%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC323+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 : n013.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 02:43:56 PM UTC 2026
% Result : Theorem 0.16s 0.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 13 unt; 0 def)
% Number of atoms : 166 ( 68 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 200 ( 74 ~; 66 |; 30 &)
% ( 3 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 36 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( neq(X4,nil)
& ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssList(X8)
=> ( app(X8,cons(X7,nil)) != X3
| app(cons(X7,nil),X8) != X4 ) ) ) )
| ( nil = X4
& nil != X3 )
| ? [X5] :
( ? [X6] :
( app(X6,X5) = X1
& app(X5,X6) = X2
& ssList(X6) )
& ssList(X5) )
| 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(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X1
& nil = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( neq(X4,nil)
& ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssList(X8)
=> ( app(X8,cons(X7,nil)) != X3
| app(cons(X7,nil),X8) != X4 ) ) ) )
| ( nil = X4
& nil != X3 )
| ? [X5] :
( ? [X6] :
( app(X6,X5) = X1
& app(X5,X6) = X2
& ssList(X6) )
& ssList(X5) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( neq(X4,nil)
& ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssList(X8)
=> ( app(X8,cons(X7,nil)) != X3
| app(cons(X7,nil),X8) != X4 ) ) ) )
| ( nil = X4
& nil != X3 )
| ? [X5] :
( ? [X6] :
( app(X6,X5) = X1
& app(X5,X6) = X2
& ssList(X6) )
& ssList(X5) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_8,negated_conjecture,
! [X13,X14] :
( ( ~ neq(esk4_0,nil)
| app(esk6_0,cons(esk5_0,nil)) = esk3_0 )
& ( ~ neq(esk4_0,nil)
| app(cons(esk5_0,nil),esk6_0) = esk4_0 )
& ( ~ neq(esk4_0,nil)
| ssList(esk6_0) )
& ( ~ neq(esk4_0,nil)
| ssItem(esk5_0) )
& ( nil != esk4_0
| nil = esk3_0 )
& ( app(X14,X13) != esk1_0
| app(X13,X14) != esk2_0
| ~ ssList(X14)
| ~ ssList(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_7])])])])])]) ).
fof(c_0_9,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_10,negated_conjecture,
( app(X2,X1) != esk1_0
| app(X1,X2) != esk2_0
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X31] :
( app(nil,X31) = X31
| ~ ssList(X31) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
fof(c_0_14,plain,
! [X43,X44] :
( ( ~ ssList(X43)
| ~ ssList(X44)
| nil = app(X43,X44)
| nil != X43
| nil != X44 )
& ( ~ ssList(X43)
| ~ ssList(X44)
| nil != app(X43,X44)
| nil = X43 )
& ( ~ ssList(X43)
| ~ ssList(X44)
| nil != app(X43,X44)
| nil = X44 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])])]) ).
fof(c_0_15,plain,
! [X19,X20] :
( ( ~ ssList(X19)
| ~ ssList(X20)
| neq(X19,X20)
| X19 = X20 )
& ( ~ ssList(X19)
| ~ ssList(X20)
| X19 != X20
| ~ neq(X19,X20) ) ),
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_9])])])])]) ).
cnf(c_0_16,negated_conjecture,
( ~ ssList(X2)
| ~ ssList(X1)
| app(X2,X1) != esk4_0
| app(X1,X2) != esk3_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
cnf(c_0_17,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_19,negated_conjecture,
ssList(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != X2
| nil != X1
| nil = app(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,negated_conjecture,
( ~ neq(esk4_0,nil)
| ssList(esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_22,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,negated_conjecture,
ssList(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_24,negated_conjecture,
app(esk3_0,nil) != esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])])]),c_0_19])]) ).
cnf(c_0_25,negated_conjecture,
( nil != esk4_0
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_26,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_20])]),c_0_18])]) ).
cnf(c_0_27,negated_conjecture,
( ssList(esk6_0)
| esk4_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_18]),c_0_23])]) ).
cnf(c_0_28,negated_conjecture,
esk4_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(esk4_0,nil)
| app(esk6_0,cons(esk5_0,nil)) = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_30,negated_conjecture,
ssList(esk6_0),
inference(sr,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
( ~ neq(esk4_0,nil)
| app(cons(esk5_0,nil),esk6_0) = esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_32,negated_conjecture,
( ~ neq(esk4_0,nil)
| ssItem(esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_33,negated_conjecture,
( ~ neq(esk4_0,nil)
| ~ ssList(cons(esk5_0,nil)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_29]),c_0_30])]),c_0_31]) ).
fof(c_0_34,plain,
! [X46,X47] :
( ssList(cons(X47,X46))
| ~ ssItem(X47)
| ~ ssList(X46) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
cnf(c_0_35,negated_conjecture,
( ssItem(esk5_0)
| esk4_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_22]),c_0_18]),c_0_23])]) ).
cnf(c_0_36,negated_conjecture,
~ ssList(cons(esk5_0,nil)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_22]),c_0_18]),c_0_23])]),c_0_28]) ).
