%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC316-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 02:43:55 PM UTC 2026
% Result : Unsatisfiable 0.17s 5.48s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of clauses : 64 ( 22 unt; 4 nHn; 64 RR)
% Number of literals : 178 ( 61 equ; 121 neg)
% Maximal clause size : 13 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_16,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
cnf(co1_7,negated_conjecture,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
cnf(co1_14,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
cnf(co1_15,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
cnf(clause120,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause120) ).
cnf(clause118,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause118) ).
cnf(co1_18,negated_conjecture,
( ~ neq(sk4,nil)
| ~ neq(sk1,nil)
| ~ neq(nil,sk1)
| ~ neq(nil,sk1)
| hd(sk1) != X4
| cons(X4,nil) != X3
| ~ ssItem(X4)
| app(X2,X3) != X1
| tl(sk1) != X2
| ~ ssList(X3)
| ~ ssList(X2)
| sk2 != X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
cnf(clause96,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause96) ).
cnf(clause97,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause97) ).
cnf(co1_17,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
cnf(clause86,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(clause98,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause98) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(co1_2,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).
cnf(clause100,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause100) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
cnf(c_0_18,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk3 ),
inference(fof_simplification,[status(thm)],[co1_16]) ).
cnf(c_0_19,negated_conjecture,
neq(sk2,nil),
inference(fof_simplification,[status(thm)],[co1_7]) ).
cnf(c_0_20,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(fof_simplification,[status(thm)],[co1_14]) ).
cnf(c_0_21,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk6) ),
inference(fof_simplification,[status(thm)],[co1_15]) ).
cnf(c_0_22,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk3 ),
c_0_18 ).
cnf(c_0_23,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_24,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_25,negated_conjecture,
neq(sk2,nil),
c_0_19 ).
cnf(c_0_26,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
inference(fof_simplification,[status(thm)],[clause120]) ).
cnf(c_0_27,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
c_0_20 ).
cnf(c_0_28,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk6) ),
c_0_21 ).
cnf(c_0_29,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
inference(fof_simplification,[status(thm)],[clause118]) ).
cnf(c_0_30,negated_conjecture,
( ~ neq(sk4,nil)
| ~ neq(sk1,nil)
| ~ neq(nil,sk1)
| ~ neq(nil,sk1)
| hd(sk1) != X4
| cons(X4,nil) != X3
| ~ ssItem(X4)
| app(X2,X3) != X1
| tl(sk1) != X2
| ~ ssList(X3)
| ~ ssList(X2)
| sk2 != X1
| ~ ssList(X1) ),
inference(fof_simplification,[status(thm)],[co1_18]) ).
cnf(c_0_31,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = X2 ),
inference(fof_simplification,[status(thm)],[clause96]) ).
cnf(c_0_32,negated_conjecture,
app(cons(sk5,nil),sk6) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]) ).
cnf(c_0_33,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
c_0_26 ).
cnf(c_0_34,negated_conjecture,
ssItem(sk5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_24]),c_0_25])]) ).
cnf(c_0_35,negated_conjecture,
ssList(sk6),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_24]),c_0_25])]) ).
cnf(c_0_36,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
inference(fof_simplification,[status(thm)],[clause97]) ).
cnf(c_0_37,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk4 ),
inference(fof_simplification,[status(thm)],[co1_17]) ).
cnf(c_0_38,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
c_0_29 ).
cnf(c_0_39,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clause86]) ).
cnf(c_0_40,negated_conjecture,
( ~ neq(sk4,nil)
| ~ neq(sk1,nil)
| ~ neq(nil,sk1)
| ~ neq(nil,sk1)
| hd(sk1) != X4
| cons(X4,nil) != X3
| ~ ssItem(X4)
| app(X2,X3) != X1
| tl(sk1) != X2
| ~ ssList(X3)
| ~ ssList(X2)
| sk2 != X1
| ~ ssList(X1) ),
c_0_30 ).
cnf(c_0_41,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| tl(cons(X1,X2)) = X2 ),
c_0_31 ).
cnf(c_0_42,negated_conjecture,
cons(sk5,sk6) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_35])]) ).
cnf(c_0_43,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
c_0_36 ).
cnf(c_0_44,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk4 ),
c_0_37 ).
