%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM710^1 : 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 : n012.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 08:16:55 AM UTC 2026
% Result : Theorem 0.08s 0.15s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 38 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 74 ( 41 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 326 ( 19 ~; 18 |; 1 &; 283 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 64 ( 18 ^; 46 !; 0 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_sort2,type,
set: $tType ).
thf(decl_23,type,
x: nat ).
thf(decl_24,type,
y: nat ).
thf(decl_25,type,
ts: nat > nat > nat ).
thf(decl_26,type,
esti: nat > set > $o ).
thf(decl_27,type,
setof: ( nat > $o ) > set ).
thf(decl_28,type,
n_1: nat ).
thf(decl_29,type,
suc: nat > nat ).
thf(decl_30,type,
pl: nat > nat > nat ).
thf(decl_31,type,
esk1_1: set > nat ).
thf(satz29,conjecture,
( ( ts @ x @ y )
= ( ts @ y @ x ) ),
file('/export/starexec/sandbox/tmp/tmp.m3J6J2S9WX/E---3.1_51578.p',satz29) ).
thf(estii,axiom,
! [X1: nat > $o,X2: nat] :
( ( X1 @ X2 )
=> ( esti @ X2 @ ( setof @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.m3J6J2S9WX/E---3.1_51578.p',estii) ).
thf(ax5,axiom,
! [X3: set] :
( ( esti @ n_1 @ X3 )
=> ( ! [X4: nat] :
( ( esti @ X4 @ X3 )
=> ( esti @ ( suc @ X4 ) @ X3 ) )
=> ! [X4: nat] : ( esti @ X4 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.m3J6J2S9WX/E---3.1_51578.p',ax5) ).
thf(satz28a,axiom,
! [X4: nat] :
( ( ts @ X4 @ n_1 )
= X4 ),
file('/export/starexec/sandbox/tmp/tmp.m3J6J2S9WX/E---3.1_51578.p',satz28a) ).
thf(satz28c,axiom,
! [X4: nat] :
( ( ts @ n_1 @ X4 )
= X4 ),
file('/export/starexec/sandbox/tmp/tmp.m3J6J2S9WX/E---3.1_51578.p',satz28c) ).
thf(estie,axiom,
! [X1: nat > $o,X2: nat] :
( ( esti @ X2 @ ( setof @ X1 ) )
=> ( X1 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.m3J6J2S9WX/E---3.1_51578.p',estie) ).
thf(satz28d,axiom,
! [X4: nat,X5: nat] :
( ( ts @ ( suc @ X4 ) @ X5 )
= ( pl @ ( ts @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox/tmp/tmp.m3J6J2S9WX/E---3.1_51578.p',satz28d) ).
thf(satz28f,axiom,
! [X4: nat,X5: nat] :
( ( pl @ ( ts @ X4 @ X5 ) @ X4 )
= ( ts @ X4 @ ( suc @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.m3J6J2S9WX/E---3.1_51578.p',satz28f) ).
thf(c_0_8,negated_conjecture,
( ( ts @ x @ y )
!= ( ts @ y @ x ) ),
inference(assume_negation,[status(cth)],[satz29]) ).
thf(c_0_9,negated_conjecture,
( ( ts @ x @ y )
!= ( ts @ y @ x ) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
thf(c_0_10,plain,
! [X24: nat > $o,X25: nat] :
( ~ ( X24 @ X25 )
| ( esti @ X25 @ ( setof @ X24 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[estii])])]) ).
thf(c_0_11,negated_conjecture,
( ( ts @ x @ y )
!= ( ts @ y @ x ) ),
inference(fof_nnf,[status(thm)],[c_0_9]) ).
thf(c_0_12,plain,
! [X21: set,X23: nat] :
( ( ( esti @ ( esk1_1 @ X21 ) @ X21 )
| ( esti @ X23 @ X21 )
| ~ ( esti @ n_1 @ X21 ) )
& ( ~ ( esti @ ( suc @ ( esk1_1 @ X21 ) ) @ X21 )
| ( esti @ X23 @ X21 )
| ~ ( esti @ n_1 @ X21 ) ) ),
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)],[ax5])])])])])]) ).
thf(c_0_13,plain,
! [X1: nat > $o,X2: nat] :
( ( esti @ X2 @ ( setof @ X1 ) )
| ~ ( X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_14,negated_conjecture,
( ( ts @ x @ y )
!= ( ts @ y @ x ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_15,plain,
! [X26: nat] :
( ( ts @ X26 @ n_1 )
= X26 ),
inference(variable_rename,[status(thm)],[satz28a]) ).
