%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SWC206+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 : n009.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 02:45:23 PM UTC 2026
% Result : Theorem 0.09s 0.42s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 17 unt; 0 def)
% Number of atoms : 118 ( 29 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 138 ( 51 ~; 44 |; 20 &)
% ( 3 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 26 ( 0 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( neq(X4,nil)
& ! [X5] :
( ssList(X5)
=> ( ~ segmentP(X3,X5)
| ~ segmentP(X4,X5)
| ~ neq(X5,nil) ) ) )
| ( nil = X4
& nil != X3 )
| neq(X1,nil)
| ~ neq(X2,nil)
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax58,axiom,
! [X1] :
( ssList(X1)
=> ( segmentP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax58) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( neq(X4,nil)
& ! [X5] :
( ssList(X5)
=> ( ~ segmentP(X3,X5)
| ~ segmentP(X4,X5)
| ~ neq(X5,nil) ) ) )
| ( nil = X4
& nil != X3 )
| neq(X1,nil)
| ~ neq(X2,nil)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( neq(X4,nil)
& ! [X5] :
( ssList(X5)
=> ( ~ segmentP(X3,X5)
| ~ segmentP(X4,X5)
| ~ neq(X5,nil) ) ) )
| ( nil = X4
& nil != X3 )
| neq(X1,nil)
| ~ neq(X2,nil)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_6,negated_conjecture,
( ( ~ neq(esk4_0,nil)
| segmentP(esk3_0,esk5_0) )
& ( ~ neq(esk4_0,nil)
| segmentP(esk4_0,esk5_0) )
& ( ~ neq(esk4_0,nil)
| neq(esk5_0,nil) )
& ( ~ neq(esk4_0,nil)
| ssList(esk5_0) )
& ( nil != esk4_0
| nil = esk3_0 )
& ~ neq(esk1_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_5])])])])]) ).
fof(c_0_7,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_8,negated_conjecture,
neq(esk2_0,nil),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
~ neq(esk1_0,nil),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_12,plain,
! [X14,X15] :
( ( ~ ssList(X14)
| ~ ssList(X15)
| neq(X14,X15)
| X14 = X15 )
& ( ~ ssList(X14)
| ~ ssList(X15)
| X14 != X15
| ~ neq(X14,X15) ) ),
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_13,negated_conjecture,
( ~ neq(esk4_0,nil)
| segmentP(esk3_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,negated_conjecture,
neq(esk4_0,nil),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_15,negated_conjecture,
~ neq(esk3_0,nil),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_18,negated_conjecture,
ssList(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_19,plain,
! [X38] :
( ( ~ ssList(X38)
| segmentP(nil,X38)
| nil != X38 )
& ( ~ ssList(X38)
| nil = X38
| ~ segmentP(nil,X38) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax58])])])]) ).
cnf(c_0_20,negated_conjecture,
segmentP(esk3_0,esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]) ).
cnf(c_0_21,negated_conjecture,
esk3_0 = nil,
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])]) ).
cnf(c_0_22,negated_conjecture,
( ~ neq(esk4_0,nil)
| ssList(esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_23,negated_conjecture,
( ~ neq(esk4_0,nil)
| neq(esk5_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_24,plain,
( ~ ssList(X1)
| ~ segmentP(nil,X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,negated_conjecture,
segmentP(nil,esk5_0),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
ssList(esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_14])]) ).
cnf(c_0_27,negated_conjecture,
neq(esk5_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_14])]) ).
cnf(c_0_28,negated_conjecture,
esk5_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_29,negated_conjecture,
~ neq(nil,nil),
inference(rw,[status(thm)],[c_0_15,c_0_21]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC206+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 08:04:57 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.42 % Version: 3.5.1
% 0.09/0.42 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.09/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.42 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.09/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.42 % Starting sh5l with 300s (1) cores
% 0.09/0.42 % new_bool_3 with pid 1271284 completed with status 0
% 0.09/0.42 % Result found by new_bool_3
% 0.09/0.42 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.09/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.42 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.09/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/0.42 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/0.42 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.09/0.42 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.42 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.42 % SubtermCWHack with pid 1271287 completed with status 0
% 0.09/0.42 % Result found by SubtermCWHack
% 0.09/0.42 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.09/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.42 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.09/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/0.42 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/0.42 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.09/0.42 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.42 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.42 % Preprocessing time : 0.002 s
% 0.09/0.42
% 0.09/0.42 % Proof found!
