%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUN024^2 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 08:19:39 AM UTC 2026
% Result : Theorem 0.28s 0.39s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 63 ( 54 equ; 0 cnn)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 193 ( 27 ~; 13 |; 25 &; 119 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 49 ( 0 ^; 46 !; 3 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
zero: $i ).
thf(decl_24,type,
s: $i > $i ).
thf(decl_25,type,
ite: $o > $i > $i > $i ).
thf(decl_26,type,
h: $i > $i ).
thf(n10,conjecture,
( ( ! [X1: $o,X2: $i,X3: $i] :
( X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X2 ) )
& ! [X1: $o,X2: $i,X3: $i] :
( ~ X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X3 ) )
& ! [X4: $i] :
( ( s @ X4 )
!= zero )
& ! [X4: $i] :
( ( s @ X4 )
!= X4 )
& ! [X4: $i] :
( ( h @ X4 )
= ( ite @ ( X4 = zero ) @ ( s @ zero ) @ zero ) ) )
=> ? [X5: $i > $i] :
( ( ( X5 @ zero )
= ( s @ zero ) )
& ( ( X5 @ ( s @ zero ) )
= zero )
& ( ( X5 @ ( s @ ( s @ zero ) ) )
= zero ) ) ),
file('/export/starexec/sandbox/tmp/tmp.x51BfwKQyB/E---3.1_680128.p',n10) ).
thf(c_0_1,negated_conjecture,
~ ( ( ! [X1: $o,X2: $i,X3: $i] :
( X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X2 ) )
& ! [X1: $o,X2: $i,X3: $i] :
( ~ X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X3 ) )
& ! [X4: $i] :
( ( s @ X4 )
!= zero )
& ! [X4: $i] :
( ( s @ X4 )
!= X4 )
& ! [X4: $i] :
( ( h @ X4 )
= ( ite @ ( X4 = zero ) @ ( s @ zero ) @ zero ) ) )
=> ? [X5: $i > $i] :
( ( ( X5 @ zero )
= ( s @ zero ) )
& ( ( X5 @ ( s @ zero ) )
= zero )
& ( ( X5 @ ( s @ ( s @ zero ) ) )
= zero ) ) ),
inference(assume_negation,[status(cth)],[n10]) ).
thf(c_0_2,negated_conjecture,
~ ( ( ! [X1: $o,X2: $i,X3: $i] :
( X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X2 ) )
& ! [X1: $o,X2: $i,X3: $i] :
( ~ X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X3 ) )
& ! [X4: $i] :
( ( s @ X4 )
!= zero )
& ! [X4: $i] :
( ( s @ X4 )
!= X4 )
& ! [X4: $i] :
( ( ( X4 != zero )
| ( ( h @ X4 )
= ( ite @ $true @ ( s @ zero ) @ zero ) ) )
& ( ( X4 = zero )
| ( ( h @ X4 )
= ( ite @ $false @ ( s @ zero ) @ zero ) ) ) ) )
=> ? [X5: $i > $i] :
( ( ( X5 @ zero )
= ( s @ zero ) )
& ( ( X5 @ ( s @ zero ) )
= zero )
& ( ( X5 @ ( s @ ( s @ zero ) ) )
= zero ) ) ),
inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[c_0_1])]) ).
thf(c_0_3,negated_conjecture,
! [X16: $o,X17: $i,X18: $i,X19: $o,X20: $i,X21: $i,X22: $i,X23: $i,X24: $i,X25: $i > $i] :
( ( ~ X16
| ( ( ite @ X16 @ X17 @ X18 )
= X17 ) )
& ( X19
| ( ( ite @ X19 @ X20 @ X21 )
= X21 ) )
& ( ( s @ X22 )
!= zero )
& ( ( s @ X23 )
!= X23 )
& ( ( X24 != zero )
| ( ( h @ X24 )
= ( ite @ $true @ ( s @ zero ) @ zero ) ) )
& ( ( X24 = zero )
| ( ( h @ X24 )
= ( ite @ $false @ ( s @ zero ) @ zero ) ) )
& ( ( ( X25 @ zero )
!= ( s @ zero ) )
| ( ( X25 @ ( s @ zero ) )
!= zero )
| ( ( X25 @ ( s @ ( s @ zero ) ) )
!= zero ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])]) ).
