%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC024+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 : n002.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 02:42:39 PM UTC 2026
% Result : Theorem 0.14s 5.87s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 13 unt; 0 def)
% Number of atoms : 180 ( 46 equ)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 225 ( 83 ~; 75 |; 40 &)
% ( 3 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 36 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( nil = X3
& nil != X4 )
| ! [X6] :
( ssList(X6)
=> ( ? [X7] :
( ? [X8] :
( ? [X9] :
( app(X9,cons(X7,nil)) = X3
& ssList(X9) )
& app(cons(X7,nil),X8) = X6
& ssList(X8) )
& ssItem(X7) )
| ~ equalelemsP(X3)
| app(X3,X6) != X4 ) )
| ? [X5] :
( frontsegP(X1,X5)
& frontsegP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| ~ 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(ax42,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax42) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( nil = X3
& nil != X4 )
| ! [X6] :
( ssList(X6)
=> ( ? [X7] :
( ? [X8] :
( ? [X9] :
( app(X9,cons(X7,nil)) = X3
& ssList(X9) )
& app(cons(X7,nil),X8) = X6
& ssList(X8) )
& ssItem(X7) )
| ~ equalelemsP(X3)
| app(X3,X6) != X4 ) )
| ? [X5] :
( frontsegP(X1,X5)
& frontsegP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| ~ neq(X2,nil)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( nil = X3
& nil != X4 )
| ! [X6] :
( ssList(X6)
=> ( ? [X7] :
( ? [X8] :
( ? [X9] :
( app(X9,cons(X7,nil)) = X3
& ssList(X9) )
& app(cons(X7,nil),X8) = X6
& ssList(X8) )
& ssItem(X7) )
| ~ equalelemsP(X3)
| app(X3,X6) != X4 ) )
| ? [X5] :
( frontsegP(X1,X5)
& frontsegP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| ~ neq(X2,nil)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_8,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
fof(c_0_9,negated_conjecture,
! [X14,X16,X17,X18] :
( ( nil != esk3_0
| nil = esk4_0 )
& ( app(X18,cons(X16,nil)) != esk3_0
| ~ ssList(X18)
| app(cons(X16,nil),X17) != esk5_0
| ~ ssList(X17)
| ~ ssItem(X16) )
& equalelemsP(esk3_0)
& app(esk3_0,esk5_0) = esk4_0
& ssList(esk5_0)
& ( ~ frontsegP(esk1_0,X14)
| ~ frontsegP(esk2_0,X14)
| ~ neq(X14,nil)
| ~ ssList(X14) )
& 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_7])])])])]) ).
fof(c_0_10,plain,
! [X64,X65,X67] :
( ( ~ ssList(X64)
| ~ ssList(X65)
| frontsegP(X64,X65)
| app(X65,X67) != X64
| ~ ssList(X67) )
& ( ~ ssList(X64)
| ~ ssList(X65)
| ~ frontsegP(X64,X65)
| app(X65,esk14_2(X64,X65)) = X64 )
& ( ~ ssList(X64)
| ~ ssList(X65)
| ~ frontsegP(X64,X65)
| ssList(esk14_2(X64,X65)) ) ),
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_11,plain,
! [X24,X25] :
( ssList(app(X24,X25))
| ~ ssList(X25)
| ~ ssList(X24) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
fof(c_0_12,plain,
! [X85,X86] :
( ( ~ ssList(X85)
| ~ ssList(X86)
| neq(X85,X86)
| X85 = X86 )
& ( ~ ssList(X85)
| ~ ssList(X86)
| X85 != X86
| ~ neq(X85,X86) ) ),
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_8])])])])]) ).
cnf(c_0_13,negated_conjecture,
neq(esk2_0,nil),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
( ~ frontsegP(esk1_0,X1)
| ~ frontsegP(esk2_0,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| app(X2,X1) != X3
| ~ ssList(X1)
| frontsegP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,negated_conjecture,
neq(esk4_0,nil),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_21,negated_conjecture,
( nil != esk3_0
| nil = esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_22,negated_conjecture,
( ~ neq(X1,nil)
| ~ ssList(X1)
| ~ frontsegP(esk4_0,X1)
| ~ frontsegP(esk3_0,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_14]) ).
cnf(c_0_23,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_24,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_25,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| frontsegP(app(X1,X2),X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_17]),c_0_18]) ).
cnf(c_0_26,negated_conjecture,
app(esk3_0,esk5_0) = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,negated_conjecture,
ssList(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_28,negated_conjecture,
ssList(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_29,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_30,negated_conjecture,
( esk3_0 != nil
| neq(nil,nil) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_31,negated_conjecture,
( ~ ssList(X1)
| ~ frontsegP(esk4_0,X1)
| ~ frontsegP(esk3_0,X1)
| X1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_32,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_27]),c_0_28])]) ).
cnf(c_0_33,negated_conjecture,
esk3_0 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_24])]) ).
fof(c_0_34,plain,
! [X73] :
( frontsegP(X73,X73)
| ~ ssList(X73) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax42])])]) ).
cnf(c_0_35,negated_conjecture,
~ frontsegP(esk3_0,esk3_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_27])]),c_0_33]) ).
