%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC039+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 : n018.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 02:42:43 PM UTC 2026
% Result : Theorem 0.26s 0.54s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 14 unt; 0 def)
% Number of atoms : 168 ( 77 equ)
% Maximal formula atoms : 44 ( 5 avg)
% Number of connectives : 195 ( 59 ~; 70 |; 39 &)
% ( 1 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 33 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( ? [X9] :
( lt(X9,X5)
& memberP(X7,X9)
& ssItem(X9) )
| ? [X8] :
( lt(X5,X8)
& memberP(X6,X8)
& ssItem(X8) )
| app(app(X6,X3),X7) != X4
| cons(X5,nil) != X3 ) ) ) ) )
| nil = X1
| X1 != X3
| X2 != X4
| nil != X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X1
& nil = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( ? [X9] :
( lt(X9,X5)
& memberP(X7,X9)
& ssItem(X9) )
| ? [X8] :
( lt(X5,X8)
& memberP(X6,X8)
& ssItem(X8) )
| app(app(X6,X3),X7) != X4
| cons(X5,nil) != X3 ) ) ) ) )
| nil = X1
| X1 != X3
| X2 != X4
| nil != X2 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( ? [X9] :
( lt(X9,X5)
& memberP(X7,X9)
& ssItem(X9) )
| ? [X8] :
( lt(X5,X8)
& memberP(X6,X8)
& ssItem(X8) )
| app(app(X6,X3),X7) != X4
| cons(X5,nil) != X3 ) ) ) ) )
| nil = X1
| X1 != X3
| X2 != X4
| nil != X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_6,negated_conjecture,
! [X17,X18] :
( ( ~ lt(X18,esk5_0)
| ~ memberP(esk7_0,X18)
| ~ ssItem(X18)
| nil = esk3_0 )
& ( ~ lt(X18,esk5_0)
| ~ memberP(esk7_0,X18)
| ~ ssItem(X18)
| nil = esk4_0 )
& ( ~ lt(esk5_0,X17)
| ~ memberP(esk6_0,X17)
| ~ ssItem(X17)
| nil = esk3_0 )
& ( ~ lt(esk5_0,X17)
| ~ memberP(esk6_0,X17)
| ~ ssItem(X17)
| nil = esk4_0 )
& ( app(app(esk6_0,esk3_0),esk7_0) = esk4_0
| nil = esk3_0 )
& ( app(app(esk6_0,esk3_0),esk7_0) = esk4_0
| nil = esk4_0 )
& ( cons(esk5_0,nil) = esk3_0
| nil = esk3_0 )
& ( cons(esk5_0,nil) = esk3_0
| nil = esk4_0 )
& ( ssList(esk7_0)
| nil = esk3_0 )
& ( ssList(esk7_0)
| nil = esk4_0 )
& ( ssList(esk6_0)
| nil = esk3_0 )
& ( ssList(esk6_0)
| nil = esk4_0 )
& ( ssItem(esk5_0)
| nil = esk3_0 )
& ( ssItem(esk5_0)
| nil = esk4_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(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_5])])])])])]) ).
cnf(c_0_7,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_8,negated_conjecture,
nil = esk2_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
nil != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,plain,
! [X69,X70] :
( ( ~ ssList(X69)
| ~ ssList(X70)
| nil = app(X69,X70)
| nil != X69
| nil != X70 )
& ( ~ ssList(X69)
| ~ ssList(X70)
| nil != app(X69,X70)
| nil = X69 )
& ( ~ ssList(X69)
| ~ ssList(X70)
| nil != app(X69,X70)
| nil = X70 ) ),
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_12,negated_conjecture,
( app(app(esk6_0,esk3_0),esk7_0) = esk4_0
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,negated_conjecture,
esk4_0 = nil,
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_14,negated_conjecture,
esk3_0 != nil,
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
( ssList(esk7_0)
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != app(X2,X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
app(app(esk6_0,esk3_0),esk7_0) = nil,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_18,negated_conjecture,
ssList(esk7_0),
inference(sr,[status(thm)],[c_0_15,c_0_14]) ).
fof(c_0_19,plain,
! [X52,X53] :
( ssList(app(X52,X53))
| ~ ssList(X53)
| ~ ssList(X52) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
cnf(c_0_20,negated_conjecture,
( ssList(esk6_0)
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_21,negated_conjecture,
( ~ ssList(app(esk6_0,esk3_0))
| esk7_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
cnf(c_0_22,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,negated_conjecture,
ssList(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_24,negated_conjecture,
ssList(esk6_0),
inference(sr,[status(thm)],[c_0_20,c_0_14]) ).
fof(c_0_25,plain,
! [X71] :
( app(X71,nil) = X71
| ~ ssList(X71) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
cnf(c_0_26,negated_conjecture,
esk7_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_24])]) ).
cnf(c_0_27,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_28,negated_conjecture,
app(app(esk6_0,esk3_0),nil) = nil,
inference(rw,[status(thm)],[c_0_17,c_0_26]) ).
