%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC416-1 : 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 : n004.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 : Unsatisfiable 0.25s 0.64s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of clauses : 56 ( 19 unt; 4 nHn; 56 RR)
% Number of literals : 140 ( 54 equ; 89 neg)
% Maximal clause size : 9 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_14,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk3) = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
cnf(co1_7,negated_conjecture,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
cnf(clause119,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause119) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
cnf(co1_13,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
cnf(clause86,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(clause120,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause120) ).
cnf(clause73,axiom,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause73) ).
cnf(clause97,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause97) ).
cnf(co1_12,negated_conjecture,
( ~ neq(sk4,nil)
| ~ neq(nil,sk2)
| hd(sk2) != X3
| cons(X3,nil) != X2
| ~ ssItem(X3)
| app(X2,sk1) != X1
| ~ ssList(X2)
| sk2 != X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
cnf(clause98,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause98) ).
cnf(co1_2,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
cnf(clause100,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).
cnf(c_0_16,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk3) = sk4 ),
inference(fof_simplification,[status(thm)],[co1_14]) ).
cnf(c_0_17,negated_conjecture,
neq(sk2,nil),
inference(fof_simplification,[status(thm)],[co1_7]) ).
cnf(c_0_18,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X2 ),
inference(fof_simplification,[status(thm)],[clause119]) ).
cnf(c_0_19,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk3) = sk4 ),
c_0_16 ).
cnf(c_0_20,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_21,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_22,negated_conjecture,
neq(sk2,nil),
c_0_17 ).
cnf(c_0_23,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(fof_simplification,[status(thm)],[co1_13]) ).
cnf(c_0_24,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X2 ),
c_0_18 ).
cnf(c_0_25,negated_conjecture,
app(cons(sk5,nil),sk1) = sk2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_21]),c_0_22])]) ).
cnf(c_0_26,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_27,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clause86]) ).
cnf(c_0_28,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
c_0_23 ).
cnf(c_0_29,negated_conjecture,
( ~ ssList(cons(sk5,nil))
| sk2 != nil
| sk1 = 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_30,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
c_0_27 ).
cnf(c_0_31,negated_conjecture,
ssItem(sk5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_21]),c_0_22])]) ).
cnf(c_0_32,axiom,
ssList(nil),
clause8 ).
cnf(c_0_33,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
inference(fof_simplification,[status(thm)],[clause120]) ).
cnf(c_0_34,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_simplification,[status(thm)],[clause73]) ).
cnf(c_0_35,negated_conjecture,
( sk2 != nil
| sk1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32])]) ).
cnf(c_0_36,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
inference(fof_simplification,[status(thm)],[clause97]) ).
cnf(c_0_37,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
c_0_33 ).
cnf(c_0_38,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
c_0_34 ).
cnf(c_0_39,negated_conjecture,
( sk2 != nil
| app(cons(sk5,nil),nil) = sk2 ),
inference(spm,[status(thm)],[c_0_25,c_0_35]) ).
cnf(c_0_40,negated_conjecture,
( ~ neq(sk4,nil)
| ~ neq(nil,sk2)
| hd(sk2) != X3
| cons(X3,nil) != X2
| ~ ssItem(X3)
| app(X2,sk1) != X1
| ~ ssList(X2)
| sk2 != X1
| ~ ssList(X1) ),
inference(fof_simplification,[status(thm)],[co1_12]) ).
cnf(c_0_41,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| hd(cons(X1,X2)) = X1 ),
c_0_36 ).
cnf(c_0_42,negated_conjecture,
cons(sk5,sk1) = sk2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_37]),c_0_31]),c_0_26])]) ).
cnf(c_0_43,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
inference(fof_simplification,[status(thm)],[clause98]) ).
cnf(c_0_44,negated_conjecture,
( ~ ssList(cons(sk5,nil))
| sk2 != nil
| cons(sk5,nil) = sk2 ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_45,negated_conjecture,
( ~ neq(sk4,nil)
| ~ neq(nil,sk2)
| hd(sk2) != X3
| cons(X3,nil) != X2
| ~ ssItem(X3)
| app(X2,sk1) != X1
| ~ ssList(X2)
| sk2 != X1
| ~ ssList(X1) ),
c_0_40 ).
cnf(c_0_46,negated_conjecture,
hd(sk2) = sk5,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_31]),c_0_26])]) ).
cnf(c_0_47,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_48,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
inference(fof_simplification,[status(thm)],[clause100]) ).
cnf(c_0_49,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
c_0_43 ).
cnf(c_0_50,negated_conjecture,
( sk2 != nil
| cons(sk5,nil) = sk2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_30]),c_0_31]),c_0_32])]) ).
cnf(c_0_51,negated_conjecture,
( ~ ssList(cons(sk5,nil))
| ~ neq(nil,sk2) ),
inference(cn,[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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46]),c_0_21]),c_0_22])])])])]),c_0_25]),c_0_31]),c_0_25]),c_0_47])]) ).
cnf(c_0_52,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
c_0_48 ).
cnf(c_0_53,negated_conjecture,
sk2 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_31]),c_0_32])]) ).
cnf(c_0_54,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_51,c_0_52]),c_0_32]),c_0_47])]),c_0_53]) ).
