%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW473+7 : 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 : 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 03:10:50 PM UTC 2026
% Result : Theorem 14.55s 2.73s
% Output : CNFRefutation 14.55s
% 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_103_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_103_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_94_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_94_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,
! [X530,X531,X532,X533] :
( ( hBOOL(hAPP(fun(X530,bool),bool,hAPP(fun(X530,bool),fun(fun(X530,bool),bool),ord_less_eq(fun(X530,bool)),hAPP(fun(X530,bool),fun(X530,bool),hAPP(X530,fun(fun(X530,bool),fun(X530,bool)),insert(X530),X531),X532)),X533))
| ~ hBOOL(hAPP(fun(X530,bool),bool,hAPP(fun(X530,bool),fun(fun(X530,bool),bool),ord_less_eq(fun(X530,bool)),X532),X533))
| ~ hBOOL(hAPP(fun(X530,bool),bool,hAPP(X530,fun(fun(X530,bool),bool),member(X530),X531),X533)) )
& ( ~ hBOOL(hAPP(fun(X530,bool),bool,hAPP(fun(X530,bool),fun(fun(X530,bool),bool),ord_less_eq(fun(X530,bool)),hAPP(fun(X530,bool),fun(X530,bool),hAPP(X530,fun(fun(X530,bool),fun(X530,bool)),insert(X530),X531),X532)),X533))
| hBOOL(hAPP(fun(X530,bool),bool,hAPP(fun(X530,bool),fun(fun(X530,bool),bool),ord_less_eq(fun(X530,bool)),X532),X533)) )
& ( ~ hBOOL(hAPP(fun(X530,bool),bool,hAPP(fun(X530,bool),fun(fun(X530,bool),bool),ord_less_eq(fun(X530,bool)),hAPP(fun(X530,bool),fun(X530,bool),hAPP(X530,fun(fun(X530,bool),fun(X530,bool)),insert(X530),X531),X532)),X533))
| hBOOL(hAPP(fun(X530,bool),bool,hAPP(X530,fun(fun(X530,bool),bool),member(X530),X531),X533)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_103_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,
! [X487,X488,X489,X490,X491] :
( hBOOL(hAPP(fun(X487,bool),bool,hAPP(X487,fun(fun(X487,bool),bool),member(X487),hAPP(X488,X487,X489,X490)),hAPP(fun(X488,bool),fun(X487,bool),hAPP(fun(X488,X487),fun(fun(X488,bool),fun(X487,bool)),image(X488,X487),X489),X491)))
| ~ hBOOL(hAPP(fun(X488,bool),bool,hAPP(X488,fun(fun(X488,bool),bool),member(X488),X490),X491)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_94_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+7 : 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 : n017.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 09:53:12 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.44 Running first-order theorem proving
% 0.14/0.44 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
% 14.55/2.73 % Version: 3.5.1
% 14.55/2.73 % Preprocessing class: FMLMSMSMSSSNFFN.
% 14.55/2.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.55/2.73 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 14.55/2.73 % Starting new_bool_3 with 300s (1) cores
% 14.55/2.73 % Starting new_bool_1 with 300s (1) cores
% 14.55/2.73 % Starting sh5l with 300s (1) cores
% 14.55/2.73 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2035756 completed with status 0
% 14.55/2.73 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 14.55/2.73 % Preprocessing class: FMLMSMSMSSSNFFN.
% 14.55/2.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.55/2.73 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 14.55/2.73 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 14.55/2.73 % No SInE strategy applied
% 14.55/2.73 % Search class: FGHSM-SMLM32-DFFFFFNN
% 14.55/2.73 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 14.55/2.73 % Starting SubtermCWHack with 136s (1) cores
% 14.55/2.73 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 14.55/2.73 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 14.55/2.73 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 14.55/2.73 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 14.55/2.73 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2035776 completed with status 0
% 14.55/2.73 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 14.55/2.73 % Preprocessing class: FMLMSMSMSSSNFFN.
% 14.55/2.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.55/2.73 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 14.55/2.73 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 14.55/2.73 % No SInE strategy applied
% 14.55/2.73 % Search class: FGHSM-SMLM32-DFFFFFNN
% 14.55/2.73 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 14.55/2.73 % Starting SubtermCWHack with 136s (1) cores
% 14.55/2.73 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 14.55/2.73 % Preprocessing time : 0.047 s
% 14.55/2.73 % Presaturation interreduction done
% 14.55/2.73
% 14.55/2.73 % Proof found!
