%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC220+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 02:43:30 PM UTC 2026
% Result : Theorem 0.26s 0.64s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 27 ( 12 unt; 0 def)
% Number of atoms : 180 ( 46 equ)
% Maximal formula atoms : 46 ( 6 avg)
% Number of connectives : 235 ( 82 ~; 86 |; 43 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 57 ( 0 sgn 28 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ! [X9] :
( ssItem(X9)
=> ! [X10] :
( ssList(X10)
=> ! [X11] :
( ssList(X11)
=> ( ? [X12] :
( leq(X9,X12)
& memberP(X11,X12)
& memberP(X10,X12)
& ~ leq(X12,X9)
& ssItem(X12) )
| app(app(X10,cons(X9,nil)),X11) != X3 ) ) ) )
& nil != X3 )
| ? [X5] :
( ? [X6] :
( ? [X7] :
( ! [X8] :
( ssItem(X8)
=> ( leq(X8,X5)
| ~ leq(X5,X8)
| ~ memberP(X7,X8)
| ~ memberP(X6,X8) ) )
& app(app(X6,cons(X5,nil)),X7) = X1
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
| nil = X1
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(c_0_1,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ! [X9] :
( ssItem(X9)
=> ! [X10] :
( ssList(X10)
=> ! [X11] :
( ssList(X11)
=> ( ? [X12] :
( leq(X9,X12)
& memberP(X11,X12)
& memberP(X10,X12)
& ~ leq(X12,X9)
& ssItem(X12) )
| app(app(X10,cons(X9,nil)),X11) != X3 ) ) ) )
& nil != X3 )
| ? [X5] :
( ? [X6] :
( ? [X7] :
( ! [X8] :
( ssItem(X8)
=> ( leq(X8,X5)
| ~ leq(X5,X8)
| ~ memberP(X7,X8)
| ~ memberP(X6,X8) ) )
& app(app(X6,cons(X5,nil)),X7) = X1
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
| nil = X1
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_2,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ! [X9] :
( ssItem(X9)
=> ! [X10] :
( ssList(X10)
=> ! [X11] :
( ssList(X11)
=> ( ? [X12] :
( leq(X9,X12)
& memberP(X11,X12)
& memberP(X10,X12)
& ~ leq(X12,X9)
& ssItem(X12) )
| app(app(X10,cons(X9,nil)),X11) != X3 ) ) ) )
& nil != X3 )
| ? [X5] :
( ? [X6] :
( ? [X7] :
( ! [X8] :
( ssItem(X8)
=> ( leq(X8,X5)
| ~ leq(X5,X8)
| ~ memberP(X7,X8)
| ~ memberP(X6,X8) ) )
& app(app(X6,cons(X5,nil)),X7) = X1
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
| nil = X1
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_3,negated_conjecture,
! [X261,X262,X263,X268] :
( ( nil = esk50_0
| ~ leq(esk53_0,X268)
| ~ memberP(esk55_0,X268)
| ~ memberP(esk54_0,X268)
| leq(X268,esk53_0)
| ~ ssItem(X268) )
& ( nil = esk50_0
| app(app(esk54_0,cons(esk53_0,nil)),esk55_0) = esk50_0 )
& ( nil = esk50_0
| ssList(esk55_0) )
& ( nil = esk50_0
| ssList(esk54_0) )
& ( nil = esk50_0
| ssItem(esk53_0) )
& ( ~ ssItem(X261)
| ~ ssList(X262)
| app(app(X262,cons(X261,nil)),X263) != esk48_0
| ~ ssList(X263)
| ~ leq(esk52_3(X261,X262,X263),X261) )
& ( ~ ssItem(X261)
| ~ ssList(X262)
| app(app(X262,cons(X261,nil)),X263) != esk48_0
| ~ ssList(X263)
| leq(X261,esk52_3(X261,X262,X263)) )
& ( ~ ssItem(X261)
| ~ ssList(X262)
| app(app(X262,cons(X261,nil)),X263) != esk48_0
| ~ ssList(X263)
| memberP(X263,esk52_3(X261,X262,X263)) )
& ( ~ ssItem(X261)
| ~ ssList(X262)
| app(app(X262,cons(X261,nil)),X263) != esk48_0
| ~ ssList(X263)
| memberP(X262,esk52_3(X261,X262,X263)) )
& ( ~ ssItem(X261)
| ~ ssList(X262)
| app(app(X262,cons(X261,nil)),X263) != esk48_0
| ~ ssList(X263)
| ssItem(esk52_3(X261,X262,X263)) )
& nil != esk48_0
& esk48_0 = esk50_0
& esk49_0 = esk51_0
& ssList(esk51_0)
& ssList(esk50_0)
& ssList(esk49_0)
& ssList(esk48_0) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])])])]) ).