thf(c_0_16,plain,
! [X27: nat] :
( ( ts @ n_1 @ X27 )
= X27 ),
inference(variable_rename,[status(thm)],[satz28c]) ).
thf(c_0_17,plain,
! [X2: nat,X3: set] :
( ( esti @ ( esk1_1 @ X3 ) @ X3 )
| ( esti @ X2 @ X3 )
| ~ ( esti @ n_1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_18,plain,
! [X2: nat] :
( ( esti @ X2
@ ( setof
@ ^ [Z0: nat] :
( ( ts @ x @ Z0 )
= ( ts @ Z0 @ x ) ) ) )
| ( ( ts @ x @ X2 )
!= ( ts @ X2 @ x ) ) ),
inference(trigger,[status(thm)],[inference(cn,[status(thm)],[]),c_0_13,c_0_14]) ).
thf(c_0_19,plain,
! [X2: nat] :
( ( ts @ X2 @ n_1 )
= X2 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_20,plain,
! [X2: nat] :
( ( ts @ n_1 @ X2 )
= X2 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_21,plain,
! [X19: nat > $o,X20: nat] :
( ~ ( esti @ X20 @ ( setof @ X19 ) )
| ( X19 @ X20 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[estie])])]) ).
thf(c_0_22,plain,
! [X2: nat] :
( ( esti
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( ( ts @ x @ Z0 )
= ( ts @ Z0 @ x ) ) ) )
@ ( setof
@ ^ [Z0: nat] :
( ( ts @ x @ Z0 )
= ( ts @ Z0 @ x ) ) ) )
| ( esti @ X2
@ ( setof
@ ^ [Z0: nat] :
( ( ts @ x @ Z0 )
= ( ts @ Z0 @ x ) ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]) ).
thf(c_0_23,plain,
! [X30: nat,X31: nat] :
( ( ts @ ( suc @ X30 ) @ X31 )
= ( pl @ ( ts @ X30 @ X31 ) @ X31 ) ),
inference(variable_rename,[status(thm)],[satz28d]) ).
thf(c_0_24,plain,
! [X2: nat,X1: nat > $o] :
( ( X1 @ X2 )
| ~ ( esti @ X2 @ ( setof @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_25,plain,
( esti
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( ( ts @ x @ Z0 )
= ( ts @ Z0 @ x ) ) ) )
@ ( setof
@ ^ [Z0: nat] :
( ( ts @ x @ Z0 )
= ( ts @ Z0 @ x ) ) ) ),
inference(ef,[status(thm)],[c_0_22]) ).
thf(c_0_26,plain,
! [X28: nat,X29: nat] :
( ( pl @ ( ts @ X28 @ X29 ) @ X28 )
= ( ts @ X28 @ ( suc @ X29 ) ) ),
inference(variable_rename,[status(thm)],[satz28f]) ).
thf(c_0_27,plain,
! [X2: nat,X3: set] :
( ( esti @ X2 @ X3 )
| ~ ( esti @ ( suc @ ( esk1_1 @ X3 ) ) @ X3 )
| ~ ( esti @ n_1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_28,plain,
! [X2: nat,X4: nat] :
( ( ts @ ( suc @ X2 ) @ X4 )
= ( pl @ ( ts @ X2 @ X4 ) @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_29,plain,
( ( ts
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( ( ts @ x @ Z0 )
= ( ts @ Z0 @ x ) ) ) )
@ x )
= ( ts @ x
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( ( ts @ x @ Z0 )
= ( ts @ Z0 @ x ) ) ) ) ) ),
inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25])]) ).
thf(c_0_30,plain,
! [X2: nat,X4: nat] :
( ( pl @ ( ts @ X2 @ X4 ) @ X2 )
= ( ts @ X2 @ ( suc @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_31,plain,
! [X2: nat] :
( ( esti @ X2
@ ( setof
@ ^ [Z0: nat] :
( ( ts @ x @ Z0 )
= ( ts @ Z0 @ x ) ) ) )
| ( ( ts
@ ( suc
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( ( ts @ x @ Z0 )
= ( ts @ Z0 @ x ) ) ) ) )
@ x )
!= ( ts @ x
@ ( suc
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( ( ts @ x @ Z0 )
= ( ts @ Z0 @ x ) ) ) ) ) ) )
| ~ ( esti @ n_1
@ ( setof
@ ^ [Z0: nat] :
( ( ts @ x @ Z0 )
= ( ts @ Z0 @ x ) ) ) ) ),
inference(spm,[status(thm)],[c_0_27,c_0_18]) ).
