%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW473+1 : 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 : n001.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 03:10:48 PM UTC 2026
% Result : Theorem 0.21s 0.50s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 18 unt; 0 def)
% Number of atoms : 33 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 10 ~; 6 |; 0 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_283_insert__mono,axiom,
! [X8,X34,X37] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X34),X37))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X8,X34)),insert_a(X8,X37))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_insert__mono) ).
fof(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) ).
fof(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) ).
fof(fact_284_image__insert,axiom,
! [X9,X8,X10] : image_pname_a(X9,insert_pname(X8,X10)) = insert_a(hAPP_pname_a(X9,X8),image_pname_a(X9,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_image__insert) ).
fof(fact_223_insert__absorb,axiom,
! [X8,X5] :
( is_fun_pname_bool(X5)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X5))
=> insert_pname(X8,X5) = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_insert__absorb) ).
fof(conj_4,hypothesis,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
fof(gsy_v_U,hypothesis,
is_fun_pname_bool(u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_U) ).
fof(c_0_7,plain,
! [X146,X147,X148] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X146,X147)),insert_a(X146,X148)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X147),X148)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_283_insert__mono])])]) ).
fof(c_0_8,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]) ).
cnf(c_0_9,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X3,X1)),insert_a(X3,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,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]) ).
fof(c_0_11,plain,
! [X199,X200,X201] : image_pname_a(X199,insert_pname(X200,X201)) = insert_a(hAPP_pname_a(X199,X200),image_pname_a(X199,X201)),
inference(variable_rename,[status(thm)],[fact_284_image__insert]) ).
fof(c_0_12,plain,
! [X108,X109] :
( insert_pname(X108,X109) = X109
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X108),X109))
| ~ is_fun_pname_bool(X109) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_223_insert__absorb])])]) ).
fof(c_0_13,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_8]) ).
cnf(c_0_14,hypothesis,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1,g)),insert_a(X1,image_pname_a(mgt_call,u)))),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,plain,
image_pname_a(X1,insert_pname(X2,X3)) = insert_a(hAPP_pname_a(X1,X2),image_pname_a(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
| ~ is_fun_pname_bool(X1)
| insert_pname(X2,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,hypothesis,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
inference(split_conjunct,[status(thm)],[conj_4]) ).
cnf(c_0_18,hypothesis,
is_fun_pname_bool(u),
inference(split_conjunct,[status(thm)],[gsy_v_U]) ).
fof(c_0_19,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_13]) ).
cnf(c_0_20,hypothesis,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,X1),g)),image_pname_a(mgt_call,insert_pname(X1,u)))),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,hypothesis,
insert_pname(pn,u) = u,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
cnf(c_0_22,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_19]) ).
cnf(c_0_23,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW473+1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n001.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 10:04:00 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.21/0.50 % Version: 3.5.1
% 0.21/0.50 % Preprocessing class: FSLMSMSMSSSNFFN.
% 0.21/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.50 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 0.21/0.50 % Starting new_bool_3 with 600s (2) cores
% 0.21/0.50 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.50 % Starting sh5l with 300s (1) cores
% 0.21/0.50 % new_bool_3 with pid 2841617 completed with status 0
% 0.21/0.50 % Result found by new_bool_3
% 0.21/0.50 % Preprocessing class: FSLMSMSMSSSNFFN.
% 0.21/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.50 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 0.21/0.50 % Starting new_bool_3 with 600s (2) cores
% 0.21/0.50 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.50 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.50 % Search class: FGHSM-FSLM32-MFFFFFNN
% 0.21/0.50 % Scheduled 12 strats onto 2 cores with 600 seconds (600 total)
% 0.21/0.50 % Starting SubtermCWHack with 55s (1) cores
% 0.21/0.50 % Starting new_bool_3 with 61s (1) cores
% 0.21/0.50 % new_bool_3 with pid 2841626 completed with status 0
% 0.21/0.50 % Result found by new_bool_3
% 0.21/0.50 % Preprocessing class: FSLMSMSMSSSNFFN.
% 0.21/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.50 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 0.21/0.50 % Starting new_bool_3 with 600s (2) cores
% 0.21/0.50 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.50 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.50 % Search class: FGHSM-FSLM32-MFFFFFNN
% 0.21/0.50 % Scheduled 12 strats onto 2 cores with 600 seconds (600 total)
% 0.21/0.50 % Starting SubtermCWHack with 55s (1) cores
% 0.21/0.50 % Starting new_bool_3 with 61s (1) cores
% 0.21/0.50 % Preprocessing time : 0.006 s
% 0.21/0.50 % Presaturation interreduction done
% 0.21/0.50
% 0.21/0.50 % Proof found!
