%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW473+5 : 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 : n003.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 0.17s 0.55s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 11 unt; 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 : 10 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-4 aty)
% Number of variables : 27 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_6,conjecture,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).
fof(fact_84_insert__subset,axiom,
! [X1,X14,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)),X13))
<=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_insert__subset) ).
fof(conj_1,hypothesis,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(fact_78_imageI,axiom,
! [X2,X1,X12,X14,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X12,X14)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_imageI) ).
fof(conj_4,hypothesis,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
fof(c_0_5,negated_conjecture,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(assume_negation,[status(cth)],[conj_6]) ).
fof(c_0_6,negated_conjecture,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_7,negated_conjecture,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(fof_nnf,[status(thm)],[c_0_6]) ).
fof(c_0_8,plain,
! [X352,X353,X354,X355] :
( ( hBOOL(hAPP(fun(X352,bool),bool,hAPP(fun(X352,bool),fun(fun(X352,bool),bool),ord_less_eq(fun(X352,bool)),hAPP(fun(X352,bool),fun(X352,bool),hAPP(X352,fun(fun(X352,bool),fun(X352,bool)),insert(X352),X353),X354)),X355))
| ~ hBOOL(hAPP(fun(X352,bool),bool,hAPP(fun(X352,bool),fun(fun(X352,bool),bool),ord_less_eq(fun(X352,bool)),X354),X355))
| ~ hBOOL(hAPP(fun(X352,bool),bool,hAPP(X352,fun(fun(X352,bool),bool),member(X352),X353),X355)) )
& ( ~ hBOOL(hAPP(fun(X352,bool),bool,hAPP(fun(X352,bool),fun(fun(X352,bool),bool),ord_less_eq(fun(X352,bool)),hAPP(fun(X352,bool),fun(X352,bool),hAPP(X352,fun(fun(X352,bool),fun(X352,bool)),insert(X352),X353),X354)),X355))
| hBOOL(hAPP(fun(X352,bool),bool,hAPP(fun(X352,bool),fun(fun(X352,bool),bool),ord_less_eq(fun(X352,bool)),X354),X355)) )
& ( ~ hBOOL(hAPP(fun(X352,bool),bool,hAPP(fun(X352,bool),fun(fun(X352,bool),bool),ord_less_eq(fun(X352,bool)),hAPP(fun(X352,bool),fun(X352,bool),hAPP(X352,fun(fun(X352,bool),fun(X352,bool)),insert(X352),X353),X354)),X355))
| hBOOL(hAPP(fun(X352,bool),bool,hAPP(X352,fun(fun(X352,bool),bool),member(X352),X353),X355)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_84_insert__subset])])])]) ).
cnf(c_0_9,negated_conjecture,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,hypothesis,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(split_conjunct,[status(thm)],[conj_1]) ).
fof(c_0_12,plain,
! [X327,X328,X329,X330,X331] :
( hBOOL(hAPP(fun(X327,bool),bool,hAPP(X327,fun(fun(X327,bool),bool),member(X327),hAPP(X328,X327,X329,X330)),hAPP(fun(X328,bool),fun(X327,bool),hAPP(fun(X328,X327),fun(fun(X328,bool),fun(X327,bool)),image(X328,X327),X329),X331)))
| ~ hBOOL(hAPP(fun(X328,bool),bool,hAPP(X328,fun(fun(X328,bool),bool),member(X328),X330),X331)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_78_imageI])])]) ).
cnf(c_0_13,negated_conjecture,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_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])]) ).
cnf(c_0_14,plain,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),hAPP(X1,X4,X5,X2)),hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X5),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,hypothesis,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),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
% 0.00/0.02 % Problem : SWW473+5 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 09:59:46 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.17/0.55 % Version: 3.5.1
% 0.17/0.55 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.17/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.55 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.17/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.55 % Starting new_bool_1 with 300s (1) cores
% 0.17/0.55 % Starting sh5l with 300s (1) cores
% 0.17/0.55 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 4006746 completed with status 0
% 0.17/0.55 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.17/0.55 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.17/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.55 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.17/0.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.17/0.55 % No SInE strategy applied
% 0.17/0.55 % Search class: FGHSM-FFLM32-DFFFFFNN
% 0.17/0.55 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.55 % Starting SubtermCWHack with 136s (1) cores
% 0.17/0.55 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.17/0.55 % Starting new_bool_3 with 277s (1) cores
% 0.17/0.55 % Starting new_bool_1 with 277s (1) cores
% 0.17/0.55 % Starting sh5l with 277s (1) cores
% 0.17/0.55 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 4006754 completed with status 0
% 0.17/0.55 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.17/0.55 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.17/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.55 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.17/0.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.17/0.55 % No SInE strategy applied
% 0.17/0.55 % Search class: FGHSM-FFLM32-DFFFFFNN
% 0.17/0.55 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.55 % Starting SubtermCWHack with 136s (1) cores
% 0.17/0.55 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.17/0.55 % Preprocessing time : 0.006 s
% 0.17/0.55 % Presaturation interreduction done
% 0.17/0.55
% 0.17/0.55 % Proof found!
