%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW473_3 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 03:10:50 PM UTC 2026
% Result : Theorem 3.39s 1.11s
% Output : CNFRefutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 30 ( 0 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 26 ( 13 ~; 8 |; 3 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 14 ( 13 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 18 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
fun_fu1471507361l_bool: $tType ).
tff(decl_sort2,type,
fun_pname_a: $tType ).
tff(decl_sort3,type,
fun_pname_bool: $tType ).
tff(decl_sort4,type,
fun_a_bool: $tType ).
tff(decl_sort5,type,
fun_fun_a_bool_bool: $tType ).
tff(decl_sort6,type,
fun_fu1430349052l_bool: $tType ).
tff(decl_sort7,type,
x_a: $tType ).
tff(decl_sort8,type,
bool: $tType ).
tff(decl_sort9,type,
fun_a_1255737515l_bool: $tType ).
tff(decl_sort10,type,
fun_fu1731003005a_bool: $tType ).
tff(decl_sort11,type,
fun_a_1752562919a_bool: $tType ).
tff(decl_sort12,type,
fun_pn422929397l_bool: $tType ).
tff(decl_sort13,type,
pname: $tType ).
tff(decl_167,type,
ord_le1311769555a_bool: fun_fu1471507361l_bool ).
tff(decl_195,type,
image_pname_a: ( fun_pname_bool * fun_pname_a ) > fun_a_bool ).
tff(decl_232,type,
insert_a: fun_a_1752562919a_bool ).
tff(decl_264,type,
hAPP_a85458249l_bool: ( x_a * fun_a_1255737515l_bool ) > fun_fun_a_bool_bool ).
tff(decl_265,type,
hAPP_a1206381875a_bool: ( x_a * fun_a_1752562919a_bool ) > fun_fu1731003005a_bool ).
tff(decl_266,type,
hAPP_pname_a: ( pname * fun_pname_a ) > x_a ).
tff(decl_273,type,
hAPP_p338031245l_bool: ( pname * fun_pn422929397l_bool ) > fun_fu1430349052l_bool ).
tff(decl_306,type,
hAPP_fun_a_bool_bool: ( fun_a_bool * fun_fun_a_bool_bool ) > bool ).
tff(decl_308,type,
hAPP_f2050579477a_bool: ( fun_a_bool * fun_fu1731003005a_bool ) > fun_a_bool ).
tff(decl_313,type,
hAPP_f1631501043l_bool: ( fun_a_bool * fun_fu1471507361l_bool ) > fun_fun_a_bool_bool ).
tff(decl_318,type,
hAPP_f1664156314l_bool: ( fun_pname_bool * fun_fu1430349052l_bool ) > bool ).
tff(decl_369,type,
hBOOL: bool > $o ).
tff(decl_370,type,
member_a: fun_a_1255737515l_bool ).
tff(decl_371,type,
member_pname: fun_pn422929397l_bool ).
tff(decl_378,type,
g: fun_a_bool ).
tff(decl_380,type,
u: fun_pname_bool ).
tff(decl_382,type,
mgt_call: fun_pname_a ).
tff(decl_384,type,
pn: pname ).
tff(conj_6,conjecture,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).
tff(fact_453_insert__subset,axiom,
! [X995: x_a,X996: fun_a_bool,X997: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X995),X996)),X997))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X996),X997))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X995),X997)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_453_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/sandbox2/benchmark/theBenchmark.p',conj_1) ).
tff(fact_434_imageI,axiom,
! [X948: fun_pname_a,X949: pname,X950: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X949),X950))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X948,X949)),image_pname_a(X948,X950))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_434_imageI) ).
tff(conj_4,hypothesis,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
tff(c_0_5,negated_conjecture,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_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_6,negated_conjecture,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
tff(c_0_7,negated_conjecture,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),
inference(fof_nnf,[status(thm)],[c_0_6]) ).
tff(c_0_8,plain,
! [X2370: x_a,X2371: fun_a_bool,X2372: fun_a_bool] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2370),X2371)),X2372))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2371),X2372))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2370),X2372)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2370),X2371)),X2372))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2371),X2372)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2370),X2371)),X2372))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2370),X2372)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_453_insert__subset])])])]) ).
tcf(c_0_9,negated_conjecture,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
tcf(c_0_10,plain,
! [X82: 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,X82),X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X82),X2)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
tcf(c_0_11,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]) ).
tff(c_0_12,plain,
! [X2826: fun_pname_a,X2827: pname,X2828: fun_pname_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X2826,X2827)),image_pname_a(X2826,X2828)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2827),X2828)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_434_imageI])])]) ).
tcf(c_0_13,negated_conjecture,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),image_pname_a(mgt_call,u))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11])]) ).
tcf(c_0_14,plain,
! [X76: pname,X66: fun_pname_a,X8: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X76),X8))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X66,X76)),image_pname_a(X66,X8))) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
tcf(c_0_15,hypothesis,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
inference(split_conjunct,[status(thm)],[conj_4]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW473_3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n026.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Mon Sep 21 10:00:36 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.42 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
% 3.39/1.11 % Version: 3.5.1
% 3.39/1.11 % Preprocessing class: FMLMSMSMSSSNFFN.
% 3.39/1.11 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.39/1.11 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.39/1.11 % Starting new_bool_3 with 300s (1) cores
% 3.39/1.11 % Starting new_bool_1 with 300s (1) cores
% 3.39/1.11 % Starting sh5l with 300s (1) cores
% 3.39/1.11 % new_bool_1 with pid 1984959 completed with status 0
% 3.39/1.11 % Result found by new_bool_1
% 3.39/1.11 % Preprocessing class: FMLMSMSMSSSNFFN.
