%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC042+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 02:42:44 PM UTC 2026
% Result : Theorem 0.23s 5.73s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 13 unt; 0 def)
% Number of atoms : 121 ( 61 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 144 ( 46 ~; 43 |; 36 &)
% ( 1 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 25 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( nil = X3
& nil != X4 )
| ! [X5] :
( ssList(X5)
=> ( ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( leq(X8,X6)
& app(X9,cons(X8,nil)) = X3
& ssList(X9) )
& ssItem(X8) )
& app(cons(X6,nil),X7) = X5
& ssList(X7) )
& ssItem(X6) )
| ~ totalorderedP(X3)
| app(X3,X5) != X4 ) )
| nil = X1
| X1 != X3
| X2 != X4
| nil != X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X1
& nil = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(c_0_3,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( nil = X3
& nil != X4 )
| ! [X5] :
( ssList(X5)
=> ( ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( leq(X8,X6)
& app(X9,cons(X8,nil)) = X3
& ssList(X9) )
& ssItem(X8) )
& app(cons(X6,nil),X7) = X5
& ssList(X7) )
& ssItem(X6) )
| ~ totalorderedP(X3)
| app(X3,X5) != X4 ) )
| nil = X1
| X1 != X3
| X2 != X4
| nil != X2 ) ) ) ) ),
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 )
| ! [X5] :
( ssList(X5)
=> ( ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( leq(X8,X6)
& app(X9,cons(X8,nil)) = X3
& ssList(X9) )
& ssItem(X8) )
& app(cons(X6,nil),X7) = X5
& ssList(X7) )
& ssItem(X6) )
| ~ totalorderedP(X3)
| app(X3,X5) != X4 ) )
| nil = X1
| X1 != X3
| X2 != X4
| nil != X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_5,negated_conjecture,
! [X15,X16,X17,X18] :
( ( nil != esk3_0
| nil = esk4_0 )
& ( ~ leq(X17,X15)
| app(X18,cons(X17,nil)) != esk3_0
| ~ ssList(X18)
| ~ ssItem(X17)
| app(cons(X15,nil),X16) != esk5_0
| ~ ssList(X16)
| ~ ssItem(X15) )
& totalorderedP(esk3_0)
& app(esk3_0,esk5_0) = esk4_0
& ssList(esk5_0)
& nil != esk1_0
& esk1_0 = esk3_0
& esk2_0 = esk4_0
& nil = esk2_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_6,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_7,negated_conjecture,
nil = esk2_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
! [X54,X55] :
( ( ~ ssList(X54)
| ~ ssList(X55)
| nil = app(X54,X55)
| nil != X54
| nil != X55 )
& ( ~ ssList(X54)
| ~ ssList(X55)
| nil != app(X54,X55)
| nil = X54 )
& ( ~ ssList(X54)
| ~ ssList(X55)
| nil != app(X54,X55)
| nil = X55 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])])]) ).
cnf(c_0_9,negated_conjecture,
app(esk3_0,esk5_0) = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
esk4_0 = nil,
inference(rw,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_11,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != app(X2,X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
app(esk3_0,esk5_0) = nil,
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,negated_conjecture,
ssList(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_14,negated_conjecture,
ssList(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_15,plain,
! [X56] :
( app(X56,nil) = X56
| ~ ssList(X56) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
cnf(c_0_16,negated_conjecture,
esk5_0 = nil,
inference(cn,[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])]) ).
cnf(c_0_17,negated_conjecture,
nil != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_19,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,negated_conjecture,
app(esk3_0,nil) = nil,
inference(rw,[status(thm)],[c_0_12,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
esk3_0 != nil,
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_13])]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC042+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/5.66 % Computer : n006.cluster.edu
% 0.20/5.66 % Model : x86_64 x86_64
% 0.20/5.66 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/5.66 % Memory : 8046.5625MB
% 0.20/5.66 % OS : Linux 6.8.0-71-generic
% 0.20/5.66 % CPULimit : 300
% 0.20/5.66 % WCLimit : 300
% 0.20/5.66 % DateTime : Mon Sep 21 07:50:51 UTC 2026
% 0.20/5.66 % CPUTime :
% 0.20/5.67 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/5.71 Running first-order theorem proving
% 0.23/5.71 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
% 0.23/5.73 % Version: 3.5.1
% 0.23/5.73 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.23/5.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/5.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.23/5.73 % Starting new_bool_3 with 300s (1) cores
% 0.23/5.73 % Starting new_bool_1 with 300s (1) cores
% 0.23/5.73 % Starting sh5l with 300s (1) cores
% 0.23/5.73 % new_bool_3 with pid 2354306 completed with status 0
% 0.23/5.73 % Result found by new_bool_3
% 0.23/5.73 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.23/5.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/5.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.23/5.73 % Starting new_bool_3 with 300s (1) cores
% 0.23/5.73 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/5.73 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/5.73 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.23/5.73 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/5.73 % Starting SubtermCWHack with 31s (1) cores
% 0.23/5.73 % SubtermCWHack with pid 2354309 completed with status 0
% 0.23/5.73 % Result found by SubtermCWHack
% 0.23/5.73 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.23/5.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/5.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.23/5.73 % Starting new_bool_3 with 300s (1) cores
% 0.23/5.73 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/5.73 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/5.73 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.23/5.73 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/5.73 % Starting SubtermCWHack with 31s (1) cores
% 0.23/5.73 % Preprocessing time : 0.002 s
% 0.23/5.73
% 0.23/5.73 % Proof found!
