%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC404+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 : n020.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 02:44:16 PM UTC 2026
% Result : Theorem 0.08s 0.45s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 13 unt; 0 def)
% Number of atoms : 178 ( 39 equ)
% Maximal formula atoms : 29 ( 6 avg)
% Number of connectives : 221 ( 69 ~; 69 |; 56 &)
% ( 1 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 73 ( 0 sgn 39 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( nil = X3
& nil != X4 )
| ! [X15] :
( ssItem(X15)
=> ( memberP(X2,X15)
| ~ memberP(X1,X15) ) )
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( ? [X11] :
( ? [X12] :
( ? [X13] :
( ? [X14] :
( lt(X13,X11)
& app(X14,cons(X13,nil)) = X3
& ssList(X14) )
& ssItem(X13) )
& app(cons(X11,nil),X12) = X6
& ssList(X12) )
& ssItem(X11) )
| ? [X7] :
( ? [X8] :
( ? [X9] :
( ? [X10] :
( lt(X7,X9)
& app(cons(X9,nil),X10) = X3
& ssList(X10) )
& ssItem(X9) )
& app(X8,cons(X7,nil)) = X5
& ssList(X8) )
& ssItem(X7) )
| ~ strictorderedP(X3)
| app(app(X5,X3),X6) != X4 ) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax36,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(app(X2,X3),X1)
<=> ( memberP(X3,X1)
| memberP(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax36) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(c_0_3,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( nil = X3
& nil != X4 )
| ! [X15] :
( ssItem(X15)
=> ( memberP(X2,X15)
| ~ memberP(X1,X15) ) )
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( ? [X11] :
( ? [X12] :
( ? [X13] :
( ? [X14] :
( lt(X13,X11)
& app(X14,cons(X13,nil)) = X3
& ssList(X14) )
& ssItem(X13) )
& app(cons(X11,nil),X12) = X6
& ssList(X12) )
& ssItem(X11) )
| ? [X7] :
( ? [X8] :
( ? [X9] :
( ? [X10] :
( lt(X7,X9)
& app(cons(X9,nil),X10) = X3
& ssList(X10) )
& ssItem(X9) )
& app(X8,cons(X7,nil)) = X5
& ssList(X8) )
& ssItem(X7) )
| ~ strictorderedP(X3)
| app(app(X5,X3),X6) != X4 ) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( nil = X3
& nil != X4 )
| ! [X15] :
( ssItem(X15)
=> ( memberP(X2,X15)
| ~ memberP(X1,X15) ) )
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( ? [X11] :
( ? [X12] :
( ? [X13] :
( ? [X14] :
( lt(X13,X11)
& app(X14,cons(X13,nil)) = X3
& ssList(X14) )
& ssItem(X13) )
& app(cons(X11,nil),X12) = X6
& ssList(X12) )
& ssItem(X11) )
| ? [X7] :
( ? [X8] :
( ? [X9] :
( ? [X10] :
( lt(X7,X9)
& app(cons(X9,nil),X10) = X3
& ssList(X10) )
& ssItem(X9) )
& app(X8,cons(X7,nil)) = X5
& ssList(X8) )
& ssItem(X7) )
| ~ strictorderedP(X3)
| app(app(X5,X3),X6) != X4 ) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_5,plain,
! [X42,X43,X44] :
( ( ~ ssItem(X42)
| ~ ssList(X43)
| ~ ssList(X44)
| memberP(app(X43,X44),X42)
| ~ memberP(X44,X42) )
& ( ~ ssItem(X42)
| ~ ssList(X43)
| ~ ssList(X44)
| memberP(app(X43,X44),X42)
| ~ memberP(X43,X42) )
& ( ~ ssItem(X42)
| ~ ssList(X43)
| ~ ssList(X44)
| memberP(X44,X42)
| memberP(X43,X42)
| ~ memberP(app(X43,X44),X42) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax36])])])])]) ).
fof(c_0_6,negated_conjecture,
! [X22,X23,X24,X25,X26,X27,X28,X29] :
( ( nil != esk3_0
| nil = esk4_0 )
& ~ memberP(esk2_0,esk7_0)
& memberP(esk1_0,esk7_0)
& ssItem(esk7_0)
& ( ~ lt(X28,X26)
| app(X29,cons(X28,nil)) != esk3_0
| ~ ssList(X29)
| ~ ssItem(X28)
| app(cons(X26,nil),X27) != esk6_0
| ~ ssList(X27)
| ~ ssItem(X26) )
& ( ~ lt(X22,X24)
| app(cons(X24,nil),X25) != esk3_0
| ~ ssList(X25)
| ~ ssItem(X24)
| app(X23,cons(X22,nil)) != esk5_0
| ~ ssList(X23)
| ~ ssItem(X22) )
& strictorderedP(esk3_0)
& app(app(esk5_0,esk3_0),esk6_0) = esk4_0
& ssList(esk6_0)
& ssList(esk5_0)
& esk1_0 = esk3_0
& esk2_0 = esk4_0
& ssList(esk4_0)
& ssList(esk3_0)
& ssList(esk2_0)
& ssList(esk1_0) ),
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_4])])])])]) ).
cnf(c_0_7,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ memberP(X1,X2)
| memberP(app(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
app(app(esk5_0,esk3_0),esk6_0) = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
ssList(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
~ memberP(esk2_0,esk7_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(app(esk5_0,esk3_0))
| ~ memberP(app(esk5_0,esk3_0),X1)
| memberP(esk4_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9])]) ).
