%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SWX048+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 03:14:26 PM UTC 2026
% Result : Theorem 245.43s 36.25s
% Output : CNFRefutation 245.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 5 unt; 0 def)
% Number of atoms : 158 ( 81 equ)
% Maximal formula atoms : 83 ( 6 avg)
% Number of connectives : 193 ( 60 ~; 87 |; 38 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 73 ( 2 sgn 37 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(id49,axiom,
! [X58,X59,X1] :
( occ_succeeds(X58,X59,X1)
<=> ( ( X1 = '0'
& X59 = nil )
| ? [X4,X5] :
( occ_succeeds(X58,X4,X5)
& X1 = s(X5)
& X59 = cons(X58,X4) )
| ? [X2,X3] :
( occ_succeeds(X58,X3,X1)
& X58 != X2
& X59 = cons(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id49) ).
fof('lemma-(occ:cons:diff)',conjecture,
! [X60,X61,X67] :
( ( X60 != X61
& list_succeeds(X67) )
=> occ(X60,cons(X61,X67)) = occ(X60,X67) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(occ:cons:diff)') ).
fof('occ/2',axiom,
! [X60,X67,X73] :
( list_succeeds(X67)
=> ( occ(X60,X67) = X73
<=> occ_succeeds(X60,X67,X73) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','occ/2') ).
fof('lemma-(occ:types)',axiom,
! [X60,X67,X72] :
( occ_succeeds(X60,X67,X72)
=> ( nat_succeeds(X72)
& list_succeeds(X67) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(occ:types)') ).
fof(c_0_4,plain,
! [X58,X59,X1] :
( occ_succeeds(X58,X59,X1)
<=> ( ( X1 = '0'
& X59 = nil )
| ? [X4,X5] :
( occ_succeeds(X58,X4,X5)
& X1 = s(X5)
& X59 = cons(X58,X4) )
| ? [X2,X3] :
( occ_succeeds(X58,X3,X1)
& X58 != X2
& X59 = cons(X2,X3) ) ) ),
inference(fof_simplification,[status(thm)],[id49]) ).
fof(c_0_5,negated_conjecture,
~ ! [X60,X61,X67] :
( ( X60 != X61
& list_succeeds(X67) )
=> occ(X60,cons(X61,X67)) = occ(X60,X67) ),
inference(assume_negation,[status(cth)],['lemma-(occ:cons:diff)']) ).
fof(c_0_6,plain,
! [X107,X108,X109,X114,X115,X116,X117,X118,X119,X120] :
( ( occ_succeeds(X114,X115,X116)
| X116 != '0'
| X115 != nil )
& ( occ_succeeds(X114,X115,X116)
| ~ occ_succeeds(X114,X119,X120)
| X116 != s(X120)
| X115 != cons(X114,X119) )
& ( occ_succeeds(X114,X115,X116)
| ~ occ_succeeds(X114,X118,X116)
| X114 = X117
| X115 != cons(X117,X118) )
& ( ~ occ_succeeds(X107,X108,X109)
| occ_succeeds(X107,esk10_3(X107,X108,X109),X109)
| occ_succeeds(X107,esk11_3(X107,X108,X109),esk12_3(X107,X108,X109))
| X109 = '0' )
& ( ~ occ_succeeds(X107,X108,X109)
| occ_succeeds(X107,esk10_3(X107,X108,X109),X109)
| occ_succeeds(X107,esk11_3(X107,X108,X109),esk12_3(X107,X108,X109))
| X108 = nil )
& ( ~ occ_succeeds(X107,X108,X109)
| occ_succeeds(X107,esk10_3(X107,X108,X109),X109)
| X109 = s(esk12_3(X107,X108,X109))
| X109 = '0' )
& ( ~ occ_succeeds(X107,X108,X109)
| occ_succeeds(X107,esk10_3(X107,X108,X109),X109)
| X109 = s(esk12_3(X107,X108,X109))
