%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM636^3 : 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 : n018.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 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 28 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 86 ( 23 ~; 13 |; 2 &; 45 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 5 ^; 25 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
one: $i ).
thf(decl_24,type,
succ: $i > $i ).
thf(decl_25,type,
m: $i > $o ).
thf(decl_26,type,
esk1_1: ( $i > $o ) > $i ).
thf(decl_27,type,
esk2_0: $i ).
thf(m_is_all,conjecture,
! [X1: $i] : ( m @ X1 ),
file('/export/starexec/sandbox2/tmp/tmp.iqxAh77X6y/E---3.1_4189300.p',m_is_all) ).
thf(m_defn,axiom,
( m
= ( ^ [X4: $i] :
( ( succ @ X4 )
!= X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iqxAh77X6y/E---3.1_4189300.p',m_defn) ).
thf(one_is_first,axiom,
! [X1: $i] :
( ( succ @ X1 )
!= one ),
file('/export/starexec/sandbox2/tmp/tmp.iqxAh77X6y/E---3.1_4189300.p',one_is_first) ).
thf(succ_injective,axiom,
! [X1: $i,X2: $i] :
( ( ( succ @ X1 )
= ( succ @ X2 ) )
=> ( X1 = X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.iqxAh77X6y/E---3.1_4189300.p',succ_injective) ).
thf(induction,axiom,
! [X3: $i > $o] :
( ( ( X3 @ one )
& ! [X1: $i] :
( ( X3 @ X1 )
=> ( X3 @ ( succ @ X1 ) ) ) )
=> ! [X2: $i] : ( X3 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.iqxAh77X6y/E---3.1_4189300.p',induction) ).
thf(c_0_5,negated_conjecture,
~ ! [X1: $i] : ( m @ X1 ),
inference(assume_negation,[status(cth)],[m_is_all]) ).
thf(c_0_6,plain,
( m
= ( ^ [Z0: $i] :
( ( succ @ Z0 )
!= Z0 ) ) ),
inference(fof_simplification,[status(thm)],[m_defn]) ).
thf(c_0_7,negated_conjecture,
~ ! [X1: $i] :
( ( succ @ X1 )
!= X1 ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[c_0_5,c_0_6])]) ).
thf(c_0_8,plain,
! [X1: $i] :
( ( succ @ X1 )
!= one ),
inference(fof_simplification,[status(thm)],[one_is_first]) ).
thf(c_0_9,plain,
! [X14: $i,X15: $i] :
( ( ( succ @ X14 )
!= ( succ @ X15 ) )
| ( X14 = X15 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[succ_injective])])]) ).
thf(c_0_10,negated_conjecture,
( ( succ @ esk2_0 )
= esk2_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
thf(c_0_11,plain,
! [X16: $i > $o,X18: $i] :
( ( ( X16 @ ( esk1_1 @ X16 ) )
| ~ ( X16 @ one )
| ( X16 @ X18 ) )
& ( ~ ( X16 @ ( succ @ ( esk1_1 @ X16 ) ) )
| ~ ( X16 @ one )
| ( X16 @ 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)],[induction])])])])])]) ).
thf(c_0_12,plain,
! [X13: $i] :
( ( succ @ X13 )
!= one ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_8])]) ).
thf(c_0_13,plain,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ( ( succ @ X1 )
!= ( succ @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,negated_conjecture,
( ( succ @ esk2_0 )
= esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_15,plain,
! [X1: $i,X3: $i > $o] :
( ( X3 @ X1 )
| ~ ( X3 @ ( succ @ ( esk1_1 @ X3 ) ) )
| ~ ( X3 @ one ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_16,plain,
! [X1: $i] :
( ( succ @ X1 )
!= one ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_17,plain,
! [X1: $i,X3: $i > $o] :
( ( X3 @ ( esk1_1 @ X3 ) )
| ( X3 @ X1 )
| ~ ( X3 @ one ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_18,negated_conjecture,
! [X1: $i] :
( ( X1 = esk2_0 )
| ( ( succ @ X1 )
!= esk2_0 ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_19,plain,
! [X1: $i] :
( ( ( succ
@ ( esk1_1
@ ^ [Z0: $i] : ( Z0 != X1 ) ) )
= X1 )
| ( one = X1 ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_15]) ).
