%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC104+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 : n026.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 02:43:01 PM UTC 2026
% Result : Theorem 0.15s 10.67s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 12 unt; 0 def)
% Number of atoms : 167 ( 46 equ)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 207 ( 74 ~; 67 |; 40 &)
% ( 3 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 34 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( frontsegP(X2,X1)
& neq(X1,nil) )
| ( 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 ) )
| ~ neq(X2,nil)
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( app(X2,X3) = X1
& ssList(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( frontsegP(X2,X1)
& neq(X1,nil) )
| ( 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 ) )
| ~ neq(X2,nil)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( frontsegP(X2,X1)
& neq(X1,nil) )
| ( 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 ) )
| ~ neq(X2,nil)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_7,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
fof(c_0_8,negated_conjecture,
! [X15,X16,X17,X18] :
( ( ~ frontsegP(esk2_0,esk1_0)
| ~ neq(esk1_0,nil) )
& ( 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)
& neq(esk2_0,nil)
& 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_6])])])])]) ).
fof(c_0_9,plain,
! [X19,X20,X22] :
( ( ~ ssList(X19)
| ~ ssList(X20)
| frontsegP(X19,X20)
| app(X20,X22) != X19
| ~ ssList(X22) )
& ( ~ ssList(X19)
| ~ ssList(X20)
| ~ frontsegP(X19,X20)
| app(X20,esk6_2(X19,X20)) = X19 )
& ( ~ ssList(X19)
| ~ ssList(X20)
| ~ frontsegP(X19,X20)
| ssList(esk6_2(X19,X20)) ) ),
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)],[ax5])])])])])]) ).
fof(c_0_10,plain,
! [X60,X61] :
( ssList(app(X60,X61))
| ~ ssList(X61)
| ~ ssList(X60) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
fof(c_0_11,plain,
! [X40,X41] :
( ( ~ ssList(X40)
| ~ ssList(X41)
| neq(X40,X41)
| X40 = X41 )
& ( ~ ssList(X40)
| ~ ssList(X41)
| X40 != X41
| ~ neq(X40,X41) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).
cnf(c_0_12,negated_conjecture,
neq(esk2_0,nil),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
( ~ frontsegP(esk2_0,esk1_0)
| ~ neq(esk1_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| app(X2,X1) != X3
| ~ ssList(X1)
| frontsegP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,negated_conjecture,
neq(esk4_0,nil),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_20,negated_conjecture,
( nil != esk3_0
| nil = esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,negated_conjecture,
( ~ neq(esk3_0,nil)
| ~ frontsegP(esk4_0,esk3_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_13]),c_0_15]) ).
cnf(c_0_22,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_23,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_24,negated_conjecture,
ssList(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| frontsegP(app(X1,X2),X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_16]),c_0_17]) ).
cnf(c_0_26,negated_conjecture,
app(esk3_0,esk5_0) = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_27,negated_conjecture,
ssList(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_28,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_29,negated_conjecture,
( esk3_0 != nil
| neq(nil,nil) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_30,negated_conjecture,
( ~ frontsegP(esk4_0,esk3_0)
| esk3_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_31,negated_conjecture,
frontsegP(esk4_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_24]),c_0_27])]) ).
cnf(c_0_32,negated_conjecture,
esk3_0 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_23])]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC104+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/10.55 % Computer : n026.cluster.edu
% 0.11/10.55 % Model : x86_64 x86_64
% 0.11/10.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.55 % Memory : 8046.5625MB
% 0.11/10.55 % OS : Linux 6.8.0-71-generic
% 0.11/10.55 % CPULimit : 300
% 0.11/10.55 % WCLimit : 300
% 0.11/10.55 % DateTime : Mon Sep 21 07:59:03 UTC 2026
% 0.11/10.55 % CPUTime :
% 0.11/10.55 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/10.61 Running first-order theorem proving
% 0.15/10.61 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
% 0.15/10.67 % Version: 3.5.1
% 0.15/10.67 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/10.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/10.67 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/10.67 % Starting new_bool_3 with 300s (1) cores
% 0.15/10.67 % Starting new_bool_1 with 300s (1) cores
% 0.15/10.67 % Starting sh5l with 300s (1) cores
% 0.15/10.67 % new_bool_3 with pid 1783777 completed with status 0
% 0.15/10.67 % Result found by new_bool_3
% 0.15/10.67 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/10.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/10.67 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/10.67 % Starting new_bool_3 with 300s (1) cores
% 0.15/10.67 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/10.67 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/10.67 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.15/10.67 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/10.67 % Starting SubtermCWHack with 31s (1) cores
% 0.15/10.67 % SubtermCWHack with pid 1783780 completed with status 0
% 0.15/10.67 % Result found by SubtermCWHack
% 0.15/10.67 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/10.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/10.67 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/10.67 % Starting new_bool_3 with 300s (1) cores
% 0.15/10.67 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/10.67 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/10.67 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.15/10.67 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/10.67 % Starting SubtermCWHack with 31s (1) cores
% 0.15/10.67 % Preprocessing time : 0.003 s
% 0.15/10.67
% 0.15/10.67 % Proof found!