cnf(c_0_4,negated_conjecture,
( nil = esk50_0
| app(app(esk54_0,cons(esk53_0,nil)),esk55_0) = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_5,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,negated_conjecture,
nil != esk48_0,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_7,negated_conjecture,
( nil = esk50_0
| ssList(esk55_0) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_8,negated_conjecture,
( nil = esk50_0
| ssList(esk54_0) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_9,negated_conjecture,
( nil = esk50_0
| ssItem(esk53_0) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_10,negated_conjecture,
( ~ leq(esk53_0,X1)
| ~ memberP(esk55_0,X1)
| ~ memberP(esk54_0,X1)
| ~ ssItem(X1)
| nil = esk50_0
| leq(X1,esk53_0) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_11,negated_conjecture,
( ~ ssItem(X2)
| ~ ssList(X1)
| app(app(X1,cons(X2,nil)),X3) != esk48_0
| ~ ssList(X3)
| memberP(X1,esk52_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_12,negated_conjecture,
app(app(esk54_0,cons(esk53_0,nil)),esk55_0) = esk48_0,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4,c_0_5]),c_0_5]),c_0_6]) ).
cnf(c_0_13,negated_conjecture,
ssList(esk55_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_5]),c_0_6]) ).
cnf(c_0_14,negated_conjecture,
ssList(esk54_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_5]),c_0_6]) ).
cnf(c_0_15,negated_conjecture,
ssItem(esk53_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_5]),c_0_6]) ).
cnf(c_0_16,negated_conjecture,
( ~ ssItem(X2)
| ~ ssList(X3)
| app(app(X3,cons(X2,nil)),X1) != esk48_0
| ~ ssList(X1)
| memberP(X1,esk52_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_17,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| app(app(X2,cons(X1,nil)),X3) != esk48_0
| ~ ssList(X3)
| ssItem(esk52_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_18,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| app(app(X2,cons(X1,nil)),X3) != esk48_0
| ~ ssList(X3)
| leq(X1,esk52_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_19,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(esk55_0,X1)
| ~ memberP(esk54_0,X1)
| ~ leq(esk53_0,X1)
| leq(X1,esk53_0) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_5]),c_0_6]) ).
cnf(c_0_20,negated_conjecture,
memberP(esk54_0,esk52_3(esk53_0,esk54_0,esk55_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14]),c_0_15])]) ).
cnf(c_0_21,negated_conjecture,
memberP(esk55_0,esk52_3(esk53_0,esk54_0,esk55_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_12]),c_0_14]),c_0_13]),c_0_15])]) ).
cnf(c_0_22,negated_conjecture,
ssItem(esk52_3(esk53_0,esk54_0,esk55_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_12]),c_0_13]),c_0_14]),c_0_15])]) ).
cnf(c_0_23,negated_conjecture,
leq(esk53_0,esk52_3(esk53_0,esk54_0,esk55_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_12]),c_0_13]),c_0_14]),c_0_15])]) ).
cnf(c_0_24,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| app(app(X2,cons(X1,nil)),X3) != esk48_0
| ~ ssList(X3)
| ~ leq(esk52_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_25,negated_conjecture,
leq(esk52_3(esk53_0,esk54_0,esk55_0),esk53_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22])]),c_0_23])]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_12]),c_0_13]),c_0_14]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC220+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.45 % Computer : n008.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 08:06:09 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.51 Running first-order theorem proving
% 0.26/0.51 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
% 0.26/0.64 % Version: 3.5.1
% 0.26/0.64 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.26/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.26/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.26/0.64 % Starting new_bool_1 with 300s (1) cores
% 0.26/0.64 % Starting sh5l with 300s (1) cores
% 0.26/0.64 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 543860 completed with status 0
% 0.26/0.64 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.26/0.64 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.26/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.26/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.26/0.64 % No SInE strategy applied
% 0.26/0.64 % Search class: FGHSF-FSLM31-MFFFFFNN
% 0.26/0.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.26/0.64 % Starting SubtermCWHack with 136s (1) cores
% 0.26/0.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.26/0.64 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.26/0.64 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.26/0.64 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S070I with 136s (1) cores
% 0.26/0.64 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 543868 completed with status 0
% 0.26/0.64 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.26/0.64 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.26/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.26/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.26/0.64 % No SInE strategy applied
% 0.26/0.64 % Search class: FGHSF-FSLM31-MFFFFFNN
% 0.26/0.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.26/0.64 % Starting SubtermCWHack with 136s (1) cores
% 0.26/0.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.26/0.64 % Preprocessing time : 0.006 s
% 0.26/0.64 % Presaturation interreduction done
% 0.26/0.64
% 0.26/0.64 % Proof found!
