%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ITP367_1 : TPTP v9.3.1. Released v8.0.0.
% 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 : Thu Sep 24 12:57:38 PM UTC 2026
% Result : Theorem 0.17s 0.51s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 30 ( 14 ~; 10 |; 4 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 8 ( 7 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 18 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$': $tType ).
tff(decl_sort2,type,
'A_ltln$': $tType ).
tff(decl_sort3,type,
'A_ltln_set_bool_fun$': $tType ).
tff(decl_sort4,type,
'A_ltln_a_ltln_set_fun$': $tType ).
tff(decl_sort5,type,
'A_ltln_set$': $tType ).
tff(decl_sort6,type,
'A_ltln_set_a_ltln_set_bool_fun_fun$': $tType ).
tff(decl_sort7,type,
'A_ltln_set_a_ltln_set_fun$': $tType ).
tff(decl_24,type,
'subformulas_nu$': 'A_ltln_a_ltln_set_fun$' ).
tff(decl_36,type,
'x$': 'A_ltln_set$' ).
tff(decl_38,type,
'fun_app$a': ( 'A_ltln_set$' * 'A_ltln_set_bool_fun$' ) > $o ).
tff(decl_40,type,
'fun_app$g': ( 'A_ltln_set$' * 'A_ltln_set_a_ltln_set_bool_fun_fun$' ) > 'A_ltln_set_bool_fun$' ).
tff(decl_50,type,
'y$': 'A_ltln_set$' ).
tff(decl_51,type,
'fun_app$h': ( 'A_ltln$' * 'A_ltln_a_ltln_set_fun$' ) > 'A_ltln_set$' ).
tff(decl_52,type,
'subformulas_mu$': 'A_ltln_a_ltln_set_fun$' ).
tff(decl_85,type,
'sup$': 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' ).
tff(decl_86,type,
'less_eq$': 'A_ltln_set_a_ltln_set_bool_fun_fun$' ).
tff(decl_89,type,
'finite$': 'A_ltln_set_bool_fun$' ).
tff(decl_93,type,
'fun_app$d': ( 'A_ltln_set$' * 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' ) > 'A_ltln_set_a_ltln_set_fun$' ).
tff(decl_96,type,
'phi$': 'A_ltln$' ).
tff(decl_97,type,
'fun_app$c': ( 'A_ltln_set$' * 'A_ltln_set_a_ltln_set_fun$' ) > 'A_ltln_set$' ).
tff(conjecture2,conjecture,
'fun_app$a'('finite$','fun_app$c'('fun_app$d'('sup$','x$'),'y$')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture2) ).
tff(axiom262,axiom,
! [X1: 'A_ltln_set$',X452: 'A_ltln_set$'] :
( ( 'fun_app$a'('fun_app$g'('less_eq$',X452),X1)
& 'fun_app$a'('finite$',X1) )
=> 'fun_app$a'('finite$',X452) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom262) ).
tff(axiom288,axiom,
! [X487: 'A_ltln$'] : 'fun_app$a'('finite$','fun_app$h'('subformulas_nu$',X487)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom288) ).
tff(axiom287,axiom,
! [X486: 'A_ltln$'] : 'fun_app$a'('finite$','fun_app$h'('subformulas_mu$',X486)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom287) ).
tff(axiom4,axiom,
! [X1: 'A_ltln_set$',X7: 'A_ltln_set$'] :
( 'fun_app$a'('finite$','fun_app$c'('fun_app$d'('sup$',X1),X7))
<=> ( 'fun_app$a'('finite$',X7)
& 'fun_app$a'('finite$',X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom4) ).
tff(axiom69,axiom,
'fun_app$a'('fun_app$g'('less_eq$','y$'),'fun_app$h'('subformulas_nu$','phi$')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom69) ).
tff(axiom70,axiom,
'fun_app$a'('fun_app$g'('less_eq$','x$'),'fun_app$h'('subformulas_mu$','phi$')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom70) ).
tff(c_0_7,negated_conjecture,
~ 'fun_app$a'('finite$','fun_app$c'('fun_app$d'('sup$','x$'),'y$')),
inference(assume_negation,[status(cth)],[conjecture2]) ).
tff(c_0_8,negated_conjecture,
~ 'fun_app$a'('finite$','fun_app$c'('fun_app$d'('sup$','x$'),'y$')),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
tff(c_0_9,plain,
! [X1283: 'A_ltln_set$',X1284: 'A_ltln_set$'] :
( 'fun_app$a'('finite$',X1284)
| ~ 'fun_app$a'('fun_app$g'('less_eq$',X1284),X1283)
| ~ 'fun_app$a'('finite$',X1283) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom262])])]) ).
