%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV299^5 : 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 : n011.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 08:35:21 AM UTC 2026
% Result : Theorem 0.28s 0.40s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 54 ( 17 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 193 ( 34 ~; 10 |; 31 &; 101 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 86 ( 86 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 81 ( 37 ^; 22 !; 22 ?; 81 :)
% 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 ) > $o ).
thf(decl_27,type,
epred2_0: ( $i > $o ) > $o ).
thf(decl_28,type,
epred3_1: ( ( ( $i > $o ) > $o ) > $o ) > ( $i > $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.eAKPD7nhwd/E---3.1_226462.p',cNAT_def) ).
thf(cZERO_def,axiom,
( cZERO
= ( ^ [X1: $i > $o] :
~ ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.eAKPD7nhwd/E---3.1_226462.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.eAKPD7nhwd/E---3.1_226462.p',cSUCC_def) ).
thf(cINDUCTION,conjecture,
! [X7: ( ( $i > $o ) > $o ) > $o] :
( ( ( X7 @ cZERO )
& ! [X8: ( $i > $o ) > $o] :
( ( X7 @ X8 )
=> ( X7 @ ( cSUCC @ X8 ) ) ) )
=> ! [X9: ( $i > $o ) > $o] :
( ( cNAT @ X9 )
=> ( X7 @ X9 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.eAKPD7nhwd/E---3.1_226462.p',cINDUCTION) ).
thf(c_0_4,plain,
( cNAT
= ( ^ [Z0: ( $i > $o ) > $o] :
! [X5: ( ( $i > $o ) > $o ) > $o] :
( ( ( X5
@ ^ [Z1: $i > $o] :
~ ? [X13: $i] : ( Z1 @ X13 ) )
& ! [X6: ( $i > $o ) > $o] :
( ( X5 @ X6 )
=> ( X5
@ ^ [Z1: $i > $o] :
? [X14: $i] :
( ( Z1 @ X14 )
& ( X6
@ ^ [Z2: $i] :
( ( Z2 != X14 )
& ( 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 ) > $o] :
( ( ( X7 @ cZERO )
& ! [X8: ( $i > $o ) > $o] :
( ( X7 @ X8 )
=> ( X7 @ ( cSUCC @ X8 ) ) ) )
=> ! [X9: ( $i > $o ) > $o] :
( ( cNAT @ X9 )
=> ( X7 @ X9 ) ) ),
inference(assume_negation,[status(cth)],[cINDUCTION]) ).
thf(c_0_8,plain,
( cNAT
= ( ^ [Z0: ( $i > $o ) > $o] :
! [X5: ( ( $i > $o ) > $o ) > $o] :
( ( ( X5
@ ^ [Z1: $i > $o] :
~ ? [X13: $i] : ( Z1 @ X13 ) )
& ! [X6: ( $i > $o ) > $o] :
( ( X5 @ X6 )
=> ( X5
@ ^ [Z1: $i > $o] :
? [X14: $i] :
( ( Z1 @ X14 )
& ( X6
@ ^ [Z2: $i] :
( ( Z2 != X14 )
& ( 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 ) > $o] :
( ( ( X7
@ ^ [Z0: $i > $o] :
~ ? [X15: $i] : ( Z0 @ X15 ) )
& ! [X8: ( $i > $o ) > $o] :
( ( X7 @ X8 )
=> ( X7
@ ^ [Z0: $i > $o] :
? [X16: $i] :
( ( Z0 @ X16 )
& ( X8
@ ^ [Z1: $i] :
( ( Z1 != X16 )
& ( Z0 @ Z1 ) ) ) ) ) ) )
=> ! [X9: ( $i > $o ) > $o] :
( ! [X17: ( ( $i > $o ) > $o ) > $o] :
( ( ( X17
@ ^ [Z0: $i > $o] :
~ ? [X18: $i] : ( Z0 @ X18 ) )
& ! [X19: ( $i > $o ) > $o] :
( ( X17 @ X19 )
=> ( X17
@ ^ [Z0: $i > $o] :
? [X20: $i] :
( ( Z0 @ X20 )
& ( X19
@ ^ [Z1: $i] :
( ( Z1 != X20 )
& ( Z0 @ Z1 ) ) ) ) ) ) )
=> ( X17 @ X9 ) )
=> ( X7 @ X9 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_7,c_0_5]),c_0_6]),c_0_8]) ).
