%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL731^5 : TPTP v9.3.1. Released v4.0.0.
% 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 08:12:06 AM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 65 ( 0 equ; 0 cnn)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 232 ( 24 ~; 31 |; 7 &; 160 @)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 77 ( 77 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 53 ( 0 ^; 45 !; 8 ?; 53 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
a: $tType ).
thf(decl_23,type,
epred1_1: ( ( a > $o ) > a ) > a > $o ).
thf(decl_24,type,
esk1_1: ( ( a > $o ) > a ) > a ).
thf(decl_25,type,
epred2_0: ( a > $o ) > $o ).
thf(decl_26,type,
esk2_1: ( a > $o ) > a ).
thf(decl_27,type,
epred3_1: ( ( a > $o ) > a ) > a > $o ).
thf(decl_28,type,
esk3_0: ( a > $o ) > a ).
thf(decl_29,type,
epred4_1: ( ( a > $o ) > $o ) > a > $o ).
thf(decl_30,type,
esk4_1: ( ( a > $o ) > $o ) > ( a > $o ) > a ).
thf(decl_31,type,
esk5_0: ( a > $o ) > a ).
thf(cTHM541,conjecture,
( ? [X1: ( a > $o ) > a] :
! [X2: a > $o] :
( ? [X3: a] : ( X2 @ X3 )
=> ( X2 @ ( X1 @ X2 ) ) )
<=> ! [X4: ( a > $o ) > $o] :
( ! [X2: a > $o] :
( ( X4 @ X2 )
=> ? [X3: a] : ( X2 @ X3 ) )
=> ? [X1: ( a > $o ) > a] :
! [X2: a > $o] :
( ( X4 @ X2 )
=> ( X2 @ ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.h02xEe78TD/E---3.1_3334850.p',cTHM541) ).
thf(c_0_1,negated_conjecture,
~ ( ? [X1: ( a > $o ) > a] :
! [X2: a > $o] :
( ? [X3: a] : ( X2 @ X3 )
=> ( X2 @ ( X1 @ X2 ) ) )
<=> ! [X4: ( a > $o ) > $o] :
( ! [X2: a > $o] :
( ( X4 @ X2 )
=> ? [X3: a] : ( X2 @ X3 ) )
=> ? [X1: ( a > $o ) > a] :
! [X2: a > $o] :
( ( X4 @ X2 )
=> ( X2 @ ( X1 @ X2 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM541]) ).
thf(c_0_2,negated_conjecture,
! [X13: ( a > $o ) > a,X17: a > $o,X19: ( a > $o ) > a,X22: a > $o,X23: a,X24: ( a > $o ) > $o,X26: a,X28: a > $o] :
( ( ~ ( epred2_0 @ X17 )
| ( X17 @ ( esk2_1 @ X17 ) )
| ( epred1_1 @ X13 @ ( esk1_1 @ X13 ) ) )
& ( ( epred2_0 @ ( epred3_1 @ X19 ) )
| ( epred1_1 @ X13 @ ( esk1_1 @ X13 ) ) )
& ( ~ ( epred3_1 @ X19 @ ( X19 @ ( epred3_1 @ X19 ) ) )
| ( epred1_1 @ X13 @ ( esk1_1 @ X13 ) ) )
& ( ~ ( epred2_0 @ X17 )
| ( X17 @ ( esk2_1 @ X17 ) )
| ~ ( epred1_1 @ X13 @ ( X13 @ ( epred1_1 @ X13 ) ) ) )
& ( ( epred2_0 @ ( epred3_1 @ X19 ) )
| ~ ( epred1_1 @ X13 @ ( X13 @ ( epred1_1 @ X13 ) ) ) )
& ( ~ ( epred3_1 @ X19 @ ( X19 @ ( epred3_1 @ X19 ) ) )
| ~ ( epred1_1 @ X13 @ ( X13 @ ( epred1_1 @ X13 ) ) ) )
& ( ( X24 @ ( epred4_1 @ X24 ) )
| ~ ( X24 @ X28 )
| ( X28 @ ( esk4_1 @ X24 @ X28 ) )
| ~ ( X22 @ X23 )
| ( X22 @ ( esk3_0 @ X22 ) ) )
& ( ~ ( epred4_1 @ X24 @ X26 )
| ~ ( X24 @ X28 )
| ( X28 @ ( esk4_1 @ X24 @ X28 ) )
| ~ ( X22 @ X23 )
| ( X22 @ ( esk3_0 @ X22 ) ) ) ),
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_1])])])])])]) ).