% 0.15/10.67 % SZS status Theorem
% 0.15/10.67 % SZS output start CNFRefutation
% See solution above
% 0.15/10.67 % Parsed axioms : 96
% 0.15/10.67 % Removed by relevancy pruning/SinE : 46
% 0.15/10.67 % Initial clauses : 91
% 0.15/10.67 % Removed in clause preprocessing : 1
% 0.15/10.67 % Initial clauses in saturation : 90
% 0.15/10.67 % Processed clauses : 100
% 0.15/10.67 % ...of these trivial : 0
% 0.15/10.67 % ...subsumed : 9
% 0.15/10.67 % ...remaining for further processing : 91
% 0.15/10.67 % Other redundant clauses eliminated : 10
% 0.15/10.67 % Clauses deleted for lack of memory : 0
% 0.15/10.67 % Backward-subsumed : 7
% 0.15/10.67 % Backward-rewritten : 5
% 0.15/10.67 % Generated clauses : 81
% 0.15/10.67 % ...of the previous two non-redundant : 58
% 0.15/10.67 % ...aggressively subsumed : 0
% 0.15/10.67 % Contextual simplify-reflections : 1
% 0.15/10.67 % Paramodulations : 71
% 0.15/10.67 % Factorizations : 0
% 0.15/10.67 % NegExts : 0
% 0.15/10.67 % Equation resolutions : 11
% 0.15/10.67 % Disequality decompositions : 0
% 0.15/10.67 % Total rewrite steps : 59
% 0.15/10.67 % ...of those cached : 49
% 0.15/10.67 % Propositional unsat checks : 0
% 0.15/10.67 % Propositional check models : 0
% 0.15/10.67 % Propositional check unsatisfiable : 0
% 0.15/10.67 % Propositional clauses : 0
% 0.15/10.67 % Propositional clauses after purity: 0
% 0.15/10.67 % Propositional unsat core size : 0
% 0.15/10.67 % Propositional preprocessing time : 0.000
% 0.15/10.67 % Propositional encoding time : 0.000
% 0.15/10.67 % Propositional solver time : 0.000
% 0.15/10.67 % Success case prop preproc time : 0.000
% 0.15/10.67 % Success case prop encoding time : 0.000
% 0.15/10.67 % Success case prop solver time : 0.000
% 0.15/10.67 % Current number of processed clauses : 72
% 0.15/10.67 % Positive orientable unit clauses : 18
% 0.15/10.67 % Positive unorientable unit clauses: 0
% 0.15/10.67 % Negative unit clauses : 4
% 0.15/10.67 % Non-unit-clauses : 50
% 0.15/10.67 % Current number of unprocessed clauses: 46
% 0.15/10.67 % ...number of literals in the above : 253
% 0.15/10.67 % Current number of archived formulas : 0
% 0.15/10.67 % Current number of archived clauses : 12
% 0.15/10.67 % Clause-clause subsumption calls (NU) : 492
% 0.15/10.67 % Rec. Clause-clause subsumption calls : 224
% 0.15/10.67 % Non-unit clause-clause subsumptions : 9
% 0.15/10.67 % Unit Clause-clause subsumption calls : 51
% 0.15/10.67 % Rewrite failures with RHS unbound : 0
% 0.15/10.67 % BW rewrite match attempts : 3
% 0.15/10.67 % BW rewrite match successes : 3
% 0.15/10.67 % Condensation attempts : 0
% 0.15/10.67 % Condensation successes : 0
% 0.15/10.67 % Termbank termtop insertions : 9812
% 0.15/10.67 % Search garbage collected termcells : 2312
% 0.15/10.67
% 0.15/10.67 % -------------------------------------------------
% 0.15/10.67 % User time : 0.020 s
% 0.15/10.67 % System time : 0.006 s
% 0.15/10.67 % Total time : 0.026 s
% 0.15/10.67 % Maximum resident set size: 3712 pages
% 0.15/10.67
% 0.15/10.67 % -------------------------------------------------
% 0.15/10.67 % User time : 0.027 s
% 0.15/10.67 % System time : 0.011 s
% 0.15/10.67 % Total time : 0.038 s
% 0.15/10.67 % Maximum resident set size: 4608 pages
% 0.15/10.67 % E exiting
%------------------------------------------------------------------------------