%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP210^3 : TPTP v9.3.1. Bugfixed v9.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 08:04:42 AM UTC 2026
% Result : Theorem 4.87s 34.20s
% Output : CNFRefutation 4.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 21 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 125 ( 46 equ; 0 cnn)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 282 ( 26 ~; 19 |; 47 &; 185 @)
% ( 3 <=>; 0 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 33 ( 33 ^; 0 !; 0 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
produc3658429121746597890et_nat: $tType ).
thf(decl_sort2,type,
assn: $tType ).
thf(decl_27,type,
abs_assn: ( produc3658429121746597890et_nat > $o ) > assn ).
thf(decl_28,type,
rep_assn: assn > produc3658429121746597890et_nat > $o ).
thf(decl_1501,type,
x: assn ).
thf(decl_1502,type,
y: assn ).
thf(decl_1736,type,
esk55_0: produc3658429121746597890et_nat ).
thf(decl_1747,type,
esk76_0: produc3658429121746597890et_nat ).
thf(conj_0,conjecture,
( ( ( x
= ( abs_assn
@ ^ [X9: produc3658429121746597890et_nat] :
( ( rep_assn @ x @ X9 )
& ( rep_assn @ y @ X9 ) ) ) )
& ( x != y ) )
<=> ( ( x
= ( abs_assn
@ ^ [X9: produc3658429121746597890et_nat] :
( ( rep_assn @ x @ X9 )
& ( rep_assn @ y @ X9 ) ) ) )
& ( y
!= ( abs_assn
@ ^ [X9: produc3658429121746597890et_nat] :
( ( rep_assn @ y @ X9 )
& ( rep_assn @ x @ X9 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.KimAtHKf2T/E---3.1_855973.p',conj_0) ).
thf(c_0_1,negated_conjecture,
~ ( ( ( x
= ( abs_assn
@ ^ [X9: produc3658429121746597890et_nat] :
( ( rep_assn @ x @ X9 )
& ( rep_assn @ y @ X9 ) ) ) )
& ( x != y ) )
<=> ( ( x
= ( abs_assn
@ ^ [X9: produc3658429121746597890et_nat] :
( ( rep_assn @ x @ X9 )
& ( rep_assn @ y @ X9 ) ) ) )
& ( y
!= ( abs_assn
@ ^ [X9: produc3658429121746597890et_nat] :
( ( rep_assn @ y @ X9 )
& ( rep_assn @ x @ X9 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_2,negated_conjecture,
~ ( ( ( x
= ( abs_assn
@ ^ [Z0: produc3658429121746597890et_nat] :
( ( rep_assn @ x @ Z0 )
& ( rep_assn @ y @ Z0 ) ) ) )
& ( x != y ) )
<=> ( ( x
= ( abs_assn
@ ^ [Z0: produc3658429121746597890et_nat] :
( ( rep_assn @ x @ Z0 )
& ( rep_assn @ y @ Z0 ) ) ) )
& ( y
!= ( abs_assn
@ ^ [Z0: produc3658429121746597890et_nat] :
( ( rep_assn @ y @ Z0 )
& ( rep_assn @ x @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_1])]) ).
thf(c_0_3,negated_conjecture,
( ( ( x
!= ( abs_assn
@ ^ [Z0: produc3658429121746597890et_nat] :
( ( rep_assn @ x @ Z0 )
& ( rep_assn @ y @ Z0 ) ) ) )
| ( x = y )
| ( x
!= ( abs_assn
@ ^ [Z0: produc3658429121746597890et_nat] :
( ( rep_assn @ x @ Z0 )
& ( rep_assn @ y @ Z0 ) ) ) )
| ( y
= ( abs_assn
@ ^ [Z0: produc3658429121746597890et_nat] :
( ( rep_assn @ y @ Z0 )
& ( rep_assn @ x @ Z0 ) ) ) ) )
& ( ( x
= ( abs_assn
@ ^ [Z0: produc3658429121746597890et_nat] :
( ( rep_assn @ x @ Z0 )
& ( rep_assn @ y @ Z0 ) ) ) )
| ( x
= ( abs_assn
@ ^ [Z0: produc3658429121746597890et_nat] :
( ( rep_assn @ x @ Z0 )
& ( rep_assn @ y @ Z0 ) ) ) ) )
& ( ( y
!= ( abs_assn
@ ^ [Z0: produc3658429121746597890et_nat] :
( ( rep_assn @ y @ Z0 )
& ( rep_assn @ x @ Z0 ) ) ) )
| ( x
= ( abs_assn
@ ^ [Z0: produc3658429121746597890et_nat] :
( ( rep_assn @ x @ Z0 )
& ( rep_assn @ y @ Z0 ) ) ) ) )
& ( ( x
= ( abs_assn
@ ^ [Z0: produc3658429121746597890et_nat] :
( ( rep_assn @ x @ Z0 )
& ( rep_assn @ y @ Z0 ) ) ) )
| ( x != y ) )
& ( ( y
!= ( abs_assn
@ ^ [Z0: produc3658429121746597890et_nat] :
( ( rep_assn @ y @ Z0 )
& ( rep_assn @ x @ Z0 ) ) ) )
| ( x != y ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])]) ).