% 14.55/2.73 % SZS status Theorem
% 14.55/2.73 % SZS output start CNFRefutation
% See solution above
% 14.55/2.73 % Parsed axioms : 1201
% 14.55/2.73 % Removed by relevancy pruning/SinE : 0
% 14.55/2.73 % Initial clauses : 1739
% 14.55/2.73 % Removed in clause preprocessing : 68
% 14.55/2.73 % Initial clauses in saturation : 1671
% 14.55/2.73 % Processed clauses : 3457
% 14.55/2.73 % ...of these trivial : 56
% 14.55/2.73 % ...subsumed : 690
% 14.55/2.73 % ...remaining for further processing : 2711
% 14.55/2.73 % Other redundant clauses eliminated : 843
% 14.55/2.73 % Clauses deleted for lack of memory : 0
% 14.55/2.73 % Backward-subsumed : 23
% 14.55/2.73 % Backward-rewritten : 35
% 14.55/2.73 % Generated clauses : 38442
% 14.55/2.73 % ...of the previous two non-redundant : 32905
% 14.55/2.73 % ...aggressively subsumed : 0
% 14.55/2.73 % Contextual simplify-reflections : 9
% 14.55/2.73 % Paramodulations : 37584
% 14.55/2.73 % Factorizations : 12
% 14.55/2.73 % NegExts : 0
% 14.55/2.73 % Equation resolutions : 854
% 14.55/2.73 % Disequality decompositions : 0
% 14.55/2.73 % Total rewrite steps : 41703
% 14.55/2.73 % ...of those cached : 37415
% 14.55/2.73 % Propositional unsat checks : 0
% 14.55/2.73 % Propositional check models : 0
% 14.55/2.73 % Propositional check unsatisfiable : 0
% 14.55/2.73 % Propositional clauses : 0
% 14.55/2.73 % Propositional clauses after purity: 0
% 14.55/2.73 % Propositional unsat core size : 0
% 14.55/2.73 % Propositional preprocessing time : 0.000
% 14.55/2.73 % Propositional encoding time : 0.000
% 14.55/2.73 % Propositional solver time : 0.000
% 14.55/2.73 % Success case prop preproc time : 0.000
% 14.55/2.73 % Success case prop encoding time : 0.000
% 14.55/2.73 % Success case prop solver time : 0.000
% 14.55/2.73 % Current number of processed clauses : 1260
% 14.55/2.73 % Positive orientable unit clauses : 339
% 14.55/2.73 % Positive unorientable unit clauses: 10
% 14.55/2.73 % Negative unit clauses : 23
% 14.55/2.73 % Non-unit-clauses : 888
% 14.55/2.73 % Current number of unprocessed clauses: 32425
% 14.55/2.73 % ...number of literals in the above : 106468
% 14.55/2.73 % Current number of archived formulas : 0
% 14.55/2.73 % Current number of archived clauses : 1395
% 14.55/2.73 % Clause-clause subsumption calls (NU) : 246712
% 14.55/2.73 % Rec. Clause-clause subsumption calls : 139750
% 14.55/2.73 % Non-unit clause-clause subsumptions : 502
% 14.55/2.73 % Unit Clause-clause subsumption calls : 1621
% 14.55/2.73 % Rewrite failures with RHS unbound : 0
% 14.55/2.73 % BW rewrite match attempts : 26137
% 14.55/2.73 % BW rewrite match successes : 186
% 14.55/2.73 % Condensation attempts : 0
% 14.55/2.73 % Condensation successes : 0
% 14.55/2.73 % Termbank termtop insertions : 2438098
% 14.55/2.73 % Search garbage collected termcells : 24248
% 14.55/2.73
% 14.55/2.73 % -------------------------------------------------
% 14.55/2.73 % User time : 2.054 s
% 14.55/2.73 % System time : 0.073 s
% 14.55/2.73 % Total time : 2.127 s
% 14.55/2.73 % Maximum resident set size: 12228 pages
% 14.55/2.73
% 14.55/2.73 % -------------------------------------------------
% 14.55/2.73 % User time : 9.812 s
% 14.55/2.73 % System time : 0.353 s
% 14.55/2.73 % Total time : 10.165 s
% 14.55/2.73 % Maximum resident set size: 6144 pages
% 14.55/2.73 % E exiting
%------------------------------------------------------------------------------