%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW473_2 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 03:10:49 PM UTC 2026
% Result : Theorem 0.90s 0.74s
% Output : CNFRefutation 0.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 7 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 25 ( 12 ~; 8 |; 3 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 12 ( 11 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 34 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
fun_pname_a: $tType ).
tff(decl_sort2,type,
fun_pname_bool: $tType ).
tff(decl_sort3,type,
fun_a_bool: $tType ).
tff(decl_sort4,type,
fun_fun_a_bool_bool: $tType ).
tff(decl_sort5,type,
fun_fu1430349052l_bool: $tType ).
tff(decl_sort6,type,
fun_a_1255737515l_bool: $tType ).
tff(decl_sort7,type,
fun_fu1471507361l_bool: $tType ).
tff(decl_sort8,type,
fun_pn422929397l_bool: $tType ).
tff(decl_sort9,type,
x_a: $tType ).
tff(decl_sort10,type,
bool: $tType ).
tff(decl_sort11,type,
pname: $tType ).
tff(decl_139,type,
ord_le1311769555a_bool: fun_fu1471507361l_bool ).
tff(decl_160,type,
image_pname_a: ( fun_pname_bool * fun_pname_a ) > fun_a_bool ).
tff(decl_181,type,
insert_a: ( fun_a_bool * x_a ) > fun_a_bool ).
tff(decl_182,type,
insert_pname: ( fun_pname_bool * pname ) > fun_pname_bool ).
tff(decl_207,type,
hAPP_a85458249l_bool: ( x_a * fun_a_1255737515l_bool ) > fun_fun_a_bool_bool ).
tff(decl_210,type,
hAPP_pname_a: ( pname * fun_pname_a ) > x_a ).
tff(decl_219,type,
hAPP_p338031245l_bool: ( pname * fun_pn422929397l_bool ) > fun_fu1430349052l_bool ).
tff(decl_235,type,
hAPP_fun_a_bool_bool: ( fun_a_bool * fun_fun_a_bool_bool ) > bool ).
tff(decl_241,type,
hAPP_f1631501043l_bool: ( fun_a_bool * fun_fu1471507361l_bool ) > fun_fun_a_bool_bool ).
tff(decl_244,type,
hAPP_f1664156314l_bool: ( fun_pname_bool * fun_fu1430349052l_bool ) > bool ).
tff(decl_276,type,
hBOOL: bool > $o ).
tff(decl_277,type,
member_a: fun_a_1255737515l_bool ).
tff(decl_278,type,
member_pname: fun_pn422929397l_bool ).
tff(decl_283,type,
g: fun_a_bool ).
tff(decl_285,type,
u: fun_pname_bool ).
tff(decl_287,type,
mgt_call: fun_pname_a ).
tff(decl_289,type,
pn: pname ).
tff(conj_6,conjecture,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_6) ).
tff(fact_232_insertI1,axiom,
! [X484: x_a,X485: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X484),insert_a(X484,X485))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_insertI1) ).
tff(fact_337_image__insert,axiom,
! [X731: fun_pname_a,X732: pname,X733: fun_pname_bool] : ( image_pname_a(X731,insert_pname(X732,X733)) = insert_a(hAPP_pname_a(X731,X732),image_pname_a(X731,X733)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_image__insert) ).
tff(fact_264_insert__absorb,axiom,
! [X556: pname,X557: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X556),X557))
=> ( insert_pname(X556,X557) = X557 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_insert__absorb) ).
tff(conj_4,hypothesis,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
tff(fact_324_insert__subset,axiom,
! [X694: x_a,X695: fun_a_bool,X696: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X694,X695)),X696))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X695),X696))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X694),X696)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_insert__subset) ).
tff(conj_1,hypothesis,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(c_0_7,negated_conjecture,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
inference(assume_negation,[status(cth)],[conj_6]) ).
tff(c_0_8,plain,
! [X1834: x_a,X1835: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1834),insert_a(X1834,X1835))),
inference(variable_rename,[status(thm)],[fact_232_insertI1]) ).
tff(c_0_9,plain,
! [X1872: fun_pname_a,X1873: pname,X1874: fun_pname_bool] : ( image_pname_a(X1872,insert_pname(X1873,X1874)) = insert_a(hAPP_pname_a(X1872,X1873),image_pname_a(X1872,X1874)) ),
inference(variable_rename,[status(thm)],[fact_337_image__insert]) ).
