%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW473+6 : 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 : 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 03:10:50 PM UTC 2026
% Result : Theorem 9.83s 2.34s
% Output : CNFRefutation 9.83s
% 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_86_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_86_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_80_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_80_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,
! [X408,X409,X410,X411] :
( ( hBOOL(hAPP(fun(X408,bool),bool,hAPP(fun(X408,bool),fun(fun(X408,bool),bool),ord_less_eq(fun(X408,bool)),hAPP(fun(X408,bool),fun(X408,bool),hAPP(X408,fun(fun(X408,bool),fun(X408,bool)),insert(X408),X409),X410)),X411))
| ~ hBOOL(hAPP(fun(X408,bool),bool,hAPP(fun(X408,bool),fun(fun(X408,bool),bool),ord_less_eq(fun(X408,bool)),X410),X411))
| ~ hBOOL(hAPP(fun(X408,bool),bool,hAPP(X408,fun(fun(X408,bool),bool),member(X408),X409),X411)) )
& ( ~ hBOOL(hAPP(fun(X408,bool),bool,hAPP(fun(X408,bool),fun(fun(X408,bool),bool),ord_less_eq(fun(X408,bool)),hAPP(fun(X408,bool),fun(X408,bool),hAPP(X408,fun(fun(X408,bool),fun(X408,bool)),insert(X408),X409),X410)),X411))
| hBOOL(hAPP(fun(X408,bool),bool,hAPP(fun(X408,bool),fun(fun(X408,bool),bool),ord_less_eq(fun(X408,bool)),X410),X411)) )
& ( ~ hBOOL(hAPP(fun(X408,bool),bool,hAPP(fun(X408,bool),fun(fun(X408,bool),bool),ord_less_eq(fun(X408,bool)),hAPP(fun(X408,bool),fun(X408,bool),hAPP(X408,fun(fun(X408,bool),fun(X408,bool)),insert(X408),X409),X410)),X411))
| hBOOL(hAPP(fun(X408,bool),bool,hAPP(X408,fun(fun(X408,bool),bool),member(X408),X409),X411)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_86_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,
! [X383,X384,X385,X386,X387] :
( hBOOL(hAPP(fun(X383,bool),bool,hAPP(X383,fun(fun(X383,bool),bool),member(X383),hAPP(X384,X383,X385,X386)),hAPP(fun(X384,bool),fun(X383,bool),hAPP(fun(X384,X383),fun(fun(X384,bool),fun(X383,bool)),image(X384,X383),X385),X387)))
| ~ hBOOL(hAPP(fun(X384,bool),bool,hAPP(X384,fun(fun(X384,bool),bool),member(X384),X386),X387)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_80_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
% 0.00/0.05 % Problem : SWW473+6 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.47 % Computer : n001.cluster.edu
% 0.21/0.47 % Model : x86_64 x86_64
% 0.21/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.47 % Memory : 8046.5625MB
% 0.21/0.47 % OS : Linux 6.8.0-71-generic
% 0.21/0.47 % CPULimit : 300
% 0.21/0.47 % WCLimit : 300
% 0.21/0.47 % DateTime : Mon Sep 21 10:03:29 UTC 2026
% 0.21/0.48 % CPUTime :
% 0.21/0.48 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.53 Running first-order theorem proving
% 0.25/0.53 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
% 9.83/2.34 % Version: 3.5.1
% 9.83/2.34 % Preprocessing class: FSLSSMSMSSSNFFN.
% 9.83/2.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.83/2.34 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 9.83/2.34 % Starting new_bool_3 with 300s (1) cores
% 9.83/2.34 % Starting new_bool_1 with 300s (1) cores
% 9.83/2.34 % Starting sh5l with 300s (1) cores
% 9.83/2.34 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2840567 completed with status 0
% 9.83/2.34 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 9.83/2.34 % Preprocessing class: FSLSSMSMSSSNFFN.
% 9.83/2.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.83/2.34 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 9.83/2.34 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 9.83/2.34 % No SInE strategy applied
% 9.83/2.34 % Search class: FGHSM-FSLM33-DFFFFFNN
% 9.83/2.34 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 9.83/2.34 % Starting SubtermCWHack with 136s (1) cores
% 9.83/2.34 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 9.83/2.34 % Starting U----_206b_01_C11_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 9.83/2.34 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 9.83/2.34 % Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 9.83/2.34 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2840574 completed with status 0
% 9.83/2.34 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 9.83/2.34 % Preprocessing class: FSLSSMSMSSSNFFN.
