%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC046+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 : 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 02:42:45 PM UTC 2026
% Result : Theorem 0.10s 0.44s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 9 unt; 0 def)
% Number of atoms : 152 ( 37 equ)
% Maximal formula atoms : 23 ( 5 avg)
% Number of connectives : 192 ( 69 ~; 69 |; 32 &)
% ( 1 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 28 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ( ( ( ? [X6] :
( segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil)))
& ssList(X6) )
| ~ memberP(X4,X5) )
& memberP(X3,X5) )
| ( memberP(X4,X5)
& ! [X6] :
( ssList(X6)
=> ~ segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) )
& ~ memberP(X3,X5) ) )
& ssItem(X5) )
| nil = X1
| X1 != X3
| X2 != X4
| nil != X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(ax37,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(cons(X2,X3),X1)
<=> ( memberP(X3,X1)
| X1 = X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(ax20,axiom,
! [X1] :
( ssList(X1)
=> ( ? [X2] :
( ? [X3] :
( cons(X3,X2) = X1
& ssItem(X3) )
& ssList(X2) )
| nil = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax20) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ( ( ( ? [X6] :
( segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil)))
& ssList(X6) )
| ~ memberP(X4,X5) )
& memberP(X3,X5) )
| ( memberP(X4,X5)
& ! [X6] :
( ssList(X6)
=> ~ segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) )
& ~ memberP(X3,X5) ) )
& ssItem(X5) )
| 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)
=> ( ? [X5] :
( ( ( ( ? [X6] :
( segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil)))
& ssList(X6) )
| ~ memberP(X4,X5) )
& memberP(X3,X5) )
| ( memberP(X4,X5)
& ! [X6] :
( ssList(X6)
=> ~ segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) )
& ~ memberP(X3,X5) ) )
& ssItem(X5) )
| nil = X1
| X1 != X3
| X2 != X4
| nil != X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_6,negated_conjecture,
! [X11,X13] :
( ( ~ ssItem(X11)
| ~ memberP(esk3_0,X11)
| ~ segmentP(esk4_0,app(app(cons(X11,nil),X13),cons(X11,nil)))
| ~ ssList(X13) )
& ( ~ ssItem(X11)
| ~ memberP(esk3_0,X11)
| memberP(esk4_0,X11) )
& ( ~ ssItem(X11)
| ~ memberP(esk4_0,X11)
| memberP(esk3_0,X11)
| segmentP(esk4_0,app(app(cons(X11,nil),esk5_1(X11)),cons(X11,nil))) )
& ( ~ ssItem(X11)
| ~ memberP(esk4_0,X11)
| memberP(esk3_0,X11)
| ssList(esk5_1(X11)) )
& 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])])])])])]) ).
fof(c_0_7,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
fof(c_0_8,plain,
! [X74,X75,X76] :
( ( ~ ssItem(X74)
| ~ ssItem(X75)
| ~ ssList(X76)
| memberP(cons(X75,X76),X74)
| ~ memberP(X76,X74) )
& ( ~ ssItem(X74)
| ~ ssItem(X75)
| ~ ssList(X76)
| memberP(cons(X75,X76),X74)
| X74 != X75 )
& ( ~ ssItem(X74)
| ~ ssItem(X75)
| ~ ssList(X76)
| memberP(X76,X74)
| X74 = X75
| ~ memberP(cons(X75,X76),X74) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])])]) ).
cnf(c_0_9,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
nil = esk2_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,plain,
! [X77] :
( ~ memberP(nil,X77)
| ~ ssItem(X77) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_12,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X60] :
( ( ~ ssList(X60)
| nil = X60
| cons(esk9_1(X60),esk8_1(X60)) = X60 )
& ( ~ ssList(X60)
| nil = X60
| ssItem(esk9_1(X60)) )
& ( ~ ssList(X60)
| nil = X60
| ssList(esk8_1(X60)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])])]) ).
cnf(c_0_14,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(esk3_0,X1)
| memberP(esk4_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,negated_conjecture,
esk4_0 = nil,
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_16,plain,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| memberP(cons(X1,X2),X1) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( ~ ssList(X1)
| nil = X1
| cons(esk9_1(X1),esk8_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(esk9_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( ~ ssList(X1)
| nil = X1
| ssList(esk8_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,negated_conjecture,
nil != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_23,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(esk3_0,X1) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_24,plain,
( ~ ssList(X1)
| memberP(X1,esk9_1(X1))
| nil = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20]) ).
cnf(c_0_25,negated_conjecture,
ssList(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_26,negated_conjecture,
esk3_0 != nil,
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,negated_conjecture,
~ ssItem(esk9_1(esk3_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_19]),c_0_25])]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC046+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n006.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 07:51:13 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.44 % Version: 3.5.1
% 0.10/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.44 % Starting sh5l with 300s (1) cores
% 0.10/0.44 % new_bool_3 with pid 2355093 completed with status 0
% 0.10/0.44 % Result found by new_bool_3
% 0.10/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.44 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.10/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.44 % SubtermCWHack with pid 2355110 completed with status 0
% 0.10/0.44 % Result found by SubtermCWHack
% 0.10/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.44 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.10/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.44 % Preprocessing time : 0.001 s
% 0.10/0.44
% 0.10/0.44 % Proof found!
