%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET624^3 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 08:22:44 AM UTC 2026
% Result : Theorem 0.10s 0.24s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 36 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 131 ( 4 equ; 0 cnn)
% Maximal formula atoms : 44 ( 3 avg)
% Number of connectives : 278 ( 33 ~; 81 |; 16 &; 145 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 33 ( 10 ^; 18 !; 5 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_28,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_35,type,
meets: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_37,type,
epred1_0: $i > $o ).
thf(decl_38,type,
epred2_0: $i > $o ).
thf(decl_39,type,
epred3_0: $i > $o ).
thf(decl_40,type,
esk1_0: $i ).
thf(decl_41,type,
esk2_0: $i ).
thf(decl_42,type,
esk3_0: $i ).
thf(thm,conjecture,
! [X22: $i > $o,X23: $i > $o,X24: $i > $o] :
( ( meets @ X22 @ ( union @ X23 @ X24 ) )
<=> ( ( meets @ X22 @ X23 )
| ( meets @ X22 @ X24 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hviheyFz9N/E---3.1_3165590.p',thm) ).
thf(union,axiom,
( union
= ( ^ [X5: $i > $o,X6: $i > $o,X4: $i] :
( ( X5 @ X4 )
| ( X6 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hviheyFz9N/E---3.1_3165590.p',union) ).
thf(meets,axiom,
( meets
= ( ^ [X18: $i > $o,X19: $i > $o] :
? [X4: $i] :
( ( X18 @ X4 )
& ( X19 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hviheyFz9N/E---3.1_3165590.p',meets) ).
thf(c_0_3,negated_conjecture,
~ ! [X22: $i > $o,X23: $i > $o,X24: $i > $o] :
( ( meets @ X22 @ ( union @ X23 @ X24 ) )
<=> ( ( meets @ X22 @ X23 )
| ( meets @ X22 @ X24 ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_4,plain,
( union
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[union]) ).
thf(c_0_5,plain,
( meets
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
? [X4: $i] :
( ( Z0 @ X4 )
& ( Z1 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[meets]) ).
thf(c_0_6,negated_conjecture,
~ ! [X22: $i > $o,X23: $i > $o,X24: $i > $o] :
( ? [X28: $i] :
( ( X22 @ X28 )
& ( ( X23 @ X28 )
| ( X24 @ X28 ) ) )
<=> ( ? [X29: $i] :
( ( X22 @ X29 )
& ( X23 @ X29 ) )
| ? [X30: $i] :
( ( X22 @ X30 )
& ( X24 @ X30 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_3,c_0_4]),c_0_5]) ).
thf(c_0_7,negated_conjecture,
! [X34: $i,X35: $i,X36: $i] :
( ( ~ ( epred1_0 @ X35 )
| ~ ( epred2_0 @ X35 )
| ~ ( epred2_0 @ X34 )
| ~ ( epred1_0 @ X34 ) )
& ( ~ ( epred1_0 @ X36 )
| ~ ( epred3_0 @ X36 )
| ~ ( epred2_0 @ X34 )
| ~ ( epred1_0 @ X34 ) )
& ( ~ ( epred1_0 @ X35 )
| ~ ( epred2_0 @ X35 )
| ~ ( epred3_0 @ X34 )
| ~ ( epred1_0 @ X34 ) )
& ( ~ ( epred1_0 @ X36 )
| ~ ( epred3_0 @ X36 )
| ~ ( epred3_0 @ X34 )
| ~ ( epred1_0 @ X34 ) )
& ( ( epred1_0 @ esk3_0 )
| ( epred1_0 @ esk2_0 )
| ( epred1_0 @ esk1_0 ) )
& ( ( epred3_0 @ esk3_0 )
| ( epred1_0 @ esk2_0 )
| ( epred1_0 @ esk1_0 ) )
& ( ( epred1_0 @ esk3_0 )
| ( epred2_0 @ esk2_0 )
| ( epred1_0 @ esk1_0 ) )
& ( ( epred3_0 @ esk3_0 )
| ( epred2_0 @ esk2_0 )
| ( epred1_0 @ esk1_0 ) )
& ( ( epred1_0 @ esk3_0 )
| ( epred1_0 @ esk2_0 )
| ( epred2_0 @ esk1_0 )
| ( epred3_0 @ esk1_0 ) )
& ( ( epred3_0 @ esk3_0 )
| ( epred1_0 @ esk2_0 )
| ( epred2_0 @ esk1_0 )
| ( epred3_0 @ esk1_0 ) )
& ( ( epred1_0 @ esk3_0 )
| ( epred2_0 @ esk2_0 )
| ( epred2_0 @ esk1_0 )
| ( epred3_0 @ esk1_0 ) )
& ( ( epred3_0 @ esk3_0 )
| ( epred2_0 @ esk2_0 )
| ( epred2_0 @ esk1_0 )
| ( epred3_0 @ esk1_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_6])])])])])]) ).