thf(c_0_10,negated_conjecture,
! [X22: ( $i > $o ) > $o,X24: ( ( $i > $o ) > $o ) > $o] :
( ( epred1_0
@ ^ [Z0: $i > $o] :
~ ? [X15: $i] : ( Z0 @ X15 ) )
& ( ~ ( epred1_0 @ X22 )
| ( epred1_0
@ ^ [Z0: $i > $o] :
? [X16: $i] :
( ( Z0 @ X16 )
& ( X22
@ ^ [Z1: $i] :
( ( Z1 != X16 )
& ( Z0 @ Z1 ) ) ) ) ) )
& ( ( X24 @ ( epred3_1 @ X24 ) )
| ~ ( X24
@ ^ [Z0: $i > $o] :
~ ? [X18: $i] : ( Z0 @ X18 ) )
| ( X24 @ epred2_0 ) )
& ( ~ ( X24
@ ^ [Z0: $i > $o] :
? [X20: $i] :
( ( Z0 @ X20 )
& ( epred3_1 @ X24
@ ^ [Z1: $i] :
( ( Z1 != X20 )
& ( Z0 @ Z1 ) ) ) ) )
| ~ ( X24
@ ^ [Z0: $i > $o] :
~ ? [X18: $i] : ( Z0 @ X18 ) )
| ( X24 @ epred2_0 ) )
& ~ ( epred1_0 @ epred2_0 ) ),
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 @ ( epred3_1 @ X5 ) )
| ( X5 @ epred2_0 )
| ~ ( X5
@ ^ [Z0: $i > $o] :
~ ? [X26: $i] : ( Z0 @ X26 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_12,negated_conjecture,
( epred1_0
@ ^ [Z0: $i > $o] :
~ ? [X27: $i] : ( Z0 @ X27 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_13,negated_conjecture,
~ ( epred1_0 @ epred2_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_14,negated_conjecture,
! [X5: ( ( $i > $o ) > $o ) > $o] :
( ( X5 @ epred2_0 )
| ~ ( X5
@ ^ [Z0: $i > $o] :
? [X28: $i] :
( ( Z0 @ X28 )
& ( epred3_1 @ X5
@ ^ [Z1: $i] :
( ( Z1 != X28 )
& ( Z0 @ Z1 ) ) ) ) )
| ~ ( X5
@ ^ [Z0: $i > $o] :
~ ? [X29: $i] : ( Z0 @ X29 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_15,negated_conjecture,
! [X3: ( $i > $o ) > $o] :
( ( epred1_0
@ ^ [Z0: $i > $o] :
? [X30: $i] :
( ( Z0 @ X30 )
& ( X3
@ ^ [Z1: $i] :
( ( Z1 != X30 )
& ( Z0 @ Z1 ) ) ) ) )
| ~ ( epred1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_16,negated_conjecture,
epred1_0 @ ( epred3_1 @ epred1_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
thf(c_0_17,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_14,c_0_15]),c_0_12]),c_0_16])]),c_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEV299^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.28 % Computer : n011.cluster.edu
% 0.11/0.28 % Model : x86_64 x86_64
% 0.11/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.28 % Memory : 8046.5625MB
% 0.11/0.28 % OS : Linux 6.8.0-71-generic
% 0.11/0.28 % CPULimit : 300
% 0.11/0.28 % WCLimit : 300
% 0.11/0.28 % DateTime : Tue Sep 29 15:32:16 UTC 2026
% 0.11/0.28 % CPUTime :
% 0.11/0.28 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.28/0.35 Running higher-order theorem proving
% 0.28/0.37 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.eAKPD7nhwd/E---3.1_226462.p
% 0.28/0.40 % Version: 3.5.1-ho
% 0.28/0.40 % Preprocessing class: HSSSSMSSSLSNHHA.
% 0.28/0.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.40 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.28/0.40 % Starting sh3l with 300s (1) cores
% 0.28/0.40 % Starting lpo6_lambda_fix with 300s (1) cores
% 0.28/0.40 % Starting full_lambda_8 with 300s (1) cores
% 0.28/0.40 % sh3l with pid 226476 completed with status 0
% 0.28/0.40 % Result found by sh3l
% 0.28/0.40 % Preprocessing class: HSSSSMSSSLSNHHA.
% 0.28/0.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.40 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.28/0.40 % Starting sh3l with 300s (1) cores
% 0.28/0.40 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf120_gu_RUU_F100_L01000)
% 0.28/0.40 % SinE strategy is gf120_gu_RUU_F100_L01000
% 0.28/0.40 % Search class: HGUNF-FFSF00-DHHFMSBN
% 0.28/0.40 % partial match(2): HGUNF-FFSF00-SHHFFSBN
% 0.28/0.40 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.40 % Starting SubtermCWHack with 28s (1) cores
% 0.28/0.40 % SubtermCWHack with pid 226479 completed with status 0
% 0.28/0.40 % Result found by SubtermCWHack
% 0.28/0.40 % Preprocessing class: HSSSSMSSSLSNHHA.
