%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC407+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 : n004.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 02:44:17 PM UTC 2026
% Result : Theorem 0.26s 0.52s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 12 unt; 0 def)
% Number of atoms : 123 ( 40 equ)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 145 ( 50 ~; 52 |; 19 &)
% ( 1 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X6] :
( ssItem(X6)
=> ( ~ memberP(X4,X6)
| cons(X6,nil) != X3 ) ) )
| ! [X5] :
( ssItem(X5)
=> ( memberP(X2,X5)
| ~ memberP(X1,X5) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
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(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X6] :
( ssItem(X6)
=> ( ~ memberP(X4,X6)
| cons(X6,nil) != X3 ) ) )
| ! [X5] :
( ssItem(X5)
=> ( memberP(X2,X5)
| ~ memberP(X1,X5) ) )
| 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)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X6] :
( ssItem(X6)
=> ( ~ memberP(X4,X6)
| cons(X6,nil) != X3 ) ) )
| ! [X5] :
( ssItem(X5)
=> ( memberP(X2,X5)
| ~ memberP(X1,X5) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_6,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
fof(c_0_7,plain,
! [X27,X28,X29] :
( ( ~ ssItem(X27)
| ~ ssItem(X28)
| ~ ssList(X29)
| memberP(cons(X28,X29),X27)
| ~ memberP(X29,X27) )
& ( ~ ssItem(X27)
| ~ ssItem(X28)
| ~ ssList(X29)
| memberP(cons(X28,X29),X27)
| X27 != X28 )
& ( ~ ssItem(X27)
| ~ ssItem(X28)
| ~ ssList(X29)
| memberP(X29,X27)
| X27 = X28
| ~ memberP(cons(X28,X29),X27) ) ),
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])])])])]) ).
fof(c_0_8,negated_conjecture,
( ( memberP(esk4_0,esk6_0)
| nil = esk3_0 )
& ( memberP(esk4_0,esk6_0)
| nil = esk4_0 )
& ( cons(esk6_0,nil) = esk3_0
| nil = esk3_0 )
& ( cons(esk6_0,nil) = esk3_0
| nil = esk4_0 )
& ( ssItem(esk6_0)
| nil = esk3_0 )
& ( ssItem(esk6_0)
| nil = esk4_0 )
& ~ memberP(esk2_0,esk5_0)
& memberP(esk1_0,esk5_0)
& ssItem(esk5_0)
& 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_9,plain,
! [X30] :
( ~ memberP(nil,X30)
| ~ ssItem(X30) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
cnf(c_0_10,plain,
( ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X3)
| memberP(X2,X3)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
( cons(esk6_0,nil) = esk3_0
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_13,negated_conjecture,
( ssItem(esk6_0)
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
memberP(esk1_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
~ memberP(esk2_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(esk3_0,X1)
| esk6_0 = X1
| esk3_0 = nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]),c_0_13]),c_0_14]) ).
cnf(c_0_20,negated_conjecture,
memberP(esk3_0,esk5_0),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
ssItem(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_22,negated_conjecture,
~ memberP(esk4_0,esk5_0),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( esk3_0 = nil
| esk5_0 = esk6_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_24,negated_conjecture,
( memberP(esk4_0,esk6_0)
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,negated_conjecture,
esk3_0 = nil,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_26,negated_conjecture,
memberP(nil,esk5_0),
inference(rw,[status(thm)],[c_0_20,c_0_25]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_26]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC407+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 : n004.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 08:22:07 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
% 0.26/0.52 % Version: 3.5.1
% 0.26/0.52 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.26/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.52 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.26/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.26/0.52 % Starting new_bool_1 with 300s (1) cores
% 0.26/0.52 % Starting sh5l with 300s (1) cores
% 0.26/0.52 % new_bool_3 with pid 2699070 completed with status 0
% 0.26/0.52 % Result found by new_bool_3
% 0.26/0.52 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.26/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.52 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.26/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.26/0.52 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.26/0.52 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.26/0.52 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.26/0.52 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.52 % Starting SubtermCWHack with 31s (1) cores
% 0.26/0.52 % SubtermCWHack with pid 2699073 completed with status 0
% 0.26/0.52 % Result found by SubtermCWHack
% 0.26/0.52 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.26/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.52 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.26/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.26/0.52 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.26/0.52 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.26/0.52 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.26/0.52 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.52 % Starting SubtermCWHack with 31s (1) cores
% 0.26/0.52 % Preprocessing time : 0.002 s
% 0.26/0.52
% 0.26/0.52 % Proof found!
