%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM814^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 08:17:10 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 26 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 179 ( 23 ~; 13 |; 19 &; 100 @)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 7 ^; 42 !; 3 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
c0: $i ).
thf(decl_24,type,
cS: $i > $i ).
thf(decl_25,type,
cEVEN1: $i > $o ).
thf(decl_26,type,
cIND: $o ).
thf(decl_27,type,
cODD1: $i > $o ).
thf(decl_28,type,
cPEANO1: $o ).
thf(decl_29,type,
esk1_1: ( $i > $o ) > $i ).
thf(decl_30,type,
esk2_2: $i > ( $i > $o ) > $i ).
thf(cODD1_def,axiom,
( cODD1
= ( ^ [X1: $i] :
~ ( cEVEN1 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TEQSLKCUJL/E---3.1_3324475.p',cODD1_def) ).
thf(cEVEN1_def,axiom,
( cEVEN1
= ( ^ [X1: $i] :
! [X2: $i > $o] :
( ( ( X2 @ c0 )
& ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( cS @ ( cS @ X3 ) ) ) ) )
=> ( X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TEQSLKCUJL/E---3.1_3324475.p',cEVEN1_def) ).
thf(cTHM404,conjecture,
( cPEANO1
=> ? [X1: $i] : ( cODD1 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.TEQSLKCUJL/E---3.1_3324475.p',cTHM404) ).
thf(cPEANO1_def,axiom,
( cPEANO1
<=> ( ! [X4: $i] :
( ( cS @ X4 )
!= c0 )
& ! [X5: $i,X6: $i] :
( ( ( cS @ X5 )
= ( cS @ X6 ) )
=> ( X5 = X6 ) )
& cIND ) ),
file('/export/starexec/sandbox/tmp/tmp.TEQSLKCUJL/E---3.1_3324475.p',cPEANO1_def) ).
thf(cIND_def,axiom,
( cIND
<=> ! [X2: $i > $o] :
( ( ( X2 @ c0 )
& ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( cS @ X3 ) ) ) )
=> ! [X3: $i] : ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TEQSLKCUJL/E---3.1_3324475.p',cIND_def) ).
thf(c_0_5,plain,
( cODD1
= ( ^ [Z0: $i] :
~ ! [X14: $i > $o] :
( ( ( X14 @ c0 )
& ! [X15: $i] :
( ( X14 @ X15 )
=> ( X14 @ ( cS @ ( cS @ X15 ) ) ) ) )
=> ( X14 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[cODD1_def]) ).
thf(c_0_6,plain,
( cEVEN1
= ( ^ [Z0: $i] :
! [X2: $i > $o] :
( ( ( X2 @ c0 )
& ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( cS @ ( cS @ X3 ) ) ) ) )
=> ( X2 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[cEVEN1_def]) ).
thf(c_0_7,negated_conjecture,
~ ( cPEANO1
=> ? [X1: $i] : ( cODD1 @ X1 ) ),
inference(assume_negation,[status(cth)],[cTHM404]) ).
thf(c_0_8,axiom,
( cPEANO1
= ( ! [X4: $i] :
( ( cS @ X4 )
!= c0 )
& ! [X5: $i,X6: $i] :
( ( ( cS @ X5 )
= ( cS @ X6 ) )
=> ( X5 = X6 ) )
& ! [X16: $i > $o] :
( ( ( X16 @ c0 )
& ! [X17: $i] :
( ( X16 @ X17 )
=> ( X16 @ ( cS @ X17 ) ) ) )
=> ! [X18: $i] : ( X16 @ X18 ) ) ) ),
inference(apply_def,[status(thm)],[cPEANO1_def,cIND_def]) ).
thf(c_0_9,plain,
( cODD1
= ( ^ [Z0: $i] :
~ ! [X14: $i > $o] :
( ( ( X14 @ c0 )
& ! [X15: $i] :
( ( X14 @ X15 )
=> ( X14 @ ( cS @ ( cS @ X15 ) ) ) ) )
=> ( X14 @ Z0 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_5,c_0_6]) ).
thf(c_0_10,negated_conjecture,
~ ( ( ! [X19: $i] :
( ( cS @ X19 )
!= c0 )
& ! [X20: $i,X21: $i] :
( ( ( cS @ X20 )
= ( cS @ X21 ) )
=> ( X20 = X21 ) )
& ! [X22: $i > $o] :
( ( ( X22 @ c0 )
& ! [X23: $i] :
( ( X22 @ X23 )
=> ( X22 @ ( cS @ X23 ) ) ) )
=> ! [X24: $i] : ( X22 @ X24 ) ) )
=> ? [X1: $i] :
~ ! [X25: $i > $o] :
( ( ( X25 @ c0 )
& ! [X26: $i] :
( ( X25 @ X26 )
=> ( X25 @ ( cS @ ( cS @ X26 ) ) ) ) )
=> ( X25 @ X1 ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_7,c_0_8]),c_0_9])]) ).
