%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET924^1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 08:22:49 AM UTC 2026
% Result : Theorem 0.28s 0.36s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 46 ( 6 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 111 ( 9 ~; 0 |; 0 &; 96 @)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 1 con; 0-3 aty)
% Number of variables : 34 ( 24 ^; 10 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mworld: $tType ).
thf(decl_25,type,
mlocal: ( mworld > $o ) > $o ).
thf(decl_26,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(decl_30,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(decl_33,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(decl_35,type,
qmltpeq: $i > $i > mworld > $o ).
thf(decl_36,type,
in: $i > $i > mworld > $o ).
thf(decl_38,type,
singleton: $i > $i ).
thf(decl_39,type,
set_difference: $i > $i > $i ).
thf(t67_zfmisc_1,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X28: $i] :
( mforall_di
@ ^ [X29: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X28 ) @ X29 ) @ ( singleton @ X28 ) ) @ ( mnot @ ( in @ X28 @ X29 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.7GmlqFtQe5/E---3.1_729375.p',t67_zfmisc_1) ).
thf(mnot_def,axiom,
( mnot
= ( ^ [X2: mworld > $o,X3: mworld] :
~ ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.7GmlqFtQe5/E---3.1_729375.p',mnot_def) ).
thf(mequiv_def,axiom,
( mequiv
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
<=> ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.7GmlqFtQe5/E---3.1_729375.p',mequiv_def) ).
thf(mforall_di_def,axiom,
( mforall_di
= ( ^ [X6: $i > mworld > $o,X3: mworld] :
! [X7: $i] : ( X6 @ X7 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.7GmlqFtQe5/E---3.1_729375.p',mforall_di_def) ).
thf(l34_zfmisc_1,axiom,
( mlocal
@ ( mforall_di
@ ^ [X30: $i] :
( mforall_di
@ ^ [X31: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X30 ) @ X31 ) @ ( singleton @ X30 ) ) @ ( mnot @ ( in @ X30 @ X31 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.7GmlqFtQe5/E---3.1_729375.p',l34_zfmisc_1) ).
thf(c_0_5,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [X28: $i] :
( mforall_di
@ ^ [X29: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X28 ) @ X29 ) @ ( singleton @ X28 ) ) @ ( mnot @ ( in @ X28 @ X29 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t67_zfmisc_1]) ).
thf(c_0_6,plain,
( mnot
= ( ^ [Z0: mworld > $o,Z1: mworld] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot_def]) ).
thf(c_0_7,plain,
( mequiv
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
<=> ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mequiv_def]) ).
thf(c_0_8,plain,
( mforall_di
= ( ^ [Z0: $i > mworld > $o,Z1: mworld] :
! [X7: $i] : ( Z0 @ X7 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mforall_di_def]) ).
thf(c_0_9,negated_conjecture,
~ ( mlocal
@ ^ [Z0: mworld] :
! [X33: $i,X32: $i] :
( ( qmltpeq @ ( set_difference @ ( singleton @ X33 ) @ X32 ) @ ( singleton @ X33 ) @ Z0 )
<=> ~ ( in @ X33 @ X32 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_5]),c_0_6]),c_0_7]),c_0_8])]) ).
thf(c_0_10,plain,
( mlocal
@ ^ [Z0: mworld] :
! [X38: $i,X37: $i] :
( ( qmltpeq @ ( set_difference @ ( singleton @ X38 ) @ X37 ) @ ( singleton @ X38 ) @ Z0 )
<=> ~ ( in @ X38 @ X37 @ Z0 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[l34_zfmisc_1]),c_0_6]),c_0_7]),c_0_8]) ).
thf(c_0_11,negated_conjecture,
~ ( mlocal
@ ^ [Z0: mworld] :
! [X58: $i,X59: $i] :
( ( qmltpeq @ ( set_difference @ ( singleton @ X58 ) @ X59 ) @ ( singleton @ X58 ) @ Z0 )
<=> ~ ( in @ X58 @ X59 @ Z0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_12,plain,
( mlocal
@ ^ [Z0: mworld] :
! [X60: $i,X61: $i] :
( ( qmltpeq @ ( set_difference @ ( singleton @ X60 ) @ X61 ) @ ( singleton @ X60 ) @ Z0 )
<=> ~ ( in @ X60 @ X61 @ Z0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_13,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET924^1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 % Computer : n006.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Tue Sep 29 13:41:09 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.30 Running higher-order theorem proving
% 0.28/0.32 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.7GmlqFtQe5/E---3.1_729375.p
% 0.28/0.36 % Version: 3.5.1-ho
% 0.28/0.36 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.28/0.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.36 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.28/0.36 % Starting post_as_ho3 with 300s (1) cores
% 0.28/0.36 % Starting new_ho_12 with 300s (1) cores
% 0.28/0.36 % Starting new_bool_2 with 300s (1) cores
% 0.28/0.36 % new_bool_2 with pid 729391 completed with status 0
% 0.28/0.36 % Result found by new_bool_2
% 0.28/0.36 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.28/0.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.36 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.28/0.36 % Starting post_as_ho3 with 300s (1) cores
% 0.28/0.36 % Starting new_ho_12 with 300s (1) cores
% 0.28/0.36 % Starting new_bool_2 with 300s (1) cores
% 0.28/0.36 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.28/0.36 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.28/0.36 % Search class: HUUNF-FFSM21-DHSSMFNN
% 0.28/0.36 % partial match(4): HGUNF-FFSF11-SHSSMFNN
% 0.28/0.36 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.36 % Starting SubtermCWHack with 28s (1) cores
% 0.28/0.36 % SubtermCWHack with pid 729392 completed with status 0
% 0.28/0.36 % Result found by SubtermCWHack
% 0.28/0.36 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.28/0.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.36 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.28/0.36 % Starting post_as_ho3 with 300s (1) cores
% 0.28/0.36 % Starting new_ho_12 with 300s (1) cores
% 0.28/0.36 % Starting new_bool_2 with 300s (1) cores
% 0.28/0.36 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.28/0.36 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.28/0.36 % Search class: HUUNF-FFSM21-DHSSMFNN
% 0.28/0.36 % partial match(4): HGUNF-FFSF11-SHSSMFNN
% 0.28/0.36 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.36 % Starting SubtermCWHack with 28s (1) cores
% 0.28/0.36 % Preprocessing time : 0.003 s
% 0.28/0.36
% 0.28/0.36 % Proof found!