cnf(c_0_13,plain,
( ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ memberP(X1,X2)
| memberP(app(X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_14,negated_conjecture,
ssList(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,negated_conjecture,
ssList(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,negated_conjecture,
memberP(esk1_0,esk7_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_18,negated_conjecture,
~ memberP(esk4_0,esk7_0),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_19,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(app(esk5_0,esk3_0))
| ~ memberP(esk3_0,X1)
| memberP(esk4_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]) ).
cnf(c_0_20,negated_conjecture,
memberP(esk3_0,esk7_0),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
ssItem(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_22,plain,
! [X64,X65] :
( ssList(app(X64,X65))
| ~ ssList(X65)
| ~ ssList(X64) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
cnf(c_0_23,negated_conjecture,
~ ssList(app(esk5_0,esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]) ).
cnf(c_0_24,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_15]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC404+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 08:22:47 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 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
% 0.08/0.45 % Version: 3.5.1
% 0.08/0.45 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.08/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.08/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.08/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.45 % Starting sh5l with 300s (1) cores
% 0.08/0.45 % new_bool_3 with pid 2478258 completed with status 0
% 0.08/0.45 % Result found by new_bool_3
% 0.08/0.45 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.08/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.08/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.08/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.08/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.08/0.45 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.08/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.45 % SubtermCWHack with pid 2478261 completed with status 0
% 0.08/0.45 % Result found by SubtermCWHack
% 0.08/0.45 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.08/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.08/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.08/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.08/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.08/0.45 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.08/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.45 % Preprocessing time : 0.002 s
% 0.08/0.45
% 0.08/0.45 % Proof found!
% 0.08/0.45 % SZS status Theorem
% 0.08/0.45 % SZS output start CNFRefutation
% See solution above
% 0.08/0.45 % Parsed axioms : 96
% 0.08/0.45 % Removed by relevancy pruning/SinE : 52
% 0.08/0.45 % Initial clauses : 88
% 0.08/0.45 % Removed in clause preprocessing : 1
% 0.08/0.45 % Initial clauses in saturation : 87
% 0.08/0.45 % Processed clauses : 229
% 0.08/0.45 % ...of these trivial : 0
% 0.08/0.45 % ...subsumed : 89
% 0.08/0.45 % ...remaining for further processing : 140
% 0.08/0.45 % Other redundant clauses eliminated : 19
% 0.08/0.45 % Clauses deleted for lack of memory : 0
% 0.08/0.45 % Backward-subsumed : 55
% 0.08/0.45 % Backward-rewritten : 2
% 0.08/0.45 % Generated clauses : 587
% 0.08/0.45 % ...of the previous two non-redundant : 429
% 0.08/0.45 % ...aggressively subsumed : 0
% 0.08/0.45 % Contextual simplify-reflections : 2
% 0.08/0.45 % Paramodulations : 564
% 0.08/0.45 % Factorizations : 0
% 0.08/0.45 % NegExts : 0
% 0.08/0.45 % Equation resolutions : 24
% 0.08/0.45 % Disequality decompositions : 0
% 0.08/0.45 % Total rewrite steps : 607
% 0.08/0.45 % ...of those cached : 597
% 0.08/0.45 % Propositional unsat checks : 0
% 0.08/0.45 % Propositional check models : 0
% 0.08/0.45 % Propositional check unsatisfiable : 0
% 0.08/0.45 % Propositional clauses : 0
% 0.08/0.45 % Propositional clauses after purity: 0
% 0.08/0.45 % Propositional unsat core size : 0
% 0.08/0.45 % Propositional preprocessing time : 0.000
% 0.08/0.45 % Propositional encoding time : 0.000
% 0.08/0.45 % Propositional solver time : 0.000
% 0.08/0.45 % Success case prop preproc time : 0.000
% 0.08/0.45 % Success case prop encoding time : 0.000
% 0.08/0.45 % Success case prop solver time : 0.000
% 0.08/0.45 % Current number of processed clauses : 79
% 0.08/0.45 % Positive orientable unit clauses : 15
% 0.08/0.45 % Positive unorientable unit clauses: 0
% 0.08/0.45 % Negative unit clauses : 6
% 0.08/0.45 % Non-unit-clauses : 58
% 0.08/0.45 % Current number of unprocessed clauses: 123
% 0.08/0.45 % ...number of literals in the above : 651
% 0.08/0.45 % Current number of archived formulas : 0
% 0.08/0.45 % Current number of archived clauses : 57
% 0.08/0.45 % Clause-clause subsumption calls (NU) : 1641
% 0.08/0.45 % Rec. Clause-clause subsumption calls : 1411
% 0.08/0.45 % Non-unit clause-clause subsumptions : 101
% 0.08/0.45 % Unit Clause-clause subsumption calls : 141
% 0.08/0.45 % Rewrite failures with RHS unbound : 0
% 0.08/0.45 % BW rewrite match attempts : 2
% 0.08/0.45 % BW rewrite match successes : 2
% 0.08/0.45 % Condensation attempts : 0
% 0.08/0.45 % Condensation successes : 0
% 0.08/0.45 % Termbank termtop insertions : 15686
% 0.08/0.45 % Search garbage collected termcells : 2340
% 0.08/0.45
% 0.08/0.45 % -------------------------------------------------
% 0.08/0.45 % User time : 0.022 s
% 0.08/0.45 % System time : 0.003 s
% 0.08/0.45 % Total time : 0.025 s
% 0.08/0.45 % Maximum resident set size: 3972 pages
% 0.08/0.45
% 0.08/0.45 % -------------------------------------------------
% 0.08/0.45 % User time : 0.026 s
% 0.08/0.45 % System time : 0.007 s
% 0.08/0.45 % Total time : 0.033 s
% 0.08/0.45 % Maximum resident set size: 4864 pages
% 0.08/0.45 % E exiting
%------------------------------------------------------------------------------