thf(c_0_3,negated_conjecture,
! [X1: ( a > $o ) > a,X5: ( a > $o ) > a] :
( ~ ( epred3_1 @ X1 @ ( X1 @ ( epred3_1 @ X1 ) ) )
| ~ ( epred1_1 @ X5 @ ( X5 @ ( epred1_1 @ X5 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_4,plain,
! [X29: a > $o,X30: a] :
( ( X29 @ ( esk5_0 @ X29 ) )
| ~ ( X29 @ X30 ) ),
inference(introduce_choice_axiom,[status(thm)],[]) ).
thf(c_0_5,negated_conjecture,
! [X1: ( a > $o ) > a,X3: a] :
( ( epred1_1 @ X1 @ ( esk5_0 @ ( epred1_1 @ X1 ) ) )
| ~ ( epred1_1 @ X1 @ X3 ) ),
inference(choice_inst,[status(thm)],[c_0_3,c_0_4]) ).
thf(c_0_6,negated_conjecture,
! [X1: ( a > $o ) > a,X5: ( a > $o ) > a] :
( ( epred2_0 @ ( epred3_1 @ X1 ) )
| ( epred1_1 @ X5 @ ( esk1_1 @ X5 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_7,negated_conjecture,
! [X1: ( a > $o ) > a,X5: ( a > $o ) > a] :
( ( epred2_0 @ ( epred3_1 @ X1 ) )
| ~ ( epred1_1 @ X5 @ ( X5 @ ( epred1_1 @ X5 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_8,negated_conjecture,
! [X1: ( a > $o ) > a,X5: ( a > $o ) > a] :
( ( epred1_1 @ X1 @ ( esk5_0 @ ( epred1_1 @ X1 ) ) )
| ( epred2_0 @ ( epred3_1 @ X5 ) ) ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
thf(c_0_9,negated_conjecture,
! [X1: ( a > $o ) > a,X5: ( a > $o ) > a] :
( ( epred2_0 @ ( epred3_1 @ X1 ) )
| ( epred2_0 @ ( epred3_1 @ X5 ) ) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
thf(c_0_10,negated_conjecture,
! [X1: ( a > $o ) > a,X2: a > $o] :
( ( X2 @ ( esk2_1 @ X2 ) )
| ( epred1_1 @ X1 @ ( esk1_1 @ X1 ) )
| ~ ( epred2_0 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_11,negated_conjecture,
! [X1: ( a > $o ) > a] : ( epred2_0 @ ( epred3_1 @ X1 ) ),
inference(ef,[status(thm)],[c_0_9]) ).
thf(c_0_12,negated_conjecture,
! [X5: ( a > $o ) > a,X1: ( a > $o ) > a] :
( ( epred1_1 @ X5 @ ( esk1_1 @ X5 ) )
| ~ ( epred3_1 @ X1 @ ( X1 @ ( epred3_1 @ X1 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_13,negated_conjecture,
! [X1: ( a > $o ) > a,X5: ( a > $o ) > a] :
( ( epred3_1 @ X1 @ ( esk2_1 @ ( epred3_1 @ X1 ) ) )
| ( epred1_1 @ X5 @ ( esk1_1 @ X5 ) ) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_14,negated_conjecture,
! [X1: ( a > $o ) > a,X5: ( a > $o ) > a] :
( ( epred1_1 @ X1 @ ( esk1_1 @ X1 ) )
| ( epred1_1 @ X5 @ ( esk1_1 @ X5 ) ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_15,negated_conjecture,
! [X1: ( a > $o ) > a] : ( epred1_1 @ X1 @ ( esk1_1 @ X1 ) ),
inference(ef,[status(thm)],[c_0_14]) ).
