%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC254+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 : 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 02:43:40 PM UTC 2026
% Result : Theorem 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 9 unt; 0 def)
% Number of atoms : 110 ( 26 equ)
% Maximal formula atoms : 30 ( 5 avg)
% Number of connectives : 134 ( 45 ~; 46 |; 23 &)
% ( 1 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 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; 7 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 21 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( singletonP(X1)
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(X6,cons(X5,nil)) != X4
| cons(X5,nil) != X3 ) ) )
| ~ neq(X2,nil) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax4,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( cons(X2,nil) = X1
& ssItem(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(c_0_2,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( singletonP(X1)
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(X6,cons(X5,nil)) != X4
| cons(X5,nil) != X3 ) ) )
| ~ neq(X2,nil) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_3,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( singletonP(X1)
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(X6,cons(X5,nil)) != X4
| cons(X5,nil) != X3 ) ) )
| ~ neq(X2,nil) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_4,negated_conjecture,
( ( ~ singletonP(esk1_0)
| ~ neq(esk4_0,nil) )
& ( ~ singletonP(esk1_0)
| neq(esk2_0,nil) )
& ( app(esk6_0,cons(esk5_0,nil)) = esk4_0
| ~ neq(esk4_0,nil) )
& ( app(esk6_0,cons(esk5_0,nil)) = esk4_0
| neq(esk2_0,nil) )
& ( cons(esk5_0,nil) = esk3_0
| ~ neq(esk4_0,nil) )
& ( cons(esk5_0,nil) = esk3_0
| neq(esk2_0,nil) )
& ( ssList(esk6_0)
| ~ neq(esk4_0,nil) )
& ( ssList(esk6_0)
| neq(esk2_0,nil) )
& ( ssItem(esk5_0)
| ~ neq(esk4_0,nil) )
& ( ssItem(esk5_0)
| neq(esk2_0,nil) )
& ( neq(esk2_0,nil)
| ~ neq(esk4_0,nil) )
& ( neq(esk2_0,nil)
| 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(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])])]) ).
cnf(c_0_5,negated_conjecture,
( neq(esk2_0,nil)
| neq(esk2_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_6,plain,
! [X22,X24] :
( ( ~ ssList(X22)
| singletonP(X22)
| cons(X24,nil) != X22
| ~ ssItem(X24) )
& ( ~ ssList(X22)
| ~ singletonP(X22)
| cons(esk9_1(X22),nil) = X22 )
& ( ~ ssList(X22)
| ~ singletonP(X22)
| ssItem(esk9_1(X22)) ) ),
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)],[ax4])])])])])]) ).
cnf(c_0_7,negated_conjecture,
neq(esk2_0,nil),
inference(cn,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,plain,
( ~ ssList(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| singletonP(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
( ~ neq(esk4_0,nil)
| cons(esk5_0,nil) = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_11,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_12,negated_conjecture,
neq(esk4_0,nil),
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_13,negated_conjecture,
( ~ neq(esk4_0,nil)
| ssItem(esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_14,negated_conjecture,
( ~ singletonP(esk1_0)
| ~ neq(esk4_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_15,plain,
( ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| singletonP(cons(X1,nil)) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_16,negated_conjecture,
cons(esk5_0,nil) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_12])]) ).
cnf(c_0_17,negated_conjecture,
ssList(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_18,negated_conjecture,
ssItem(esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_12])]) ).
cnf(c_0_19,negated_conjecture,
~ singletonP(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_12])]) ).
cnf(c_0_20,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_15,c_0_16]),c_0_17]),c_0_18])]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC254+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n026.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 08:12:06 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.41 % Version: 3.5.1
% 0.13/0.41 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.41 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/0.41 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.41 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.41 % Starting sh5l with 300s (1) cores
% 0.13/0.41 % new_bool_3 with pid 1806678 completed with status 0
% 0.13/0.41 % Result found by new_bool_3
% 0.13/0.41 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.41 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/0.41 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.41 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.13/0.41 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.41 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.13/0.41 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.41 % Starting SubtermCWHack with 28s (1) cores
% 0.13/0.41 % SubtermCWHack with pid 1806681 completed with status 0
% 0.13/0.41 % Result found by SubtermCWHack
% 0.13/0.41 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.41 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/0.41 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.41 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.13/0.41 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.41 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.13/0.41 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.41 % Starting SubtermCWHack with 28s (1) cores
% 0.13/0.41 % Preprocessing time : 0.002 s
% 0.13/0.41
% 0.13/0.41 % Proof found!
