%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC417+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 : n018.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 02:44:20 PM UTC 2026
% Result : Theorem 0.15s 0.68s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 12 unt; 0 def)
% Number of atoms : 151 ( 48 equ)
% Maximal formula atoms : 38 ( 4 avg)
% Number of connectives : 182 ( 65 ~; 63 |; 32 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 4 ( 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 : 49 ( 0 sgn 29 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ( app(X9,cons(X8,nil)) != X3
| app(cons(X8,nil),X9) != X4 ) ) )
| ? [X5] :
( ? [X6] :
( ? [X7] :
( app(app(X7,cons(X5,nil)),X6) = X1
& app(app(X6,cons(X5,nil)),X7) = X2
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
| ~ neq(X2,nil) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
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(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ( app(X9,cons(X8,nil)) != X3
| app(cons(X8,nil),X9) != X4 ) ) )
| ? [X5] :
( ? [X6] :
( ? [X7] :
( app(app(X7,cons(X5,nil)),X6) = X1
& app(app(X6,cons(X5,nil)),X7) = X2
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
| ~ neq(X2,nil) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ( app(X9,cons(X8,nil)) != X3
| app(cons(X8,nil),X9) != X4 ) ) )
| ? [X5] :
( ? [X6] :
( ? [X7] :
( app(app(X7,cons(X5,nil)),X6) = X1
& app(app(X6,cons(X5,nil)),X7) = X2
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
| ~ neq(X2,nil) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_7,negated_conjecture,
! [X14,X15,X16] :
( ( app(esk6_0,cons(esk5_0,nil)) = esk3_0
| ~ neq(esk4_0,nil) )
& ( app(esk6_0,cons(esk5_0,nil)) = esk3_0
| neq(esk2_0,nil) )
& ( app(cons(esk5_0,nil),esk6_0) = esk4_0
| ~ neq(esk4_0,nil) )
& ( app(cons(esk5_0,nil),esk6_0) = esk4_0
| neq(esk2_0,nil) )
& ( ssList(esk6_0)
| ~ neq(esk4_0,nil) )
& ( ssList(esk6_0)
| neq(esk2_0,nil) )
& ( ssItem(esk5_0)
| ~ neq(esk4_0,nil) )
& ( ssItem(esk5_0)
| neq(esk2_0,nil) )
& ( app(app(X16,cons(X14,nil)),X15) != esk1_0
| app(app(X15,cons(X14,nil)),X16) != esk2_0
| ~ ssList(X16)
| ~ ssList(X15)
| ~ ssItem(X14)
| ~ neq(esk4_0,nil) )
& ( app(app(X16,cons(X14,nil)),X15) != esk1_0
| app(app(X15,cons(X14,nil)),X16) != esk2_0
| ~ ssList(X16)
| ~ ssList(X15)
| ~ ssItem(X14)
| neq(esk2_0,nil) )
& ( neq(esk2_0,nil)
| ~ neq(esk4_0,nil) )
& ( neq(esk2_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(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])])]) ).
cnf(c_0_8,negated_conjecture,
( neq(esk2_0,nil)
| neq(esk2_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_9,negated_conjecture,
( app(app(X3,cons(X1,nil)),X2) != esk1_0
| app(app(X2,cons(X1,nil)),X3) != esk2_0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ neq(esk4_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
neq(esk2_0,nil),
inference(cn,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
( ~ neq(esk4_0,nil)
| app(esk6_0,cons(esk5_0,nil)) = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,negated_conjecture,
( ~ neq(esk4_0,nil)
| ssList(esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,negated_conjecture,
( ~ neq(esk4_0,nil)
| ssItem(esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,negated_conjecture,
( ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| app(app(X3,cons(X2,nil)),X1) != esk2_0
| app(app(X1,cons(X2,nil)),X3) != esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_11])]) ).
cnf(c_0_17,negated_conjecture,
app(esk6_0,cons(esk5_0,nil)) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_10]),c_0_11])]) ).
cnf(c_0_18,negated_conjecture,
ssList(esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_10]),c_0_11])]) ).
cnf(c_0_19,negated_conjecture,
ssItem(esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_10]),c_0_11])]) ).
fof(c_0_20,plain,
! [X33] :
( app(nil,X33) = X33
| ~ ssList(X33) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
cnf(c_0_21,negated_conjecture,
( ~ neq(esk4_0,nil)
| app(cons(esk5_0,nil),esk6_0) = esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,negated_conjecture,
( ~ ssList(X1)
| app(esk1_0,X1) != esk1_0
| app(app(X1,cons(esk5_0,nil)),esk6_0) != esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[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_23,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,negated_conjecture,
app(cons(esk5_0,nil),esk6_0) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_10]),c_0_10]),c_0_11])]) ).
cnf(c_0_25,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_26,plain,
! [X48,X49] :
( ssList(cons(X49,X48))
| ~ ssItem(X49)
| ~ ssList(X48) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
cnf(c_0_27,negated_conjecture,
( ~ ssList(cons(esk5_0,nil))
| app(esk1_0,nil) != esk1_0 ),
inference(cn,[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])]) ).
cnf(c_0_28,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_29,plain,
! [X47] :
( app(X47,nil) = X47
| ~ ssList(X47) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
cnf(c_0_30,negated_conjecture,
app(esk1_0,nil) != esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_25]),c_0_19])]) ).
