%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET557^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 08:22:27 AM UTC 2026
% Result : Theorem 0.28s 0.26s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 15 ( 4 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 52 ( 11 ~; 4 |; 0 &; 36 @)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 22 ( 4 ^; 14 !; 4 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
epred1_0: $i > $i > $o ).
thf(decl_24,type,
esk1_1: ( $i > $o ) > $i ).
thf(surjectiveCantorThm,conjecture,
~ ? [X1: $i > $i > $o] :
! [X2: $i > $o] :
? [X3: $i] :
( ( X1 @ X3 )
= X2 ),
file('/export/starexec/sandbox/tmp/tmp.mapais782G/E---3.1_1251048.p',surjectiveCantorThm) ).
thf(c_0_1,negated_conjecture,
~ ~ ? [X1: $i > $i > $o] :
! [X2: $i > $o] :
? [X3: $i] :
( ( X1 @ X3 )
= X2 ),
inference(assume_negation,[status(cth)],[surjectiveCantorThm]) ).
thf(c_0_2,negated_conjecture,
! [X8: $i > $o] :
( ( epred1_0 @ ( esk1_1 @ X8 ) )
= X8 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])]) ).
thf(c_0_3,negated_conjecture,
! [X2: $i > $o] :
( ( epred1_0 @ ( esk1_1 @ X2 ) )
= X2 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_4,negated_conjecture,
! [X2: $i > $o,X10: $i] :
( ( epred1_0 @ ( esk1_1 @ X2 ) @ X10 )
<=> ( X2 @ X10 ) ),
inference(arg_cong,[status(thm)],[c_0_3]) ).
thf(c_0_5,negated_conjecture,
! [X2: $i > $o,X3: $i] :
( ( epred1_0 @ ( esk1_1 @ X2 ) @ X3 )
| ~ ( X2 @ X3 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_4]) ).
thf(c_0_6,negated_conjecture,
! [X2: $i > $o,X3: $i] :
( ( X2 @ X3 )
| ~ ( epred1_0 @ ( esk1_1 @ X2 ) @ X3 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_4]) ).
thf(c_0_7,negated_conjecture,
! [X2: $i > $o,X3: $i] :
( ( epred1_0
@ ( esk1_1
@ ^ [Z0: $i] :
~ ( X2 @ Z0 ) )
@ X3 )
| ( X2 @ X3 ) ),
inference(primitive_enumeration,[status(thm)],[inference(cn,[status(thm)],[]),c_0_5]) ).
thf(c_0_8,negated_conjecture,
! [X2: $i > $o,X3: $i] :
( ~ ( epred1_0
@ ( esk1_1
@ ^ [Z0: $i] :
~ ( X2 @ Z0 ) )
@ X3 )
| ~ ( X2 @ X3 ) ),
inference(primitive_enumeration,[status(thm)],[inference(cn,[status(thm)],[]),c_0_6]) ).
thf(c_0_9,negated_conjecture,
( epred1_0
@ ( esk1_1
@ ^ [Z0: $i] :
~ ( epred1_0 @ Z0 @ Z0 ) )
@ ( esk1_1
@ ^ [Z0: $i] :
~ ( epred1_0 @ Z0 @ Z0 ) ) ),
inference(ef,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_9])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET557^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n001.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 13:43:20 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
% 0.07/0.24 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.mapais782G/E---3.1_1251048.p
% 0.28/0.26 % Version: 3.5.1-ho
% 0.28/0.26 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.28/0.26 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.26 % Starting post_as_ho12 with 300s (1) cores
% 0.28/0.26 % Starting new_bool_9 with 300s (1) cores
% 0.28/0.26 % Starting post_as_ho1 with 300s (1) cores
% 0.28/0.26 % Starting post_as_ho4 with 300s (1) cores
% 0.28/0.26 % Starting post_as_ho2 with 300s (1) cores
% 0.28/0.26 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.28/0.26 % Starting full_lambda_10 with 300s (1) cores
% 0.28/0.26 % Starting new_ho_8 with 300s (1) cores
% 0.28/0.26 % post_as_ho2 with pid 1251065 completed with status 0
% 0.28/0.26 % Result found by post_as_ho2
% 0.28/0.26 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.28/0.26 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.26 % Starting post_as_ho12 with 300s (1) cores
% 0.28/0.26 % Starting new_bool_9 with 300s (1) cores
% 0.28/0.26 % Starting post_as_ho1 with 300s (1) cores
% 0.28/0.26 % Starting post_as_ho4 with 300s (1) cores
% 0.28/0.26 % Starting post_as_ho2 with 300s (1) cores
% 0.28/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.28/0.26 % No SInE strategy applied
% 0.28/0.26 % Search class: HUUPF-FFSF11-SSSFFFBN
% 0.28/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.28/0.26 % SubtermCWHack with pid 1251070 completed with status 10
% 0.28/0.26 % Starting post_as_ho2 with 31s (1) cores
% 0.28/0.26 % post_as_ho2 with pid 1251074 completed with status 10
% 0.28/0.26 % Starting post_as_ho4 with 28s (1) cores
% 0.28/0.26 % post_as_ho4 with pid 1251081 completed with status 0
% 0.28/0.26 % Result found by post_as_ho4
% 0.28/0.26 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.28/0.26 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.26 % Starting post_as_ho12 with 300s (1) cores
% 0.28/0.26 % Starting new_bool_9 with 300s (1) cores
% 0.28/0.26 % Starting post_as_ho1 with 300s (1) cores
% 0.28/0.26 % Starting post_as_ho4 with 300s (1) cores
% 0.28/0.26 % Starting post_as_ho2 with 300s (1) cores
% 0.28/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.28/0.26 % No SInE strategy applied
% 0.28/0.26 % Search class: HUUPF-FFSF11-SSSFFFBN
% 0.28/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.28/0.26 % SubtermCWHack with pid 1251070 completed with status 10
% 0.28/0.26 % Starting post_as_ho2 with 31s (1) cores
% 0.28/0.26 % post_as_ho2 with pid 1251074 completed with status 10
% 0.28/0.26 % Starting post_as_ho4 with 28s (1) cores
% 0.28/0.26 % Preprocessing time : 0.001 s
% 0.28/0.26 % Presaturation interreduction done
% 0.28/0.26
% 0.28/0.26 % Proof found!