cnf(c_0_55,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_30]),c_0_31]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC416-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.44 % Computer : n004.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Mon Sep 21 08:22:34 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.54 Running first-order theorem proving
% 0.25/0.54 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
% 0.25/0.64 % Version: 3.5.1
% 0.25/0.64 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.25/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.64 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.25/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.64 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.64 % Starting sh5l with 300s (1) cores
% 0.25/0.64 % new_bool_3 with pid 2700136 completed with status 0
% 0.25/0.64 % Result found by new_bool_3
% 0.25/0.64 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.25/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.64 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.25/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.64 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.25/0.64 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.25/0.64 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.25/0.64 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.64 % Starting SubtermCWHack with 31s (1) cores
% 0.25/0.64 % SubtermCWHack with pid 2700139 completed with status 0
% 0.25/0.64 % Result found by SubtermCWHack
% 0.25/0.64 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.25/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.64 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.25/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.64 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.25/0.64 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.25/0.64 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.25/0.64 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.64 % Starting SubtermCWHack with 31s (1) cores
% 0.25/0.64 % Preprocessing time : 0.003 s
% 0.25/0.64
% 0.25/0.64 % Proof found!
% 0.25/0.64 % SZS status Unsatisfiable
% 0.25/0.64 % SZS output start CNFRefutation
% See solution above
% 0.25/0.64 % Parsed axioms : 199
% 0.25/0.64 % Removed by relevancy pruning/SinE : 135
% 0.25/0.64 % Initial clauses : 64
% 0.25/0.64 % Removed in clause preprocessing : 0
% 0.25/0.64 % Initial clauses in saturation : 64
% 0.25/0.64 % Processed clauses : 156
% 0.25/0.64 % ...of these trivial : 4
% 0.25/0.64 % ...subsumed : 39
% 0.25/0.64 % ...remaining for further processing : 113
% 0.25/0.64 % Other redundant clauses eliminated : 14
% 0.25/0.64 % Clauses deleted for lack of memory : 0
% 0.25/0.64 % Backward-subsumed : 15
% 0.25/0.64 % Backward-rewritten : 5
% 0.25/0.64 % Generated clauses : 292
% 0.25/0.64 % ...of the previous two non-redundant : 222
% 0.25/0.64 % ...aggressively subsumed : 0
% 0.25/0.64 % Contextual simplify-reflections : 1
% 0.25/0.64 % Paramodulations : 277
% 0.25/0.64 % Factorizations : 0
% 0.25/0.64 % NegExts : 0
% 0.25/0.64 % Equation resolutions : 18
% 0.25/0.64 % Disequality decompositions : 0
% 0.25/0.64 % Total rewrite steps : 294
% 0.25/0.64 % ...of those cached : 281
% 0.25/0.64 % Propositional unsat checks : 0
% 0.25/0.64 % Propositional check models : 0
% 0.25/0.64 % Propositional check unsatisfiable : 0
% 0.25/0.64 % Propositional clauses : 0
% 0.25/0.64 % Propositional clauses after purity: 0
% 0.25/0.64 % Propositional unsat core size : 0
% 0.25/0.64 % Propositional preprocessing time : 0.000
% 0.25/0.64 % Propositional encoding time : 0.000
% 0.25/0.64 % Propositional solver time : 0.000
% 0.25/0.64 % Success case prop preproc time : 0.000
% 0.25/0.64 % Success case prop encoding time : 0.000
% 0.25/0.64 % Success case prop solver time : 0.000
% 0.25/0.64 % Current number of processed clauses : 86
% 0.25/0.64 % Positive orientable unit clauses : 15
% 0.25/0.64 % Positive unorientable unit clauses: 0
% 0.25/0.64 % Negative unit clauses : 4
% 0.25/0.64 % Non-unit-clauses : 67
% 0.25/0.64 % Current number of unprocessed clauses: 122
% 0.25/0.64 % ...number of literals in the above : 654
% 0.25/0.64 % Current number of archived formulas : 0
% 0.25/0.64 % Current number of archived clauses : 20
% 0.25/0.64 % Clause-clause subsumption calls (NU) : 804
% 0.25/0.64 % Rec. Clause-clause subsumption calls : 262
% 0.25/0.64 % Non-unit clause-clause subsumptions : 35
% 0.25/0.64 % Unit Clause-clause subsumption calls : 33
% 0.25/0.64 % Rewrite failures with RHS unbound : 0
% 0.25/0.64 % BW rewrite match attempts : 3
% 0.25/0.64 % BW rewrite match successes : 3
% 0.25/0.64 % Condensation attempts : 0
% 0.25/0.64 % Condensation successes : 0
% 0.25/0.64 % Termbank termtop insertions : 8937
% 0.25/0.64 % Search garbage collected termcells : 885
% 0.25/0.64
% 0.25/0.64 % -------------------------------------------------
% 0.25/0.64 % User time : 0.022 s
% 0.25/0.64 % System time : 0.005 s
% 0.25/0.64 % Total time : 0.027 s
% 0.25/0.64 % Maximum resident set size: 4068 pages
% 0.25/0.64
% 0.25/0.64 % -------------------------------------------------
% 0.25/0.64 % User time : 0.028 s
% 0.25/0.64 % System time : 0.013 s
% 0.25/0.64 % Total time : 0.041 s
% 0.25/0.64 % Maximum resident set size: 5120 pages
% 0.25/0.64 % E exiting
%------------------------------------------------------------------------------