% 0.10/0.44 % SZS status Theorem
% 0.10/0.44 % SZS output start CNFRefutation
% See solution above
% 0.10/0.44 % Parsed axioms : 96
% 0.10/0.44 % Removed by relevancy pruning/SinE : 68
% 0.10/0.44 % Initial clauses : 57
% 0.10/0.44 % Removed in clause preprocessing : 0
% 0.10/0.44 % Initial clauses in saturation : 57
% 0.10/0.44 % Processed clauses : 68
% 0.10/0.44 % ...of these trivial : 0
% 0.10/0.44 % ...subsumed : 14
% 0.10/0.44 % ...remaining for further processing : 54
% 0.10/0.44 % Other redundant clauses eliminated : 10
% 0.10/0.44 % Clauses deleted for lack of memory : 0
% 0.10/0.44 % Backward-subsumed : 0
% 0.10/0.44 % Backward-rewritten : 3
% 0.10/0.44 % Generated clauses : 64
% 0.10/0.44 % ...of the previous two non-redundant : 36
% 0.10/0.44 % ...aggressively subsumed : 0
% 0.10/0.44 % Contextual simplify-reflections : 5
% 0.10/0.44 % Paramodulations : 52
% 0.10/0.44 % Factorizations : 0
% 0.10/0.44 % NegExts : 0
% 0.10/0.44 % Equation resolutions : 13
% 0.10/0.44 % Disequality decompositions : 0
% 0.10/0.44 % Total rewrite steps : 44
% 0.10/0.44 % ...of those cached : 39
% 0.10/0.44 % Propositional unsat checks : 0
% 0.10/0.44 % Propositional check models : 0
% 0.10/0.44 % Propositional check unsatisfiable : 0
% 0.10/0.44 % Propositional clauses : 0
% 0.10/0.44 % Propositional clauses after purity: 0
% 0.10/0.44 % Propositional unsat core size : 0
% 0.10/0.44 % Propositional preprocessing time : 0.000
% 0.10/0.44 % Propositional encoding time : 0.000
% 0.10/0.44 % Propositional solver time : 0.000
% 0.10/0.44 % Success case prop preproc time : 0.000
% 0.10/0.44 % Success case prop encoding time : 0.000
% 0.10/0.44 % Success case prop solver time : 0.000
% 0.10/0.44 % Current number of processed clauses : 48
% 0.10/0.44 % Positive orientable unit clauses : 9
% 0.10/0.44 % Positive unorientable unit clauses: 0
% 0.10/0.44 % Negative unit clauses : 3
% 0.10/0.44 % Non-unit-clauses : 36
% 0.10/0.44 % Current number of unprocessed clauses: 25
% 0.10/0.44 % ...number of literals in the above : 137
% 0.10/0.44 % Current number of archived formulas : 0
% 0.10/0.44 % Current number of archived clauses : 3
% 0.10/0.44 % Clause-clause subsumption calls (NU) : 188
% 0.10/0.44 % Rec. Clause-clause subsumption calls : 87
% 0.10/0.44 % Non-unit clause-clause subsumptions : 19
% 0.10/0.44 % Unit Clause-clause subsumption calls : 13
% 0.10/0.44 % Rewrite failures with RHS unbound : 0
% 0.10/0.44 % BW rewrite match attempts : 3
% 0.10/0.44 % BW rewrite match successes : 3
% 0.10/0.44 % Condensation attempts : 0
% 0.10/0.44 % Condensation successes : 0
% 0.10/0.44 % Termbank termtop insertions : 6741
% 0.10/0.44 % Search garbage collected termcells : 1724
% 0.10/0.44
% 0.10/0.44 % -------------------------------------------------
% 0.10/0.44 % User time : 0.008 s
% 0.10/0.44 % System time : 0.003 s
% 0.10/0.44 % Total time : 0.011 s
% 0.10/0.44 % Maximum resident set size: 3708 pages
% 0.10/0.44
% 0.10/0.44 % -------------------------------------------------
% 0.10/0.44 % User time : 0.010 s
% 0.10/0.44 % System time : 0.010 s
% 0.10/0.44 % Total time : 0.020 s
% 0.10/0.44 % Maximum resident set size: 4608 pages
% 0.10/0.44 % E exiting
%------------------------------------------------------------------------------