%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC098+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 : n020.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 02:42:59 PM UTC 2026
% Result : Theorem 0.09s 0.44s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 37 ( 10 unt; 0 def)
% Number of atoms : 200 ( 86 equ)
% Maximal formula atoms : 46 ( 5 avg)
% Number of connectives : 261 ( 98 ~; 99 |; 42 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 26 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X7] :
( ssItem(X7)
=> ( ? [X8] :
( leq(X7,X8)
& memberP(X4,X8)
& X7 != X8
& ssItem(X8) )
| ~ memberP(X4,X7)
| cons(X7,nil) != X3 ) ) )
| ( nil = X1
& nil = X2 )
| ? [X5] :
( memberP(X2,X5)
& ! [X6] :
( ssItem(X6)
=> ( X5 = X6
| ~ leq(X5,X6)
| ~ memberP(X2,X6) ) )
& cons(X5,nil) = X1
& ssItem(X5) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(c_0_3,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X7] :
( ssItem(X7)
=> ( ? [X8] :
( leq(X7,X8)
& memberP(X4,X8)
& X7 != X8
& ssItem(X8) )
| ~ memberP(X4,X7)
| cons(X7,nil) != X3 ) ) )
| ( nil = X1
& nil = X2 )
| ? [X5] :
( memberP(X2,X5)
& ! [X6] :
( ssItem(X6)
=> ( X5 = X6
| ~ leq(X5,X6)
| ~ memberP(X2,X6) ) )
& cons(X5,nil) = X1
& ssItem(X5) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X7] :
( ssItem(X7)
=> ( ? [X8] :
( leq(X7,X8)
& memberP(X4,X8)
& X7 != X8
& ssItem(X8) )
| ~ memberP(X4,X7)
| cons(X7,nil) != X3 ) ) )
| ( nil = X1
& nil = X2 )
| ? [X5] :
( memberP(X2,X5)
& ! [X6] :
( ssItem(X6)
=> ( X5 = X6
| ~ leq(X5,X6)
| ~ memberP(X2,X6) ) )
& cons(X5,nil) = X1
& ssItem(X5) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_5,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
fof(c_0_6,negated_conjecture,
! [X13,X16] :
( ( ~ leq(esk6_0,X16)
| ~ memberP(esk4_0,X16)
| esk6_0 = X16
| ~ ssItem(X16)
| nil = esk3_0 )
& ( ~ leq(esk6_0,X16)
| ~ memberP(esk4_0,X16)
| esk6_0 = X16
| ~ ssItem(X16)
| nil = esk4_0 )
& ( 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 )
& ( nil != esk1_0
| nil != esk2_0 )
& ( ~ memberP(esk2_0,X13)
| cons(X13,nil) != esk1_0
| ~ ssItem(X13)
| X13 != esk5_1(X13) )
& ( ~ memberP(esk2_0,X13)
| cons(X13,nil) != esk1_0
| ~ ssItem(X13)
| leq(X13,esk5_1(X13)) )
& ( ~ memberP(esk2_0,X13)
| cons(X13,nil) != esk1_0
| ~ ssItem(X13)
| memberP(esk2_0,esk5_1(X13)) )
& ( ~ memberP(esk2_0,X13)
| cons(X13,nil) != esk1_0
| ~ ssItem(X13)
| ssItem(esk5_1(X13)) )
& 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(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])])]) ).
fof(c_0_7,plain,
! [X20,X21] :
( nil != cons(X21,X20)
| ~ ssItem(X21)
| ~ ssList(X20) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
cnf(c_0_8,negated_conjecture,
( nil != esk1_0
| nil != esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( nil != cons(X2,X1)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
( cons(esk6_0,nil) = esk3_0
| nil = esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_14,negated_conjecture,
( ssItem(esk6_0)
| nil = esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,negated_conjecture,
( esk4_0 != nil
| esk3_0 != nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( ~ leq(esk6_0,X1)
| ~ memberP(esk4_0,X1)
| ~ ssItem(X1)
| esk6_0 = X1
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,negated_conjecture,
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_11,c_0_12]),c_0_13])]),c_0_14]),c_0_15]) ).
