%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM636^2 : 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 08:16:38 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 44 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 149 ( 39 ~; 17 |; 2 &; 88 @)
% ( 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 : 6 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 14 ^; 28 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
one: $i ).
thf(decl_24,type,
succ: $i > $i ).
thf(decl_25,type,
esk1_1: ( $i > $o ) > $i ).
thf(decl_26,type,
esk2_0: $i ).
thf(satz2,conjecture,
! [X1: $i] :
( ( succ @ X1 )
!= X1 ),
file('/export/starexec/sandbox2/tmp/tmp.e8i602sJOp/E---3.1_3268662.p',satz2) ).
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.e8i602sJOp/E---3.1_3268662.p',induction) ).
thf(one_is_first,axiom,
! [X1: $i] :
( ( succ @ X1 )
!= one ),
file('/export/starexec/sandbox2/tmp/tmp.e8i602sJOp/E---3.1_3268662.p',one_is_first) ).
thf(succ_injective,axiom,
! [X1: $i,X2: $i] :
( ( ( succ @ X1 )
= ( succ @ X2 ) )
=> ( X1 = X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.e8i602sJOp/E---3.1_3268662.p',succ_injective) ).
thf(c_0_4,negated_conjecture,
~ ! [X1: $i] :
( ( succ @ X1 )
!= X1 ),
inference(assume_negation,[status(cth)],[satz2]) ).
thf(c_0_5,negated_conjecture,
~ ! [X1: $i] :
( ( succ @ X1 )
!= X1 ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
thf(c_0_6,plain,
! [X14: $i > $o,X16: $i] :
( ( ( X14 @ ( esk1_1 @ X14 ) )
| ~ ( X14 @ one )
| ( X14 @ X16 ) )
& ( ~ ( X14 @ ( succ @ ( esk1_1 @ X14 ) ) )
| ~ ( X14 @ one )
| ( X14 @ X16 ) ) ),
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_7,negated_conjecture,
( ( succ @ esk2_0 )
= esk2_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
thf(c_0_8,plain,
! [X1: $i] :
( ( succ @ X1 )
!= one ),
inference(fof_simplification,[status(thm)],[one_is_first]) ).
thf(c_0_9,plain,
! [X1: $i,X3: $i > $o] :
( ( X3 @ X1 )
| ~ ( X3 @ ( succ @ ( esk1_1 @ X3 ) ) )
| ~ ( X3 @ one ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,negated_conjecture,
( ( succ @ esk2_0 )
= esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
! [X11: $i] :
( ( succ @ X11 )
!= one ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_8])]) ).
thf(c_0_12,plain,
! [X1: $i] :
( ( X1
!= ( succ @ X1 ) )
| ( one
= ( succ @ one ) )
| ( ( succ
@ ( esk1_1
@ ^ [Z0: $i] :
( Z0
!= ( succ @ Z0 ) ) ) )
= ( succ
@ ( succ
@ ( esk1_1
@ ^ [Z0: $i] :
( Z0
!= ( succ @ Z0 ) ) ) ) ) ) ),
inference(trigger,[status(thm)],[inference(cn,[status(thm)],[]),c_0_9,c_0_10]) ).
thf(c_0_13,plain,
! [X1: $i] :
( ( succ @ X1 )
!= one ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_14,plain,
! [X12: $i,X13: $i] :
( ( ( succ @ X12 )
!= ( succ @ X13 ) )
| ( X12 = X13 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[succ_injective])])]) ).
thf(c_0_15,plain,
! [X1: $i] :
( ( ( succ
@ ( succ
@ ( esk1_1
@ ^ [Z0: $i] :
( Z0
!= ( succ @ Z0 ) ) ) ) )
= ( succ
@ ( esk1_1
@ ^ [Z0: $i] :
( Z0
!= ( succ @ Z0 ) ) ) ) )
| ( ( succ @ X1 )
!= X1 ) ),
inference(sr,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_16,plain,
! [X1: $i,X3: $i > $o] :
( ( X3 @ ( esk1_1 @ X3 ) )
| ( X3 @ X1 )
| ~ ( X3 @ one ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_17,plain,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ( ( succ @ X1 )
!= ( succ @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_18,negated_conjecture,
( ( succ
@ ( succ
@ ( esk1_1
@ ^ [Z0: $i] :
( Z0
!= ( succ @ Z0 ) ) ) ) )
= ( succ
@ ( esk1_1
@ ^ [Z0: $i] :
( Z0
!= ( succ @ Z0 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_15,c_0_10]) ).