thf(c_0_4,negated_conjecture,
! [X2: $i] :
( ( X2 = zero )
| ( ( h @ X2 )
= ( ite @ ~ $true @ ( s @ zero ) @ zero ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_5,negated_conjecture,
! [X2: $i,X3: $i] :
( ( ite @ ~ $true @ X2 @ X3 )
= X3 ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_3])])]) ).
thf(c_0_6,negated_conjecture,
! [X2: $i] :
( ( ( h @ X2 )
= ( ite @ $true @ ( s @ zero ) @ zero ) )
| ( X2 != zero ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_7,negated_conjecture,
! [X3: $i,X2: $i] :
( ( ite @ $true @ X2 @ X3 )
= X2 ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_3])])]) ).
thf(c_0_8,negated_conjecture,
! [X5: $i > $i] :
( ( ( X5 @ zero )
!= ( s @ zero ) )
| ( ( X5 @ ( s @ zero ) )
!= zero )
| ( ( X5 @ ( s @ ( s @ zero ) ) )
!= zero ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_9,negated_conjecture,
! [X2: $i] :
( ( ( h @ X2 )
= zero )
| ( X2 = zero ) ),
inference(rw,[status(thm)],[c_0_4,c_0_5]) ).
thf(c_0_10,negated_conjecture,
( ( h @ zero )
= ( s @ zero ) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7])]) ).
thf(c_0_11,negated_conjecture,
! [X2: $i] :
( ( s @ X2 )
!= zero ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_12,negated_conjecture,
( ( h @ ( s @ zero ) )
!= zero ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10])]),c_0_11]) ).
thf(c_0_13,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_9]),c_0_11]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUN024^2 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.27 % Computer : n006.cluster.edu
% 0.11/0.27 % Model : x86_64 x86_64
% 0.11/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.27 % Memory : 8046.5625MB
% 0.11/0.27 % 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 13:05:54 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.x51BfwKQyB/E---3.1_680128.p
% 0.28/0.39 % Version: 3.5.1-ho
% 0.28/0.39 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.28/0.39 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.39 % Starting post_as_ho12 with 300s (1) cores
% 0.28/0.39 % Starting new_bool_9 with 300s (1) cores
% 0.28/0.39 % Starting post_as_ho1 with 300s (1) cores
% 0.28/0.39 % Starting post_as_ho4 with 300s (1) cores
% 0.28/0.39 % Starting post_as_ho2 with 300s (1) cores
% 0.28/0.39 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.28/0.39 % Starting full_lambda_10 with 300s (1) cores
% 0.28/0.39 % Starting new_ho_8 with 300s (1) cores
% 0.28/0.39 % post_as_ho2 with pid 680145 completed with status 0
% 0.28/0.39 % Result found by post_as_ho2
% 0.28/0.39 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.28/0.39 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.39 % Starting post_as_ho12 with 300s (1) cores
% 0.28/0.39 % Starting new_bool_9 with 300s (1) cores
% 0.28/0.39 % Starting post_as_ho1 with 300s (1) cores
% 0.28/0.39 % Starting post_as_ho4 with 300s (1) cores
% 0.28/0.39 % Starting post_as_ho2 with 300s (1) cores
% 0.28/0.39 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.28/0.39 % No SInE strategy applied
% 0.28/0.39 % Search class: HGHPS-FFSF31-MSSFFSNN
% 0.28/0.39 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.39 % Starting SubtermCWHack with 28s (1) cores
% 0.28/0.39 % SubtermCWHack with pid 680149 completed with status 0
% 0.28/0.39 % Result found by SubtermCWHack
% 0.28/0.39 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.28/0.39 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.39 % Starting post_as_ho12 with 300s (1) cores
% 0.28/0.39 % Starting new_bool_9 with 300s (1) cores
% 0.28/0.39 % Starting post_as_ho1 with 300s (1) cores
% 0.28/0.39 % Starting post_as_ho4 with 300s (1) cores
% 0.28/0.39 % Starting post_as_ho2 with 300s (1) cores
% 0.28/0.39 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.28/0.39 % No SInE strategy applied
% 0.28/0.39 % Search class: HGHPS-FFSF31-MSSFFSNN
% 0.28/0.39 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.39 % Starting SubtermCWHack with 28s (1) cores
% 0.28/0.39 % Preprocessing time : 0.001 s
% 0.28/0.39
% 0.28/0.39 % Proof found!