% 9.83/2.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.83/2.34 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 9.83/2.34 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 9.83/2.34 % No SInE strategy applied
% 9.83/2.34 % Search class: FGHSM-FSLM33-DFFFFFNN
% 9.83/2.34 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 9.83/2.34 % Starting SubtermCWHack with 136s (1) cores
% 9.83/2.34 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 9.83/2.34 % Preprocessing time : 0.036 s
% 9.83/2.34 % Presaturation interreduction done
% 9.83/2.34
% 9.83/2.34 % Proof found!
% 9.83/2.34 % SZS status Theorem
% 9.83/2.34 % SZS output start CNFRefutation
% See solution above
% 9.83/2.34 % Parsed axioms : 609
% 9.83/2.34 % Removed by relevancy pruning/SinE : 0
% 9.83/2.34 % Initial clauses : 839
% 9.83/2.34 % Removed in clause preprocessing : 24
% 9.83/2.34 % Initial clauses in saturation : 815
% 9.83/2.34 % Processed clauses : 1696
% 9.83/2.34 % ...of these trivial : 17
% 9.83/2.34 % ...subsumed : 404
% 9.83/2.34 % ...remaining for further processing : 1275
% 9.83/2.34 % Other redundant clauses eliminated : 222
% 9.83/2.34 % Clauses deleted for lack of memory : 0
% 9.83/2.34 % Backward-subsumed : 8
% 9.83/2.34 % Backward-rewritten : 28
% 9.83/2.34 % Generated clauses : 13781
% 9.83/2.34 % ...of the previous two non-redundant : 11796
% 9.83/2.34 % ...aggressively subsumed : 0
% 9.83/2.34 % Contextual simplify-reflections : 6
% 9.83/2.34 % Paramodulations : 13549
% 9.83/2.34 % Factorizations : 9
% 9.83/2.34 % NegExts : 0
% 9.83/2.34 % Equation resolutions : 227
% 9.83/2.34 % Disequality decompositions : 0
% 9.83/2.34 % Total rewrite steps : 14111
% 9.83/2.34 % ...of those cached : 11692
% 9.83/2.34 % Propositional unsat checks : 0
% 9.83/2.34 % Propositional check models : 0
% 9.83/2.34 % Propositional check unsatisfiable : 0
% 9.83/2.34 % Propositional clauses : 0
% 9.83/2.34 % Propositional clauses after purity: 0
% 9.83/2.34 % Propositional unsat core size : 0
% 9.83/2.34 % Propositional preprocessing time : 0.000
% 9.83/2.34 % Propositional encoding time : 0.000
% 9.83/2.34 % Propositional solver time : 0.000
% 9.83/2.34 % Success case prop preproc time : 0.000
% 9.83/2.34 % Success case prop encoding time : 0.000
% 9.83/2.34 % Success case prop solver time : 0.000
% 9.83/2.34 % Current number of processed clauses : 595
% 9.83/2.34 % Positive orientable unit clauses : 159
% 9.83/2.34 % Positive unorientable unit clauses: 6
% 9.83/2.34 % Negative unit clauses : 17
% 9.83/2.34 % Non-unit-clauses : 413
% 9.83/2.34 % Current number of unprocessed clauses: 11508
% 9.83/2.34 % ...number of literals in the above : 38916
% 9.83/2.34 % Current number of archived formulas : 0
% 9.83/2.34 % Current number of archived clauses : 659
% 9.83/2.34 % Clause-clause subsumption calls (NU) : 86478
% 9.83/2.34 % Rec. Clause-clause subsumption calls : 48566
% 9.83/2.34 % Non-unit clause-clause subsumptions : 301
% 9.83/2.34 % Unit Clause-clause subsumption calls : 340
% 9.83/2.34 % Rewrite failures with RHS unbound : 0
% 9.83/2.34 % BW rewrite match attempts : 11522
% 9.83/2.34 % BW rewrite match successes : 81
% 9.83/2.34 % Condensation attempts : 0
% 9.83/2.34 % Condensation successes : 0
% 9.83/2.34 % Termbank termtop insertions : 991637
% 9.83/2.34 % Search garbage collected termcells : 12133
% 9.83/2.34
% 9.83/2.34 % -------------------------------------------------
% 9.83/2.34 % User time : 1.334 s
% 9.83/2.34 % System time : 0.048 s
% 9.83/2.34 % Total time : 1.381 s
% 9.83/2.34 % Maximum resident set size: 7824 pages
% 9.83/2.34
% 9.83/2.34 % -------------------------------------------------
% 9.83/2.34 % User time : 6.997 s
% 9.83/2.34 % System time : 0.258 s
% 9.83/2.34 % Total time : 7.255 s
% 9.83/2.34 % Maximum resident set size: 5376 pages
% 9.83/2.34 % E exiting
%------------------------------------------------------------------------------