thf(c_0_8,negated_conjecture,
! [X1: $i,X3: $i] :
( ~ ( epred1_0 @ X1 )
| ~ ( epred3_0 @ X1 )
| ~ ( epred3_0 @ X3 )
| ~ ( epred1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i,X3: $i] :
( ~ ( epred1_0 @ X1 )
| ~ ( epred2_0 @ X1 )
| ~ ( epred2_0 @ X3 )
| ~ ( epred1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i] :
( ~ ( epred1_0 @ X1 )
| ~ ( epred3_0 @ X1 ) ),
inference(condense,[status(thm)],[c_0_8]) ).
thf(c_0_11,negated_conjecture,
( ( epred3_0 @ esk3_0 )
| ( epred1_0 @ esk2_0 )
| ( epred1_0 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_12,negated_conjecture,
( ( epred1_0 @ esk3_0 )
| ( epred1_0 @ esk2_0 )
| ( epred1_0 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i] :
( ~ ( epred1_0 @ X1 )
| ~ ( epred2_0 @ X1 ) ),
inference(condense,[status(thm)],[c_0_9]) ).
thf(c_0_14,negated_conjecture,
( ( epred3_0 @ esk3_0 )
| ( epred2_0 @ esk2_0 )
| ( epred1_0 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_15,negated_conjecture,
( ( epred1_0 @ esk2_0 )
| ( epred1_0 @ esk1_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
thf(c_0_16,negated_conjecture,
( ( epred3_0 @ esk3_0 )
| ( epred1_0 @ esk1_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
thf(c_0_17,negated_conjecture,
( ( epred1_0 @ esk3_0 )
| ( epred2_0 @ esk2_0 )
| ( epred1_0 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_18,negated_conjecture,
( ( epred1_0 @ esk1_0 )
| ~ ( epred1_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_10,c_0_16]) ).
thf(c_0_19,negated_conjecture,
( ( epred3_0 @ esk3_0 )
| ( epred1_0 @ esk2_0 )
| ( epred2_0 @ esk1_0 )
| ( epred3_0 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_20,negated_conjecture,
epred1_0 @ esk1_0,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_17]),c_0_15]),c_0_18]) ).
thf(c_0_21,negated_conjecture,
( ( epred3_0 @ esk3_0 )
| ( epred3_0 @ esk1_0 )
| ( epred1_0 @ esk2_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_19]),c_0_20])]) ).
thf(c_0_22,negated_conjecture,
( ( epred1_0 @ esk2_0 )
| ( epred3_0 @ esk1_0 )
| ~ ( epred1_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_10,c_0_21]) ).
thf(c_0_23,negated_conjecture,
( ( epred1_0 @ esk3_0 )
| ( epred1_0 @ esk2_0 )
| ( epred2_0 @ esk1_0 )
| ( epred3_0 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_24,negated_conjecture,
( ( epred1_0 @ esk2_0 )
| ~ ( epred1_0 @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_22]),c_0_20])]) ).
thf(c_0_25,negated_conjecture,
( ( epred3_0 @ esk1_0 )
| ( epred1_0 @ esk2_0 ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_23]),c_0_20])]),c_0_24]) ).
thf(c_0_26,negated_conjecture,
( ( epred1_0 @ esk3_0 )
| ( epred2_0 @ esk2_0 )
| ( epred2_0 @ esk1_0 )
| ( epred3_0 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_27,negated_conjecture,
epred1_0 @ esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_25]),c_0_20])]) ).
thf(c_0_28,negated_conjecture,
( ( epred3_0 @ esk3_0 )
| ( epred2_0 @ esk2_0 )
| ( epred2_0 @ esk1_0 )
| ( epred3_0 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_29,negated_conjecture,
( ( epred3_0 @ esk1_0 )
| ( epred2_0 @ esk1_0 )
| ( epred1_0 @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_26]),c_0_27])]) ).
thf(c_0_30,negated_conjecture,
( ( epred3_0 @ esk3_0 )
| ( epred3_0 @ esk1_0 )
| ( epred2_0 @ esk1_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_28]),c_0_27])]) ).
thf(c_0_31,negated_conjecture,
( ( epred1_0 @ esk3_0 )
| ( epred3_0 @ esk1_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_29]),c_0_20])]) ).
thf(c_0_32,negated_conjecture,
( ( epred3_0 @ esk1_0 )
| ( epred3_0 @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_30]),c_0_20])]) ).
thf(c_0_33,negated_conjecture,
epred1_0 @ esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_31]),c_0_20])]) ).