% 0.28/0.39 % SZS status Theorem
% 0.28/0.39 % SZS output start CNFRefutation
% See solution above
% 0.28/0.39 % Parsed axioms : 5
% 0.28/0.39 % Removed by relevancy pruning/SinE : 0
% 0.28/0.39 % Initial clauses : 11
% 0.28/0.39 % Removed in clause preprocessing : 4
% 0.28/0.39 % Initial clauses in saturation : 7
% 0.28/0.39 % Processed clauses : 10
% 0.28/0.39 % ...of these trivial : 0
% 0.28/0.39 % ...subsumed : 1
% 0.28/0.39 % ...remaining for further processing : 9
% 0.28/0.39 % Other redundant clauses eliminated : 2
% 0.28/0.39 % Clauses deleted for lack of memory : 0
% 0.28/0.39 % Backward-subsumed : 0
% 0.28/0.39 % Backward-rewritten : 0
% 0.28/0.39 % Generated clauses : 6
% 0.28/0.39 % ...of the previous two non-redundant : 4
% 0.28/0.39 % ...aggressively subsumed : 0
% 0.28/0.39 % Contextual simplify-reflections : 0
% 0.28/0.39 % Paramodulations : 4
% 0.28/0.39 % Factorizations : 0
% 0.28/0.39 % NegExts : 0
% 0.28/0.39 % Equation resolutions : 2
% 0.28/0.39 % Disequality decompositions : 0
% 0.28/0.39 % Total rewrite steps : 7
% 0.28/0.39 % ...of those cached : 0
% 0.28/0.39 % Propositional unsat checks : 0
% 0.28/0.39 % Propositional check models : 0
% 0.28/0.39 % Propositional check unsatisfiable : 0
% 0.28/0.39 % Propositional clauses : 0
% 0.28/0.39 % Propositional clauses after purity: 0
% 0.28/0.39 % Propositional unsat core size : 0
% 0.28/0.39 % Propositional preprocessing time : 0.000
% 0.28/0.39 % Propositional encoding time : 0.000
% 0.28/0.39 % Propositional solver time : 0.000
% 0.28/0.39 % Success case prop preproc time : 0.000
% 0.28/0.39 % Success case prop encoding time : 0.000
% 0.28/0.39 % Success case prop solver time : 0.000
% 0.28/0.39 % Current number of processed clauses : 8
% 0.28/0.39 % Positive orientable unit clauses : 3
% 0.28/0.39 % Positive unorientable unit clauses: 0
% 0.28/0.39 % Negative unit clauses : 3
% 0.28/0.39 % Non-unit-clauses : 2
% 0.28/0.39 % Current number of unprocessed clauses: 1
% 0.28/0.39 % ...number of literals in the above : 2
% 0.28/0.39 % Current number of archived formulas : 0
% 0.28/0.39 % Current number of archived clauses : 0
% 0.28/0.39 % Clause-clause subsumption calls (NU) : 1
% 0.28/0.39 % Rec. Clause-clause subsumption calls : 1
% 0.28/0.39 % Non-unit clause-clause subsumptions : 0
% 0.28/0.39 % Unit Clause-clause subsumption calls : 2
% 0.28/0.39 % Rewrite failures with RHS unbound : 0
% 0.28/0.39 % BW rewrite match attempts : 0
% 0.28/0.39 % BW rewrite match successes : 0
% 0.28/0.39 % Condensation attempts : 0
% 0.28/0.39 % Condensation successes : 0
% 0.28/0.39 % Termbank termtop insertions : 903
% 0.28/0.39 % Search garbage collected termcells : 255
% 0.28/0.39
% 0.28/0.39 % -------------------------------------------------
% 0.28/0.39 % User time : 0.002 s
% 0.28/0.39 % System time : 0.002 s
% 0.28/0.39 % Total time : 0.004 s
% 0.28/0.39 % Maximum resident set size: 3892 pages
% 0.28/0.39
% 0.28/0.39 % -------------------------------------------------
% 0.28/0.39 % User time : 0.004 s
% 0.28/0.39 % System time : 0.009 s
% 0.28/0.39 % Total time : 0.013 s
% 0.28/0.39 % Maximum resident set size: 4864 pages
% 0.28/0.39 % E exiting
%------------------------------------------------------------------------------