%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV289^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 08:35:20 AM UTC 2026
% Result : Theorem 0.10s 0.24s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 64 ( 20 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 205 ( 38 ~; 11 |; 35 &; 108 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 79 ( 79 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 86 ( 43 ^; 18 !; 25 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
cNAT: ( ( $i > $o ) > $o ) > $o ).
thf(decl_24,type,
cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
thf(decl_25,type,
cZERO: ( $i > $o ) > $o ).
thf(decl_26,type,
epred1_0: ( $i > $o ) > $o ).
thf(decl_27,type,
epred2_1: ( ( ( $i > $o ) > $o ) > $o ) > ( $i > $o ) > $o ).
thf(decl_28,type,
epred3_0: ( ( $i > $o ) > $o ) > $o ).
thf(cNAT_def,axiom,
( cNAT
= ( ^ [X3: ( $i > $o ) > $o] :
! [X5: ( ( $i > $o ) > $o ) > $o] :
( ( ( X5 @ cZERO )
& ! [X6: ( $i > $o ) > $o] :
( ( X5 @ X6 )
=> ( X5 @ ( cSUCC @ X6 ) ) ) )
=> ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1SxiJ07aQi/E---3.1_3665750.p',cNAT_def) ).
thf(cZERO_def,axiom,
( cZERO
= ( ^ [X1: $i > $o] :
~ ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1SxiJ07aQi/E---3.1_3665750.p',cZERO_def) ).
thf(cSUCC_def,axiom,
( cSUCC
= ( ^ [X3: ( $i > $o ) > $o,X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ( X3
@ ^ [X4: $i] :
( ( X4 != X2 )
& ( X1 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1SxiJ07aQi/E---3.1_3665750.p',cSUCC_def) ).
thf(cTTTP6101,conjecture,
! [X7: ( $i > $o ) > $o] :
( ( cNAT @ X7 )
=> ( cNAT @ ( cSUCC @ X7 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1SxiJ07aQi/E---3.1_3665750.p',cTTTP6101) ).
thf(c_0_4,plain,
( cNAT
= ( ^ [Z0: ( $i > $o ) > $o] :
! [X5: ( ( $i > $o ) > $o ) > $o] :
( ( ( X5
@ ^ [Z1: $i > $o] :
~ ? [X9: $i] : ( Z1 @ X9 ) )
& ! [X6: ( $i > $o ) > $o] :
( ( X5 @ X6 )
=> ( X5
@ ^ [Z1: $i > $o] :
? [X10: $i] :
( ( Z1 @ X10 )
& ( X6
@ ^ [Z2: $i] :
( ( Z2 != X10 )
& ( Z1 @ Z2 ) ) ) ) ) ) )
=> ( X5 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[cNAT_def]) ).
thf(c_0_5,plain,
( cZERO
= ( ^ [Z0: $i > $o] :
~ ? [X2: $i] : ( Z0 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[cZERO_def]) ).
thf(c_0_6,plain,
( cSUCC
= ( ^ [Z0: ( $i > $o ) > $o,Z1: $i > $o] :
? [X2: $i] :
( ( Z1 @ X2 )
& ( Z0
@ ^ [Z2: $i] :
( ( Z2 != X2 )
& ( Z1 @ Z2 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[cSUCC_def]) ).
thf(c_0_7,negated_conjecture,
~ ! [X7: ( $i > $o ) > $o] :
( ( cNAT @ X7 )
=> ( cNAT @ ( cSUCC @ X7 ) ) ),
inference(assume_negation,[status(cth)],[cTTTP6101]) ).
thf(c_0_8,plain,
( cNAT
= ( ^ [Z0: ( $i > $o ) > $o] :
! [X5: ( ( $i > $o ) > $o ) > $o] :
( ( ( X5
@ ^ [Z1: $i > $o] :
~ ? [X9: $i] : ( Z1 @ X9 ) )
& ! [X6: ( $i > $o ) > $o] :
( ( X5 @ X6 )
=> ( X5
@ ^ [Z1: $i > $o] :
? [X10: $i] :
( ( Z1 @ X10 )
& ( X6
@ ^ [Z2: $i] :
( ( Z2 != X10 )
& ( Z1 @ Z2 ) ) ) ) ) ) )
=> ( X5 @ Z0 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,c_0_5]),c_0_6]) ).