thf(c_0_11,negated_conjecture,
! [X27: $i,X28: $i,X29: $i,X30: $i > $o,X32: $i,X33: $i,X34: $i > $o] :
( ( ( cS @ X27 )
!= c0 )
& ( ( ( cS @ X28 )
!= ( cS @ X29 ) )
| ( X28 = X29 ) )
& ( ( X30 @ ( esk1_1 @ X30 ) )
| ~ ( X30 @ c0 )
| ( X30 @ X32 ) )
& ( ~ ( X30 @ ( cS @ ( esk1_1 @ X30 ) ) )
| ~ ( X30 @ c0 )
| ( X30 @ X32 ) )
& ( ( X34 @ ( esk2_2 @ X33 @ X34 ) )
| ~ ( X34 @ c0 )
| ( X34 @ X33 ) )
& ( ~ ( X34 @ ( cS @ ( cS @ ( esk2_2 @ X33 @ X34 ) ) ) )
| ~ ( X34 @ c0 )
| ( X34 @ X33 ) ) ),
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_10])])])])])]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i,X2: $i > $o] :
( ( X2 @ X1 )
| ~ ( X2 @ ( cS @ ( cS @ ( esk2_2 @ X1 @ X2 ) ) ) )
| ~ ( X2 @ c0 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i,X3: $i] :
( ( X1 = X3 )
| ( ( cS @ X1 )
!= ( cS @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i] :
( ( ( cS
@ ( cS
@ ( esk2_2 @ X1
@ ^ [Z0: $i] : ( Z0 != X1 ) ) ) )
= X1 )
| ( c0 = X1 ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_12]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i] :
( ( cS @ X1 )
!= c0 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i] :
( ( cS
@ ( esk2_2 @ ( cS @ X1 )
@ ^ [Z0: $i] :
( Z0
!= ( cS @ X1 ) ) ) )
= X1 ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14])]),c_0_15]) ).
thf(c_0_17,negated_conjecture,
$false,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM814^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n007.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 13:00:39 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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.TEQSLKCUJL/E---3.1_3324475.p
% 0.21/0.27 % Version: 3.5.1-ho
% 0.21/0.27 % Preprocessing class: HSSSSLSSSLSNSFA.
% 0.21/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.27 % Starting post_as_ho5 with 1500s (5) cores
% 0.21/0.27 % Starting post_as_ho10 with 300s (1) cores
% 0.21/0.27 % Starting post_as_ho4 with 300s (1) cores
% 0.21/0.27 % Starting sh5l with 300s (1) cores
% 0.21/0.27 % sh5l with pid 3324491 completed with status 0
% 0.21/0.27 % Result found by sh5l
% 0.21/0.27 % Preprocessing class: HSSSSLSSSLSNSFA.
% 0.21/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.27 % Starting post_as_ho5 with 1500s (5) cores
% 0.21/0.27 % Starting post_as_ho10 with 300s (1) cores
% 0.21/0.27 % Starting post_as_ho4 with 300s (1) cores
% 0.21/0.27 % Starting sh5l with 300s (1) cores
% 0.21/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.21/0.27 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.21/0.27 % Search class: HGUSF-FFSF21-MSFFMMBN
% 0.21/0.27 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.27 % Starting SubtermCWHack with 31s (1) cores
% 0.21/0.27 % SubtermCWHack with pid 3324495 completed with status 10
% 0.21/0.27 % Starting ho_unfolding_3 with 181s (1) cores
% 0.21/0.27 % ho_unfolding_3 with pid 3324501 completed with status 0
% 0.21/0.27 % Result found by ho_unfolding_3
% 0.21/0.27 % Preprocessing class: HSSSSLSSSLSNSFA.
% 0.21/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.27 % Starting post_as_ho5 with 1500s (5) cores
% 0.21/0.27 % Starting post_as_ho10 with 300s (1) cores
% 0.21/0.27 % Starting post_as_ho4 with 300s (1) cores
% 0.21/0.27 % Starting sh5l with 300s (1) cores
% 0.21/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.21/0.27 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.21/0.27 % Search class: HGUSF-FFSF21-MSFFMMBN
% 0.21/0.27 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.27 % Starting SubtermCWHack with 31s (1) cores
% 0.21/0.27 % SubtermCWHack with pid 3324495 completed with status 10
% 0.21/0.27 % Starting ho_unfolding_3 with 181s (1) cores
% 0.21/0.27 % Preprocessing time : 0.001 s
% 0.21/0.27 % Presaturation interreduction done
% 0.21/0.27
% 0.21/0.27 % Proof found!