% 0.17/0.55 % SZS status Theorem
% 0.17/0.55 % SZS output start CNFRefutation
% See solution above
% 0.17/0.55 % Parsed axioms : 161
% 0.17/0.55 % Removed by relevancy pruning/SinE : 0
% 0.17/0.55 % Initial clauses : 200
% 0.17/0.55 % Removed in clause preprocessing : 3
% 0.17/0.55 % Initial clauses in saturation : 197
% 0.17/0.55 % Processed clauses : 442
% 0.17/0.55 % ...of these trivial : 2
% 0.17/0.55 % ...subsumed : 87
% 0.17/0.55 % ...remaining for further processing : 353
% 0.17/0.55 % Other redundant clauses eliminated : 2
% 0.17/0.55 % Clauses deleted for lack of memory : 0
% 0.17/0.55 % Backward-subsumed : 0
% 0.17/0.55 % Backward-rewritten : 1
% 0.17/0.55 % Generated clauses : 1106
% 0.17/0.55 % ...of the previous two non-redundant : 867
% 0.17/0.55 % ...aggressively subsumed : 0
% 0.17/0.55 % Contextual simplify-reflections : 0
% 0.17/0.55 % Paramodulations : 1099
% 0.17/0.55 % Factorizations : 2
% 0.17/0.55 % NegExts : 0
% 0.17/0.55 % Equation resolutions : 5
% 0.17/0.55 % Disequality decompositions : 0
% 0.17/0.55 % Total rewrite steps : 659
% 0.17/0.55 % ...of those cached : 344
% 0.17/0.55 % Propositional unsat checks : 0
% 0.17/0.55 % Propositional check models : 0
% 0.17/0.55 % Propositional check unsatisfiable : 0
% 0.17/0.55 % Propositional clauses : 0
% 0.17/0.55 % Propositional clauses after purity: 0
% 0.17/0.55 % Propositional unsat core size : 0
% 0.17/0.55 % Propositional preprocessing time : 0.000
% 0.17/0.55 % Propositional encoding time : 0.000
% 0.17/0.55 % Propositional solver time : 0.000
% 0.17/0.55 % Success case prop preproc time : 0.000
% 0.17/0.55 % Success case prop encoding time : 0.000
% 0.17/0.55 % Success case prop solver time : 0.000
% 0.17/0.55 % Current number of processed clauses : 182
% 0.17/0.55 % Positive orientable unit clauses : 59
% 0.17/0.55 % Positive unorientable unit clauses: 2
% 0.17/0.55 % Negative unit clauses : 8
% 0.17/0.55 % Non-unit-clauses : 113
% 0.17/0.55 % Current number of unprocessed clauses: 789
% 0.17/0.55 % ...number of literals in the above : 1921
% 0.17/0.55 % Current number of archived formulas : 0
% 0.17/0.55 % Current number of archived clauses : 170
% 0.17/0.55 % Clause-clause subsumption calls (NU) : 4715
% 0.17/0.55 % Rec. Clause-clause subsumption calls : 4466
% 0.17/0.55 % Non-unit clause-clause subsumptions : 83
% 0.17/0.55 % Unit Clause-clause subsumption calls : 68
% 0.17/0.55 % Rewrite failures with RHS unbound : 0
% 0.17/0.55 % BW rewrite match attempts : 2257
% 0.17/0.55 % BW rewrite match successes : 14
% 0.17/0.55 % Condensation attempts : 0
% 0.17/0.55 % Condensation successes : 0
% 0.17/0.55 % Termbank termtop insertions : 101837
% 0.17/0.55 % Search garbage collected termcells : 2090
% 0.17/0.55
% 0.17/0.55 % -------------------------------------------------
% 0.17/0.55 % User time : 0.092 s
% 0.17/0.55 % System time : 0.013 s
% 0.17/0.55 % Total time : 0.104 s
% 0.17/0.55 % Maximum resident set size: 4644 pages
% 0.17/0.55
% 0.17/0.55 % -------------------------------------------------
% 0.17/0.55 % User time : 0.410 s
% 0.17/0.55 % System time : 0.048 s
% 0.17/0.55 % Total time : 0.458 s
% 0.17/0.55 % Maximum resident set size: 5120 pages
% 0.17/0.55 % E exiting
%------------------------------------------------------------------------------