% 0.28/0.26 % SZS status Theorem
% 0.28/0.26 % SZS output start CNFRefutation
% See solution above
% 0.28/0.26 % Parsed axioms : 1
% 0.28/0.26 % Removed by relevancy pruning/SinE : 0
% 0.28/0.26 % Initial clauses : 1
% 0.28/0.26 % Removed in clause preprocessing : 0
% 0.28/0.26 % Initial clauses in saturation : 1
% 0.28/0.26 % Processed clauses : 15
% 0.28/0.26 % ...of these trivial : 1
% 0.28/0.26 % ...subsumed : 1
% 0.28/0.26 % ...remaining for further processing : 13
% 0.28/0.26 % Other redundant clauses eliminated : 0
% 0.28/0.26 % Clauses deleted for lack of memory : 0
% 0.28/0.26 % Backward-subsumed : 0
% 0.28/0.26 % Backward-rewritten : 0
% 0.28/0.26 % Generated clauses : 39
% 0.28/0.26 % ...of the previous two non-redundant : 31
% 0.28/0.26 % ...aggressively subsumed : 0
% 0.28/0.26 % Contextual simplify-reflections : 0
% 0.28/0.26 % Paramodulations : 20
% 0.28/0.26 % Factorizations : 8
% 0.28/0.26 % NegExts : 0
% 0.28/0.26 % Equation resolutions : 2
% 0.28/0.26 % Disequality decompositions : 0
% 0.28/0.26 % Total rewrite steps : 5
% 0.28/0.26 % ...of those cached : 2
% 0.28/0.26 % Propositional unsat checks : 0
% 0.28/0.26 % Propositional check models : 0
% 0.28/0.26 % Propositional check unsatisfiable : 0
% 0.28/0.26 % Propositional clauses : 0
% 0.28/0.26 % Propositional clauses after purity: 0
% 0.28/0.26 % Propositional unsat core size : 0
% 0.28/0.26 % Propositional preprocessing time : 0.000
% 0.28/0.26 % Propositional encoding time : 0.000
% 0.28/0.26 % Propositional solver time : 0.000
% 0.28/0.26 % Success case prop preproc time : 0.000
% 0.28/0.26 % Success case prop encoding time : 0.000
% 0.28/0.26 % Success case prop solver time : 0.000
% 0.28/0.26 % Current number of processed clauses : 11
% 0.28/0.26 % Positive orientable unit clauses : 5
% 0.28/0.26 % Positive unorientable unit clauses: 0
% 0.28/0.26 % Negative unit clauses : 2
% 0.28/0.26 % Non-unit-clauses : 4
% 0.28/0.26 % Current number of unprocessed clauses: 17
% 0.28/0.26 % ...number of literals in the above : 26
% 0.28/0.26 % Current number of archived formulas : 0
% 0.28/0.26 % Current number of archived clauses : 2
% 0.28/0.26 % Clause-clause subsumption calls (NU) : 7
% 0.28/0.26 % Rec. Clause-clause subsumption calls : 7
% 0.28/0.26 % Non-unit clause-clause subsumptions : 0
% 0.28/0.26 % Unit Clause-clause subsumption calls : 6
% 0.28/0.26 % Rewrite failures with RHS unbound : 0
% 0.28/0.26 % BW rewrite match attempts : 5
% 0.28/0.26 % BW rewrite match successes : 0
% 0.28/0.26 % Condensation attempts : 15
% 0.28/0.26 % Condensation successes : 0
% 0.28/0.26 % Termbank termtop insertions : 2042
% 0.28/0.26 % Search garbage collected termcells : 15
% 0.28/0.26
% 0.28/0.26 % -------------------------------------------------
% 0.28/0.26 % User time : 0.004 s
% 0.28/0.26 % System time : 0.003 s
% 0.28/0.26 % Total time : 0.007 s
% 0.28/0.26 % Maximum resident set size: 3576 pages
% 0.28/0.26
% 0.28/0.26 % -------------------------------------------------
% 0.28/0.26 % User time : 0.007 s
% 0.28/0.26 % System time : 0.006 s
% 0.28/0.26 % Total time : 0.013 s
% 0.28/0.26 % Maximum resident set size: 4608 pages
% 0.28/0.26 % E exiting
%------------------------------------------------------------------------------