thf(c_0_16,negated_conjecture,
! [X1: ( a > $o ) > a] : ( epred1_1 @ X1 @ ( esk5_0 @ ( epred1_1 @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_5,c_0_15]) ).
thf(c_0_17,negated_conjecture,
! [X2: a > $o,X1: ( a > $o ) > a] :
( ( X2 @ ( esk2_1 @ X2 ) )
| ~ ( epred2_0 @ X2 )
| ~ ( epred1_1 @ X1 @ ( X1 @ ( epred1_1 @ X1 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_18,negated_conjecture,
! [X1: ( a > $o ) > a] :
~ ( epred3_1 @ X1 @ ( X1 @ ( epred3_1 @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_3,c_0_16]) ).
thf(c_0_19,negated_conjecture,
! [X2: a > $o] :
( ( X2 @ ( esk2_1 @ X2 ) )
| ~ ( epred2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
thf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_11])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL731^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n015.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 10:06:32 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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.h02xEe78TD/E---3.1_3334850.p
% 0.07/0.26 % Version: 3.5.1-ho
% 0.07/0.26 % Preprocessing class: HSSSSMSSSSSNHHA.
% 0.07/0.26 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting sh2lt with 1200s (4) cores
% 0.07/0.26 % Starting new_ho_10_unif with 300s (1) cores
% 0.07/0.26 % Starting full_lambda_6 with 300s (1) cores
% 0.07/0.26 % Starting post_as_ho1 with 300s (1) cores
% 0.07/0.26 % Starting ehoh_best3_rw with 300s (1) cores
% 0.07/0.26 % sh2lt with pid 3334863 completed with status 0
% 0.07/0.26 % Result found by sh2lt
% 0.07/0.26 % Preprocessing class: HSSSSMSSSSSNHHA.
% 0.07/0.26 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting sh2lt with 1200s (4) cores
% 0.07/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,5,,4,20000,1.0,true))
% 0.07/0.26 % SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 0.07/0.26 % Search class: HGHNF-FFSF11-SHHFFMBN
% 0.07/0.26 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 0.07/0.26 % Starting SubtermCWHack with 109s (1) cores
% 0.07/0.26 % Starting sh2lt with 121s (1) cores
% 0.07/0.26 % Starting post_as_ho1 with 109s (1) cores
% 0.07/0.26 % Starting ehoh_best_sine_rwall with 109s (1) cores
% 0.07/0.26 % post_as_ho1 with pid 3334871 completed with status 0
% 0.07/0.26 % Result found by post_as_ho1
% 0.07/0.26 % Preprocessing class: HSSSSMSSSSSNHHA.
% 0.07/0.26 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting sh2lt with 1200s (4) cores
% 0.07/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,5,,4,20000,1.0,true))
% 0.07/0.26 % SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 0.07/0.26 % Search class: HGHNF-FFSF11-SHHFFMBN
% 0.07/0.26 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 0.07/0.26 % Starting SubtermCWHack with 109s (1) cores
% 0.07/0.26 % Starting sh2lt with 121s (1) cores
% 0.07/0.26 % Starting post_as_ho1 with 109s (1) cores
% 0.07/0.26 % Preprocessing time : 0.001 s
% 0.07/0.26 % Presaturation interreduction done
% 0.07/0.26
% 0.07/0.26 % Proof found!