tff(c_0_10,plain,
! [X1352: 'A_ltln$'] : 'fun_app$a'('finite$','fun_app$h'('subformulas_nu$',X1352)),
inference(variable_rename,[status(thm)],[axiom288]) ).
tff(c_0_11,plain,
! [X1425: 'A_ltln$'] : 'fun_app$a'('finite$','fun_app$h'('subformulas_mu$',X1425)),
inference(variable_rename,[status(thm)],[axiom287]) ).
tff(c_0_12,negated_conjecture,
~ 'fun_app$a'('finite$','fun_app$c'('fun_app$d'('sup$','x$'),'y$')),
inference(fof_nnf,[status(thm)],[c_0_8]) ).
tff(c_0_13,plain,
! [X1271: 'A_ltln_set$',X1272: 'A_ltln_set$'] :
( ( 'fun_app$a'('finite$','fun_app$c'('fun_app$d'('sup$',X1271),X1272))
| ~ 'fun_app$a'('finite$',X1272)
| ~ 'fun_app$a'('finite$',X1271) )
& ( ~ 'fun_app$a'('finite$','fun_app$c'('fun_app$d'('sup$',X1271),X1272))
| 'fun_app$a'('finite$',X1272) )
& ( ~ 'fun_app$a'('finite$','fun_app$c'('fun_app$d'('sup$',X1271),X1272))
| 'fun_app$a'('finite$',X1271) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom4])])])]) ).
tcf(c_0_14,plain,
! [X4: 'A_ltln_set$',X1: 'A_ltln_set$'] :
( ~ 'fun_app$a'('fun_app$g'('less_eq$',X4),X1)
| ~ 'fun_app$a'('finite$',X1)
| 'fun_app$a'('finite$',X4) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tcf(c_0_15,plain,
'fun_app$a'('fun_app$g'('less_eq$','y$'),'fun_app$h'('subformulas_nu$','phi$')),
inference(split_conjunct,[status(thm)],[axiom69]) ).
tcf(c_0_16,plain,
! [X2: 'A_ltln$'] : 'fun_app$a'('finite$','fun_app$h'('subformulas_nu$',X2)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
tcf(c_0_17,plain,
'fun_app$a'('fun_app$g'('less_eq$','x$'),'fun_app$h'('subformulas_mu$','phi$')),
inference(split_conjunct,[status(thm)],[axiom70]) ).
tcf(c_0_18,plain,
! [X2: 'A_ltln$'] : 'fun_app$a'('finite$','fun_app$h'('subformulas_mu$',X2)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
tcf(c_0_19,negated_conjecture,
~ 'fun_app$a'('finite$','fun_app$c'('fun_app$d'('sup$','x$'),'y$')),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
tcf(c_0_20,plain,
! [X1: 'A_ltln_set$',X4: 'A_ltln_set$'] :
( ~ 'fun_app$a'('finite$',X4)
| ~ 'fun_app$a'('finite$',X1)
| 'fun_app$a'('finite$','fun_app$c'('fun_app$d'('sup$',X1),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
tcf(c_0_21,plain,
'fun_app$a'('finite$','y$'),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).
tcf(c_0_22,plain,
'fun_app$a'('finite$','x$'),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_17]),c_0_18])]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP367_1 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n018.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 22:37:44 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.51 % Version: 3.5.1
% 0.17/0.51 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.17/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.51 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.17/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.51 % Starting new_bool_1 with 300s (1) cores
% 0.17/0.51 % Starting sh5l with 300s (1) cores
% 0.17/0.51 % new_bool_3 with pid 342452 completed with status 0
% 0.17/0.51 % Result found by new_bool_3
% 0.17/0.51 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.17/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.51 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.17/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/0.51 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.51 % Search class: FGHSM-FSLS31-DFFFFFNN
% 0.17/0.51 % partial match(1): FGHSM-FSLM31-DFFFFFNN
% 0.17/0.51 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.51 % Starting SubtermCWHack with 28s (1) cores
% 0.17/0.51 % SubtermCWHack with pid 342455 completed with status 0
% 0.17/0.51 % Result found by SubtermCWHack
% 0.17/0.51 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.17/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.51 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.17/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/0.51 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.51 % Search class: FGHSM-FSLS31-DFFFFFNN
% 0.17/0.51 % partial match(1): FGHSM-FSLM31-DFFFFFNN
% 0.17/0.51 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.51 % Starting SubtermCWHack with 28s (1) cores
% 0.17/0.51 % Preprocessing time : 0.008 s
% 0.17/0.51
% 0.17/0.51 % Proof found!