% 0.28/0.36 % SZS status Theorem
% 0.28/0.36 % SZS output start CNFRefutation
% See solution above
% 0.28/0.36 % Parsed axioms : 42
% 0.28/0.36 % Removed by relevancy pruning/SinE : 26
% 0.28/0.36 % Initial clauses : 11
% 0.28/0.36 % Removed in clause preprocessing : 0
% 0.28/0.36 % Initial clauses in saturation : 11
% 0.28/0.36 % Processed clauses : 6
% 0.28/0.36 % ...of these trivial : 0
% 0.28/0.36 % ...subsumed : 0
% 0.28/0.36 % ...remaining for further processing : 5
% 0.28/0.36 % Other redundant clauses eliminated : 0
% 0.28/0.36 % Clauses deleted for lack of memory : 0
% 0.28/0.36 % Backward-subsumed : 0
% 0.28/0.36 % Backward-rewritten : 0
% 0.28/0.36 % Generated clauses : 0
% 0.28/0.36 % ...of the previous two non-redundant : 0
% 0.28/0.36 % ...aggressively subsumed : 0
% 0.28/0.36 % Contextual simplify-reflections : 0
% 0.28/0.36 % Paramodulations : 0
% 0.28/0.36 % Factorizations : 0
% 0.28/0.36 % NegExts : 0
% 0.28/0.36 % Equation resolutions : 0
% 0.28/0.36 % Disequality decompositions : 0
% 0.28/0.36 % Total rewrite steps : 1
% 0.28/0.36 % ...of those cached : 0
% 0.28/0.36 % Propositional unsat checks : 0
% 0.28/0.36 % Propositional check models : 0
% 0.28/0.36 % Propositional check unsatisfiable : 0
% 0.28/0.36 % Propositional clauses : 0
% 0.28/0.36 % Propositional clauses after purity: 0
% 0.28/0.36 % Propositional unsat core size : 0
% 0.28/0.36 % Propositional preprocessing time : 0.000
% 0.28/0.36 % Propositional encoding time : 0.000
% 0.28/0.36 % Propositional solver time : 0.000
% 0.28/0.36 % Success case prop preproc time : 0.000
% 0.28/0.36 % Success case prop encoding time : 0.000
% 0.28/0.36 % Success case prop solver time : 0.000
% 0.28/0.36 % Current number of processed clauses : 5
% 0.28/0.36 % Positive orientable unit clauses : 5
% 0.28/0.36 % Positive unorientable unit clauses: 0
% 0.28/0.36 % Negative unit clauses : 0
% 0.28/0.36 % Non-unit-clauses : 0
% 0.28/0.36 % Current number of unprocessed clauses: 5
% 0.28/0.36 % ...number of literals in the above : 5
% 0.28/0.36 % Current number of archived formulas : 0
% 0.28/0.36 % Current number of archived clauses : 0
% 0.28/0.36 % Clause-clause subsumption calls (NU) : 0
% 0.28/0.36 % Rec. Clause-clause subsumption calls : 0
% 0.28/0.36 % Non-unit clause-clause subsumptions : 0
% 0.28/0.36 % Unit Clause-clause subsumption calls : 0
% 0.28/0.36 % Rewrite failures with RHS unbound : 0
% 0.28/0.36 % BW rewrite match attempts : 10
% 0.28/0.36 % BW rewrite match successes : 0
% 0.28/0.36 % Condensation attempts : 0
% 0.28/0.36 % Condensation successes : 0
% 0.28/0.36 % Termbank termtop insertions : 2669
% 0.28/0.36 % Search garbage collected termcells : 1111
% 0.28/0.36
% 0.28/0.36 % -------------------------------------------------
% 0.28/0.36 % User time : 0.006 s
% 0.28/0.36 % System time : 0.003 s
% 0.28/0.36 % Total time : 0.009 s
% 0.28/0.36 % Maximum resident set size: 3632 pages
% 0.28/0.36
% 0.28/0.36 % -------------------------------------------------
% 0.28/0.36 % User time : 0.007 s
% 0.28/0.36 % System time : 0.011 s
% 0.28/0.36 % Total time : 0.019 s
% 0.28/0.36 % Maximum resident set size: 4608 pages
% 0.28/0.36 % E exiting
%------------------------------------------------------------------------------