cnf(c_0_37,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_38,negated_conjecture,
ssItem(esk5_0),
inference(sr,[status(thm)],[c_0_35,c_0_28]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_18]),c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC323+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n013.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 08:15:21 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.16/0.40 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
% 0.16/0.46 % Version: 3.5.1
% 0.16/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.46 % Starting sh5l with 300s (1) cores
% 0.16/0.46 % new_bool_3 with pid 339727 completed with status 0
% 0.16/0.46 % Result found by new_bool_3
% 0.16/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.46 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.16/0.46 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.46 % Starting SubtermCWHack with 28s (1) cores
% 0.16/0.46 % SubtermCWHack with pid 339731 completed with status 0
% 0.16/0.46 % Result found by SubtermCWHack
% 0.16/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.46 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.16/0.46 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.46 % Starting SubtermCWHack with 28s (1) cores
% 0.16/0.46 % Preprocessing time : 0.002 s
% 0.16/0.46
% 0.16/0.46 % Proof found!
% 0.16/0.46 % SZS status Theorem
% 0.16/0.46 % SZS output start CNFRefutation
% See solution above
% 0.16/0.46 % Parsed axioms : 96
% 0.16/0.46 % Removed by relevancy pruning/SinE : 77
% 0.16/0.46 % Initial clauses : 39
% 0.16/0.46 % Removed in clause preprocessing : 0
% 0.16/0.46 % Initial clauses in saturation : 39
% 0.16/0.46 % Processed clauses : 166
% 0.16/0.46 % ...of these trivial : 2
% 0.16/0.46 % ...subsumed : 48
% 0.16/0.46 % ...remaining for further processing : 116
% 0.16/0.46 % Other redundant clauses eliminated : 16
% 0.16/0.46 % Clauses deleted for lack of memory : 0
% 0.16/0.46 % Backward-subsumed : 19
% 0.16/0.46 % Backward-rewritten : 10
% 0.16/0.46 % Generated clauses : 468
% 0.16/0.46 % ...of the previous two non-redundant : 347
% 0.16/0.46 % ...aggressively subsumed : 0
% 0.16/0.46 % Contextual simplify-reflections : 7
% 0.16/0.46 % Paramodulations : 446
% 0.16/0.46 % Factorizations : 0
% 0.16/0.46 % NegExts : 0
% 0.16/0.46 % Equation resolutions : 20
% 0.16/0.46 % Disequality decompositions : 0
% 0.16/0.46 % Total rewrite steps : 468
% 0.16/0.46 % ...of those cached : 454
% 0.16/0.46 % Propositional unsat checks : 0
% 0.16/0.46 % Propositional check models : 0
% 0.16/0.46 % Propositional check unsatisfiable : 0
% 0.16/0.46 % Propositional clauses : 0
% 0.16/0.46 % Propositional clauses after purity: 0
% 0.16/0.46 % Propositional unsat core size : 0
% 0.16/0.46 % Propositional preprocessing time : 0.000
% 0.16/0.46 % Propositional encoding time : 0.000
% 0.16/0.46 % Propositional solver time : 0.000
% 0.16/0.46 % Success case prop preproc time : 0.000
% 0.16/0.46 % Success case prop encoding time : 0.000
% 0.16/0.46 % Success case prop solver time : 0.000
% 0.16/0.46 % Current number of processed clauses : 81
% 0.16/0.46 % Positive orientable unit clauses : 16
% 0.16/0.46 % Positive unorientable unit clauses: 0
% 0.16/0.46 % Negative unit clauses : 9
% 0.16/0.46 % Non-unit-clauses : 56
% 0.16/0.46 % Current number of unprocessed clauses: 199
% 0.16/0.46 % ...number of literals in the above : 940
% 0.16/0.46 % Current number of archived formulas : 0
% 0.16/0.46 % Current number of archived clauses : 32
% 0.16/0.46 % Clause-clause subsumption calls (NU) : 385
% 0.16/0.46 % Rec. Clause-clause subsumption calls : 287
% 0.16/0.46 % Non-unit clause-clause subsumptions : 45
% 0.16/0.46 % Unit Clause-clause subsumption calls : 129
% 0.16/0.46 % Rewrite failures with RHS unbound : 0
% 0.16/0.46 % BW rewrite match attempts : 8
% 0.16/0.46 % BW rewrite match successes : 8
% 0.16/0.46 % Condensation attempts : 0
% 0.16/0.46 % Condensation successes : 0
% 0.16/0.46 % Termbank termtop insertions : 10926
% 0.16/0.46 % Search garbage collected termcells : 1400
% 0.16/0.46
% 0.16/0.46 % -------------------------------------------------
% 0.16/0.46 % User time : 0.013 s
% 0.16/0.46 % System time : 0.005 s
% 0.16/0.46 % Total time : 0.018 s
% 0.16/0.46 % Maximum resident set size: 3708 pages
% 0.16/0.46
% 0.16/0.46 % -------------------------------------------------
% 0.16/0.46 % User time : 0.017 s
% 0.16/0.46 % System time : 0.010 s
% 0.16/0.46 % Total time : 0.026 s
% 0.16/0.46 % Maximum resident set size: 4608 pages
% 0.16/0.46 % E exiting
%------------------------------------------------------------------------------