| X108 = nil )
& ( ~ occ_succeeds(X107,X108,X109)
| occ_succeeds(X107,esk10_3(X107,X108,X109),X109)
| X108 = cons(X107,esk11_3(X107,X108,X109))
| X109 = '0' )
& ( ~ occ_succeeds(X107,X108,X109)
| occ_succeeds(X107,esk10_3(X107,X108,X109),X109)
| X108 = cons(X107,esk11_3(X107,X108,X109))
| X108 = nil )
& ( ~ occ_succeeds(X107,X108,X109)
| X107 != esk9_3(X107,X108,X109)
| occ_succeeds(X107,esk11_3(X107,X108,X109),esk12_3(X107,X108,X109))
| X109 = '0' )
& ( ~ occ_succeeds(X107,X108,X109)
| X107 != esk9_3(X107,X108,X109)
| occ_succeeds(X107,esk11_3(X107,X108,X109),esk12_3(X107,X108,X109))
| X108 = nil )
& ( ~ occ_succeeds(X107,X108,X109)
| X107 != esk9_3(X107,X108,X109)
| X109 = s(esk12_3(X107,X108,X109))
| X109 = '0' )
& ( ~ occ_succeeds(X107,X108,X109)
| X107 != esk9_3(X107,X108,X109)
| X109 = s(esk12_3(X107,X108,X109))
| X108 = nil )
& ( ~ occ_succeeds(X107,X108,X109)
| X107 != esk9_3(X107,X108,X109)
| X108 = cons(X107,esk11_3(X107,X108,X109))
| X109 = '0' )
& ( ~ occ_succeeds(X107,X108,X109)
| X107 != esk9_3(X107,X108,X109)
| X108 = cons(X107,esk11_3(X107,X108,X109))
| X108 = nil )
& ( ~ occ_succeeds(X107,X108,X109)
| X108 = cons(esk9_3(X107,X108,X109),esk10_3(X107,X108,X109))
| occ_succeeds(X107,esk11_3(X107,X108,X109),esk12_3(X107,X108,X109))
| X109 = '0' )
& ( ~ occ_succeeds(X107,X108,X109)
| X108 = cons(esk9_3(X107,X108,X109),esk10_3(X107,X108,X109))
| occ_succeeds(X107,esk11_3(X107,X108,X109),esk12_3(X107,X108,X109))
| X108 = nil )
& ( ~ occ_succeeds(X107,X108,X109)
| X108 = cons(esk9_3(X107,X108,X109),esk10_3(X107,X108,X109))
| X109 = s(esk12_3(X107,X108,X109))
| X109 = '0' )
& ( ~ occ_succeeds(X107,X108,X109)
| X108 = cons(esk9_3(X107,X108,X109),esk10_3(X107,X108,X109))
| X109 = s(esk12_3(X107,X108,X109))
| X108 = nil )
& ( ~ occ_succeeds(X107,X108,X109)
| X108 = cons(esk9_3(X107,X108,X109),esk10_3(X107,X108,X109))
| X108 = cons(X107,esk11_3(X107,X108,X109))
| X109 = '0' )
& ( ~ occ_succeeds(X107,X108,X109)
| X108 = cons(esk9_3(X107,X108,X109),esk10_3(X107,X108,X109))
| X108 = cons(X107,esk11_3(X107,X108,X109))
| X108 = nil ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])])])]) ).
fof(c_0_7,plain,
! [X80,X81,X82] :
( ( ~ list_succeeds(X81)
| occ(X80,X81) = X82
| ~ occ_succeeds(X80,X81,X82) )
& ( ~ list_succeeds(X81)
| occ_succeeds(X80,X81,X82)
| occ(X80,X81) != X82 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['occ/2'])])])]) ).
fof(c_0_8,negated_conjecture,
~ ! [X60,X61,X67] :
( ( X60 != X61
& list_succeeds(X67) )
=> occ(X60,cons(X61,X67)) = occ(X60,X67) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_9,plain,
! [X124,X125,X126] :
( ( ~ occ_succeeds(X124,X125,X126)
| nat_succeeds(X126) )
& ( ~ occ_succeeds(X124,X125,X126)
| list_succeeds(X125) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['lemma-(occ:types)'])])])]) ).