% 0.26/0.64 % SZS status Theorem
% 0.26/0.64 % SZS output start CNFRefutation
% See solution above
% 0.26/0.64 % Parsed axioms : 96
% 0.26/0.64 % Removed by relevancy pruning/SinE : 0
% 0.26/0.64 % Initial clauses : 207
% 0.26/0.64 % Removed in clause preprocessing : 2
% 0.26/0.64 % Initial clauses in saturation : 205
% 0.26/0.64 % Processed clauses : 476
% 0.26/0.64 % ...of these trivial : 2
% 0.26/0.64 % ...subsumed : 19
% 0.26/0.64 % ...remaining for further processing : 455
% 0.26/0.64 % Other redundant clauses eliminated : 59
% 0.26/0.64 % Clauses deleted for lack of memory : 0
% 0.26/0.64 % Backward-subsumed : 1
% 0.26/0.64 % Backward-rewritten : 6
% 0.26/0.64 % Generated clauses : 772
% 0.26/0.64 % ...of the previous two non-redundant : 664
% 0.26/0.64 % ...aggressively subsumed : 0
% 0.26/0.64 % Contextual simplify-reflections : 2
% 0.26/0.64 % Paramodulations : 710
% 0.26/0.64 % Factorizations : 0
% 0.26/0.64 % NegExts : 0
% 0.26/0.64 % Equation resolutions : 64
% 0.26/0.64 % Disequality decompositions : 0
% 0.26/0.64 % Total rewrite steps : 473
% 0.26/0.64 % ...of those cached : 444
% 0.26/0.64 % Propositional unsat checks : 0
% 0.26/0.64 % Propositional check models : 0
% 0.26/0.64 % Propositional check unsatisfiable : 0
% 0.26/0.64 % Propositional clauses : 0
% 0.26/0.64 % Propositional clauses after purity: 0
% 0.26/0.64 % Propositional unsat core size : 0
% 0.26/0.64 % Propositional preprocessing time : 0.000
% 0.26/0.64 % Propositional encoding time : 0.000
% 0.26/0.64 % Propositional solver time : 0.000
% 0.26/0.64 % Success case prop preproc time : 0.000
% 0.26/0.64 % Success case prop encoding time : 0.000
% 0.26/0.64 % Success case prop solver time : 0.000
% 0.26/0.64 % Current number of processed clauses : 226
% 0.26/0.64 % Positive orientable unit clauses : 43
% 0.26/0.64 % Positive unorientable unit clauses: 0
% 0.26/0.64 % Negative unit clauses : 3
% 0.26/0.64 % Non-unit-clauses : 180
% 0.26/0.64 % Current number of unprocessed clauses: 584
% 0.26/0.64 % ...number of literals in the above : 3596
% 1.05/0.64 % Current number of archived formulas : 0
% 1.05/0.64 % Current number of archived clauses : 206
% 1.05/0.64 % Clause-clause subsumption calls (NU) : 19088
% 1.05/0.64 % Rec. Clause-clause subsumption calls : 3889
% 1.05/0.64 % Non-unit clause-clause subsumptions : 9
% 1.05/0.64 % Unit Clause-clause subsumption calls : 76
% 1.05/0.64 % Rewrite failures with RHS unbound : 0
% 1.05/0.64 % BW rewrite match attempts : 4
% 1.05/0.64 % BW rewrite match successes : 4
% 1.05/0.64 % Condensation attempts : 0
% 1.05/0.64 % Condensation successes : 0
% 1.05/0.64 % Termbank termtop insertions : 36575
% 1.05/0.64 % Search garbage collected termcells : 4508
% 1.05/0.64
% 1.05/0.64 % -------------------------------------------------
% 1.05/0.64 % User time : 0.093 s
% 1.05/0.64 % System time : 0.014 s
% 1.05/0.64 % Total time : 0.108 s
% 1.05/0.64 % Maximum resident set size: 4276 pages
% 1.05/0.64
% 1.05/0.64 % -------------------------------------------------
% 1.05/0.64 % User time : 0.419 s
% 1.05/0.64 % System time : 0.044 s
% 1.05/0.64 % Total time : 0.463 s
% 1.05/0.64 % Maximum resident set size: 4608 pages
% 1.05/0.64 % E exiting
%------------------------------------------------------------------------------