cnf(c_0_18,negated_conjecture,
( ~ memberP(esk2_0,X1)
| cons(X1,nil) != esk1_0
| ~ ssItem(X1)
| leq(X1,esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
( cons(esk6_0,nil) = esk3_0
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_20,negated_conjecture,
( memberP(esk4_0,esk6_0)
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_21,negated_conjecture,
( ssItem(esk6_0)
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(esk4_0,X1)
| ~ leq(esk6_0,X1)
| esk6_0 = X1 ),
inference(sr,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(esk4_0,X1)
| cons(X1,nil) != esk3_0
| leq(X1,esk5_1(X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_9]),c_0_10]) ).
cnf(c_0_24,negated_conjecture,
cons(esk6_0,nil) = esk3_0,
inference(sr,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_25,negated_conjecture,
memberP(esk4_0,esk6_0),
inference(sr,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_26,negated_conjecture,
ssItem(esk6_0),
inference(sr,[status(thm)],[c_0_21,c_0_17]) ).
cnf(c_0_27,negated_conjecture,
( ~ memberP(esk2_0,X1)
| cons(X1,nil) != esk1_0
| ~ ssItem(X1)
| memberP(esk2_0,esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_28,negated_conjecture,
( ~ ssItem(esk5_1(esk6_0))
| ~ memberP(esk4_0,esk5_1(esk6_0))
| esk5_1(esk6_0) = esk6_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25]),c_0_26])]) ).
cnf(c_0_29,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(esk4_0,X1)
| cons(X1,nil) != esk3_0
| memberP(esk4_0,esk5_1(X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_10]),c_0_9]),c_0_10]) ).
cnf(c_0_30,negated_conjecture,
( ~ memberP(esk2_0,X1)
| cons(X1,nil) != esk1_0
| ~ ssItem(X1)
| ssItem(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_31,negated_conjecture,
( ~ memberP(esk2_0,X1)
| cons(X1,nil) != esk1_0
| ~ ssItem(X1)
| X1 != esk5_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_32,negated_conjecture,
( ~ ssItem(esk5_1(esk6_0))
| esk5_1(esk6_0) = esk6_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_24]),c_0_25]),c_0_26])]) ).
cnf(c_0_33,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(esk4_0,X1)
| cons(X1,nil) != esk3_0
| ssItem(esk5_1(X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_9]),c_0_10]) ).
cnf(c_0_34,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(esk4_0,X1)
| esk5_1(X1) != X1
| cons(X1,nil) != esk3_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_9]),c_0_10]) ).
cnf(c_0_35,negated_conjecture,
esk5_1(esk6_0) = esk6_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_24]),c_0_25]),c_0_26])]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_24]),c_0_25]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC098+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n020.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 07:56:34 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.44 % Version: 3.5.1
% 0.09/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.09/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.09/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.44 % Starting sh5l with 300s (1) cores
% 0.09/0.44 % new_bool_1 with pid 2429674 completed with status 0
% 0.09/0.44 % Result found by new_bool_1
% 0.09/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.09/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.09/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/0.44 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.09/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.44 % SubtermCWHack with pid 2429680 completed with status 0
% 0.09/0.44 % Result found by SubtermCWHack
% 0.09/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.09/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.09/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/0.44 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.09/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.44 % Preprocessing time : 0.001 s
% 0.09/0.44
% 0.09/0.44 % Proof found!