thf(c_0_9,negated_conjecture,
~ ! [X7: ( $i > $o ) > $o] :
( ! [X11: ( ( $i > $o ) > $o ) > $o] :
( ( ( X11
@ ^ [Z0: $i > $o] :
~ ? [X12: $i] : ( Z0 @ X12 ) )
& ! [X13: ( $i > $o ) > $o] :
( ( X11 @ X13 )
=> ( X11
@ ^ [Z0: $i > $o] :
? [X14: $i] :
( ( Z0 @ X14 )
& ( X13
@ ^ [Z1: $i] :
( ( Z1 != X14 )
& ( Z0 @ Z1 ) ) ) ) ) ) )
=> ( X11 @ X7 ) )
=> ! [X16: ( ( $i > $o ) > $o ) > $o] :
( ( ( X16
@ ^ [Z0: $i > $o] :
~ ? [X17: $i] : ( Z0 @ X17 ) )
& ! [X18: ( $i > $o ) > $o] :
( ( X16 @ X18 )
=> ( X16
@ ^ [Z0: $i > $o] :
? [X19: $i] :
( ( Z0 @ X19 )
& ( X18
@ ^ [Z1: $i] :
( ( Z1 != X19 )
& ( Z0 @ Z1 ) ) ) ) ) ) )
=> ( X16
@ ^ [Z0: $i > $o] :
? [X15: $i] :
( ( Z0 @ X15 )
& ( X7
@ ^ [Z1: $i] :
( ( Z1 != X15 )
& ( Z0 @ Z1 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_7,c_0_6]),c_0_8]) ).
thf(c_0_10,negated_conjecture,
! [X21: ( ( $i > $o ) > $o ) > $o,X24: ( $i > $o ) > $o] :
( ( ( X21 @ ( epred2_1 @ X21 ) )
| ~ ( X21
@ ^ [Z0: $i > $o] :
~ ? [X12: $i] : ( Z0 @ X12 ) )
| ( X21 @ epred1_0 ) )
& ( ~ ( X21
@ ^ [Z0: $i > $o] :
? [X14: $i] :
( ( Z0 @ X14 )
& ( epred2_1 @ X21
@ ^ [Z1: $i] :
( ( Z1 != X14 )
& ( Z0 @ Z1 ) ) ) ) )
| ~ ( X21
@ ^ [Z0: $i > $o] :
~ ? [X12: $i] : ( Z0 @ X12 ) )
| ( X21 @ epred1_0 ) )
& ( epred3_0
@ ^ [Z0: $i > $o] :
~ ? [X17: $i] : ( Z0 @ X17 ) )
& ( ~ ( epred3_0 @ X24 )
| ( epred3_0
@ ^ [Z0: $i > $o] :
? [X19: $i] :
( ( Z0 @ X19 )
& ( X24
@ ^ [Z1: $i] :
( ( Z1 != X19 )
& ( Z0 @ Z1 ) ) ) ) ) )
& ~ ( epred3_0
@ ^ [Z0: $i > $o] :
? [X15: $i] :
( ( Z0 @ X15 )
& ( epred1_0
@ ^ [Z1: $i] :
( ( Z1 != X15 )
& ( Z0 @ Z1 ) ) ) ) ) ),
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_9])])])])])]) ).
