%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP165^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 08:04:33 AM UTC 2026
% Result : Theorem 0.22s 0.33s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 88 ( 10 equ; 0 cnn)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 184 ( 26 ~; 17 |; 6 &; 132 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
set_a: $tType ).
thf(decl_sort2,type,
refine424419629nres_a: $tType ).
thf(decl_sort3,type,
a: $tType ).
thf(decl_26,type,
if_Ref1724547303nres_a: $o > refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
thf(decl_38,type,
ord_le519537037nres_a: refine424419629nres_a > refine424419629nres_a > $o ).
thf(decl_65,type,
refine1198353288_RES_a: set_a > refine424419629nres_a ).
thf(decl_70,type,
collect_a: ( a > $o ) > set_a ).
thf(decl_75,type,
s1: refine424419629nres_a ).
thf(decl_76,type,
s2: refine424419629nres_a ).
thf(decl_77,type,
phi: a > $o ).
thf(decl_78,type,
b: $o ).
thf(conj_2,conjecture,
ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ b @ s1 @ s2 ) @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ),
file('/export/starexec/sandbox2/tmp/tmp.1i0y80f2Hb/E---3.1_1785764.p',conj_2) ).
thf(help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
! [X865: refine424419629nres_a,X866: refine424419629nres_a] :
( ( if_Ref1724547303nres_a @ ~ $true @ X865 @ X866 )
= X866 ),
file('/export/starexec/sandbox2/tmp/tmp.1i0y80f2Hb/E---3.1_1785764.p',help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T) ).
thf(conj_1,hypothesis,
( ~ b
=> ( ord_le519537037nres_a @ s2 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1i0y80f2Hb/E---3.1_1785764.p',conj_1) ).
thf(help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
! [X867: refine424419629nres_a,X868: refine424419629nres_a] :
( ( if_Ref1724547303nres_a @ $true @ X867 @ X868 )
= X867 ),
file('/export/starexec/sandbox2/tmp/tmp.1i0y80f2Hb/E---3.1_1785764.p',help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T) ).
thf(conj_0,hypothesis,
( b
=> ( ord_le519537037nres_a @ s1 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1i0y80f2Hb/E---3.1_1785764.p',conj_0) ).
thf(c_0_5,negated_conjecture,
~ ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ b @ s1 @ s2 ) @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ),
inference(assume_negation,[status(cth)],[conj_2]) ).
thf(c_0_6,negated_conjecture,
~ ( ( ~ b
| ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ $true @ s1 @ s2 ) @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) )
& ( b
| ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ $false @ s1 @ s2 ) @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ) ),
inference(fool_unroll,[status(thm)],[c_0_5]) ).
thf(c_0_7,axiom,
! [X865: refine424419629nres_a,X866: refine424419629nres_a] :
( ( ~ ~ $true
| ( ( if_Ref1724547303nres_a @ $true @ X865 @ X866 )
= X866 ) )
& ( ~ $true
| ( ( if_Ref1724547303nres_a @ $false @ X865 @ X866 )
= X866 ) ) ),
inference(fool_unroll,[status(thm)],[help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T]) ).
thf(c_0_8,hypothesis,
( ~ b
=> ( ord_le519537037nres_a @ s2 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ),
inference(fof_simplification,[status(thm)],[conj_1]) ).
thf(c_0_9,negated_conjecture,
( ( ~ b
| b )
& ( ~ ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ $false @ s1 @ s2 ) @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) )
| b )
& ( ~ b
| ~ ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ $true @ s1 @ s2 ) @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) )
& ( ~ ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ $false @ s1 @ s2 ) @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) )
| ~ ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ $true @ s1 @ s2 ) @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
thf(c_0_10,plain,
! [X1421: refine424419629nres_a,X1422: refine424419629nres_a] :
( ( if_Ref1724547303nres_a @ $true @ X1421 @ X1422 )
= X1421 ),
inference(variable_rename,[status(thm)],[help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T]) ).
thf(c_0_11,hypothesis,
( ~ b
| ( ord_le519537037nres_a @ s1 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_0])]) ).