% 0.23/5.73 % SZS status Theorem
% 0.23/5.73 % SZS output start CNFRefutation
% See solution above
% 0.23/5.73 % Parsed axioms : 96
% 0.23/5.73 % Removed by relevancy pruning/SinE : 56
% 0.23/5.73 % Initial clauses : 74
% 0.23/5.73 % Removed in clause preprocessing : 1
% 0.23/5.73 % Initial clauses in saturation : 73
% 0.23/5.73 % Processed clauses : 57
% 0.23/5.73 % ...of these trivial : 1
% 0.23/5.73 % ...subsumed : 4
% 0.23/5.73 % ...remaining for further processing : 52
% 0.23/5.73 % Other redundant clauses eliminated : 4
% 0.23/5.73 % Clauses deleted for lack of memory : 0
% 0.23/5.73 % Backward-subsumed : 0
% 0.23/5.73 % Backward-rewritten : 5
% 0.23/5.73 % Generated clauses : 25
% 0.23/5.73 % ...of the previous two non-redundant : 13
% 0.23/5.73 % ...aggressively subsumed : 0
% 0.23/5.73 % Contextual simplify-reflections : 0
% 0.23/5.73 % Paramodulations : 22
% 0.23/5.73 % Factorizations : 0
% 0.23/5.73 % NegExts : 0
% 0.23/5.73 % Equation resolutions : 4
% 0.23/5.73 % Disequality decompositions : 0
% 0.23/5.73 % Total rewrite steps : 29
% 0.23/5.73 % ...of those cached : 22
% 0.23/5.73 % Propositional unsat checks : 0
% 0.23/5.73 % Propositional check models : 0
% 0.23/5.73 % Propositional check unsatisfiable : 0
% 0.23/5.73 % Propositional clauses : 0
% 0.23/5.73 % Propositional clauses after purity: 0
% 0.23/5.73 % Propositional unsat core size : 0
% 0.23/5.73 % Propositional preprocessing time : 0.000
% 0.23/5.73 % Propositional encoding time : 0.000
% 0.23/5.73 % Propositional solver time : 0.000
% 0.23/5.73 % Success case prop preproc time : 0.000
% 0.23/5.73 % Success case prop encoding time : 0.000
% 0.23/5.73 % Success case prop solver time : 0.000
% 0.23/5.73 % Current number of processed clauses : 44
% 0.23/5.73 % Positive orientable unit clauses : 12
% 0.23/5.73 % Positive unorientable unit clauses: 0
% 0.23/5.73 % Negative unit clauses : 2
% 0.23/5.73 % Non-unit-clauses : 30
% 0.23/5.73 % Current number of unprocessed clauses: 29
% 0.23/5.73 % ...number of literals in the above : 150
% 0.23/5.73 % Current number of archived formulas : 0
% 0.23/5.73 % Current number of archived clauses : 5
% 0.23/5.73 % Clause-clause subsumption calls (NU) : 59
% 0.23/5.73 % Rec. Clause-clause subsumption calls : 28
% 0.23/5.73 % Non-unit clause-clause subsumptions : 4
% 0.23/5.73 % Unit Clause-clause subsumption calls : 14
% 0.23/5.73 % Rewrite failures with RHS unbound : 0
% 0.23/5.73 % BW rewrite match attempts : 4
% 0.23/5.73 % BW rewrite match successes : 4
% 0.23/5.73 % Condensation attempts : 0
% 0.23/5.73 % Condensation successes : 0
% 0.23/5.73 % Termbank termtop insertions : 7324
% 0.23/5.73 % Search garbage collected termcells : 1983
% 0.23/5.73
% 0.23/5.73 % -------------------------------------------------
% 0.23/5.73 % User time : 0.007 s
% 0.23/5.73 % System time : 0.002 s
% 0.23/5.73 % Total time : 0.009 s
% 0.23/5.73 % Maximum resident set size: 3728 pages
% 0.23/5.73
% 0.23/5.73 % -------------------------------------------------
% 0.23/5.73 % User time : 0.011 s
% 0.23/5.73 % System time : 0.006 s
% 0.23/5.73 % Total time : 0.017 s
% 0.23/5.73 % Maximum resident set size: 4608 pages
% 0.23/5.73 % E exiting
%------------------------------------------------------------------------------