thf(c_0_19,plain,
! [X1: $i] :
( ( X1
!= ( succ @ X1 ) )
| ( ( esk1_1
@ ^ [Z0: $i] :
( Z0
!= ( succ @ Z0 ) ) )
!= ( succ
@ ( esk1_1
@ ^ [Z0: $i] :
( Z0
!= ( succ @ Z0 ) ) ) ) )
| ( one
= ( succ @ one ) ) ),
inference(trigger,[status(thm)],[inference(cn,[status(thm)],[]),c_0_16,c_0_10]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i] :
( ( ( succ
@ ( esk1_1
@ ^ [Z0: $i] :
( Z0
!= ( succ @ Z0 ) ) ) )
= X1 )
| ( ( succ
@ ( esk1_1
@ ^ [Z0: $i] :
( Z0
!= ( succ @ Z0 ) ) ) )
!= ( succ @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_21,plain,
! [X1: $i] :
( ( ( succ
@ ( esk1_1
@ ^ [Z0: $i] :
( Z0
!= ( succ @ Z0 ) ) ) )
!= ( esk1_1
@ ^ [Z0: $i] :
( Z0
!= ( succ @ Z0 ) ) ) )
| ( ( succ @ X1 )
!= X1 ) ),
inference(sr,[status(thm)],[c_0_19,c_0_13]) ).
thf(c_0_22,negated_conjecture,
( ( succ
@ ( esk1_1
@ ^ [Z0: $i] :
( Z0
!= ( succ @ Z0 ) ) ) )
= ( esk1_1
@ ^ [Z0: $i] :
( Z0
!= ( succ @ Z0 ) ) ) ),
inference(er,[status(thm)],[c_0_20]) ).
thf(c_0_23,plain,
! [X1: $i] :
( ( succ @ X1 )
!= X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]) ).
thf(c_0_24,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_10,c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM636^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/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 12:01:40 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.e8i602sJOp/E---3.1_3268662.p
% 0.08/0.25 % Version: 3.5.1-ho
% 0.08/0.25 % Preprocessing class: HSSSSMSSSSSNSFA.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting new_ho_14 with 1500s (5) cores
% 0.08/0.25 % Starting full_lambda_8 with 300s (1) cores
% 0.08/0.25 % Starting new_ho_13 with 300s (1) cores
% 0.08/0.25 % Starting ho_unfolding_3 with 300s (1) cores
% 0.08/0.25 % new_ho_13 with pid 3268677 completed with status 0
% 0.08/0.25 % Result found by new_ho_13
% 0.08/0.25 % Preprocessing class: HSSSSMSSSSSNSFA.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting new_ho_14 with 1500s (5) cores
% 0.08/0.25 % Starting full_lambda_8 with 300s (1) cores
% 0.08/0.25 % Starting new_ho_13 with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.25 % No SInE strategy applied
% 0.08/0.25 % Search class: HGUSF-FFSF11-DSFFFSBN
% 0.08/0.25 % partial match(1): HGUSF-FFSF11-SSFFFSBN
% 0.08/0.25 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.25 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.25 % SubtermCWHack with pid 3268682 completed with status 0
% 0.08/0.25 % Result found by SubtermCWHack
% 0.08/0.25 % Preprocessing class: HSSSSMSSSSSNSFA.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting new_ho_14 with 1500s (5) cores
% 0.08/0.25 % Starting full_lambda_8 with 300s (1) cores
% 0.08/0.25 % Starting new_ho_13 with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.25 % No SInE strategy applied
% 0.08/0.25 % Search class: HGUSF-FFSF11-DSFFFSBN
% 0.08/0.25 % partial match(1): HGUSF-FFSF11-SSFFFSBN
% 0.08/0.25 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.25 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.25 % Preprocessing time : 0.001 s
% 0.08/0.25
% 0.08/0.25 % Proof found!