cnf(c_0_45,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
inference(fof_simplification,[status(thm)],[clause98]) ).
cnf(c_0_46,negated_conjecture,
( ~ ssList(cons(sk5,nil))
| sk1 != nil
| cons(sk5,nil) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_32]),c_0_35])]) ).
cnf(c_0_47,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
c_0_39 ).
cnf(c_0_48,axiom,
ssList(nil),
clause8 ).
cnf(c_0_49,negated_conjecture,
( ~ neq(sk4,nil)
| ~ neq(sk1,nil)
| ~ neq(nil,sk1)
| ~ ssItem(X4)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| cons(X4,nil) != X3
| app(X2,X3) != X1
| hd(sk1) != X4
| tl(sk1) != X2
| sk2 != X1 ),
inference(cn,[status(thm)],[c_0_40]) ).
cnf(c_0_50,negated_conjecture,
tl(sk1) = sk6,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_34]),c_0_35])]) ).
cnf(c_0_51,negated_conjecture,
hd(sk1) = sk5,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_42]),c_0_34]),c_0_35])]) ).
cnf(c_0_52,negated_conjecture,
app(sk6,cons(sk5,nil)) = sk2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_24]),c_0_24]),c_0_25])]) ).
cnf(c_0_53,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_54,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
inference(fof_simplification,[status(thm)],[clause100]) ).
cnf(c_0_55,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
c_0_45 ).
cnf(c_0_56,negated_conjecture,
( sk1 != nil
| cons(sk5,nil) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_34]),c_0_48])]) ).
cnf(c_0_57,negated_conjecture,
( ~ ssList(cons(sk5,nil))
| ~ neq(sk1,nil)
| ~ neq(nil,sk1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_24]),c_0_25])])])])])]),c_0_52]),c_0_34]),c_0_35]),c_0_52]),c_0_53])]) ).
cnf(c_0_58,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
c_0_54 ).
cnf(c_0_59,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_60,negated_conjecture,
sk1 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_34]),c_0_48])]) ).
cnf(c_0_61,negated_conjecture,
( ~ ssList(cons(sk5,nil))
| ~ neq(nil,sk1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]),c_0_48])]),c_0_60]) ).
cnf(c_0_62,negated_conjecture,
~ ssList(cons(sk5,nil)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_58]),c_0_48]),c_0_59])]),c_0_60]) ).
cnf(c_0_63,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_47]),c_0_34]),c_0_48])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC316-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/5.39 % Computer : n017.cluster.edu
% 0.13/5.39 % Model : x86_64 x86_64
% 0.13/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.39 % Memory : 8046.5625MB
% 0.13/5.39 % OS : Linux 6.8.0-71-generic
% 0.13/5.39 % CPULimit : 300
% 0.13/5.39 % WCLimit : 300
% 0.13/5.39 % DateTime : Mon Sep 21 08:10:18 UTC 2026
% 0.13/5.39 % CPUTime :
% 0.13/5.39 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/5.44 Running first-order theorem proving
% 0.17/5.44 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
% 0.17/5.48 % Version: 3.5.1
% 0.17/5.48 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.17/5.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/5.48 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.17/5.48 % Starting new_bool_3 with 300s (1) cores
% 0.17/5.48 % Starting new_bool_1 with 300s (1) cores
% 0.17/5.48 % Starting sh5l with 300s (1) cores
% 0.17/5.48 % new_bool_3 with pid 1864925 completed with status 0
% 0.17/5.48 % Result found by new_bool_3
% 0.17/5.48 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.17/5.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/5.48 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.17/5.48 % Starting new_bool_3 with 300s (1) cores
% 0.17/5.48 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/5.48 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/5.48 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.17/5.48 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.17/5.48 % Starting SubtermCWHack with 31s (1) cores
% 0.17/5.48 % SubtermCWHack with pid 1864928 completed with status 0
% 0.17/5.48 % Result found by SubtermCWHack
% 0.17/5.48 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.17/5.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/5.48 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.17/5.48 % Starting new_bool_3 with 300s (1) cores
% 0.17/5.48 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/5.48 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/5.48 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.17/5.48 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.17/5.48 % Starting SubtermCWHack with 31s (1) cores
% 0.17/5.48 % Preprocessing time : 0.002 s
% 0.17/5.48
% 0.17/5.48 % Proof found!
