%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU803^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:25:41 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 12 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 167 ( 11 ~; 6 |; 7 &; 125 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 36 ( 6 ^; 27 !; 3 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
funcSet: $i > $i > $i ).
thf(decl_25,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_26,type,
surjective: $i > $i > $i > $o ).
thf(decl_27,type,
esk1_0: $i ).
thf(decl_28,type,
esk2_0: $i ).
thf(decl_29,type,
esk3_0: $i > $i ).
thf(decl_30,type,
esk4_0: $i ).
thf(decl_31,type,
esk5_0: $i ).
thf(leftInvIsSurj,conjecture,
! [X1: $i,X2: $i,X6: $i > $i] :
( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in @ ( X6 @ X4 ) @ X2 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( funcSet @ X2 @ X1 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( ap @ X2 @ X1 @ X7 @ ( X6 @ X4 ) )
= X4 ) )
=> ( surjective @ X2 @ X1 @ X7 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LsgIjLv9fp/E---3.1_163943.p',leftInvIsSurj) ).
thf(surjective,axiom,
( surjective
= ( ^ [X1: $i,X2: $i,X3: $i] :
! [X4: $i] :
( ( in @ X4 @ X2 )
=> ? [X5: $i] :
( ( in @ X5 @ X1 )
& ( ( ap @ X1 @ X2 @ X3 @ X5 )
= X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LsgIjLv9fp/E---3.1_163943.p',surjective) ).
thf(c_0_2,negated_conjecture,
~ ! [X1: $i,X2: $i,X6: $i > $i] :
( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in @ ( X6 @ X4 ) @ X2 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( funcSet @ X2 @ X1 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( ap @ X2 @ X1 @ X7 @ ( X6 @ X4 ) )
= X4 ) )
=> ( surjective @ X2 @ X1 @ X7 ) ) ) ),
inference(assume_negation,[status(cth)],[leftInvIsSurj]) ).
thf(c_0_3,plain,
( surjective
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
! [X4: $i] :
( ( in @ X4 @ Z1 )
=> ? [X5: $i] :
( ( in @ X5 @ Z0 )
& ( ( ap @ Z0 @ Z1 @ Z2 @ X5 )
= X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[surjective]) ).
thf(c_0_4,negated_conjecture,
~ ! [X1: $i,X2: $i,X6: $i > $i] :
( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in @ ( X6 @ X4 ) @ X2 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( funcSet @ X2 @ X1 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( ap @ X2 @ X1 @ X7 @ ( X6 @ X4 ) )
= X4 ) )
=> ! [X14: $i] :
( ( in @ X14 @ X1 )
=> ? [X15: $i] :
( ( in @ X15 @ X2 )
& ( ( ap @ X2 @ X1 @ X7 @ X15 )
= X14 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_2,c_0_3]) ).
thf(c_0_5,negated_conjecture,
! [X19: $i,X21: $i,X23: $i] :
( ( ~ ( in @ X19 @ esk1_0 )
| ( in @ ( esk3_0 @ X19 ) @ esk2_0 ) )
& ( in @ esk4_0 @ ( funcSet @ esk2_0 @ esk1_0 ) )
& ( ~ ( in @ X21 @ esk1_0 )
| ( ( ap @ esk2_0 @ esk1_0 @ esk4_0 @ ( esk3_0 @ X21 ) )
= X21 ) )
& ( in @ esk5_0 @ esk1_0 )
& ( ~ ( in @ X23 @ esk2_0 )
| ( ( ap @ esk2_0 @ esk1_0 @ esk4_0 @ X23 )
!= esk5_0 ) ) ),
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_4])])])])]) ).
thf(c_0_6,negated_conjecture,
! [X1: $i] :
( ~ ( in @ X1 @ esk2_0 )
| ( ( ap @ esk2_0 @ esk1_0 @ esk4_0 @ X1 )
!= esk5_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_7,negated_conjecture,
! [X1: $i] :
( ( ( ap @ esk2_0 @ esk1_0 @ esk4_0 @ ( esk3_0 @ X1 ) )
= X1 )
| ~ ( in @ X1 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
in @ esk5_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_9,negated_conjecture,
~ ( in @ ( esk3_0 @ esk5_0 ) @ esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7])]),c_0_8])]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i] :
( ( in @ ( esk3_0 @ X1 ) @ esk2_0 )
| ~ ( in @ X1 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_11,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_8])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU803^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n018.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 14:34:26 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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.LsgIjLv9fp/E---3.1_163943.p
% 0.08/0.25 % Version: 3.5.1-ho
% 0.08/0.25 % Preprocessing class: HSSSSMSSSLSNSSN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting ehoh_best3_fo with 1500s (5) cores
% 0.08/0.25 % Starting post_as_ho12 with 300s (1) cores
% 0.08/0.25 % Starting post_as_ho4 with 300s (1) cores
% 0.08/0.25 % Starting ehoh_best6_lambda with 300s (1) cores
% 0.08/0.25 % post_as_ho12 with pid 163957 completed with status 0
% 0.08/0.25 % Result found by post_as_ho12
% 0.08/0.25 % Preprocessing class: HSSSSMSSSLSNSSN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting ehoh_best3_fo with 1500s (5) cores
% 0.08/0.25 % Starting post_as_ho12 with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.25 % No SInE strategy applied
% 0.08/0.25 % Search class: HHHSF-FFSF33-SSSFMFNN
% 0.08/0.25 % partial match(3): HHHSF-FFSF11-SHSFMFNN
% 0.08/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.25 % SubtermCWHack with pid 163960 completed with status 0
% 0.08/0.25 % Result found by SubtermCWHack
% 0.08/0.25 % Preprocessing class: HSSSSMSSSLSNSSN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting ehoh_best3_fo with 1500s (5) cores
% 0.08/0.25 % Starting post_as_ho12 with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.25 % No SInE strategy applied
% 0.08/0.25 % Search class: HHHSF-FFSF33-SSSFMFNN
% 0.08/0.25 % partial match(3): HHHSF-FFSF11-SHSFMFNN
% 0.08/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.25 % Preprocessing time : 0.001 s
% 0.08/0.25
% 0.08/0.25 % Proof found!
