ( lessis @ esk2_0 @ X1 )
| ~ ( p @ X1 )
| ~ ( some
@ ^ [Z0: nat] :
~ ( ! [X26: nat] :
( ( p @ X26 )
=> ( lessis @ Z0 @ X26 ) )
=> ~ ( p @ Z0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_22,negated_conjecture,
( ( p @ esk2_0 )
| ~ ( some
@ ^ [Z0: nat] :
~ ( ! [X27: nat] :
( ( p @ X27 )
=> ( lessis @ Z0 @ X27 ) )
=> ~ ( p @ Z0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_23,negated_conjecture,
( ( p @ esk1_0 )
| ~ ( some
@ ^ [Z0: nat] :
~ ( ! [X28: nat] :
( ( p @ X28 )
=> ( lessis @ Z0 @ X28 ) )
=> ~ ( p @ Z0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_24,negated_conjecture,
( ( esk1_0 != esk2_0 )
| ~ ( some
@ ^ [Z0: nat] :
~ ( ! [X29: nat] :
( ( p @ X29 )
=> ( lessis @ Z0 @ X29 ) )
=> ~ ( p @ Z0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_25,negated_conjecture,
! [X1: nat] :
( ( X1 = esk1_0 )
| ~ ( lessis @ X1 @ esk1_0 )
| ~ ( p @ X1 ) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_26,negated_conjecture,
! [X1: nat] :
( ( lessis @ esk2_0 @ X1 )
| ~ ( p @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_17]),c_0_18])]) ).
thf(c_0_27,negated_conjecture,
p @ esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_17]),c_0_18])]) ).
thf(c_0_28,negated_conjecture,
p @ esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_17]),c_0_18])]) ).
thf(c_0_29,negated_conjecture,
esk2_0 != esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_17]),c_0_18])]) ).
thf(c_0_30,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28])]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM705^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.16 % Computer : n007.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 12:40:26 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
% 0.10/0.22 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.z7eernOlll/E---3.1_3302001.p
% 0.10/0.24 % Version: 3.5.1-ho
% 0.10/0.24 % Preprocessing class: HSMSSMSSSSMNSSN.
% 0.10/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.24 % Starting sh5l with 300s (1) cores
% 0.10/0.24 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.10/0.24 % Starting lpo1_def_fix with 300s (1) cores
% 0.10/0.24 % sh5l with pid 3302031 completed with status 0
% 0.10/0.24 % Result found by sh5l
% 0.10/0.24 % Preprocessing class: HSMSSMSSSSMNSSN.
% 0.10/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.24 % Starting sh5l with 300s (1) cores
% 0.10/0.24 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.10/0.24 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.10/0.24 % Search class: HGHSF-FFSF00-DSSFFFBN
% 0.10/0.24 % partial match(2): HGHSF-FFSF00-SSSFFSBN
% 0.10/0.24 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.24 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.24 % SubtermCWHack with pid 3302035 completed with status 0
% 0.10/0.24 % Result found by SubtermCWHack
% 0.10/0.24 % Preprocessing class: HSMSSMSSSSMNSSN.
% 0.10/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.24 % Starting sh5l with 300s (1) cores
% 0.10/0.24 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.10/0.24 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.10/0.24 % Search class: HGHSF-FFSF00-DSSFFFBN
% 0.10/0.24 % partial match(2): HGHSF-FFSF00-SSSFFSBN
% 0.10/0.24 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.24 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.24 % Preprocessing time : 0.001 s
% 0.10/0.24
% 0.10/0.24 % Proof found!