% 0.09/0.42 % SZS status Theorem
% 0.09/0.42 % SZS output start CNFRefutation
% See solution above
% 0.09/0.42 % Parsed axioms : 96
% 0.09/0.42 % Removed by relevancy pruning/SinE : 70
% 0.09/0.42 % Initial clauses : 51
% 0.09/0.42 % Removed in clause preprocessing : 0
% 0.09/0.42 % Initial clauses in saturation : 51
% 0.09/0.42 % Processed clauses : 42
% 0.09/0.42 % ...of these trivial : 0
% 0.09/0.42 % ...subsumed : 0
% 0.09/0.42 % ...remaining for further processing : 42
% 0.09/0.42 % Other redundant clauses eliminated : 1
% 0.09/0.42 % Clauses deleted for lack of memory : 0
% 0.09/0.42 % Backward-subsumed : 4
% 0.09/0.42 % Backward-rewritten : 11
% 0.09/0.42 % Generated clauses : 15
% 0.09/0.42 % ...of the previous two non-redundant : 14
% 0.09/0.42 % ...aggressively subsumed : 0
% 0.09/0.42 % Contextual simplify-reflections : 1
% 0.09/0.42 % Paramodulations : 14
% 0.09/0.42 % Factorizations : 0
% 0.09/0.42 % NegExts : 0
% 0.09/0.42 % Equation resolutions : 1
% 0.09/0.42 % Disequality decompositions : 0
% 0.09/0.42 % Total rewrite steps : 31
% 0.09/0.42 % ...of those cached : 21
% 0.09/0.42 % Propositional unsat checks : 0
% 0.09/0.42 % Propositional check models : 0
% 0.09/0.42 % Propositional check unsatisfiable : 0
% 0.09/0.42 % Propositional clauses : 0
% 0.09/0.42 % Propositional clauses after purity: 0
% 0.09/0.42 % Propositional unsat core size : 0
% 0.09/0.42 % Propositional preprocessing time : 0.000
% 0.09/0.42 % Propositional encoding time : 0.000
% 0.09/0.42 % Propositional solver time : 0.000
% 0.09/0.42 % Success case prop preproc time : 0.000
% 0.09/0.42 % Success case prop encoding time : 0.000
% 0.09/0.42 % Success case prop solver time : 0.000
% 0.09/0.42 % Current number of processed clauses : 26
% 0.09/0.42 % Positive orientable unit clauses : 10
% 0.09/0.42 % Positive unorientable unit clauses: 0
% 0.09/0.42 % Negative unit clauses : 3
% 0.09/0.42 % Non-unit-clauses : 13
% 0.09/0.42 % Current number of unprocessed clauses: 20
% 0.09/0.42 % ...number of literals in the above : 92
% 0.09/0.42 % Current number of archived formulas : 0
% 0.09/0.42 % Current number of archived clauses : 15
% 0.09/0.42 % Clause-clause subsumption calls (NU) : 21
% 0.09/0.42 % Rec. Clause-clause subsumption calls : 20
% 0.09/0.42 % Non-unit clause-clause subsumptions : 1
% 0.09/0.42 % Unit Clause-clause subsumption calls : 21
% 0.09/0.42 % Rewrite failures with RHS unbound : 0
% 0.09/0.42 % BW rewrite match attempts : 4
% 0.09/0.42 % BW rewrite match successes : 4
% 0.09/0.42 % Condensation attempts : 0
% 0.09/0.42 % Condensation successes : 0
% 0.09/0.42 % Termbank termtop insertions : 5016
% 0.09/0.42 % Search garbage collected termcells : 1530
% 0.09/0.42
% 0.09/0.42 % -------------------------------------------------
% 0.09/0.42 % User time : 0.007 s
% 0.09/0.42 % System time : 0.003 s
% 0.09/0.42 % Total time : 0.010 s
% 0.09/0.42 % Maximum resident set size: 4016 pages
% 0.09/0.42
% 0.09/0.42 % -------------------------------------------------
% 0.09/0.42 % User time : 0.009 s
% 0.09/0.42 % System time : 0.007 s
% 0.09/0.42 % Total time : 0.015 s
% 0.09/0.42 % Maximum resident set size: 4864 pages
% 0.09/0.42 % E exiting
%------------------------------------------------------------------------------