thf(c_0_20,negated_conjecture,
one != esk2_0,
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
thf(c_0_21,plain,
! [X1: $i] :
( ( one = X1 )
| ( ( esk1_1
@ ^ [Z0: $i] : ( Z0 != X1 ) )
!= X1 ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_17]) ).
thf(c_0_22,negated_conjecture,
( ( esk1_1
@ ^ [Z0: $i] : ( Z0 != esk2_0 ) )
= esk2_0 ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19])]),c_0_20]) ).
thf(c_0_23,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM636^3 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n018.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 12:10:11 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.22 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.iqxAh77X6y/E---3.1_4189300.p
% 0.07/0.25 % Version: 3.5.1-ho
% 0.07/0.25 % Preprocessing class: HSSSSMSSSLSNSFA.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting post_as_ho4 with 1200s (4) cores
% 0.07/0.25 % Starting post_as_ho5 with 600s (2) cores
% 0.07/0.25 % Starting new_ho_8 with 300s (1) cores
% 0.07/0.25 % Starting new_ho_4 with 300s (1) cores
% 0.07/0.25 % post_as_ho4 with pid 4189313 completed with status 0
% 0.07/0.25 % Result found by post_as_ho4
% 0.07/0.25 % Preprocessing class: HSSSSMSSSLSNSFA.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting post_as_ho4 with 1200s (4) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.25 % No SInE strategy applied
% 0.07/0.25 % Search class: HGUSF-FFSF11-SSFFMSBN
% 0.07/0.25 % partial match(1): HGUNF-FFSF11-SSFFMSBN
% 0.07/0.25 % Scheduled 6 strats onto 4 cores with 1200 seconds (1200 total)
% 0.07/0.25 % Starting SubtermCWHack with 121s (1) cores
% 0.07/0.25 % Starting post_as_ho12 with 481s (1) cores
% 0.07/0.25 % Starting new_ho_8 with 181s (1) cores
% 0.07/0.25 % Starting new_ho_4 with 181s (1) cores
% 0.07/0.25 % SubtermCWHack with pid 4189319 completed with status 10
% 0.07/0.25 % Starting post_as_ho5 with 181s (1) cores
% 0.07/0.25 % new_ho_8 with pid 4189322 completed with status 10
% 0.07/0.25 % Starting post_as_ho4 with 55s (1) cores
% 0.07/0.25 % post_as_ho12 with pid 4189320 completed with status 10
% 0.07/0.25 % new_ho_4 with pid 4189324 completed with status 10
% 0.07/0.25 % post_as_ho5 with pid 4189327 completed with status 0
% 0.07/0.25 % Result found by post_as_ho5
% 0.07/0.25 % Preprocessing class: HSSSSMSSSLSNSFA.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting post_as_ho4 with 1200s (4) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.25 % No SInE strategy applied
% 0.07/0.25 % Search class: HGUSF-FFSF11-SSFFMSBN
% 0.07/0.25 % partial match(1): HGUNF-FFSF11-SSFFMSBN
% 0.07/0.25 % Scheduled 6 strats onto 4 cores with 1200 seconds (1200 total)
% 0.07/0.25 % Starting SubtermCWHack with 121s (1) cores
% 0.07/0.25 % Starting post_as_ho12 with 481s (1) cores
% 0.07/0.25 % Starting new_ho_8 with 181s (1) cores
% 0.07/0.25 % Starting new_ho_4 with 181s (1) cores
% 0.07/0.25 % SubtermCWHack with pid 4189319 completed with status 10
% 0.07/0.25 % Starting post_as_ho5 with 181s (1) cores
% 0.07/0.25 % Preprocessing time : 0.001 s
% 0.07/0.25 % Presaturation interreduction done
% 0.07/0.25
% 0.07/0.25 % Proof found!