cnf(c_0_36,plain,
( ~ ssList(X1)
| frontsegP(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC024+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/5.80 % Computer : n002.cluster.edu
% 0.12/5.80 % Model : x86_64 x86_64
% 0.12/5.80 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.80 % Memory : 8046.5625MB
% 0.12/5.80 % OS : Linux 6.8.0-71-generic
% 0.12/5.80 % CPULimit : 300
% 0.14/5.80 % WCLimit : 300
% 0.14/5.80 % DateTime : Mon Sep 21 07:52:39 UTC 2026
% 0.14/5.80 % CPUTime :
% 0.14/5.80 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/5.84 Running first-order theorem proving
% 0.14/5.84 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
% 0.14/5.86 % Version: 3.5.1
% 0.14/5.86 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/5.86 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.86 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/5.86 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.86 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.86 % Starting sh5l with 300s (1) cores
% 0.14/5.86 % new_bool_3 with pid 2803872 completed with status 0
% 0.14/5.86 % Result found by new_bool_3
% 0.14/5.86 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/5.86 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.86 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/5.86 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.86 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/5.86 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/5.86 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.14/5.86 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/5.86 % Starting SubtermCWHack with 31s (1) cores
% 0.14/5.86 % SubtermCWHack with pid 2803875 completed with status 0
% 0.14/5.86 % Result found by SubtermCWHack
% 0.14/5.87 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/5.87 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.87 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/5.87 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.87 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/5.87 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/5.87 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.14/5.87 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/5.87 % Starting SubtermCWHack with 31s (1) cores
% 0.14/5.87 % Preprocessing time : 0.002 s
% 0.14/5.87
% 0.14/5.87 % Proof found!
% 0.14/5.87 % SZS status Theorem
% 0.14/5.87 % SZS output start CNFRefutation
% See solution above
% 0.14/5.87 % Parsed axioms : 96
% 0.14/5.87 % Removed by relevancy pruning/SinE : 66
% 0.14/5.87 % Initial clauses : 62
% 0.14/5.87 % Removed in clause preprocessing : 0
% 0.14/5.87 % Initial clauses in saturation : 62
% 0.14/5.87 % Processed clauses : 65
% 0.14/5.87 % ...of these trivial : 0
% 0.14/5.87 % ...subsumed : 4
% 0.14/5.87 % ...remaining for further processing : 61
% 0.14/5.87 % Other redundant clauses eliminated : 6
% 0.14/5.87 % Clauses deleted for lack of memory : 0
% 0.14/5.87 % Backward-subsumed : 4
% 0.14/5.87 % Backward-rewritten : 2
% 0.14/5.87 % Generated clauses : 38
% 0.14/5.87 % ...of the previous two non-redundant : 27
% 0.14/5.87 % ...aggressively subsumed : 0
% 0.14/5.87 % Contextual simplify-reflections : 1
% 0.14/5.87 % Paramodulations : 33
% 0.14/5.87 % Factorizations : 0
% 0.14/5.87 % NegExts : 0
% 0.14/5.87 % Equation resolutions : 6
% 0.14/5.87 % Disequality decompositions : 0
% 0.14/5.87 % Total rewrite steps : 39
% 0.14/5.87 % ...of those cached : 32
% 0.14/5.87 % Propositional unsat checks : 0
% 0.14/5.87 % Propositional check models : 0
% 0.14/5.87 % Propositional check unsatisfiable : 0
% 0.14/5.87 % Propositional clauses : 0
% 0.14/5.87 % Propositional clauses after purity: 0
% 0.14/5.87 % Propositional unsat core size : 0
% 0.14/5.87 % Propositional preprocessing time : 0.000
% 0.14/5.87 % Propositional encoding time : 0.000
% 0.14/5.87 % Propositional solver time : 0.000
% 0.14/5.87 % Success case prop preproc time : 0.000
% 0.14/5.87 % Success case prop encoding time : 0.000
% 0.14/5.87 % Success case prop solver time : 0.000
% 0.14/5.87 % Current number of processed clauses : 50
% 0.14/5.87 % Positive orientable unit clauses : 15
% 0.14/5.87 % Positive unorientable unit clauses: 0
% 0.14/5.87 % Negative unit clauses : 5
% 0.14/5.87 % Non-unit-clauses : 30
% 0.14/5.87 % Current number of unprocessed clauses: 24
% 0.14/5.87 % ...number of literals in the above : 116
% 0.14/5.87 % Current number of archived formulas : 0
% 0.14/5.87 % Current number of archived clauses : 6
% 0.14/5.87 % Clause-clause subsumption calls (NU) : 134
% 0.14/5.87 % Rec. Clause-clause subsumption calls : 64
% 0.14/5.87 % Non-unit clause-clause subsumptions : 3
% 0.14/5.87 % Unit Clause-clause subsumption calls : 24
% 0.14/5.87 % Rewrite failures with RHS unbound : 0
% 0.14/5.87 % BW rewrite match attempts : 2
% 0.14/5.87 % BW rewrite match successes : 2
% 0.14/5.87 % Condensation attempts : 0
% 0.14/5.87 % Condensation successes : 0
% 0.14/5.87 % Termbank termtop insertions : 6503
% 0.14/5.87 % Search garbage collected termcells : 1817
% 0.14/5.87
% 0.14/5.87 % -------------------------------------------------
% 0.14/5.87 % User time : 0.006 s
% 0.14/5.87 % System time : 0.004 s
% 0.14/5.87 % Total time : 0.010 s
% 0.14/5.87 % Maximum resident set size: 4020 pages
% 0.14/5.87
% 0.14/5.87 % -------------------------------------------------
% 0.14/5.87 % User time : 0.010 s
% 0.14/5.87 % System time : 0.008 s
% 0.14/5.87 % Total time : 0.018 s
% 0.14/5.87 % Maximum resident set size: 4864 pages
% 0.14/5.87 % E exiting
%------------------------------------------------------------------------------