% 0.28/0.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.40 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.28/0.40 % Starting sh3l with 300s (1) cores
% 0.28/0.40 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf120_gu_RUU_F100_L01000)
% 0.28/0.40 % SinE strategy is gf120_gu_RUU_F100_L01000
% 0.28/0.40 % Search class: HGUNF-FFSF00-DHHFMSBN
% 0.28/0.40 % partial match(2): HGUNF-FFSF00-SHHFFSBN
% 0.28/0.40 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.40 % Starting SubtermCWHack with 28s (1) cores
% 0.28/0.40 % Preprocessing time : 0.002 s
% 0.28/0.40
% 0.28/0.40 % Proof found!
% 0.28/0.40 % SZS status Theorem
% 0.28/0.40 % SZS output start CNFRefutation
% See solution above
% 0.28/0.40 % Parsed axioms : 7
% 0.28/0.40 % Removed by relevancy pruning/SinE : 3
% 0.28/0.40 % Initial clauses : 5
% 0.28/0.40 % Removed in clause preprocessing : 0
% 0.28/0.40 % Initial clauses in saturation : 5
% 0.28/0.40 % Processed clauses : 6
% 0.28/0.40 % ...of these trivial : 0
% 0.28/0.40 % ...subsumed : 0
% 0.28/0.40 % ...remaining for further processing : 6
% 0.28/0.40 % Other redundant clauses eliminated : 0
% 0.28/0.40 % Clauses deleted for lack of memory : 0
% 0.28/0.40 % Backward-subsumed : 0
% 0.28/0.40 % Backward-rewritten : 0
% 0.28/0.40 % Generated clauses : 2
% 0.28/0.40 % ...of the previous two non-redundant : 1
% 0.28/0.40 % ...aggressively subsumed : 0
% 0.28/0.40 % Contextual simplify-reflections : 0
% 0.28/0.40 % Paramodulations : 2
% 0.28/0.40 % Factorizations : 0
% 0.28/0.40 % NegExts : 0
% 0.28/0.40 % Equation resolutions : 0
% 0.28/0.40 % Disequality decompositions : 0
% 0.28/0.40 % Total rewrite steps : 2
% 0.28/0.40 % ...of those cached : 0
% 0.28/0.40 % Propositional unsat checks : 0
% 0.28/0.40 % Propositional check models : 0
% 0.28/0.40 % Propositional check unsatisfiable : 0
% 0.28/0.40 % Propositional clauses : 0
% 0.28/0.40 % Propositional clauses after purity: 0
% 0.28/0.40 % Propositional unsat core size : 0
% 0.28/0.40 % Propositional preprocessing time : 0.000
% 0.28/0.40 % Propositional encoding time : 0.000
% 0.28/0.40 % Propositional solver time : 0.000
% 0.28/0.40 % Success case prop preproc time : 0.000
% 0.28/0.40 % Success case prop encoding time : 0.000
% 0.28/0.40 % Success case prop solver time : 0.000
% 0.28/0.40 % Current number of processed clauses : 6
% 0.28/0.40 % Positive orientable unit clauses : 2
% 0.28/0.40 % Positive unorientable unit clauses: 0
% 0.28/0.40 % Negative unit clauses : 1
% 0.28/0.40 % Non-unit-clauses : 3
% 0.28/0.40 % Current number of unprocessed clauses: 0
% 0.28/0.40 % ...number of literals in the above : 0
% 0.28/0.40 % Current number of archived formulas : 0
% 0.28/0.40 % Current number of archived clauses : 0
% 0.28/0.40 % Clause-clause subsumption calls (NU) : 1
% 0.28/0.40 % Rec. Clause-clause subsumption calls : 1
% 0.28/0.40 % Non-unit clause-clause subsumptions : 0
% 0.28/0.40 % Unit Clause-clause subsumption calls : 0
% 0.28/0.40 % Rewrite failures with RHS unbound : 0
% 0.28/0.40 % BW rewrite match attempts : 0
% 0.28/0.40 % BW rewrite match successes : 0
% 0.28/0.40 % Condensation attempts : 0
% 0.28/0.40 % Condensation successes : 0
% 0.28/0.40 % Termbank termtop insertions : 1242
% 0.28/0.40 % Search garbage collected termcells : 303
% 0.28/0.40
% 0.28/0.40 % -------------------------------------------------
% 0.28/0.40 % User time : 0.005 s
% 0.28/0.40 % System time : 0.002 s
% 0.28/0.40 % Total time : 0.007 s
% 0.28/0.40 % Maximum resident set size: 3640 pages
% 0.28/0.40
% 0.28/0.40 % -------------------------------------------------
% 0.28/0.40 % User time : 0.008 s
% 0.28/0.40 % System time : 0.007 s
% 0.28/0.40 % Total time : 0.015 s
% 0.28/0.40 % Maximum resident set size: 4608 pages
% 0.28/0.40 % E exiting
%------------------------------------------------------------------------------