thf(c_0_4,negated_conjecture,
( ( x
= ( abs_assn
@ ^ [Z0: produc3658429121746597890et_nat] :
( ( rep_assn @ x @ Z0 )
& ( rep_assn @ y @ Z0 ) ) ) )
| ( x
= ( abs_assn
@ ^ [Z0: produc3658429121746597890et_nat] :
( ( rep_assn @ x @ Z0 )
& ( rep_assn @ y @ Z0 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_5,negated_conjecture,
( ( y
!= ( abs_assn
@ ^ [Z0: produc3658429121746597890et_nat] :
( ( rep_assn @ y @ Z0 )
& ( rep_assn @ x @ Z0 ) ) ) )
| ( x != y ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_6,negated_conjecture,
( x
= ( abs_assn
@ ^ [Z0: produc3658429121746597890et_nat] :
( ( rep_assn @ x @ Z0 )
& ( rep_assn @ y @ Z0 ) ) ) ),
inference(cn,[status(thm)],[c_0_4]) ).
thf(c_0_7,plain,
( ( ( ^ [Z0: produc3658429121746597890et_nat] :
( ( rep_assn @ y @ Z0 )
& ( rep_assn @ x @ Z0 ) ) )
!= ( ^ [Z0: produc3658429121746597890et_nat] :
( ( rep_assn @ x @ Z0 )
& ( rep_assn @ y @ Z0 ) ) ) )
| ( y != x ) ),
inference(ext_sup,[status(thm)],[c_0_5,c_0_6]) ).
thf(c_0_8,negated_conjecture,
( ( x = y )
| ( y
= ( abs_assn
@ ^ [Z0: produc3658429121746597890et_nat] :
( ( rep_assn @ y @ Z0 )
& ( rep_assn @ x @ Z0 ) ) ) )
| ( x
!= ( abs_assn
@ ^ [Z0: produc3658429121746597890et_nat] :
( ( rep_assn @ x @ Z0 )
& ( rep_assn @ y @ Z0 ) ) ) )
| ( x
!= ( abs_assn
@ ^ [Z0: produc3658429121746597890et_nat] :
( ( rep_assn @ x @ Z0 )
& ( rep_assn @ y @ Z0 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_9,plain,
( ( ( ( rep_assn @ y @ esk55_0 )
& ( rep_assn @ x @ esk55_0 ) )
<~> ( ( rep_assn @ x @ esk55_0 )
& ( rep_assn @ y @ esk55_0 ) ) )
| ( y != x ) ),
inference(neg_ext,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
( ( y = x )
| ( y
= ( abs_assn
@ ^ [Z0: produc3658429121746597890et_nat] :
( ( rep_assn @ y @ Z0 )
& ( rep_assn @ x @ Z0 ) ) ) )
| ( x
!= ( abs_assn
@ ^ [Z0: produc3658429121746597890et_nat] :
( ( rep_assn @ x @ Z0 )
& ( rep_assn @ y @ Z0 ) ) ) ) ),
inference(cn,[status(thm)],[c_0_8]) ).
thf(c_0_11,plain,
( ( rep_assn @ x @ esk55_0 )
| ( y != x ) ),
inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_9])]) ).
thf(c_0_12,plain,
( ( rep_assn @ y @ esk55_0 )
| ( y != x ) ),
inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_9])]) ).
thf(c_0_13,negated_conjecture,
( ( ( abs_assn
@ ^ [Z0: produc3658429121746597890et_nat] :
( ( rep_assn @ y @ Z0 )
& ( rep_assn @ x @ Z0 ) ) )
= y )
| ( y = x ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_6])]) ).