cnf(c_0_10,plain,
( ~ occ_succeeds(X4,X3,X5)
| X1 != cons(X2,X3)
| occ_succeeds(X4,X1,X5)
| X4 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( ~ list_succeeds(X2)
| occ(X1,X2) != X3
| occ_succeeds(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,negated_conjecture,
( occ(esk1_0,cons(esk2_0,esk3_0)) != occ(esk1_0,esk3_0)
& esk1_0 != esk2_0
& list_succeeds(esk3_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
cnf(c_0_13,plain,
( ~ list_succeeds(X2)
| ~ occ_succeeds(X1,X2,X3)
| occ(X1,X2) = X3 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
( ~ occ_succeeds(X2,X1,X3)
| list_succeeds(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( ~ occ_succeeds(X2,X3,X4)
| occ_succeeds(X2,cons(X1,X3),X4)
| X1 = X2 ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( ~ list_succeeds(X2)
| occ_succeeds(X1,X2,occ(X1,X2)) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
occ(esk1_0,cons(esk2_0,esk3_0)) != occ(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( ~ occ_succeeds(X1,X2,X3)
| occ(X1,X2) = X3 ),
inference(csr,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
( ~ list_succeeds(X3)
| occ_succeeds(X2,cons(X1,X3),occ(X2,X3))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
list_succeeds(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,negated_conjecture,
~ occ_succeeds(esk1_0,cons(esk2_0,esk3_0),occ(esk1_0,esk3_0)),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18])]) ).
cnf(c_0_22,negated_conjecture,
( occ_succeeds(X2,cons(X1,esk3_0),occ(X2,esk3_0))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
esk1_0 != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX048+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.44 % Computer : n011.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 10:24:41 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.52 Running first-order theorem proving
% 0.27/0.52 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 245.43/36.25 % Version: 3.5.1
% 245.43/36.25 % Preprocessing class: FSLSSMSSSSSNFFN.
% 245.43/36.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 245.43/36.25 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 245.43/36.25 % Starting new_bool_3 with 300s (1) cores
% 245.43/36.25 % Starting new_bool_1 with 300s (1) cores
% 245.43/36.25 % Starting sh5l with 300s (1) cores
% 245.43/36.25 % new_bool_3 with pid 1662038 completed with status 0
% 245.43/36.25 % Result found by new_bool_3
% 245.43/36.25 % Preprocessing class: FSLSSMSSSSSNFFN.
% 245.43/36.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 245.43/36.25 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 245.43/36.25 % Starting new_bool_3 with 300s (1) cores
% 245.43/36.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 245.43/36.25 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 245.43/36.25 % Search class: FGHSM-FSLS32-MFFFFFNN
% 245.43/36.25 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 245.43/36.25 % Starting SubtermCWHack with 31s (1) cores
% 245.43/36.25 % SubtermCWHack with pid 1662041 completed with status 8
% 245.43/36.25 % Starting G-E--_200_C45_F1_SE_CS_SP_PI_CO_S5PRR_S0V with 150s (1) cores
% 245.43/36.25 % G-E--_200_C45_F1_SE_CS_SP_PI_CO_S5PRR_S0V with pid 1662054 completed with status 0
% 245.43/36.25 % Result found by G-E--_200_C45_F1_SE_CS_SP_PI_CO_S5PRR_S0V
% 245.43/36.25 % Preprocessing class: FSLSSMSSSSSNFFN.
% 245.43/36.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 245.43/36.25 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 245.43/36.25 % Starting new_bool_3 with 300s (1) cores
% 245.43/36.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 245.43/36.25 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 245.43/36.25 % Search class: FGHSM-FSLS32-MFFFFFNN
% 245.43/36.25 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 245.43/36.25 % Starting SubtermCWHack with 31s (1) cores
% 245.43/36.25 % SubtermCWHack with pid 1662041 completed with status 8
% 245.43/36.25 % Starting G-E--_200_C45_F1_SE_CS_SP_PI_CO_S5PRR_S0V with 150s (1) cores
% 245.43/36.25 % Preprocessing time : 0.003 s
% 245.43/36.25
% 245.43/36.25 % Proof found!