tff(c_0_10,plain,
! [X1820: pname,X1821: fun_pname_bool] :
( ( insert_pname(X1820,X1821) = X1821 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1820),X1821)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_264_insert__absorb])])]) ).
tff(c_0_11,negated_conjecture,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
tcf(c_0_12,plain,
! [X47: x_a,X1: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X47),insert_a(X47,X1))),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
tcf(c_0_13,plain,
! [X43: pname,X37: fun_pname_a,X7: fun_pname_bool] : image_pname_a(X37,insert_pname(X43,X7)) = insert_a(hAPP_pname_a(X37,X43),image_pname_a(X37,X7)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tcf(c_0_14,plain,
! [X43: pname,X7: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X43),X7))
| ( insert_pname(X43,X7) = X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
tcf(c_0_15,hypothesis,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
inference(split_conjunct,[status(thm)],[conj_4]) ).
tff(c_0_16,negated_conjecture,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
inference(fof_nnf,[status(thm)],[c_0_11]) ).
tff(c_0_17,plain,
! [X1847: x_a,X1848: fun_a_bool,X1849: fun_a_bool] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1847,X1848)),X1849))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1848),X1849))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1847),X1849)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1847,X1848)),X1849))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1848),X1849)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1847,X1848)),X1849))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1847),X1849)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_324_insert__subset])])])]) ).
tcf(c_0_18,plain,
! [X43: pname,X37: fun_pname_a,X7: fun_pname_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X37,X43)),image_pname_a(X37,insert_pname(X43,X7)))),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
tcf(c_0_19,hypothesis,
insert_pname(pn,u) = u,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
tcf(c_0_20,negated_conjecture,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
tcf(c_0_21,plain,
! [X47: x_a,X2: fun_a_bool,X1: fun_a_bool] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X47),X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X47,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
tcf(c_0_22,hypothesis,
! [X37: fun_pname_a] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X37,pn)),image_pname_a(X37,u))),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
tcf(c_0_23,hypothesis,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
inference(split_conjunct,[status(thm)],[conj_1]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW473_2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 % Computer : n017.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Mon Sep 21 09:53:28 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 Running first-order theorem proving
% 0.17/0.43 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.90/0.74 % Version: 3.5.1
% 0.90/0.74 % Preprocessing class: FMLMSMSMSSSNFFN.
% 0.90/0.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.90/0.74 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.90/0.74 % Starting new_bool_3 with 300s (1) cores
% 0.90/0.74 % Starting new_bool_1 with 300s (1) cores
% 0.90/0.74 % Starting sh5l with 300s (1) cores
% 0.90/0.74 % new_bool_1 with pid 2036533 completed with status 0
% 0.90/0.74 % Result found by new_bool_1
% 0.90/0.74 % Preprocessing class: FMLMSMSMSSSNFFN.
% 0.90/0.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.90/0.74 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.90/0.74 % Starting new_bool_3 with 300s (1) cores
% 0.90/0.74 % Starting new_bool_1 with 300s (1) cores
% 0.90/0.74 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.90/0.74 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.90/0.74 % Search class: FGHSM-FSLM32-MFFFFFNN
% 0.90/0.74 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.90/0.74 % Starting SubtermCWHack with 28s (1) cores
% 0.90/0.74 % SubtermCWHack with pid 2036549 completed with status 0
% 0.90/0.74 % Result found by SubtermCWHack
% 0.90/0.74 % Preprocessing class: FMLMSMSMSSSNFFN.
% 0.90/0.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.90/0.74 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.90/0.74 % Starting new_bool_3 with 300s (1) cores
% 0.90/0.74 % Starting new_bool_1 with 300s (1) cores
% 0.90/0.74 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.90/0.74 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.90/0.74 % Search class: FGHSM-FSLM32-MFFFFFNN
% 0.90/0.74 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.90/0.74 % Starting SubtermCWHack with 28s (1) cores
% 0.90/0.74 % Preprocessing time : 0.015 s
% 0.90/0.74
% 0.90/0.74 % Proof found!