thf(c_0_14,plain,
y != x,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_9])]),c_0_11]),c_0_12]) ).
thf(c_0_15,negated_conjecture,
( ( abs_assn
@ ^ [Z0: produc3658429121746597890et_nat] :
( ( rep_assn @ y @ Z0 )
& ( rep_assn @ x @ Z0 ) ) )
= y ),
inference(sr,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_16,plain,
( ( ^ [Z0: produc3658429121746597890et_nat] :
( ( rep_assn @ y @ Z0 )
& ( rep_assn @ x @ Z0 ) ) )
!= ( ^ [Z0: produc3658429121746597890et_nat] :
( ( rep_assn @ x @ Z0 )
& ( rep_assn @ y @ Z0 ) ) ) ),
inference(sr,[status(thm)],[inference(ext_sup,[status(thm)],[c_0_15,c_0_6]),c_0_14]) ).
thf(c_0_17,plain,
( ( ( rep_assn @ y @ esk76_0 )
& ( rep_assn @ x @ esk76_0 ) )
<~> ( ( rep_assn @ x @ esk76_0 )
& ( rep_assn @ y @ esk76_0 ) ) ),
inference(neg_ext,[status(thm)],[c_0_16]) ).
thf(c_0_18,plain,
rep_assn @ y @ esk76_0,
inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_17])]) ).
thf(c_0_19,plain,
rep_assn @ x @ esk76_0,
inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_17])]) ).
thf(c_0_20,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_17])]),c_0_18]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP210^3 : TPTP v9.3.1. Bugfixed v9.2.1.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n016.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 20:19:05 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 4.85/4.90 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.KimAtHKf2T/E---3.1_855973.p
% 4.87/34.20 % Version: 3.5.1-ho
% 4.87/34.20 % partial match(3): HMLLSMSLSSMCHSA
% 4.87/34.20 % Preprocessing class: HMLLSLLLSSLCHSA.
% 4.87/34.20 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 4.87/34.20 % Starting new_ho_10 with 1495s (5) cores
% 4.87/34.20 % Starting sh5l with 299s (1) cores
% 4.87/34.20 % Starting new_bool_1 with 299s (1) cores
% 4.87/34.20 % Starting new_bool_2 with 299s (1) cores
% 4.87/34.20 % new_bool_1 with pid 855989 completed with status 0
% 4.87/34.20 % Result found by new_bool_1
% 4.87/34.20 % partial match(3): HMLLSMSLSSMCHSA
% 4.87/34.20 % Preprocessing class: HMLLSLLLSSLCHSA.
% 4.87/34.20 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 4.87/34.20 % Starting new_ho_10 with 1495s (5) cores
% 4.87/34.20 % Starting sh5l with 299s (1) cores
% 4.87/34.20 % Starting new_bool_1 with 299s (1) cores
% 4.87/34.20 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 4.87/34.20 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 4.87/34.20 % Search class: HGHSM-FSLM32-DHSFFSBN
% 4.87/34.20 % Scheduled 7 strats onto 1 cores with 299 seconds (299 total)
% 4.87/34.20 % Starting SubtermCWHack with 27s (1) cores
% 4.87/34.20 % SubtermCWHack with pid 855991 completed with status 8
% 4.87/34.20 % Starting new_bool_1 with 30s (1) cores
% 4.87/34.20 % new_bool_1 with pid 856004 completed with status 0
% 4.87/34.20 % Result found by new_bool_1
% 4.87/34.20 % partial match(3): HMLLSMSLSSMCHSA
% 4.87/34.20 % Preprocessing class: HMLLSLLLSSLCHSA.
% 4.87/34.20 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 4.87/34.20 % Starting new_ho_10 with 1495s (5) cores
% 4.87/34.20 % Starting sh5l with 299s (1) cores
% 4.87/34.20 % Starting new_bool_1 with 299s (1) cores
% 4.87/34.20 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 4.87/34.20 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 4.87/34.20 % Search class: HGHSM-FSLM32-DHSFFSBN
% 4.87/34.20 % Scheduled 7 strats onto 1 cores with 299 seconds (299 total)
% 4.87/34.20 % Starting SubtermCWHack with 27s (1) cores
% 4.87/34.20 % SubtermCWHack with pid 855991 completed with status 8
% 4.87/34.20 % Starting new_bool_1 with 30s (1) cores
% 4.87/34.20 % Preprocessing time : 0.041 s
% 4.87/34.20 % Presaturation interreduction done
% 4.87/34.20
% 4.87/34.20 % Proof found!