thf(c_0_12,plain,
! [X1419: refine424419629nres_a,X1420: refine424419629nres_a] :
( ( $true
| ( ( if_Ref1724547303nres_a @ $true @ X1419 @ X1420 )
= X1420 ) )
& ( ~ $true
| ( ( if_Ref1724547303nres_a @ $false @ X1419 @ X1420 )
= X1420 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
thf(c_0_13,hypothesis,
( b
| ( ord_le519537037nres_a @ s2 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ),
inference(fof_nnf,[status(thm)],[c_0_8]) ).
thf(c_0_14,negated_conjecture,
( ~ b
| ~ ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ $true @ s1 @ s2 ) @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_15,plain,
! [X23: refine424419629nres_a,X22: refine424419629nres_a] :
( ( if_Ref1724547303nres_a @ $true @ X22 @ X23 )
= X22 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_16,hypothesis,
( ( ord_le519537037nres_a @ s1 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) )
| ~ b ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_17,plain,
! [X22: refine424419629nres_a,X23: refine424419629nres_a] :
( ( ( if_Ref1724547303nres_a @ ~ $true @ X22 @ X23 )
= X23 )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_18,hypothesis,
( b
| ( ord_le519537037nres_a @ s2 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_19,negated_conjecture,
~ b,
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
thf(c_0_20,negated_conjecture,
( b
| ~ ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ ~ $true @ s1 @ s2 ) @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_21,plain,
! [X22: refine424419629nres_a,X23: refine424419629nres_a] :
( ( if_Ref1724547303nres_a @ ~ $true @ X22 @ X23 )
= X23 ),
inference(cn,[status(thm)],[c_0_17]) ).
thf(c_0_22,hypothesis,
ord_le519537037nres_a @ s2 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ),
inference(sr,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_23,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_22])]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP165^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n002.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 20:07:07 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.22/0.27 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.1i0y80f2Hb/E---3.1_1785764.p
% 0.22/0.33 % Version: 3.5.1-ho
% 0.22/0.33 % Preprocessing class: HSLSSMSMSSMCHSA.
% 0.22/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.33 % Starting post_as_ho6 with 1500s (5) cores
% 0.22/0.33 % Starting post_as_ho8 with 300s (1) cores
% 0.22/0.33 % Starting new_bool_3 with 300s (1) cores
% 0.22/0.33 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.33 % post_as_ho6 with pid 1785777 completed with status 0
% 0.22/0.33 % Result found by post_as_ho6
% 0.22/0.33 % Preprocessing class: HSLSSMSMSSMCHSA.
% 0.22/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.33 % Starting post_as_ho6 with 1500s (5) cores
% 0.22/0.33 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,2.0,0,3,20000,1.0,true))
% 0.22/0.33 % SinE strategy is GSinE(CountFormulas,,true,2.0,0,3,20000,1.0,true)
% 0.22/0.33 % Search class: HGHSM-FSLF33-SHSFFSBN
% 0.22/0.33 % partial match(1): HGHSM-FSLM33-SHSFFSBN
% 0.22/0.33 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.33 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.33 % Starting post_as_ho6 with 151s (1) cores
% 0.22/0.33 % Starting sh5l with 136s (1) cores
% 0.22/0.33 % Starting lpo9_lambda_fix with 136s (1) cores
% 0.22/0.33 % Starting full_lambda_6 with 136s (1) cores
% 0.22/0.33 % post_as_ho6 with pid 1785784 completed with status 0
% 0.22/0.33 % Result found by post_as_ho6
% 0.22/0.33 % Preprocessing class: HSLSSMSMSSMCHSA.
% 0.22/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.33 % Starting post_as_ho6 with 1500s (5) cores
% 0.22/0.33 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,2.0,0,3,20000,1.0,true))
% 0.22/0.33 % SinE strategy is GSinE(CountFormulas,,true,2.0,0,3,20000,1.0,true)
% 0.22/0.33 % Search class: HGHSM-FSLF33-SHSFFSBN
% 0.22/0.33 % partial match(1): HGHSM-FSLM33-SHSFFSBN
% 0.22/0.33 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.33 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.33 % Starting post_as_ho6 with 151s (1) cores
% 0.22/0.33 % Preprocessing time : 0.004 s
% 0.22/0.33 % Presaturation interreduction done
% 0.22/0.33
% 0.22/0.33 % Proof found!