% 245.43/36.25 % SZS status Theorem
% 245.43/36.25 % SZS output start CNFRefutation
% See solution above
% 245.43/36.25 % Parsed axioms : 288
% 245.43/36.25 % Removed by relevancy pruning/SinE : 185
% 245.43/36.25 % Initial clauses : 162
% 245.43/36.25 % Removed in clause preprocessing : 0
% 245.43/36.25 % Initial clauses in saturation : 162
% 245.43/36.25 % Processed clauses : 16336
% 245.43/36.25 % ...of these trivial : 31
% 245.43/36.25 % ...subsumed : 12620
% 245.43/36.25 % ...remaining for further processing : 3685
% 245.43/36.25 % Other redundant clauses eliminated : 1094
% 245.43/36.25 % Clauses deleted for lack of memory : 0
% 245.43/36.25 % Backward-subsumed : 310
% 245.43/36.25 % Backward-rewritten : 116
% 245.43/36.25 % Generated clauses : 204708
% 245.43/36.25 % ...of the previous two non-redundant : 200636
% 245.43/36.25 % ...aggressively subsumed : 0
% 245.43/36.25 % Contextual simplify-reflections : 468
% 245.43/36.25 % Paramodulations : 203537
% 245.43/36.25 % Factorizations : 62
% 245.43/36.25 % NegExts : 0
% 245.43/36.25 % Equation resolutions : 1116
% 245.43/36.25 % Disequality decompositions : 0
% 245.43/36.25 % Total rewrite steps : 24535
% 245.43/36.25 % ...of those cached : 23801
% 245.43/36.25 % Propositional unsat checks : 0
% 245.43/36.25 % Propositional check models : 0
% 245.43/36.25 % Propositional check unsatisfiable : 0
% 245.43/36.25 % Propositional clauses : 0
% 245.43/36.25 % Propositional clauses after purity: 0
% 245.43/36.25 % Propositional unsat core size : 0
% 245.43/36.25 % Propositional preprocessing time : 0.000
% 245.43/36.25 % Propositional encoding time : 0.000
% 245.43/36.25 % Propositional solver time : 0.000
% 245.43/36.25 % Success case prop preproc time : 0.000
% 245.43/36.25 % Success case prop encoding time : 0.000
% 245.43/36.25 % Success case prop solver time : 0.000
% 245.43/36.25 % Current number of processed clauses : 3243
% 245.43/36.25 % Positive orientable unit clauses : 60
% 245.43/36.25 % Positive unorientable unit clauses: 0
% 245.43/36.25 % Negative unit clauses : 83
% 245.43/36.25 % Non-unit-clauses : 3100
% 245.43/36.25 % Current number of unprocessed clauses: 183098
% 245.43/36.25 % ...number of literals in the above : 870737
% 245.43/36.25 % Current number of archived formulas : 0
% 245.43/36.25 % Current number of archived clauses : 426
% 245.43/36.25 % Clause-clause subsumption calls (NU) : 1106012
% 245.43/36.25 % Rec. Clause-clause subsumption calls : 492705
% 245.43/36.25 % Non-unit clause-clause subsumptions : 8376
% 245.43/36.25 % Unit Clause-clause subsumption calls : 14207
% 245.43/36.25 % Rewrite failures with RHS unbound : 0
% 245.43/36.25 % BW rewrite match attempts : 113
% 245.43/36.25 % BW rewrite match successes : 27
% 245.43/36.25 % Condensation attempts : 16336
% 245.43/36.25 % Condensation successes : 160
% 245.43/36.25 % Termbank termtop insertions : 3245958
% 245.43/36.25 % Search garbage collected termcells : 4070
% 245.43/36.25
% 245.43/36.25 % -------------------------------------------------
% 245.43/36.25 % User time : 33.881 s
% 245.43/36.25 % System time : 1.273 s
% 245.43/36.25 % Total time : 35.154 s
% 245.43/36.25 % Maximum resident set size: 4528 pages
% 245.43/36.25
% 245.43/36.25 % -------------------------------------------------
% 245.43/36.25 % User time : 33.896 s
% 245.43/36.25 % System time : 1.282 s
% 245.43/36.25 % Total time : 35.177 s
% 245.43/36.25 % Maximum resident set size: 4864 pages
% 245.43/36.25 % E exiting
%------------------------------------------------------------------------------