cnf(c_0_31,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_32,negated_conjecture,
ssList(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC417+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.57 % Computer : n018.cluster.edu
% 0.11/0.57 % Model : x86_64 x86_64
% 0.11/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.57 % Memory : 8046.5625MB
% 0.11/0.57 % OS : Linux 6.8.0-71-generic
% 0.11/0.57 % CPULimit : 300
% 0.11/0.57 % WCLimit : 300
% 0.11/0.57 % DateTime : Mon Sep 21 08:24:44 UTC 2026
% 0.11/0.57 % CPUTime :
% 0.11/0.57 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.62 Running first-order theorem proving
% 0.11/0.62 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
% 0.15/0.68 % Version: 3.5.1
% 0.15/0.68 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.68 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.68 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.68 % Starting sh5l with 300s (1) cores
% 0.15/0.68 % new_bool_3 with pid 1440132 completed with status 0
% 0.15/0.68 % Result found by new_bool_3
% 0.15/0.68 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.68 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.68 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.68 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.68 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.15/0.68 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.68 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.68 % SubtermCWHack with pid 1440138 completed with status 0
% 0.15/0.68 % Result found by SubtermCWHack
% 0.15/0.68 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.68 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.68 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.68 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.68 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.15/0.68 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.68 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.68 % Preprocessing time : 0.002 s
% 0.15/0.68
% 0.15/0.68 % Proof found!
% 0.15/0.68 % SZS status Theorem
% 0.15/0.68 % SZS output start CNFRefutation
% See solution above
% 0.15/0.68 % Parsed axioms : 96
% 0.15/0.68 % Removed by relevancy pruning/SinE : 77
% 0.15/0.68 % Initial clauses : 45
% 0.15/0.68 % Removed in clause preprocessing : 0
% 0.15/0.68 % Initial clauses in saturation : 45
% 0.15/0.68 % Processed clauses : 527
% 0.15/0.68 % ...of these trivial : 13
% 0.15/0.68 % ...subsumed : 282
% 0.15/0.68 % ...remaining for further processing : 232
% 0.15/0.68 % Other redundant clauses eliminated : 20
% 0.15/0.68 % Clauses deleted for lack of memory : 0
% 0.15/0.68 % Backward-subsumed : 32
% 0.15/0.68 % Backward-rewritten : 8
% 0.15/0.68 % Generated clauses : 1251
% 0.15/0.68 % ...of the previous two non-redundant : 929
% 0.15/0.68 % ...aggressively subsumed : 0
% 0.15/0.68 % Contextual simplify-reflections : 33
% 0.15/0.68 % Paramodulations : 1227
% 0.15/0.68 % Factorizations : 0
% 0.15/0.68 % NegExts : 0
% 0.15/0.68 % Equation resolutions : 25
% 0.15/0.68 % Disequality decompositions : 0
% 0.15/0.68 % Total rewrite steps : 1321
% 0.15/0.68 % ...of those cached : 1296
% 0.15/0.68 % Propositional unsat checks : 0
% 0.15/0.68 % Propositional check models : 0
% 0.15/0.68 % Propositional check unsatisfiable : 0
% 0.15/0.68 % Propositional clauses : 0
% 0.15/0.68 % Propositional clauses after purity: 0
% 0.15/0.68 % Propositional unsat core size : 0
% 0.15/0.68 % Propositional preprocessing time : 0.000
% 0.15/0.68 % Propositional encoding time : 0.000
% 0.15/0.68 % Propositional solver time : 0.000
% 0.15/0.68 % Success case prop preproc time : 0.000
% 0.15/0.68 % Success case prop encoding time : 0.000
% 0.15/0.68 % Success case prop solver time : 0.000
% 0.15/0.68 % Current number of processed clauses : 189
% 0.15/0.68 % Positive orientable unit clauses : 31
% 0.15/0.68 % Positive unorientable unit clauses: 0
% 0.15/0.68 % Negative unit clauses : 17
% 0.15/0.68 % Non-unit-clauses : 141
% 0.15/0.68 % Current number of unprocessed clauses: 419
% 0.15/0.68 % ...number of literals in the above : 2151
% 0.15/0.68 % Current number of archived formulas : 0
% 0.15/0.68 % Current number of archived clauses : 40
% 0.15/0.68 % Clause-clause subsumption calls (NU) : 3902
% 0.15/0.68 % Rec. Clause-clause subsumption calls : 1824
% 0.15/0.68 % Non-unit clause-clause subsumptions : 279
% 0.15/0.68 % Unit Clause-clause subsumption calls : 173
% 0.15/0.68 % Rewrite failures with RHS unbound : 0
% 0.15/0.68 % BW rewrite match attempts : 6
% 0.15/0.68 % BW rewrite match successes : 6
% 0.15/0.68 % Condensation attempts : 0
% 0.15/0.68 % Condensation successes : 0
% 0.15/0.68 % Termbank termtop insertions : 23554
% 0.15/0.68 % Search garbage collected termcells : 1410
% 0.15/0.68
% 0.15/0.68 % -------------------------------------------------
% 0.15/0.68 % User time : 0.033 s
% 0.15/0.68 % System time : 0.004 s
% 0.15/0.68 % Total time : 0.037 s
% 0.15/0.68 % Maximum resident set size: 3760 pages
% 0.15/0.68
% 0.15/0.68 % -------------------------------------------------
% 0.15/0.68 % User time : 0.038 s
% 0.15/0.68 % System time : 0.007 s
% 0.15/0.68 % Total time : 0.045 s
% 0.15/0.68 % Maximum resident set size: 4864 pages
% 0.15/0.68 % E exiting
%------------------------------------------------------------------------------