% 0.13/0.41 % SZS status Theorem
% 0.13/0.41 % SZS output start CNFRefutation
% See solution above
% 0.13/0.41 % Parsed axioms : 96
% 0.13/0.41 % Removed by relevancy pruning/SinE : 75
% 0.13/0.41 % Initial clauses : 49
% 0.13/0.41 % Removed in clause preprocessing : 0
% 0.13/0.41 % Initial clauses in saturation : 49
% 0.13/0.41 % Processed clauses : 47
% 0.13/0.41 % ...of these trivial : 6
% 0.13/0.41 % ...subsumed : 3
% 0.13/0.41 % ...remaining for further processing : 38
% 0.13/0.41 % Other redundant clauses eliminated : 7
% 0.13/0.41 % Clauses deleted for lack of memory : 0
% 0.13/0.41 % Backward-subsumed : 0
% 0.13/0.41 % Backward-rewritten : 2
% 0.13/0.41 % Generated clauses : 18
% 0.13/0.41 % ...of the previous two non-redundant : 8
% 0.13/0.41 % ...aggressively subsumed : 0
% 0.13/0.41 % Contextual simplify-reflections : 0
% 0.13/0.41 % Paramodulations : 12
% 0.13/0.41 % Factorizations : 0
% 0.13/0.41 % NegExts : 0
% 0.13/0.41 % Equation resolutions : 7
% 0.13/0.41 % Disequality decompositions : 0
% 0.13/0.41 % Total rewrite steps : 49
% 0.13/0.41 % ...of those cached : 40
% 0.13/0.41 % Propositional unsat checks : 0
% 0.13/0.41 % Propositional check models : 0
% 0.13/0.41 % Propositional check unsatisfiable : 0
% 0.13/0.41 % Propositional clauses : 0
% 0.13/0.41 % Propositional clauses after purity: 0
% 0.13/0.41 % Propositional unsat core size : 0
% 0.13/0.41 % Propositional preprocessing time : 0.000
% 0.13/0.41 % Propositional encoding time : 0.000
% 0.13/0.41 % Propositional solver time : 0.000
% 0.13/0.41 % Success case prop preproc time : 0.000
% 0.13/0.41 % Success case prop encoding time : 0.000
% 0.13/0.41 % Success case prop solver time : 0.000
% 0.13/0.41 % Current number of processed clauses : 32
% 0.13/0.41 % Positive orientable unit clauses : 13
% 0.13/0.41 % Positive unorientable unit clauses: 0
% 0.13/0.41 % Negative unit clauses : 4
% 0.13/0.41 % Non-unit-clauses : 15
% 0.13/0.41 % Current number of unprocessed clauses: 10
% 0.13/0.41 % ...number of literals in the above : 44
% 0.13/0.41 % Current number of archived formulas : 0
% 0.13/0.41 % Current number of archived clauses : 2
% 0.13/0.41 % Clause-clause subsumption calls (NU) : 24
% 0.13/0.41 % Rec. Clause-clause subsumption calls : 5
% 0.13/0.41 % Non-unit clause-clause subsumptions : 0
% 0.13/0.41 % Unit Clause-clause subsumption calls : 1
% 0.13/0.41 % Rewrite failures with RHS unbound : 0
% 0.13/0.41 % BW rewrite match attempts : 2
% 0.13/0.41 % BW rewrite match successes : 2
% 0.13/0.41 % Condensation attempts : 0
% 0.13/0.41 % Condensation successes : 0
% 0.13/0.41 % Termbank termtop insertions : 4477
% 0.13/0.41 % Search garbage collected termcells : 1391
% 0.13/0.41
% 0.13/0.41 % -------------------------------------------------
% 0.13/0.41 % User time : 0.007 s
% 0.13/0.41 % System time : 0.003 s
% 0.13/0.41 % Total time : 0.010 s
% 0.13/0.41 % Maximum resident set size: 3960 pages
% 0.13/0.41
% 0.13/0.41 % -------------------------------------------------
% 0.13/0.41 % User time : 0.010 s
% 0.13/0.41 % System time : 0.008 s
% 0.13/0.41 % Total time : 0.018 s
% 0.13/0.41 % Maximum resident set size: 4608 pages
% 0.13/0.41 % E exiting
%------------------------------------------------------------------------------