% 0.08/0.25 % SZS status Theorem
% 0.08/0.25 % SZS output start CNFRefutation
% See solution above
% 0.08/0.25 % Parsed axioms : 6
% 0.08/0.25 % Removed by relevancy pruning/SinE : 0
% 0.08/0.25 % Initial clauses : 9
% 0.08/0.25 % Removed in clause preprocessing : 4
% 0.08/0.25 % Initial clauses in saturation : 5
% 0.08/0.25 % Processed clauses : 6
% 0.08/0.25 % ...of these trivial : 0
% 0.08/0.25 % ...subsumed : 0
% 0.08/0.25 % ...remaining for further processing : 6
% 0.08/0.25 % Other redundant clauses eliminated : 1
% 0.08/0.25 % Clauses deleted for lack of memory : 0
% 0.08/0.25 % Backward-subsumed : 0
% 0.08/0.25 % Backward-rewritten : 0
% 0.08/0.25 % Generated clauses : 3
% 0.08/0.25 % ...of the previous two non-redundant : 1
% 0.08/0.25 % ...aggressively subsumed : 0
% 0.08/0.25 % Contextual simplify-reflections : 0
% 0.08/0.25 % Paramodulations : 2
% 0.08/0.25 % Factorizations : 0
% 0.08/0.25 % NegExts : 0
% 0.08/0.25 % Equation resolutions : 1
% 0.08/0.25 % Disequality decompositions : 0
% 0.08/0.25 % Total rewrite steps : 2
% 0.08/0.25 % ...of those cached : 1
% 0.08/0.25 % Propositional unsat checks : 0
% 0.08/0.25 % Propositional check models : 0
% 0.08/0.25 % Propositional check unsatisfiable : 0
% 0.08/0.25 % Propositional clauses : 0
% 0.08/0.25 % Propositional clauses after purity: 0
% 0.08/0.25 % Propositional unsat core size : 0
% 0.08/0.25 % Propositional preprocessing time : 0.000
% 0.08/0.25 % Propositional encoding time : 0.000
% 0.08/0.25 % Propositional solver time : 0.000
% 0.08/0.25 % Success case prop preproc time : 0.000
% 0.08/0.25 % Success case prop encoding time : 0.000
% 0.08/0.25 % Success case prop solver time : 0.000
% 0.08/0.25 % Current number of processed clauses : 6
% 0.08/0.25 % Positive orientable unit clauses : 2
% 0.08/0.25 % Positive unorientable unit clauses: 0
% 0.08/0.25 % Negative unit clauses : 1
% 0.08/0.25 % Non-unit-clauses : 3
% 0.08/0.25 % Current number of unprocessed clauses: 0
% 0.08/0.25 % ...number of literals in the above : 0
% 0.08/0.25 % Current number of archived formulas : 0
% 0.08/0.25 % Current number of archived clauses : 0
% 0.08/0.25 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.25 % Rec. Clause-clause subsumption calls : 0
% 0.08/0.25 % Non-unit clause-clause subsumptions : 0
% 0.08/0.25 % Unit Clause-clause subsumption calls : 1
% 0.08/0.25 % Rewrite failures with RHS unbound : 0
% 0.08/0.25 % BW rewrite match attempts : 0
% 0.08/0.25 % BW rewrite match successes : 0
% 0.08/0.25 % Condensation attempts : 0
% 0.08/0.25 % Condensation successes : 0
% 0.08/0.25 % Termbank termtop insertions : 622
% 0.08/0.25 % Search garbage collected termcells : 204
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.003 s
% 0.08/0.25 % System time : 0.001 s
% 0.08/0.25 % Total time : 0.004 s
% 0.08/0.25 % Maximum resident set size: 3636 pages
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.005 s
% 0.08/0.25 % System time : 0.005 s
% 0.08/0.25 % Total time : 0.010 s
% 0.08/0.25 % Maximum resident set size: 4864 pages
% 0.08/0.25 % E exiting
%------------------------------------------------------------------------------