% 0.07/0.25 % SZS status Theorem
% 0.07/0.25 % SZS output start CNFRefutation
% See solution above
% 0.07/0.25 % Parsed axioms : 10
% 0.07/0.25 % Removed by relevancy pruning/SinE : 0
% 0.07/0.25 % Initial clauses : 10
% 0.07/0.25 % Removed in clause preprocessing : 3
% 0.07/0.25 % Initial clauses in saturation : 7
% 0.07/0.25 % Processed clauses : 25
% 0.07/0.25 % ...of these trivial : 0
% 0.07/0.25 % ...subsumed : 5
% 0.07/0.25 % ...remaining for further processing : 20
% 0.07/0.25 % Other redundant clauses eliminated : 5
% 0.07/0.25 % Clauses deleted for lack of memory : 0
% 0.07/0.25 % Backward-subsumed : 3
% 0.07/0.25 % Backward-rewritten : 0
% 0.07/0.25 % Generated clauses : 53
% 0.07/0.25 % ...of the previous two non-redundant : 38
% 0.07/0.25 % ...aggressively subsumed : 0
% 0.07/0.25 % Contextual simplify-reflections : 0
% 0.07/0.25 % Paramodulations : 35
% 0.07/0.25 % Factorizations : 4
% 0.07/0.25 % NegExts : 0
% 0.07/0.25 % Equation resolutions : 8
% 0.07/0.25 % Disequality decompositions : 0
% 0.07/0.25 % Total rewrite steps : 2
% 0.07/0.25 % ...of those cached : 0
% 0.07/0.25 % Propositional unsat checks : 0
% 0.07/0.25 % Propositional check models : 0
% 0.07/0.25 % Propositional check unsatisfiable : 0
% 0.07/0.25 % Propositional clauses : 0
% 0.07/0.25 % Propositional clauses after purity: 0
% 0.07/0.25 % Propositional unsat core size : 0
% 0.07/0.25 % Propositional preprocessing time : 0.000
% 0.07/0.25 % Propositional encoding time : 0.000
% 0.07/0.25 % Propositional solver time : 0.000
% 0.07/0.25 % Success case prop preproc time : 0.000
% 0.07/0.25 % Success case prop encoding time : 0.000
% 0.07/0.25 % Success case prop solver time : 0.000
% 0.07/0.25 % Current number of processed clauses : 12
% 0.07/0.25 % Positive orientable unit clauses : 3
% 0.07/0.25 % Positive unorientable unit clauses: 0
% 0.07/0.25 % Negative unit clauses : 2
% 0.07/0.25 % Non-unit-clauses : 7
% 0.07/0.25 % Current number of unprocessed clauses: 17
% 0.07/0.25 % ...number of literals in the above : 46
% 0.07/0.25 % Current number of archived formulas : 0
% 0.07/0.25 % Current number of archived clauses : 8
% 0.07/0.25 % Clause-clause subsumption calls (NU) : 8
% 0.07/0.25 % Rec. Clause-clause subsumption calls : 8
% 0.07/0.25 % Non-unit clause-clause subsumptions : 3
% 0.07/0.25 % Unit Clause-clause subsumption calls : 3
% 0.07/0.25 % Rewrite failures with RHS unbound : 0
% 0.07/0.25 % BW rewrite match attempts : 1
% 0.07/0.25 % BW rewrite match successes : 1
% 0.07/0.25 % Condensation attempts : 0
% 0.07/0.25 % Condensation successes : 0
% 0.07/0.25 % Termbank termtop insertions : 1954
% 0.07/0.25 % Search garbage collected termcells : 148
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.015 s
% 0.07/0.25 % System time : 0.007 s
% 0.07/0.25 % Total time : 0.022 s
% 0.07/0.25 % Maximum resident set size: 3632 pages
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.018 s
% 0.07/0.25 % System time : 0.008 s
% 0.07/0.25 % Total time : 0.027 s
% 0.07/0.25 % Maximum resident set size: 4864 pages
% 0.07/0.25 % E exiting
%------------------------------------------------------------------------------