thf(c_0_11,negated_conjecture,
! [X5: ( ( $i > $o ) > $o ) > $o] :
( ( X5 @ ( epred2_1 @ X5 ) )
| ( X5 @ epred1_0 )
| ~ ( X5
@ ^ [Z0: $i > $o] :
~ ? [X25: $i] : ( Z0 @ X25 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_12,negated_conjecture,
( epred3_0
@ ^ [Z0: $i > $o] :
~ ? [X26: $i] : ( Z0 @ X26 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_13,negated_conjecture,
~ ( epred3_0
@ ^ [Z0: $i > $o] :
? [X27: $i] :
( ( Z0 @ X27 )
& ( epred1_0
@ ^ [Z1: $i] :
( ( Z1 != X27 )
& ( Z0 @ Z1 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_14,negated_conjecture,
! [X3: ( $i > $o ) > $o] :
( ( epred3_0
@ ^ [Z0: $i > $o] :
? [X28: $i] :
( ( Z0 @ X28 )
& ( X3
@ ^ [Z1: $i] :
( ( Z1 != X28 )
& ( Z0 @ Z1 ) ) ) ) )
| ~ ( epred3_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_15,negated_conjecture,
( ( epred3_0 @ ( epred2_1 @ epred3_0 ) )
| ( epred3_0 @ epred1_0 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_16,negated_conjecture,
~ ( epred3_0 @ epred1_0 ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_17,negated_conjecture,
! [X5: ( ( $i > $o ) > $o ) > $o] :
( ( X5 @ epred1_0 )
| ~ ( X5
@ ^ [Z0: $i > $o] :
? [X29: $i] :
( ( Z0 @ X29 )
& ( epred2_1 @ X5
@ ^ [Z1: $i] :
( ( Z1 != X29 )
& ( Z0 @ Z1 ) ) ) ) )
| ~ ( X5
@ ^ [Z0: $i > $o] :
~ ? [X30: $i] : ( Z0 @ X30 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_18,negated_conjecture,
epred3_0 @ ( epred2_1 @ epred3_0 ),
inference(sr,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_19,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_14]),c_0_12]),c_0_18])]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV289^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.16 % Computer : n015.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Sep 29 15:34:47 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 Running higher-order theorem proving
% 0.10/0.22 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.1SxiJ07aQi/E---3.1_3665750.p
% 0.10/0.24 % Version: 3.5.1-ho
% 0.10/0.24 % Preprocessing class: HSSSSMSSSLSNHHN.
% 0.10/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.24 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.10/0.24 % Starting sh5l with 300s (1) cores
% 0.10/0.24 % Starting full_lambda_10 with 300s (1) cores
% 0.10/0.24 % Starting full_lambda_6 with 300s (1) cores
% 0.10/0.24 % full_lambda_10 with pid 3665782 completed with status 0
% 0.10/0.24 % Result found by full_lambda_10
% 0.10/0.24 % Preprocessing class: HSSSSMSSSLSNHHN.
% 0.10/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.24 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.10/0.24 % Starting sh5l with 300s (1) cores
% 0.10/0.24 % Starting full_lambda_10 with 300s (1) cores
% 0.10/0.24 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,5,,5,20000,3.0,true))
% 0.10/0.24 % SinE strategy is GSinE(CountFormulas,hypos,5,,5,20000,3.0,true)
% 0.10/0.24 % Search class: HGUNF-FFSF00-DHHFMSBN
% 0.10/0.24 % partial match(2): HGUNF-FFSF00-SHHFFSBN
% 0.10/0.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.24 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.24 % SubtermCWHack with pid 3665786 completed with status 0
% 0.10/0.24 % Result found by SubtermCWHack
% 0.10/0.24 % Preprocessing class: HSSSSMSSSLSNHHN.
% 0.10/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.24 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.10/0.24 % Starting sh5l with 300s (1) cores
% 0.10/0.24 % Starting full_lambda_10 with 300s (1) cores
% 0.10/0.24 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,5,,5,20000,3.0,true))
% 0.10/0.24 % SinE strategy is GSinE(CountFormulas,hypos,5,,5,20000,3.0,true)
% 0.10/0.24 % Search class: HGUNF-FFSF00-DHHFMSBN
% 0.10/0.24 % partial match(2): HGUNF-FFSF00-SHHFFSBN
% 0.10/0.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.24 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.24 % Preprocessing time : 0.001 s
% 0.10/0.24
% 0.10/0.24 % Proof found!