% 0.22/0.33 % SZS status Theorem
% 0.22/0.33 % SZS output start CNFRefutation
% See solution above
% 0.22/0.33 % Parsed axioms : 424
% 0.22/0.33 % Removed by relevancy pruning/SinE : 296
% 0.22/0.33 % Initial clauses : 219
% 0.22/0.33 % Removed in clause preprocessing : 18
% 0.22/0.33 % Initial clauses in saturation : 201
% 0.22/0.33 % Processed clauses : 27
% 0.22/0.33 % ...of these trivial : 3
% 0.22/0.33 % ...subsumed : 5
% 0.22/0.33 % ...remaining for further processing : 19
% 0.22/0.33 % Other redundant clauses eliminated : 2
% 0.22/0.33 % Clauses deleted for lack of memory : 0
% 0.22/0.33 % Backward-subsumed : 1
% 0.22/0.33 % Backward-rewritten : 4
% 0.22/0.33 % Generated clauses : 3
% 0.22/0.33 % ...of the previous two non-redundant : 6
% 0.22/0.33 % ...aggressively subsumed : 0
% 0.22/0.33 % Contextual simplify-reflections : 1
% 0.22/0.33 % Paramodulations : 0
% 0.22/0.33 % Factorizations : 0
% 0.22/0.33 % NegExts : 0
% 0.22/0.33 % Equation resolutions : 2
% 0.22/0.33 % Disequality decompositions : 0
% 0.22/0.33 % Total rewrite steps : 9
% 0.22/0.33 % ...of those cached : 3
% 0.22/0.33 % Propositional unsat checks : 0
% 0.22/0.33 % Propositional check models : 0
% 0.22/0.33 % Propositional check unsatisfiable : 0
% 0.22/0.33 % Propositional clauses : 0
% 0.22/0.33 % Propositional clauses after purity: 0
% 0.22/0.33 % Propositional unsat core size : 0
% 0.22/0.33 % Propositional preprocessing time : 0.000
% 0.22/0.33 % Propositional encoding time : 0.000
% 0.22/0.33 % Propositional solver time : 0.000
% 0.22/0.33 % Success case prop preproc time : 0.000
% 0.22/0.33 % Success case prop encoding time : 0.000
% 0.22/0.33 % Success case prop solver time : 0.000
% 0.22/0.33 % Current number of processed clauses : 11
% 0.22/0.33 % Positive orientable unit clauses : 7
% 0.22/0.33 % Positive unorientable unit clauses: 0
% 0.22/0.33 % Negative unit clauses : 2
% 0.22/0.33 % Non-unit-clauses : 2
% 0.22/0.33 % Current number of unprocessed clauses: 179
% 0.22/0.33 % ...number of literals in the above : 547
% 0.22/0.33 % Current number of archived formulas : 0
% 0.22/0.33 % Current number of archived clauses : 6
% 0.22/0.33 % Clause-clause subsumption calls (NU) : 15
% 0.22/0.33 % Rec. Clause-clause subsumption calls : 15
% 0.22/0.33 % Non-unit clause-clause subsumptions : 3
% 0.22/0.33 % Unit Clause-clause subsumption calls : 10
% 0.22/0.33 % Rewrite failures with RHS unbound : 0
% 0.22/0.33 % BW rewrite match attempts : 6
% 0.22/0.33 % BW rewrite match successes : 2
% 0.22/0.33 % Condensation attempts : 27
% 0.22/0.33 % Condensation successes : 0
% 0.22/0.33 % Termbank termtop insertions : 24060
% 0.22/0.33 % Search garbage collected termcells : 9387
% 0.22/0.33
% 0.22/0.33 % -------------------------------------------------
% 0.22/0.33 % User time : 0.022 s
% 0.22/0.33 % System time : 0.007 s
% 0.22/0.33 % Total time : 0.029 s
% 0.22/0.33 % Maximum resident set size: 5464 pages
% 0.22/0.33
% 0.22/0.33 % -------------------------------------------------
% 0.22/0.33 % User time : 0.053 s
% 0.22/0.33 % System time : 0.020 s
% 0.22/0.33 % Total time : 0.072 s
% 0.22/0.33 % Maximum resident set size: 5632 pages
% 0.22/0.33 % E exiting
%------------------------------------------------------------------------------