% 0.17/5.48 % SZS status Unsatisfiable
% 0.17/5.48 % SZS output start CNFRefutation
% See solution above
% 0.17/5.48 % Parsed axioms : 203
% 0.17/5.48 % Removed by relevancy pruning/SinE : 129
% 0.17/5.48 % Initial clauses : 74
% 0.17/5.48 % Removed in clause preprocessing : 0
% 0.17/5.48 % Initial clauses in saturation : 74
% 0.17/5.48 % Processed clauses : 206
% 0.17/5.48 % ...of these trivial : 8
% 0.17/5.48 % ...subsumed : 46
% 0.17/5.48 % ...remaining for further processing : 152
% 0.17/5.48 % Other redundant clauses eliminated : 23
% 0.17/5.48 % Clauses deleted for lack of memory : 0
% 0.17/5.48 % Backward-subsumed : 35
% 0.17/5.48 % Backward-rewritten : 5
% 0.17/5.48 % Generated clauses : 510
% 0.17/5.48 % ...of the previous two non-redundant : 367
% 0.17/5.48 % ...aggressively subsumed : 0
% 0.17/5.48 % Contextual simplify-reflections : 3
% 0.17/5.48 % Paramodulations : 486
% 0.17/5.48 % Factorizations : 0
% 0.17/5.48 % NegExts : 0
% 0.17/5.48 % Equation resolutions : 28
% 0.17/5.48 % Disequality decompositions : 0
% 0.17/5.48 % Total rewrite steps : 522
% 0.17/5.48 % ...of those cached : 504
% 0.17/5.48 % Propositional unsat checks : 0
% 0.17/5.48 % Propositional check models : 0
% 0.17/5.48 % Propositional check unsatisfiable : 0
% 0.17/5.48 % Propositional clauses : 0
% 0.17/5.48 % Propositional clauses after purity: 0
% 0.17/5.48 % Propositional unsat core size : 0
% 0.17/5.48 % Propositional preprocessing time : 0.000
% 0.17/5.48 % Propositional encoding time : 0.000
% 0.17/5.48 % Propositional solver time : 0.000
% 0.17/5.48 % Success case prop preproc time : 0.000
% 0.17/5.48 % Success case prop encoding time : 0.000
% 0.17/5.48 % Success case prop solver time : 0.000
% 0.17/5.48 % Current number of processed clauses : 105
% 0.17/5.48 % Positive orientable unit clauses : 19
% 0.17/5.48 % Positive unorientable unit clauses: 0
% 0.17/5.48 % Negative unit clauses : 5
% 0.17/5.48 % Non-unit-clauses : 81
% 0.17/5.48 % Current number of unprocessed clauses: 207
% 0.17/5.48 % ...number of literals in the above : 1110
% 0.17/5.48 % Current number of archived formulas : 0
% 0.17/5.48 % Current number of archived clauses : 40
% 0.17/5.48 % Clause-clause subsumption calls (NU) : 1417
% 0.17/5.48 % Rec. Clause-clause subsumption calls : 568
% 0.17/5.48 % Non-unit clause-clause subsumptions : 47
% 0.17/5.48 % Unit Clause-clause subsumption calls : 144
% 0.17/5.48 % Rewrite failures with RHS unbound : 0
% 0.17/5.48 % BW rewrite match attempts : 3
% 0.17/5.48 % BW rewrite match successes : 3
% 0.17/5.48 % Condensation attempts : 0
% 0.17/5.48 % Condensation successes : 0
% 0.17/5.48 % Termbank termtop insertions : 12515
% 0.17/5.48 % Search garbage collected termcells : 885
% 0.17/5.48
% 0.17/5.48 % -------------------------------------------------
% 0.17/5.48 % User time : 0.018 s
% 0.17/5.48 % System time : 0.004 s
% 0.17/5.48 % Total time : 0.023 s
% 0.17/5.48 % Maximum resident set size: 4072 pages
% 0.17/5.48
% 0.17/5.48 % -------------------------------------------------
% 0.17/5.48 % User time : 0.023 s
% 0.17/5.48 % System time : 0.009 s
% 0.17/5.48 % Total time : 0.032 s
% 0.17/5.48 % Maximum resident set size: 4864 pages
% 0.17/5.48 % E exiting
%------------------------------------------------------------------------------