% 0.08/0.25 % SZS status Theorem
% 0.08/0.25 % SZS output start CNFRefutation
% See solution above
% 0.08/0.25 % Parsed axioms : 6
% 0.08/0.25 % Removed by relevancy pruning/SinE : 0
% 0.08/0.25 % Initial clauses : 7
% 0.08/0.25 % Removed in clause preprocessing : 2
% 0.08/0.25 % Initial clauses in saturation : 9
% 0.08/0.25 % Processed clauses : 16
% 0.08/0.25 % ...of these trivial : 0
% 0.08/0.25 % ...subsumed : 2
% 0.08/0.25 % ...remaining for further processing : 14
% 0.08/0.25 % Other redundant clauses eliminated : 0
% 0.08/0.25 % Clauses deleted for lack of memory : 0
% 0.08/0.25 % Backward-subsumed : 1
% 0.08/0.25 % Backward-rewritten : 4
% 0.08/0.25 % Generated clauses : 17
% 0.08/0.25 % ...of the previous two non-redundant : 13
% 0.08/0.25 % ...aggressively subsumed : 0
% 0.08/0.25 % Contextual simplify-reflections : 0
% 0.08/0.25 % Paramodulations : 13
% 0.08/0.25 % Factorizations : 0
% 0.08/0.25 % NegExts : 0
% 0.08/0.25 % Equation resolutions : 2
% 0.08/0.25 % Disequality decompositions : 0
% 0.08/0.25 % Total rewrite steps : 8
% 0.08/0.25 % ...of those cached : 6
% 0.08/0.25 % Propositional unsat checks : 0
% 0.08/0.25 % Propositional check models : 0
% 0.08/0.25 % Propositional check unsatisfiable : 0
% 0.08/0.25 % Propositional clauses : 0
% 0.08/0.25 % Propositional clauses after purity: 0
% 0.08/0.25 % Propositional unsat core size : 0
% 0.08/0.25 % Propositional preprocessing time : 0.000
% 0.08/0.25 % Propositional encoding time : 0.000
% 0.08/0.25 % Propositional solver time : 0.000
% 0.08/0.25 % Success case prop preproc time : 0.000
% 0.08/0.25 % Success case prop encoding time : 0.000
% 0.08/0.25 % Success case prop solver time : 0.000
% 0.08/0.25 % Current number of processed clauses : 7
% 0.08/0.25 % Positive orientable unit clauses : 0
% 0.08/0.25 % Positive unorientable unit clauses: 0
% 0.08/0.25 % Negative unit clauses : 3
% 0.08/0.25 % Non-unit-clauses : 4
% 0.08/0.25 % Current number of unprocessed clauses: 6
% 0.08/0.25 % ...number of literals in the above : 12
% 0.08/0.25 % Current number of archived formulas : 0
% 0.08/0.25 % Current number of archived clauses : 8
% 0.08/0.25 % Clause-clause subsumption calls (NU) : 11
% 0.08/0.25 % Rec. Clause-clause subsumption calls : 11
% 0.08/0.25 % Non-unit clause-clause subsumptions : 1
% 0.08/0.25 % Unit Clause-clause subsumption calls : 6
% 0.08/0.25 % Rewrite failures with RHS unbound : 0
% 0.08/0.25 % BW rewrite match attempts : 3
% 0.08/0.25 % BW rewrite match successes : 2
% 0.08/0.25 % Condensation attempts : 0
% 0.08/0.25 % Condensation successes : 0
% 0.08/0.25 % Termbank termtop insertions : 795
% 0.08/0.25 % Search garbage collected termcells : 116
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.005 s
% 0.08/0.25 % System time : 0.001 s
% 0.08/0.25 % Total time : 0.007 s
% 0.08/0.25 % Maximum resident set size: 3888 pages
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.006 s
% 0.08/0.25 % System time : 0.004 s
% 0.08/0.25 % Total time : 0.010 s
% 0.08/0.25 % Maximum resident set size: 4864 pages
% 0.08/0.25 % E exiting
%------------------------------------------------------------------------------