% 0.90/0.74 % SZS status Theorem
% 0.90/0.74 % SZS output start CNFRefutation
% See solution above
% 0.90/0.74 % Parsed axioms : 1168
% 0.90/0.74 % Removed by relevancy pruning/SinE : 758
% 0.90/0.74 % Initial clauses : 591
% 0.90/0.74 % Removed in clause preprocessing : 37
% 0.90/0.74 % Initial clauses in saturation : 554
% 0.90/0.74 % Processed clauses : 3223
% 0.90/0.74 % ...of these trivial : 260
% 0.90/0.74 % ...subsumed : 2219
% 0.90/0.74 % ...remaining for further processing : 744
% 0.90/0.74 % Other redundant clauses eliminated : 156
% 0.90/0.74 % Clauses deleted for lack of memory : 0
% 0.90/0.74 % Backward-subsumed : 0
% 0.90/0.74 % Backward-rewritten : 9
% 0.90/0.74 % Generated clauses : 12107
% 0.90/0.74 % ...of the previous two non-redundant : 7421
% 0.90/0.74 % ...aggressively subsumed : 0
% 0.90/0.74 % Contextual simplify-reflections : 0
% 0.90/0.74 % Paramodulations : 11933
% 0.90/0.74 % Factorizations : 4
% 0.90/0.74 % NegExts : 0
% 0.90/0.74 % Equation resolutions : 173
% 0.90/0.74 % Disequality decompositions : 0
% 0.90/0.74 % Total rewrite steps : 6400
% 0.90/0.74 % ...of those cached : 5500
% 0.90/0.74 % Propositional unsat checks : 0
% 0.90/0.74 % Propositional check models : 0
% 0.90/0.74 % Propositional check unsatisfiable : 0
% 0.90/0.74 % Propositional clauses : 0
% 0.90/0.74 % Propositional clauses after purity: 0
% 0.90/0.74 % Propositional unsat core size : 0
% 0.90/0.74 % Propositional preprocessing time : 0.000
% 0.90/0.74 % Propositional encoding time : 0.000
% 0.90/0.74 % Propositional solver time : 0.000
% 0.90/0.74 % Success case prop preproc time : 0.000
% 0.90/0.74 % Success case prop encoding time : 0.000
% 0.90/0.74 % Success case prop solver time : 0.000
% 0.90/0.74 % Current number of processed clauses : 651
% 0.90/0.74 % Positive orientable unit clauses : 238
% 0.90/0.74 % Positive unorientable unit clauses: 12
% 0.90/0.74 % Negative unit clauses : 60
% 0.90/0.74 % Non-unit-clauses : 341
% 0.90/0.74 % Current number of unprocessed clauses: 4703
% 0.90/0.74 % ...number of literals in the above : 9792
% 0.90/0.74 % Current number of archived formulas : 0
% 0.90/0.74 % Current number of archived clauses : 9
% 0.90/0.74 % Clause-clause subsumption calls (NU) : 23621
% 0.90/0.74 % Rec. Clause-clause subsumption calls : 20752
% 0.90/0.74 % Non-unit clause-clause subsumptions : 1386
% 0.90/0.74 % Unit Clause-clause subsumption calls : 747
% 0.90/0.74 % Rewrite failures with RHS unbound : 105
% 0.90/0.74 % BW rewrite match attempts : 1304
% 0.90/0.74 % BW rewrite match successes : 26
% 0.90/0.74 % Condensation attempts : 0
% 0.90/0.74 % Condensation successes : 0
% 0.90/0.74 % Termbank termtop insertions : 184442
% 0.90/0.74 % Search garbage collected termcells : 12941
% 0.90/0.74
% 0.90/0.74 % -------------------------------------------------
% 0.90/0.74 % User time : 0.175 s
% 0.90/0.74 % System time : 0.026 s
% 0.90/0.74 % Total time : 0.201 s
% 0.90/0.74 % Maximum resident set size: 7580 pages
% 0.90/0.74
% 0.90/0.74 % -------------------------------------------------
% 0.90/0.74 % User time : 0.213 s
% 0.90/0.74 % System time : 0.033 s
% 0.90/0.74 % Total time : 0.246 s
% 0.90/0.74 % Maximum resident set size: 6656 pages
% 0.90/0.74 % E exiting
%------------------------------------------------------------------------------