%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM636^1 : 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 : n006.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 08:16:38 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 76 ( 46 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 244 ( 48 ~; 21 |; 1 &; 167 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 60 ( 21 ^; 39 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_sort2,type,
set: $tType ).
thf(decl_23,type,
x: nat ).
thf(decl_24,type,
suc: nat > nat ).
thf(decl_25,type,
esti: nat > set > $o ).
thf(decl_26,type,
setof: ( nat > $o ) > set ).
thf(decl_27,type,
n_1: nat ).
thf(decl_28,type,
esk1_1: set > nat ).
thf(satz2,conjecture,
( ( suc @ x )
!= x ),
file('/export/starexec/sandbox2/tmp/tmp.FLF1d0G3EH/E---3.1_623214.p',satz2) ).
thf(estii,axiom,
! [X1: nat > $o,X2: nat] :
( ( X1 @ X2 )
=> ( esti @ X2 @ ( setof @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.FLF1d0G3EH/E---3.1_623214.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/sandbox2/tmp/tmp.FLF1d0G3EH/E---3.1_623214.p',ax5) ).
thf(ax3,axiom,
! [X4: nat] :
( ( suc @ X4 )
!= n_1 ),
file('/export/starexec/sandbox2/tmp/tmp.FLF1d0G3EH/E---3.1_623214.p',ax3) ).
thf(estie,axiom,
! [X1: nat > $o,X2: nat] :
( ( esti @ X2 @ ( setof @ X1 ) )
=> ( X1 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.FLF1d0G3EH/E---3.1_623214.p',estie) ).
thf(satz1,axiom,
! [X4: nat,X5: nat] :
( ( X4 != X5 )
=> ( ( suc @ X4 )
!= ( suc @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.FLF1d0G3EH/E---3.1_623214.p',satz1) ).
thf(c_0_6,negated_conjecture,
~ ( ( ( suc @ x )
!= x ) ),
inference(assume_negation,[status(cth)],[satz2]) ).
thf(c_0_7,plain,
! [X21: nat > $o,X22: nat] :
( ~ ( X21 @ X22 )
| ( esti @ X22 @ ( setof @ X21 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[estii])])]) ).
thf(c_0_8,negated_conjecture,
( ( suc @ x )
= x ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
thf(c_0_9,plain,
! [X18: set,X20: nat] :
( ( ( esti @ ( esk1_1 @ X18 ) @ X18 )
| ( esti @ X20 @ X18 )
| ~ ( esti @ n_1 @ X18 ) )
& ( ~ ( esti @ ( suc @ ( esk1_1 @ X18 ) ) @ X18 )
| ( esti @ X20 @ X18 )
| ~ ( esti @ n_1 @ X18 ) ) ),
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_10,plain,
! [X1: nat > $o,X2: nat] :
( ( esti @ X2 @ ( setof @ X1 ) )
| ~ ( X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,negated_conjecture,
( ( suc @ x )
= x ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,plain,
! [X4: nat] :
( ( suc @ X4 )
!= n_1 ),
inference(fof_simplification,[status(thm)],[ax3]) ).
thf(c_0_13,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_9]) ).
thf(c_0_14,plain,
! [X2: nat] :
( ( esti @ X2
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( suc @ Z0 ) ) ) )
| ( X2
= ( suc @ X2 ) ) ),
inference(trigger,[status(thm)],[inference(cn,[status(thm)],[]),c_0_10,c_0_11]) ).
thf(c_0_15,plain,
! [X23: nat] :
( ( suc @ X23 )
!= n_1 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_12])]) ).
thf(c_0_16,plain,
! [X16: nat > $o,X17: nat] :
( ~ ( esti @ X17 @ ( setof @ X16 ) )
| ( X16 @ X17 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[estie])])]) ).
thf(c_0_17,plain,
! [X2: nat] :
( ( ( suc
@ ( suc
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( suc @ Z0 ) ) ) ) ) )
= ( suc
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( suc @ Z0 ) ) ) ) ) )
| ( esti @ X2
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( suc @ Z0 ) ) ) )
| ~ ( esti @ n_1
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( suc @ Z0 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_18,plain,
! [X2: nat] :
( ( suc @ X2 )
!= n_1 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_19,plain,
! [X4: nat,X5: nat] :
( ( X4 != X5 )
=> ( ( suc @ X4 )
!= ( suc @ X5 ) ) ),
inference(fof_simplification,[status(thm)],[satz1]) ).