% 0.26/0.52 % SZS status Theorem
% 0.26/0.52 % SZS output start CNFRefutation
% See solution above
% 0.26/0.52 % Parsed axioms : 96
% 0.26/0.52 % Removed by relevancy pruning/SinE : 75
% 0.26/0.52 % Initial clauses : 49
% 0.26/0.52 % Removed in clause preprocessing : 0
% 0.26/0.52 % Initial clauses in saturation : 49
% 0.26/0.52 % Processed clauses : 1190
% 0.26/0.52 % ...of these trivial : 6
% 0.26/0.52 % ...subsumed : 889
% 0.26/0.52 % ...remaining for further processing : 295
% 0.26/0.52 % Other redundant clauses eliminated : 27
% 0.26/0.52 % Clauses deleted for lack of memory : 0
% 0.26/0.52 % Backward-subsumed : 19
% 0.26/0.52 % Backward-rewritten : 178
% 0.26/0.52 % Generated clauses : 4687
% 0.26/0.52 % ...of the previous two non-redundant : 4093
% 0.26/0.52 % ...aggressively subsumed : 0
% 0.26/0.52 % Contextual simplify-reflections : 117
% 0.26/0.52 % Paramodulations : 4655
% 0.26/0.52 % Factorizations : 0
% 0.26/0.52 % NegExts : 0
% 0.26/0.52 % Equation resolutions : 33
% 0.26/0.52 % Disequality decompositions : 0
% 0.26/0.52 % Total rewrite steps : 4057
% 0.26/0.52 % ...of those cached : 4048
% 0.26/0.52 % Propositional unsat checks : 0
% 0.26/0.52 % Propositional check models : 0
% 0.26/0.52 % Propositional check unsatisfiable : 0
% 0.26/0.52 % Propositional clauses : 0
% 0.26/0.52 % Propositional clauses after purity: 0
% 0.26/0.52 % Propositional unsat core size : 0
% 0.26/0.52 % Propositional preprocessing time : 0.000
% 0.26/0.52 % Propositional encoding time : 0.000
% 0.26/0.52 % Propositional solver time : 0.000
% 0.26/0.52 % Success case prop preproc time : 0.000
% 0.26/0.52 % Success case prop encoding time : 0.000
% 0.26/0.52 % Success case prop solver time : 0.000
% 0.26/0.52 % Current number of processed clauses : 95
% 0.26/0.52 % Positive orientable unit clauses : 8
% 0.26/0.52 % Positive unorientable unit clauses: 0
% 0.26/0.52 % Negative unit clauses : 1
% 0.26/0.52 % Non-unit-clauses : 86
% 0.26/0.52 % Current number of unprocessed clauses: 2937
% 0.26/0.52 % ...number of literals in the above : 15581
% 0.26/0.52 % Current number of archived formulas : 0
% 0.26/0.52 % Current number of archived clauses : 197
% 0.26/0.52 % Clause-clause subsumption calls (NU) : 9154
% 0.26/0.52 % Rec. Clause-clause subsumption calls : 5286
% 0.26/0.52 % Non-unit clause-clause subsumptions : 1025
% 0.26/0.52 % Unit Clause-clause subsumption calls : 30
% 0.26/0.52 % Rewrite failures with RHS unbound : 0
% 0.26/0.52 % BW rewrite match attempts : 4
% 0.26/0.52 % BW rewrite match successes : 4
% 0.26/0.52 % Condensation attempts : 0
% 0.26/0.52 % Condensation successes : 0
% 0.26/0.52 % Termbank termtop insertions : 81711
% 0.26/0.52 % Search garbage collected termcells : 1486
% 0.26/0.52
% 0.26/0.52 % -------------------------------------------------
% 0.26/0.52 % User time : 0.089 s
% 0.26/0.52 % System time : 0.005 s
% 0.26/0.52 % Total time : 0.094 s
% 0.26/0.52 % Maximum resident set size: 3760 pages
% 0.26/0.52
% 0.26/0.52 % -------------------------------------------------
% 0.26/0.52 % User time : 0.095 s
% 0.26/0.52 % System time : 0.008 s
% 0.26/0.52 % Total time : 0.103 s
% 0.26/0.52 % Maximum resident set size: 4608 pages
% 0.26/0.52 % E exiting
%------------------------------------------------------------------------------