thf(c_0_32,plain,
( ( ts
@ ( suc
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( ( ts @ x @ Z0 )
= ( ts @ Z0 @ x ) ) ) ) )
@ x )
= ( ts @ x
@ ( suc
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( ( ts @ x @ Z0 )
= ( ts @ Z0 @ x ) ) ) ) ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
thf(c_0_33,plain,
! [X2: nat] :
( ( esti @ X2
@ ( setof
@ ^ [Z0: nat] :
( ( ts @ x @ Z0 )
= ( ts @ Z0 @ x ) ) ) )
| ~ ( esti @ n_1
@ ( setof
@ ^ [Z0: nat] :
( ( ts @ x @ Z0 )
= ( ts @ Z0 @ x ) ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]) ).
thf(c_0_34,plain,
! [X2: nat] :
( ( ( ts @ x @ X2 )
= ( ts @ X2 @ x ) )
| ~ ( esti @ X2
@ ( setof
@ ^ [Z0: nat] :
( ( ts @ x @ Z0 )
= ( ts @ Z0 @ x ) ) ) ) ),
inference(trigger,[status(thm)],[inference(cn,[status(thm)],[]),c_0_24,c_0_14]) ).
thf(c_0_35,plain,
! [X2: nat] :
( esti @ X2
@ ( setof
@ ^ [Z0: nat] :
( ( ts @ x @ Z0 )
= ( ts @ Z0 @ x ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_13])]),c_0_19]),c_0_20])]) ).
thf(c_0_36,plain,
! [X2: nat] :
( ( ts @ x @ X2 )
= ( ts @ X2 @ x ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]) ).
thf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM710^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 12:43:03 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.13 Running higher-order theorem proving
% 0.08/0.13 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.m3J6J2S9WX/E---3.1_51578.p
% 0.08/0.15 % Version: 3.5.1-ho
% 0.08/0.15 % Preprocessing class: HSMSSMSSSSSNSFA.
% 0.08/0.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.15 % Starting new_ho_14 with 1200s (4) cores
% 0.08/0.15 % Starting new_ho_13 with 600s (2) cores
% 0.08/0.15 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.08/0.15 % Starting new_bool_3 with 300s (1) cores
% 0.08/0.15 % new_ho_13 with pid 51592 completed with status 0
% 0.08/0.15 % Result found by new_ho_13
% 0.08/0.15 % Preprocessing class: HSMSSMSSSSSNSFA.
% 0.08/0.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.15 % Starting new_ho_14 with 1200s (4) cores
% 0.08/0.15 % Starting new_ho_13 with 600s (2) cores
% 0.08/0.15 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.15 % No SInE strategy applied
% 0.08/0.15 % Search class: HGUSM-FFMF21-MSFFFSBN
% 0.08/0.15 % partial match(2): HGUSM-FFSF21-SSFFFSBN
% 0.08/0.15 % Scheduled 5 strats onto 2 cores with 600 seconds (600 total)
% 0.08/0.15 % Starting SubtermCWHack with 61s (1) cores
% 0.08/0.15 % Starting new_ho_14 with 361s (1) cores
% 0.08/0.15 % SubtermCWHack with pid 51596 completed with status 0
% 0.08/0.15 % Result found by SubtermCWHack
% 0.08/0.15 % Preprocessing class: HSMSSMSSSSSNSFA.
% 0.08/0.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.15 % Starting new_ho_14 with 1200s (4) cores
% 0.08/0.15 % Starting new_ho_13 with 600s (2) cores
% 0.08/0.15 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.15 % No SInE strategy applied
% 0.08/0.15 % Search class: HGUSM-FFMF21-MSFFFSBN
% 0.08/0.15 % partial match(2): HGUSM-FFSF21-SSFFFSBN
% 0.08/0.15 % Scheduled 5 strats onto 2 cores with 600 seconds (600 total)
% 0.08/0.15 % Starting SubtermCWHack with 61s (1) cores
% 0.08/0.15 % Preprocessing time : 0.001 s
% 0.08/0.15
% 0.08/0.15 % Proof found!