% 0.17/0.51 % SZS status Theorem
% 0.17/0.51 % SZS output start CNFRefutation
% See solution above
% 0.17/0.51 % Parsed axioms : 734
% 0.17/0.51 % Removed by relevancy pruning/SinE : 438
% 0.17/0.51 % Initial clauses : 508
% 0.17/0.51 % Removed in clause preprocessing : 35
% 0.17/0.51 % Initial clauses in saturation : 473
% 0.17/0.51 % Processed clauses : 371
% 0.17/0.51 % ...of these trivial : 38
% 0.17/0.51 % ...subsumed : 161
% 0.17/0.51 % ...remaining for further processing : 172
% 0.17/0.51 % Other redundant clauses eliminated : 40
% 0.17/0.51 % Clauses deleted for lack of memory : 0
% 0.17/0.51 % Backward-subsumed : 0
% 0.17/0.51 % Backward-rewritten : 1
% 0.17/0.51 % Generated clauses : 791
% 0.17/0.51 % ...of the previous two non-redundant : 366
% 0.17/0.51 % ...aggressively subsumed : 0
% 0.17/0.51 % Contextual simplify-reflections : 0
% 0.17/0.51 % Paramodulations : 755
% 0.17/0.51 % Factorizations : 0
% 0.17/0.51 % NegExts : 0
% 0.17/0.51 % Equation resolutions : 41
% 0.17/0.51 % Disequality decompositions : 0
% 0.17/0.51 % Total rewrite steps : 406
% 0.17/0.51 % ...of those cached : 304
% 0.17/0.51 % Propositional unsat checks : 0
% 0.17/0.51 % Propositional check models : 0
% 0.17/0.51 % Propositional check unsatisfiable : 0
% 0.17/0.51 % Propositional clauses : 0
% 0.17/0.51 % Propositional clauses after purity: 0
% 0.17/0.51 % Propositional unsat core size : 0
% 0.17/0.51 % Propositional preprocessing time : 0.000
% 0.17/0.51 % Propositional encoding time : 0.000
% 0.17/0.51 % Propositional solver time : 0.000
% 0.17/0.51 % Success case prop preproc time : 0.000
% 0.17/0.51 % Success case prop encoding time : 0.000
% 0.17/0.51 % Success case prop solver time : 0.000
% 0.17/0.51 % Current number of processed clauses : 141
% 0.17/0.51 % Positive orientable unit clauses : 53
% 0.17/0.51 % Positive unorientable unit clauses: 1
% 0.17/0.51 % Negative unit clauses : 3
% 0.17/0.51 % Non-unit-clauses : 84
% 0.17/0.51 % Current number of unprocessed clauses: 468
% 0.17/0.51 % ...number of literals in the above : 1221
% 0.17/0.51 % Current number of archived formulas : 0
% 0.17/0.51 % Current number of archived clauses : 1
% 0.17/0.51 % Clause-clause subsumption calls (NU) : 966
% 0.17/0.51 % Rec. Clause-clause subsumption calls : 796
% 0.17/0.51 % Non-unit clause-clause subsumptions : 120
% 0.17/0.51 % Unit Clause-clause subsumption calls : 15
% 0.17/0.51 % Rewrite failures with RHS unbound : 0
% 0.17/0.51 % BW rewrite match attempts : 37
% 0.17/0.51 % BW rewrite match successes : 13
% 0.17/0.51 % Condensation attempts : 0
% 0.17/0.51 % Condensation successes : 0
% 0.17/0.51 % Termbank termtop insertions : 53106
% 0.17/0.51 % Search garbage collected termcells : 10501
% 0.17/0.51
% 0.17/0.51 % -------------------------------------------------
% 0.17/0.51 % User time : 0.049 s
% 0.17/0.51 % System time : 0.007 s
% 0.17/0.51 % Total time : 0.056 s
% 0.17/0.51 % Maximum resident set size: 6144 pages
% 0.17/0.51
% 0.17/0.51 % -------------------------------------------------
% 0.17/0.51 % User time : 0.086 s
% 0.17/0.51 % System time : 0.016 s
% 0.17/0.51 % Total time : 0.102 s
% 0.17/0.51 % Maximum resident set size: 5888 pages
% 0.17/0.51 % E exiting
%------------------------------------------------------------------------------