% 0.07/0.26 % SZS status Theorem
% 0.07/0.26 % SZS output start CNFRefutation
% See solution above
% 0.07/0.26 % Parsed axioms : 2
% 0.07/0.26 % Removed by relevancy pruning/SinE : 1
% 0.07/0.26 % Initial clauses : 8
% 0.07/0.26 % Removed in clause preprocessing : 0
% 0.07/0.26 % Initial clauses in saturation : 8
% 0.07/0.26 % Processed clauses : 33
% 0.07/0.26 % ...of these trivial : 0
% 0.07/0.26 % ...subsumed : 3
% 0.07/0.26 % ...remaining for further processing : 30
% 0.07/0.26 % Other redundant clauses eliminated : 2
% 0.07/0.26 % Clauses deleted for lack of memory : 0
% 0.07/0.26 % Backward-subsumed : 7
% 0.07/0.26 % Backward-rewritten : 4
% 0.07/0.26 % Generated clauses : 43
% 0.07/0.26 % ...of the previous two non-redundant : 39
% 0.07/0.26 % ...aggressively subsumed : 0
% 0.07/0.26 % Contextual simplify-reflections : 0
% 0.07/0.26 % Paramodulations : 23
% 0.07/0.26 % Factorizations : 4
% 0.07/0.26 % NegExts : 2
% 0.07/0.26 % Equation resolutions : 2
% 0.07/0.26 % Disequality decompositions : 0
% 0.07/0.26 % Total rewrite steps : 6
% 0.07/0.26 % ...of those cached : 0
% 0.07/0.26 % Propositional unsat checks : 0
% 0.07/0.26 % Propositional check models : 0
% 0.07/0.26 % Propositional check unsatisfiable : 0
% 0.07/0.26 % Propositional clauses : 0
% 0.07/0.26 % Propositional clauses after purity: 0
% 0.07/0.26 % Propositional unsat core size : 0
% 0.07/0.26 % Propositional preprocessing time : 0.000
% 0.07/0.26 % Propositional encoding time : 0.000
% 0.07/0.26 % Propositional solver time : 0.000
% 0.07/0.26 % Success case prop preproc time : 0.000
% 0.07/0.26 % Success case prop encoding time : 0.000
% 0.07/0.26 % Success case prop solver time : 0.000
% 0.07/0.26 % Current number of processed clauses : 11
% 0.07/0.26 % Positive orientable unit clauses : 3
% 0.07/0.26 % Positive unorientable unit clauses: 0
% 0.07/0.26 % Negative unit clauses : 1
% 0.07/0.26 % Non-unit-clauses : 7
% 0.07/0.26 % Current number of unprocessed clauses: 16
% 0.07/0.26 % ...number of literals in the above : 53
% 0.07/0.26 % Current number of archived formulas : 0
% 0.07/0.26 % Current number of archived clauses : 20
% 0.07/0.26 % Clause-clause subsumption calls (NU) : 11
% 0.07/0.26 % Rec. Clause-clause subsumption calls : 10
% 0.07/0.26 % Non-unit clause-clause subsumptions : 4
% 0.07/0.26 % Unit Clause-clause subsumption calls : 8
% 0.07/0.26 % Rewrite failures with RHS unbound : 0
% 0.07/0.26 % BW rewrite match attempts : 5
% 0.07/0.26 % BW rewrite match successes : 5
% 0.07/0.26 % Condensation attempts : 0
% 0.07/0.26 % Condensation successes : 0
% 0.07/0.26 % Termbank termtop insertions : 2218
% 0.07/0.26 % Search garbage collected termcells : 283
% 0.07/0.26
% 0.07/0.26 % -------------------------------------------------
% 0.07/0.26 % User time : 0.004 s
% 0.07/0.26 % System time : 0.005 s
% 0.07/0.26 % Total time : 0.009 s
% 0.07/0.26 % Maximum resident set size: 3632 pages
% 0.07/0.26
% 0.07/0.26 % -------------------------------------------------
% 0.07/0.26 % User time : 0.013 s
% 0.07/0.26 % System time : 0.016 s
% 0.07/0.26 % Total time : 0.029 s
% 0.07/0.26 % Maximum resident set size: 4864 pages
% 0.07/0.26 % E exiting
%------------------------------------------------------------------------------