% 0.21/0.50 % SZS status Theorem
% 0.21/0.50 % SZS output start CNFRefutation
% See solution above
% 0.21/0.50 % Parsed axioms : 449
% 0.21/0.50 % Removed by relevancy pruning/SinE : 258
% 0.21/0.50 % Initial clauses : 264
% 0.21/0.50 % Removed in clause preprocessing : 5
% 0.21/0.50 % Initial clauses in saturation : 259
% 0.21/0.50 % Processed clauses : 442
% 0.21/0.50 % ...of these trivial : 10
% 0.21/0.50 % ...subsumed : 58
% 0.21/0.50 % ...remaining for further processing : 374
% 0.21/0.50 % Other redundant clauses eliminated : 33
% 0.21/0.50 % Clauses deleted for lack of memory : 0
% 0.21/0.50 % Backward-subsumed : 2
% 0.21/0.50 % Backward-rewritten : 0
% 0.21/0.50 % Generated clauses : 457
% 0.21/0.50 % ...of the previous two non-redundant : 271
% 0.21/0.50 % ...aggressively subsumed : 0
% 0.21/0.50 % Contextual simplify-reflections : 0
% 0.21/0.50 % Paramodulations : 423
% 0.21/0.50 % Factorizations : 0
% 0.21/0.50 % NegExts : 0
% 0.21/0.50 % Equation resolutions : 34
% 0.21/0.50 % Disequality decompositions : 0
% 0.21/0.50 % Total rewrite steps : 198
% 0.21/0.50 % ...of those cached : 124
% 0.21/0.50 % Propositional unsat checks : 0
% 0.21/0.50 % Propositional check models : 0
% 0.21/0.50 % Propositional check unsatisfiable : 0
% 0.21/0.50 % Propositional clauses : 0
% 0.21/0.50 % Propositional clauses after purity: 0
% 0.21/0.50 % Propositional unsat core size : 0
% 0.21/0.50 % Propositional preprocessing time : 0.000
% 0.21/0.50 % Propositional encoding time : 0.000
% 0.21/0.50 % Propositional solver time : 0.000
% 0.21/0.50 % Success case prop preproc time : 0.000
% 0.21/0.50 % Success case prop encoding time : 0.000
% 0.21/0.50 % Success case prop solver time : 0.000
% 0.21/0.50 % Current number of processed clauses : 152
% 0.21/0.50 % Positive orientable unit clauses : 62
% 0.21/0.50 % Positive unorientable unit clauses: 4
% 0.21/0.50 % Negative unit clauses : 9
% 0.21/0.50 % Non-unit-clauses : 77
% 0.21/0.50 % Current number of unprocessed clauses: 270
% 0.21/0.50 % ...number of literals in the above : 520
% 0.21/0.50 % Current number of archived formulas : 0
% 0.21/0.50 % Current number of archived clauses : 189
% 0.21/0.50 % Clause-clause subsumption calls (NU) : 4220
% 0.21/0.50 % Rec. Clause-clause subsumption calls : 3063
% 0.21/0.50 % Non-unit clause-clause subsumptions : 56
% 0.21/0.50 % Unit Clause-clause subsumption calls : 142
% 0.21/0.50 % Rewrite failures with RHS unbound : 0
% 0.21/0.50 % BW rewrite match attempts : 158
% 0.21/0.50 % BW rewrite match successes : 18
% 0.21/0.50 % Condensation attempts : 0
% 0.21/0.50 % Condensation successes : 0
% 0.21/0.50 % Termbank termtop insertions : 35518
% 0.21/0.50 % Search garbage collected termcells : 5432
% 0.21/0.50
% 0.21/0.50 % -------------------------------------------------
% 0.21/0.50 % User time : 0.050 s
% 0.21/0.50 % System time : 0.005 s
% 0.21/0.50 % Total time : 0.056 s
% 0.21/0.50 % Maximum resident set size: 5268 pages
% 0.21/0.50
% 0.21/0.50 % -------------------------------------------------
% 0.21/0.50 % User time : 0.094 s
% 0.21/0.50 % System time : 0.020 s
% 0.21/0.50 % Total time : 0.115 s
% 0.21/0.50 % Maximum resident set size: 5376 pages
% 0.21/0.50 % E exiting
%------------------------------------------------------------------------------