thf(c_0_20,plain,
! [X2: nat,X1: nat > $o] :
( ( X1 @ X2 )
| ~ ( esti @ X2 @ ( setof @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_21,plain,
! [X2: nat] :
( ( ( suc
@ ( suc
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( suc @ Z0 ) ) ) ) ) )
= ( suc
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( suc @ Z0 ) ) ) ) ) )
| ( esti @ X2
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( suc @ Z0 ) ) ) ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_10])]),c_0_18]) ).
thf(c_0_22,plain,
! [X2: nat,X3: set] :
( ( esti @ ( esk1_1 @ X3 ) @ X3 )
| ( esti @ X2 @ X3 )
| ~ ( esti @ n_1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_23,plain,
! [X24: nat,X25: nat] :
( ( X24 = X25 )
| ( ( suc @ X24 )
!= ( suc @ X25 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
thf(c_0_24,plain,
! [X2: nat] :
( ( ( suc
@ ( suc
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( suc @ Z0 ) ) ) ) ) )
= ( suc
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( suc @ Z0 ) ) ) ) ) )
| ( ( suc @ X2 )
!= X2 ) ),
inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21])]) ).
thf(c_0_25,plain,
! [X2: nat] :
( ( esti
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( suc @ Z0 ) ) ) )
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( suc @ Z0 ) ) ) )
| ( esti @ X2
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( suc @ Z0 ) ) ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_14]),c_0_18]) ).
thf(c_0_26,plain,
! [X2: nat,X4: nat] :
( ( X2 = X4 )
| ( ( suc @ X2 )
!= ( suc @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_27,negated_conjecture,
( ( suc
@ ( suc
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( suc @ Z0 ) ) ) ) ) )
= ( suc
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( suc @ Z0 ) ) ) ) ) ),
inference(spm,[status(thm)],[c_0_24,c_0_11]) ).
thf(c_0_28,plain,
( esti
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( suc @ Z0 ) ) ) )
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( suc @ Z0 ) ) ) ),
inference(ef,[status(thm)],[c_0_25]) ).
thf(c_0_29,negated_conjecture,
! [X2: nat] :
( ( X2
= ( suc
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( suc @ Z0 ) ) ) ) ) )
| ( ( suc @ X2 )
!= ( suc
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( suc @ Z0 ) ) ) ) ) ) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
thf(c_0_30,plain,
( ( suc
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( suc @ Z0 ) ) ) ) )
!= ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( suc @ Z0 ) ) ) ) ),
inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_28])]) ).
thf(c_0_31,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_29]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM636^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n006.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 12:02:09 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.FLF1d0G3EH/E---3.1_623214.p
% 0.08/0.26 % Version: 3.5.1-ho
% 0.08/0.26 % Preprocessing class: HSSSSMSSSSSNSFA.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting new_ho_14 with 1500s (5) cores
% 0.08/0.26 % Starting full_lambda_8 with 300s (1) cores
% 0.08/0.26 % Starting new_ho_13 with 300s (1) cores
% 0.08/0.26 % Starting ho_unfolding_3 with 300s (1) cores
% 0.08/0.26 % new_ho_13 with pid 623229 completed with status 0
% 0.08/0.26 % Result found by new_ho_13
% 0.08/0.26 % Preprocessing class: HSSSSMSSSSSNSFA.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting new_ho_14 with 1500s (5) cores
% 0.08/0.26 % Starting full_lambda_8 with 300s (1) cores
% 0.08/0.26 % Starting new_ho_13 with 300s (1) cores
% 0.08/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.26 % No SInE strategy applied
% 0.08/0.26 % Search class: HGHSF-FFSF11-MSFFFSBN
% 0.08/0.26 % partial match(2): HGUSF-FFSF11-SSFFFSBN
% 0.08/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.26 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.26 % SubtermCWHack with pid 623231 completed with status 0
% 0.08/0.26 % Result found by SubtermCWHack
% 0.08/0.26 % Preprocessing class: HSSSSMSSSSSNSFA.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting new_ho_14 with 1500s (5) cores
% 0.08/0.26 % Starting full_lambda_8 with 300s (1) cores
% 0.08/0.26 % Starting new_ho_13 with 300s (1) cores
% 0.08/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.26 % No SInE strategy applied
% 0.08/0.26 % Search class: HGHSF-FFSF11-MSFFFSBN
% 0.08/0.26 % partial match(2): HGUSF-FFSF11-SSFFFSBN
% 0.08/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.26 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.26 % Preprocessing time : 0.001 s
% 0.08/0.26
% 0.08/0.26 % Proof found!