% 0.10/0.24 % SZS status Theorem
% 0.10/0.24 % SZS output start CNFRefutation
% See solution above
% 0.10/0.24 % Parsed axioms : 11
% 0.10/0.24 % Removed by relevancy pruning/SinE : 6
% 0.10/0.24 % Initial clauses : 9
% 0.10/0.24 % Removed in clause preprocessing : 0
% 0.10/0.24 % Initial clauses in saturation : 9
% 0.10/0.24 % Processed clauses : 16
% 0.10/0.24 % ...of these trivial : 0
% 0.10/0.24 % ...subsumed : 0
% 0.10/0.24 % ...remaining for further processing : 16
% 0.10/0.24 % Other redundant clauses eliminated : 0
% 0.10/0.24 % Clauses deleted for lack of memory : 0
% 0.10/0.24 % Backward-subsumed : 3
% 0.10/0.24 % Backward-rewritten : 2
% 0.10/0.24 % Generated clauses : 9
% 0.10/0.24 % ...of the previous two non-redundant : 7
% 0.10/0.24 % ...aggressively subsumed : 0
% 0.10/0.24 % Contextual simplify-reflections : 0
% 0.10/0.24 % Paramodulations : 9
% 0.10/0.24 % Factorizations : 0
% 0.10/0.24 % NegExts : 0
% 0.10/0.24 % Equation resolutions : 0
% 0.10/0.24 % Disequality decompositions : 0
% 0.10/0.24 % Total rewrite steps : 9
% 0.10/0.24 % ...of those cached : 6
% 0.10/0.24 % Propositional unsat checks : 0
% 0.10/0.24 % Propositional check models : 0
% 0.10/0.24 % Propositional check unsatisfiable : 0
% 0.10/0.24 % Propositional clauses : 0
% 0.10/0.24 % Propositional clauses after purity: 0
% 0.10/0.24 % Propositional unsat core size : 0
% 0.10/0.24 % Propositional preprocessing time : 0.000
% 0.10/0.24 % Propositional encoding time : 0.000
% 0.10/0.24 % Propositional solver time : 0.000
% 0.10/0.24 % Success case prop preproc time : 0.000
% 0.10/0.24 % Success case prop encoding time : 0.000
% 0.10/0.24 % Success case prop solver time : 0.000
% 0.10/0.24 % Current number of processed clauses : 11
% 0.10/0.24 % Positive orientable unit clauses : 3
% 0.10/0.24 % Positive unorientable unit clauses: 0
% 0.10/0.24 % Negative unit clauses : 1
% 0.10/0.24 % Non-unit-clauses : 7
% 0.10/0.24 % Current number of unprocessed clauses: 0
% 0.10/0.24 % ...number of literals in the above : 0
% 0.10/0.24 % Current number of archived formulas : 0
% 0.10/0.24 % Current number of archived clauses : 5
% 0.10/0.24 % Clause-clause subsumption calls (NU) : 6
% 0.10/0.24 % Rec. Clause-clause subsumption calls : 5
% 0.10/0.24 % Non-unit clause-clause subsumptions : 2
% 0.10/0.24 % Unit Clause-clause subsumption calls : 3
% 0.10/0.24 % Rewrite failures with RHS unbound : 0
% 0.10/0.24 % BW rewrite match attempts : 2
% 0.10/0.24 % BW rewrite match successes : 2
% 0.10/0.24 % Condensation attempts : 0
% 0.10/0.24 % Condensation successes : 0
% 0.10/0.24 % Termbank termtop insertions : 1406
% 0.10/0.24 % Search garbage collected termcells : 284
% 0.10/0.24
% 0.10/0.24 % -------------------------------------------------
% 0.10/0.24 % User time : 0.005 s
% 0.10/0.24 % System time : 0.001 s
% 0.10/0.24 % Total time : 0.006 s
% 0.10/0.24 % Maximum resident set size: 3588 pages
% 0.10/0.24
% 0.10/0.24 % -------------------------------------------------
% 0.10/0.24 % User time : 0.008 s
% 0.10/0.24 % System time : 0.001 s
% 0.10/0.24 % Total time : 0.009 s
% 0.10/0.24 % Maximum resident set size: 4864 pages
% 0.10/0.24 % E exiting
%------------------------------------------------------------------------------