% 0.10/0.24 % SZS status Theorem
% 0.10/0.24 % SZS output start CNFRefutation
% See solution above
% 0.10/0.24 % Parsed axioms : 7
% 0.10/0.24 % Removed by relevancy pruning/SinE : 3
% 0.10/0.24 % Initial clauses : 5
% 0.10/0.24 % Removed in clause preprocessing : 0
% 0.10/0.24 % Initial clauses in saturation : 5
% 0.10/0.24 % Processed clauses : 8
% 0.10/0.24 % ...of these trivial : 0
% 0.10/0.24 % ...subsumed : 0
% 0.10/0.24 % ...remaining for further processing : 8
% 0.10/0.24 % Other redundant clauses eliminated : 0
% 0.10/0.24 % Clauses deleted for lack of memory : 0
% 0.10/0.24 % Backward-subsumed : 0
% 0.10/0.24 % Backward-rewritten : 0
% 0.10/0.24 % Generated clauses : 4
% 0.10/0.24 % ...of the previous two non-redundant : 3
% 0.10/0.24 % ...aggressively subsumed : 0
% 0.10/0.24 % Contextual simplify-reflections : 0
% 0.10/0.24 % Paramodulations : 3
% 0.10/0.24 % Factorizations : 0
% 0.10/0.24 % NegExts : 0
% 0.10/0.24 % Equation resolutions : 0
% 0.10/0.24 % Disequality decompositions : 0
% 0.10/0.24 % Total rewrite steps : 2
% 0.10/0.24 % ...of those cached : 0
% 0.10/0.24 % Propositional unsat checks : 0
% 0.10/0.24 % Propositional check models : 0
% 0.10/0.24 % Propositional check unsatisfiable : 0
% 0.10/0.24 % Propositional clauses : 0
% 0.10/0.24 % Propositional clauses after purity: 0
% 0.10/0.24 % Propositional unsat core size : 0
% 0.10/0.24 % Propositional preprocessing time : 0.000
% 0.10/0.24 % Propositional encoding time : 0.000
% 0.10/0.24 % Propositional solver time : 0.000
% 0.10/0.24 % Success case prop preproc time : 0.000
% 0.10/0.24 % Success case prop encoding time : 0.000
% 0.10/0.24 % Success case prop solver time : 0.000
% 0.10/0.24 % Current number of processed clauses : 7
% 0.10/0.24 % Positive orientable unit clauses : 2
% 0.10/0.24 % Positive unorientable unit clauses: 0
% 0.10/0.24 % Negative unit clauses : 2
% 0.10/0.24 % Non-unit-clauses : 3
% 0.10/0.24 % Current number of unprocessed clauses: 0
% 0.10/0.24 % ...number of literals in the above : 0
% 0.10/0.24 % Current number of archived formulas : 0
% 0.10/0.24 % Current number of archived clauses : 1
% 0.10/0.24 % Clause-clause subsumption calls (NU) : 2
% 0.10/0.24 % Rec. Clause-clause subsumption calls : 2
% 0.10/0.24 % Non-unit clause-clause subsumptions : 0
% 0.10/0.24 % Unit Clause-clause subsumption calls : 2
% 0.10/0.24 % Rewrite failures with RHS unbound : 0
% 0.10/0.24 % BW rewrite match attempts : 0
% 0.10/0.24 % BW rewrite match successes : 0
% 0.10/0.24 % Condensation attempts : 0
% 0.10/0.24 % Condensation successes : 0
% 0.10/0.24 % Termbank termtop insertions : 1375
% 0.10/0.24 % Search garbage collected termcells : 320
% 0.10/0.24
% 0.10/0.24 % -------------------------------------------------
% 0.10/0.24 % User time : 0.003 s
% 0.10/0.24 % System time : 0.002 s
% 0.10/0.24 % Total time : 0.006 s
% 0.10/0.24 % Maximum resident set size: 3640 pages
% 0.10/0.24
% 0.10/0.24 % -------------------------------------------------
% 0.10/0.24 % User time : 0.004 s
% 0.10/0.24 % System time : 0.008 s
% 0.10/0.24 % Total time : 0.012 s
% 0.10/0.24 % Maximum resident set size: 4608 pages
% 0.10/0.24 % E exiting
%------------------------------------------------------------------------------