% 4.87/34.20 % SZS status Theorem
% 4.87/34.20 % SZS output start CNFRefutation
% See solution above
% 4.87/34.20 % Parsed axioms : 11329
% 4.87/34.20 % Removed by relevancy pruning/SinE : 10672
% 4.87/34.20 % Initial clauses : 993
% 4.87/34.20 % Removed in clause preprocessing : 23
% 4.87/34.20 % Initial clauses in saturation : 970
% 4.87/34.20 % Processed clauses : 1176
% 4.87/34.20 % ...of these trivial : 85
% 4.87/34.20 % ...subsumed : 298
% 4.87/34.20 % ...remaining for further processing : 792
% 4.87/34.20 % Other redundant clauses eliminated : 88
% 4.87/34.20 % Clauses deleted for lack of memory : 0
% 4.87/34.20 % Backward-subsumed : 20
% 4.87/34.20 % Backward-rewritten : 8
% 4.87/34.20 % Generated clauses : 216
% 4.87/34.20 % ...of the previous two non-redundant : 173
% 4.87/34.20 % ...aggressively subsumed : 0
% 4.87/34.20 % Contextual simplify-reflections : 8
% 4.87/34.20 % Paramodulations : 35
% 4.87/34.20 % Factorizations : 0
% 4.87/34.20 % NegExts : 18
% 4.87/34.20 % Equation resolutions : 89
% 4.87/34.20 % Disequality decompositions : 0
% 4.87/34.20 % Total rewrite steps : 203
% 4.87/34.20 % ...of those cached : 113
% 4.87/34.20 % Propositional unsat checks : 0
% 4.87/34.20 % Propositional check models : 0
% 4.87/34.20 % Propositional check unsatisfiable : 0
% 4.87/34.20 % Propositional clauses : 0
% 4.87/34.20 % Propositional clauses after purity: 0
% 4.87/34.20 % Propositional unsat core size : 0
% 4.87/34.20 % Propositional preprocessing time : 0.000
% 4.87/34.20 % Propositional encoding time : 0.000
% 4.87/34.20 % Propositional solver time : 0.000
% 4.87/34.20 % Success case prop preproc time : 0.000
% 4.87/34.20 % Success case prop encoding time : 0.000
% 4.87/34.20 % Success case prop solver time : 0.000
% 4.87/34.20 % Current number of processed clauses : 102
% 4.87/34.20 % Positive orientable unit clauses : 45
% 4.87/34.20 % Positive unorientable unit clauses: 0
% 4.87/34.20 % Negative unit clauses : 22
% 4.87/34.20 % Non-unit-clauses : 35
% 4.87/34.20 % Current number of unprocessed clauses: 547
% 4.87/34.20 % ...number of literals in the above : 1370
% 4.87/34.20 % Current number of archived formulas : 0
% 4.87/34.20 % Current number of archived clauses : 612
% 4.87/34.20 % Clause-clause subsumption calls (NU) : 34660
% 4.87/34.20 % Rec. Clause-clause subsumption calls : 22484
% 4.87/34.20 % Non-unit clause-clause subsumptions : 251
% 4.87/34.20 % Unit Clause-clause subsumption calls : 327
% 4.87/34.20 % Rewrite failures with RHS unbound : 0
% 4.87/34.20 % BW rewrite match attempts : 589
% 4.87/34.20 % BW rewrite match successes : 94
% 4.87/34.20 % Condensation attempts : 0
% 4.87/34.20 % Condensation successes : 0
% 4.87/34.20 % Termbank termtop insertions : 286992
% 4.87/34.20 % Search garbage collected termcells : 121876
% 4.87/34.20
% 4.87/34.20 % -------------------------------------------------
% 4.87/34.20 % User time : 26.746 s
% 4.87/34.20 % System time : 0.853 s
% 4.87/34.20 % Total time : 27.599 s
% 4.87/34.20 % Maximum resident set size: 35640 pages
% 4.87/34.20
% 4.87/34.20 % -------------------------------------------------
% 4.87/34.20 % User time : 28.294 s
% 4.87/34.20 % System time : 0.908 s
% 4.87/34.20 % Total time : 29.202 s
% 4.87/34.20 % Maximum resident set size: 30976 pages
% 4.87/34.20 % E exiting
%------------------------------------------------------------------------------