% 0.09/0.44 % SZS status Theorem
% 0.09/0.44 % SZS output start CNFRefutation
% See solution above
% 0.09/0.44 % Parsed axioms : 96
% 0.09/0.44 % Removed by relevancy pruning/SinE : 66
% 0.09/0.44 % Initial clauses : 64
% 0.09/0.44 % Removed in clause preprocessing : 0
% 0.09/0.44 % Initial clauses in saturation : 64
% 0.09/0.44 % Processed clauses : 78
% 0.09/0.44 % ...of these trivial : 0
% 0.09/0.44 % ...subsumed : 13
% 0.09/0.44 % ...remaining for further processing : 65
% 0.09/0.44 % Other redundant clauses eliminated : 8
% 0.09/0.44 % Clauses deleted for lack of memory : 0
% 0.09/0.44 % Backward-subsumed : 5
% 0.09/0.44 % Backward-rewritten : 3
% 0.09/0.44 % Generated clauses : 74
% 0.09/0.44 % ...of the previous two non-redundant : 48
% 0.09/0.44 % ...aggressively subsumed : 0
% 0.09/0.44 % Contextual simplify-reflections : 2
% 0.09/0.44 % Paramodulations : 62
% 0.09/0.44 % Factorizations : 0
% 0.09/0.44 % NegExts : 0
% 0.09/0.44 % Equation resolutions : 10
% 0.09/0.44 % Disequality decompositions : 0
% 0.09/0.44 % Total rewrite steps : 80
% 0.09/0.44 % ...of those cached : 71
% 0.09/0.44 % Propositional unsat checks : 0
% 0.09/0.44 % Propositional check models : 0
% 0.09/0.44 % Propositional check unsatisfiable : 0
% 0.09/0.44 % Propositional clauses : 0
% 0.09/0.44 % Propositional clauses after purity: 0
% 0.09/0.44 % Propositional unsat core size : 0
% 0.09/0.44 % Propositional preprocessing time : 0.000
% 0.09/0.44 % Propositional encoding time : 0.000
% 0.09/0.44 % Propositional solver time : 0.000
% 0.09/0.44 % Success case prop preproc time : 0.000
% 0.09/0.44 % Success case prop encoding time : 0.000
% 0.09/0.44 % Success case prop solver time : 0.000
% 0.09/0.44 % Current number of processed clauses : 51
% 0.09/0.44 % Positive orientable unit clauses : 13
% 0.09/0.44 % Positive unorientable unit clauses: 0
% 0.09/0.44 % Negative unit clauses : 2
% 0.09/0.44 % Non-unit-clauses : 36
% 0.09/0.44 % Current number of unprocessed clauses: 34
% 0.09/0.44 % ...number of literals in the above : 166
% 0.09/0.44 % Current number of archived formulas : 0
% 0.09/0.44 % Current number of archived clauses : 11
% 0.09/0.44 % Clause-clause subsumption calls (NU) : 152
% 0.09/0.44 % Rec. Clause-clause subsumption calls : 65
% 0.09/0.44 % Non-unit clause-clause subsumptions : 13
% 0.09/0.44 % Unit Clause-clause subsumption calls : 10
% 0.09/0.44 % Rewrite failures with RHS unbound : 0
% 0.09/0.44 % BW rewrite match attempts : 6
% 0.09/0.44 % BW rewrite match successes : 6
% 0.09/0.44 % Condensation attempts : 0
% 0.09/0.44 % Condensation successes : 0
% 0.09/0.44 % Termbank termtop insertions : 7167
% 0.09/0.44 % Search garbage collected termcells : 1866
% 0.09/0.44
% 0.09/0.44 % -------------------------------------------------
% 0.09/0.44 % User time : 0.006 s
% 0.09/0.44 % System time : 0.005 s
% 0.09/0.44 % Total time : 0.011 s
% 0.09/0.44 % Maximum resident set size: 3764 pages
% 0.09/0.44
% 0.09/0.44 % -------------------------------------------------
% 0.09/0.44 % User time : 0.011 s
% 0.09/0.44 % System time : 0.009 s
% 0.09/0.44 % Total time : 0.020 s
% 0.09/0.44 % Maximum resident set size: 4864 pages
% 0.09/0.44 % E exiting
%------------------------------------------------------------------------------