cnf(c_0_29,negated_conjecture,
( ~ ssList(app(esk6_0,esk3_0))
| app(esk6_0,esk3_0) = nil ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_30,negated_conjecture,
app(esk6_0,esk3_0) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_22]),c_0_23]),c_0_24])]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_30]),c_0_24]),c_0_23])]),c_0_14]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC039+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.40 % Computer : n018.cluster.edu
% 0.17/0.40 % Model : x86_64 x86_64
% 0.17/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.40 % Memory : 8046.5625MB
% 0.17/0.40 % OS : Linux 6.8.0-71-generic
% 0.17/0.40 % CPULimit : 300
% 0.17/0.40 % WCLimit : 300
% 0.17/0.40 % DateTime : Mon Sep 21 07:52:45 UTC 2026
% 0.17/0.41 % CPUTime :
% 0.17/0.41 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.47 Running first-order theorem proving
% 0.21/0.47 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
% 0.26/0.54 % Version: 3.5.1
% 0.26/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.26/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.26/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.26/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.26/0.54 % Starting sh5l with 300s (1) cores
% 0.26/0.54 % new_bool_1 with pid 1381640 completed with status 0
% 0.26/0.54 % Result found by new_bool_1
% 0.26/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.26/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.26/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.26/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.26/0.54 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.26/0.54 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.26/0.54 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.26/0.54 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.54 % Starting SubtermCWHack with 31s (1) cores
% 0.26/0.54 % SubtermCWHack with pid 1381642 completed with status 0
% 0.26/0.54 % Result found by SubtermCWHack
% 0.26/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.26/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.26/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.26/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.26/0.54 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.26/0.54 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.26/0.54 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.26/0.54 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.54 % Starting SubtermCWHack with 31s (1) cores
% 0.26/0.54 % Preprocessing time : 0.003 s
% 0.26/0.54
% 0.26/0.54 % Proof found!
% 0.26/0.54 % SZS status Theorem
% 0.26/0.54 % SZS output start CNFRefutation
% See solution above
% 0.26/0.54 % Parsed axioms : 96
% 0.26/0.54 % Removed by relevancy pruning/SinE : 66
% 0.26/0.54 % Initial clauses : 67
% 0.26/0.54 % Removed in clause preprocessing : 0
% 0.26/0.54 % Initial clauses in saturation : 67
% 0.26/0.54 % Processed clauses : 56
% 0.26/0.54 % ...of these trivial : 7
% 0.26/0.54 % ...subsumed : 4
% 0.26/0.54 % ...remaining for further processing : 45
% 0.26/0.54 % Other redundant clauses eliminated : 3
% 0.26/0.54 % Clauses deleted for lack of memory : 0
% 0.26/0.54 % Backward-subsumed : 0
% 0.26/0.54 % Backward-rewritten : 9
% 0.26/0.54 % Generated clauses : 23
% 0.26/0.54 % ...of the previous two non-redundant : 13
% 0.26/0.54 % ...aggressively subsumed : 0
% 0.26/0.54 % Contextual simplify-reflections : 0
% 0.26/0.54 % Paramodulations : 21
% 0.26/0.54 % Factorizations : 0
% 0.26/0.54 % NegExts : 0
% 0.26/0.54 % Equation resolutions : 3
% 0.26/0.54 % Disequality decompositions : 0
% 0.26/0.54 % Total rewrite steps : 63
% 0.26/0.54 % ...of those cached : 50
% 0.26/0.54 % Propositional unsat checks : 0
% 0.26/0.54 % Propositional check models : 0
% 0.26/0.54 % Propositional check unsatisfiable : 0
% 0.26/0.54 % Propositional clauses : 0
% 0.26/0.54 % Propositional clauses after purity: 0
% 0.26/0.54 % Propositional unsat core size : 0
% 0.26/0.54 % Propositional preprocessing time : 0.000
% 0.26/0.54 % Propositional encoding time : 0.000
% 0.26/0.54 % Propositional solver time : 0.000
% 0.26/0.54 % Success case prop preproc time : 0.000
% 0.26/0.54 % Success case prop encoding time : 0.000
% 0.26/0.54 % Success case prop solver time : 0.000
% 0.26/0.54 % Current number of processed clauses : 34
% 0.26/0.54 % Positive orientable unit clauses : 13
% 0.26/0.54 % Positive unorientable unit clauses: 0
% 0.26/0.54 % Negative unit clauses : 2
% 0.26/0.54 % Non-unit-clauses : 19
% 0.26/0.54 % Current number of unprocessed clauses: 23
% 0.26/0.54 % ...number of literals in the above : 115
% 0.26/0.54 % Current number of archived formulas : 0
% 0.26/0.54 % Current number of archived clauses : 9
% 0.26/0.54 % Clause-clause subsumption calls (NU) : 73
% 0.26/0.54 % Rec. Clause-clause subsumption calls : 35
% 0.26/0.54 % Non-unit clause-clause subsumptions : 2
% 0.26/0.54 % Unit Clause-clause subsumption calls : 6
% 0.26/0.54 % Rewrite failures with RHS unbound : 0
% 0.26/0.54 % BW rewrite match attempts : 5
% 0.26/0.54 % BW rewrite match successes : 5
% 0.26/0.54 % Condensation attempts : 0
% 0.26/0.54 % Condensation successes : 0
% 0.26/0.54 % Termbank termtop insertions : 6351
% 0.26/0.54 % Search garbage collected termcells : 1834
% 0.26/0.54
% 0.26/0.54 % -------------------------------------------------
% 0.26/0.54 % User time : 0.014 s
% 0.26/0.54 % System time : 0.005 s
% 0.26/0.54 % Total time : 0.018 s
% 0.26/0.54 % Maximum resident set size: 3760 pages
% 0.26/0.54
% 0.26/0.54 % -------------------------------------------------
% 0.26/0.54 % User time : 0.020 s
% 0.26/0.54 % System time : 0.011 s
% 0.26/0.54 % Total time : 0.031 s
% 0.26/0.54 % Maximum resident set size: 4608 pages
% 0.26/0.54 % E exiting
%------------------------------------------------------------------------------