% 0.08/0.26 % SZS status Theorem
% 0.08/0.26 % SZS output start CNFRefutation
% See solution above
% 0.08/0.26 % Parsed axioms : 13
% 0.08/0.26 % Removed by relevancy pruning/SinE : 0
% 0.08/0.26 % Initial clauses : 14
% 0.08/0.26 % Removed in clause preprocessing : 7
% 0.08/0.26 % Initial clauses in saturation : 9
% 0.08/0.26 % Processed clauses : 26
% 0.08/0.26 % ...of these trivial : 0
% 0.08/0.26 % ...subsumed : 5
% 0.08/0.26 % ...remaining for further processing : 21
% 0.08/0.26 % Other redundant clauses eliminated : 0
% 0.08/0.26 % Clauses deleted for lack of memory : 0
% 0.08/0.26 % Backward-subsumed : 3
% 0.08/0.26 % Backward-rewritten : 1
% 0.08/0.26 % Generated clauses : 37
% 0.08/0.26 % ...of the previous two non-redundant : 29
% 0.08/0.26 % ...aggressively subsumed : 0
% 0.08/0.26 % Contextual simplify-reflections : 0
% 0.08/0.26 % Paramodulations : 33
% 0.08/0.26 % Factorizations : 2
% 0.08/0.26 % NegExts : 0
% 0.08/0.26 % Equation resolutions : 2
% 0.08/0.26 % Disequality decompositions : 0
% 0.08/0.26 % Total rewrite steps : 1
% 0.08/0.26 % ...of those cached : 0
% 0.08/0.26 % Propositional unsat checks : 0
% 0.08/0.26 % Propositional check models : 0
% 0.08/0.26 % Propositional check unsatisfiable : 0
% 0.08/0.26 % Propositional clauses : 0
% 0.08/0.26 % Propositional clauses after purity: 0
% 0.08/0.26 % Propositional unsat core size : 0
% 0.08/0.26 % Propositional preprocessing time : 0.000
% 0.08/0.26 % Propositional encoding time : 0.000
% 0.08/0.26 % Propositional solver time : 0.000
% 0.08/0.26 % Success case prop preproc time : 0.000
% 0.08/0.26 % Success case prop encoding time : 0.000
% 0.08/0.26 % Success case prop solver time : 0.000
% 0.08/0.26 % Current number of processed clauses : 17
% 0.08/0.26 % Positive orientable unit clauses : 3
% 0.08/0.26 % Positive unorientable unit clauses: 0
% 0.08/0.26 % Negative unit clauses : 3
% 0.08/0.26 % Non-unit-clauses : 11
% 0.08/0.26 % Current number of unprocessed clauses: 5
% 0.08/0.26 % ...number of literals in the above : 12
% 0.08/0.26 % Current number of archived formulas : 0
% 0.08/0.26 % Current number of archived clauses : 4
% 0.08/0.26 % Clause-clause subsumption calls (NU) : 36
% 0.08/0.26 % Rec. Clause-clause subsumption calls : 36
% 0.08/0.26 % Non-unit clause-clause subsumptions : 3
% 0.08/0.26 % Unit Clause-clause subsumption calls : 3
% 0.08/0.26 % Rewrite failures with RHS unbound : 0
% 0.08/0.26 % BW rewrite match attempts : 2
% 0.08/0.26 % BW rewrite match successes : 2
% 0.08/0.26 % Condensation attempts : 0
% 0.08/0.26 % Condensation successes : 0
% 0.08/0.26 % Termbank termtop insertions : 1328
% 0.08/0.26 % Search garbage collected termcells : 148
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.004 s
% 0.08/0.26 % System time : 0.001 s
% 0.08/0.26 % Total time : 0.005 s
% 0.08/0.26 % Maximum resident set size: 3636 pages
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.006 s
% 0.08/0.26 % System time : 0.006 s
% 0.08/0.26 % Total time : 0.011 s
% 0.08/0.26 % Maximum resident set size: 4864 pages
% 0.08/0.26 % E exiting
%------------------------------------------------------------------------------