% 0.21/0.27 % SZS status Theorem
% 0.21/0.27 % SZS output start CNFRefutation
% See solution above
% 0.21/0.27 % Parsed axioms : 11
% 0.21/0.27 % Removed by relevancy pruning/SinE : 6
% 0.21/0.27 % Initial clauses : 6
% 0.21/0.27 % Removed in clause preprocessing : 0
% 0.21/0.27 % Initial clauses in saturation : 6
% 0.21/0.27 % Processed clauses : 31
% 0.21/0.27 % ...of these trivial : 1
% 0.21/0.27 % ...subsumed : 5
% 0.21/0.27 % ...remaining for further processing : 25
% 0.21/0.27 % Other redundant clauses eliminated : 9
% 0.21/0.27 % Clauses deleted for lack of memory : 0
% 0.21/0.27 % Backward-subsumed : 0
% 0.21/0.27 % Backward-rewritten : 0
% 0.21/0.27 % Generated clauses : 55
% 0.21/0.27 % ...of the previous two non-redundant : 34
% 0.21/0.27 % ...aggressively subsumed : 0
% 0.21/0.27 % Contextual simplify-reflections : 0
% 0.21/0.27 % Paramodulations : 29
% 0.21/0.27 % Factorizations : 0
% 0.21/0.27 % NegExts : 1
% 0.21/0.27 % Equation resolutions : 10
% 0.21/0.27 % Disequality decompositions : 0
% 0.21/0.27 % Total rewrite steps : 2
% 0.21/0.27 % ...of those cached : 0
% 0.21/0.27 % Propositional unsat checks : 0
% 0.21/0.27 % Propositional check models : 0
% 0.21/0.27 % Propositional check unsatisfiable : 0
% 0.21/0.27 % Propositional clauses : 0
% 0.21/0.27 % Propositional clauses after purity: 0
% 0.21/0.27 % Propositional unsat core size : 0
% 0.21/0.27 % Propositional preprocessing time : 0.000
% 0.21/0.27 % Propositional encoding time : 0.000
% 0.21/0.27 % Propositional solver time : 0.000
% 0.21/0.27 % Success case prop preproc time : 0.000
% 0.21/0.27 % Success case prop encoding time : 0.000
% 0.21/0.27 % Success case prop solver time : 0.000
% 0.21/0.27 % Current number of processed clauses : 19
% 0.21/0.27 % Positive orientable unit clauses : 4
% 0.21/0.27 % Positive unorientable unit clauses: 0
% 0.21/0.27 % Negative unit clauses : 2
% 0.21/0.27 % Non-unit-clauses : 13
% 0.21/0.27 % Current number of unprocessed clauses: 8
% 0.21/0.27 % ...number of literals in the above : 19
% 0.21/0.27 % Current number of archived formulas : 0
% 0.21/0.27 % Current number of archived clauses : 6
% 0.21/0.27 % Clause-clause subsumption calls (NU) : 12
% 0.21/0.27 % Rec. Clause-clause subsumption calls : 12
% 0.21/0.27 % Non-unit clause-clause subsumptions : 1
% 0.21/0.27 % Unit Clause-clause subsumption calls : 6
% 0.21/0.27 % Rewrite failures with RHS unbound : 0
% 0.21/0.27 % BW rewrite match attempts : 0
% 0.21/0.27 % BW rewrite match successes : 0
% 0.21/0.27 % Condensation attempts : 31
% 0.21/0.27 % Condensation successes : 1
% 0.21/0.27 % Termbank termtop insertions : 1603
% 0.21/0.27 % Search garbage collected termcells : 348
% 0.21/0.27
% 0.21/0.27 % -------------------------------------------------
% 0.21/0.27 % User time : 0.006 s
% 0.21/0.27 % System time : 0.004 s
% 0.21/0.27 % Total time : 0.010 s
% 0.21/0.27 % Maximum resident set size: 3892 pages
% 0.21/0.27
% 0.21/0.27 % -------------------------------------------------
% 0.21/0.27 % User time : 0.008 s
% 0.21/0.27 % System time : 0.008 s
% 0.21/0.27 % Total time : 0.016 s
% 0.21/0.27 % Maximum resident set size: 4864 pages
% 0.21/0.27 % E exiting
%------------------------------------------------------------------------------