% 0.08/0.15 % SZS status Theorem
% 0.08/0.15 % SZS output start CNFRefutation
% See solution above
% 0.08/0.15 % Parsed axioms : 18
% 0.08/0.15 % Removed by relevancy pruning/SinE : 0
% 0.08/0.15 % Initial clauses : 19
% 0.08/0.15 % Removed in clause preprocessing : 10
% 0.08/0.15 % Initial clauses in saturation : 17
% 0.08/0.15 % Processed clauses : 73
% 0.08/0.15 % ...of these trivial : 1
% 0.08/0.15 % ...subsumed : 24
% 0.08/0.15 % ...remaining for further processing : 48
% 0.08/0.15 % Other redundant clauses eliminated : 0
% 0.08/0.15 % Clauses deleted for lack of memory : 0
% 0.08/0.15 % Backward-subsumed : 3
% 0.08/0.15 % Backward-rewritten : 7
% 0.08/0.15 % Generated clauses : 127
% 0.08/0.15 % ...of the previous two non-redundant : 77
% 0.08/0.15 % ...aggressively subsumed : 0
% 0.08/0.15 % Contextual simplify-reflections : 0
% 0.08/0.15 % Paramodulations : 124
% 0.08/0.15 % Factorizations : 2
% 0.08/0.15 % NegExts : 0
% 0.08/0.15 % Equation resolutions : 0
% 0.08/0.15 % Disequality decompositions : 0
% 0.08/0.15 % Total rewrite steps : 118
% 0.08/0.15 % ...of those cached : 23
% 0.08/0.15 % Propositional unsat checks : 0
% 0.08/0.15 % Propositional check models : 0
% 0.08/0.15 % Propositional check unsatisfiable : 0
% 0.08/0.15 % Propositional clauses : 0
% 0.08/0.15 % Propositional clauses after purity: 0
% 0.08/0.15 % Propositional unsat core size : 0
% 0.08/0.15 % Propositional preprocessing time : 0.000
% 0.08/0.15 % Propositional encoding time : 0.000
% 0.08/0.15 % Propositional solver time : 0.000
% 0.08/0.15 % Success case prop preproc time : 0.000
% 0.08/0.15 % Success case prop encoding time : 0.000
% 0.08/0.15 % Success case prop solver time : 0.000
% 0.08/0.15 % Current number of processed clauses : 37
% 0.08/0.15 % Positive orientable unit clauses : 16
% 0.08/0.15 % Positive unorientable unit clauses: 10
% 0.08/0.15 % Negative unit clauses : 0
% 0.08/0.15 % Non-unit-clauses : 11
% 0.08/0.15 % Current number of unprocessed clauses: 18
% 0.08/0.15 % ...number of literals in the above : 29
% 0.08/0.15 % Current number of archived formulas : 0
% 0.08/0.15 % Current number of archived clauses : 11
% 0.08/0.15 % Clause-clause subsumption calls (NU) : 66
% 0.08/0.15 % Rec. Clause-clause subsumption calls : 66
% 0.08/0.15 % Non-unit clause-clause subsumptions : 0
% 0.08/0.15 % Unit Clause-clause subsumption calls : 203
% 0.08/0.15 % Rewrite failures with RHS unbound : 0
% 0.08/0.15 % BW rewrite match attempts : 207
% 0.08/0.15 % BW rewrite match successes : 14
% 0.08/0.15 % Condensation attempts : 0
% 0.08/0.15 % Condensation successes : 0
% 0.08/0.15 % Termbank termtop insertions : 10416
% 0.08/0.15 % Search garbage collected termcells : 134
% 0.08/0.15
% 0.08/0.15 % -------------------------------------------------
% 0.08/0.15 % User time : 0.005 s
% 0.08/0.15 % System time : 0.002 s
% 0.08/0.15 % Total time : 0.008 s
% 0.08/0.15 % Maximum resident set size: 3640 pages
% 0.08/0.15
% 0.08/0.15 % -------------------------------------------------
% 0.08/0.15 % User time : 0.011 s
% 0.08/0.15 % System time : 0.006 s
% 0.08/0.15 % Total time : 0.017 s
% 0.08/0.15 % Maximum resident set size: 4864 pages
% 0.08/0.15 % E exiting
%------------------------------------------------------------------------------