thf(c_0_34,negated_conjecture,
epred3_0 @ esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_32]),c_0_33])]) ).
thf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_34]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET624^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n008.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 13:40:24 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.10/0.22 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.hviheyFz9N/E---3.1_3165590.p
% 0.10/0.24 % Version: 3.5.1-ho
% 0.10/0.24 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.10/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.24 % Starting new_ho_9 with 1500s (5) cores
% 0.10/0.24 % Starting post_as_ho1 with 300s (1) cores
% 0.10/0.24 % Starting sh1l with 300s (1) cores
% 0.10/0.24 % Starting post_as_ho10 with 300s (1) cores
% 0.10/0.24 % new_ho_9 with pid 3165617 completed with status 0
% 0.10/0.24 % Result found by new_ho_9
% 0.10/0.24 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.10/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.24 % Starting new_ho_9 with 1500s (5) cores
% 0.10/0.24 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.24 % No SInE strategy applied
% 0.10/0.24 % Search class: HGHNF-FFSM00-SHSSMFNN
% 0.10/0.24 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.24 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.24 % Starting new_ho_9 with 151s (1) cores
% 0.10/0.24 % Starting sh5l with 136s (1) cores
% 0.10/0.24 % Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.10/0.24 % Starting lpo1_def_fix with 136s (1) cores
% 0.10/0.24 % sh5l with pid 3165624 completed with status 0
% 0.10/0.24 % Result found by sh5l
% 0.10/0.24 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.10/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.24 % Starting new_ho_9 with 1500s (5) cores
% 0.10/0.24 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.24 % No SInE strategy applied
% 0.10/0.24 % Search class: HGHNF-FFSM00-SHSSMFNN
% 0.10/0.24 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.24 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.24 % Starting new_ho_9 with 151s (1) cores
% 0.10/0.24 % Starting sh5l with 136s (1) cores
% 0.10/0.24 % Preprocessing time : 0.001 s
% 0.10/0.24 % Presaturation interreduction done
% 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 : 29
% 0.10/0.24 % Removed by relevancy pruning/SinE : 0
% 0.10/0.24 % Initial clauses : 26
% 0.10/0.24 % Removed in clause preprocessing : 14
% 0.10/0.24 % Initial clauses in saturation : 12
% 0.10/0.24 % Processed clauses : 37
% 0.10/0.24 % ...of these trivial : 0
% 0.10/0.24 % ...subsumed : 2
% 0.10/0.24 % ...remaining for further processing : 35
% 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 : 11
% 0.10/0.24 % Backward-rewritten : 8
% 0.10/0.24 % Generated clauses : 16
% 0.10/0.24 % ...of the previous two non-redundant : 15
% 0.10/0.24 % ...aggressively subsumed : 0
% 0.10/0.24 % Contextual simplify-reflections : 5
% 0.10/0.24 % Paramodulations : 16
% 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 : 19
% 0.10/0.24 % ...of those cached : 15
% 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 : 6
% 0.10/0.24 % Positive orientable unit clauses : 4
% 0.10/0.24 % Positive unorientable unit clauses: 0
% 0.10/0.24 % Negative unit clauses : 0
% 0.10/0.24 % Non-unit-clauses : 2
% 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 : 29
% 0.10/0.24 % Clause-clause subsumption calls (NU) : 45
% 0.10/0.24 % Rec. Clause-clause subsumption calls : 24
% 0.10/0.24 % Non-unit clause-clause subsumptions : 20
% 0.10/0.24 % Unit Clause-clause subsumption calls : 3
% 0.10/0.24 % Rewrite failures with RHS unbound : 0
% 0.10/0.24 % BW rewrite match attempts : 4
% 0.10/0.24 % BW rewrite match successes : 4
% 0.10/0.24 % Condensation attempts : 37
% 0.10/0.24 % Condensation successes : 2
% 0.10/0.24 % Termbank termtop insertions : 1724
% 0.10/0.24 % Search garbage collected termcells : 336
% 0.10/0.24
% 0.10/0.24 % -------------------------------------------------
% 0.10/0.24 % User time : 0.003 s
% 0.10/0.24 % System time : 0.001 s
% 0.10/0.24 % Total time : 0.005 s
% 0.10/0.24 % Maximum resident set size: 3916 pages
% 0.10/0.24
% 0.10/0.24 % -------------------------------------------------
% 0.10/0.24 % User time : 0.013 s
% 0.10/0.24 % System time : 0.012 s
% 0.10/0.24 % Total time : 0.025 s
% 0.10/0.24 % Maximum resident set size: 4864 pages
% 0.10/0.24 % E exiting
%------------------------------------------------------------------------------