% 3.39/1.11 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.39/1.11 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.39/1.11 % Starting new_bool_3 with 300s (1) cores
% 3.39/1.11 % Starting new_bool_1 with 300s (1) cores
% 3.39/1.11 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 3.39/1.11 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 3.39/1.11 % Search class: FGHSM-FSLM31-DFFFFFNN
% 3.39/1.11 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 3.39/1.11 % Starting SubtermCWHack with 28s (1) cores
% 3.39/1.11 % SubtermCWHack with pid 1984973 completed with status 0
% 3.39/1.11 % Result found by SubtermCWHack
% 3.39/1.11 % Preprocessing class: FMLMSMSMSSSNFFN.
% 3.39/1.11 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.39/1.11 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.39/1.11 % Starting new_bool_3 with 300s (1) cores
% 3.39/1.11 % Starting new_bool_1 with 300s (1) cores
% 3.39/1.11 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 3.39/1.11 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 3.39/1.11 % Search class: FGHSM-FSLM31-DFFFFFNN
% 3.39/1.11 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 3.39/1.11 % Starting SubtermCWHack with 28s (1) cores
% 3.39/1.11 % Preprocessing time : 0.013 s
% 3.39/1.11
% 3.39/1.11 % Proof found!
% 3.39/1.11 % SZS status Theorem
% 3.39/1.11 % SZS output start CNFRefutation
% See solution above
% 3.39/1.11 % Parsed axioms : 1811
% 3.39/1.11 % Removed by relevancy pruning/SinE : 1309
% 3.39/1.11 % Initial clauses : 778
% 3.39/1.11 % Removed in clause preprocessing : 39
% 3.39/1.11 % Initial clauses in saturation : 739
% 3.39/1.11 % Processed clauses : 5403
% 3.39/1.11 % ...of these trivial : 74
% 3.39/1.11 % ...subsumed : 4036
% 3.39/1.11 % ...remaining for further processing : 1293
% 3.39/1.11 % Other redundant clauses eliminated : 434
% 3.39/1.11 % Clauses deleted for lack of memory : 0
% 3.39/1.11 % Backward-subsumed : 16
% 3.39/1.11 % Backward-rewritten : 29
% 3.39/1.11 % Generated clauses : 26587
% 3.39/1.11 % ...of the previous two non-redundant : 21771
% 3.39/1.11 % ...aggressively subsumed : 0
% 3.39/1.11 % Contextual simplify-reflections : 1
% 3.39/1.11 % Paramodulations : 26144
% 3.39/1.11 % Factorizations : 6
% 3.39/1.11 % NegExts : 0
% 3.39/1.11 % Equation resolutions : 447
% 3.39/1.11 % Disequality decompositions : 0
% 3.39/1.11 % Total rewrite steps : 11163
% 3.39/1.11 % ...of those cached : 10017
% 3.39/1.11 % Propositional unsat checks : 0
% 3.39/1.11 % Propositional check models : 0
% 3.39/1.11 % Propositional check unsatisfiable : 0
% 3.39/1.11 % Propositional clauses : 0
% 3.39/1.11 % Propositional clauses after purity: 0
% 3.39/1.11 % Propositional unsat core size : 0
% 3.39/1.11 % Propositional preprocessing time : 0.000
% 3.39/1.11 % Propositional encoding time : 0.000
% 3.39/1.11 % Propositional solver time : 0.000
% 3.39/1.11 % Success case prop preproc time : 0.000
% 3.39/1.11 % Success case prop encoding time : 0.000
% 3.39/1.11 % Success case prop solver time : 0.000
% 3.39/1.11 % Current number of processed clauses : 1163
% 3.39/1.11 % Positive orientable unit clauses : 228
% 3.39/1.11 % Positive unorientable unit clauses: 6
% 3.39/1.11 % Negative unit clauses : 123
% 3.39/1.11 % Non-unit-clauses : 806
% 3.39/1.11 % Current number of unprocessed clauses: 17036
% 3.39/1.11 % ...number of literals in the above : 44988
% 3.39/1.11 % Current number of archived formulas : 0
% 3.39/1.11 % Current number of archived clauses : 45
% 3.39/1.11 % Clause-clause subsumption calls (NU) : 79593
% 3.39/1.11 % Rec. Clause-clause subsumption calls : 64055
% 3.39/1.11 % Non-unit clause-clause subsumptions : 2206
% 3.39/1.11 % Unit Clause-clause subsumption calls : 3242
% 3.39/1.11 % Rewrite failures with RHS unbound : 0
% 3.39/1.11 % BW rewrite match attempts : 1157
% 3.39/1.11 % BW rewrite match successes : 54
% 3.39/1.11 % Condensation attempts : 0
% 3.39/1.11 % Condensation successes : 0
% 3.39/1.11 % Termbank termtop insertions : 471825
% 3.39/1.11 % Search garbage collected termcells : 21097
% 3.39/1.11
% 3.39/1.11 % -------------------------------------------------
% 3.39/1.11 % User time : 0.460 s
% 3.39/1.11 % System time : 0.032 s
% 3.39/1.11 % Total time : 0.492 s
% 3.39/1.11 % Maximum resident set size: 9672 pages
% 3.39/1.11
% 3.39/1.11 % -------------------------------------------------
% 3.39/1.11 % User time : 0.532 s
% 3.39/1.11 % System time : 0.041 s
% 3.39/1.11 % Total time : 0.574 s
% 3.39/1.11 % Maximum resident set size: 8448 pages
% 3.39/1.11 % E exiting
%------------------------------------------------------------------------------