%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC029-1 : 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 : n010.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 02:42:41 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.64s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of clauses : 60 ( 16 unt; 6 nHn; 60 RR)
% Number of literals : 127 ( 59 equ; 65 neg)
% Maximal clause size : 4 ( 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; 7 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_7,negated_conjecture,
( nil != sk4
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
cnf(co1_12,negated_conjecture,
( nil = sk1
| nil = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
cnf(co1_15,negated_conjecture,
( nil != sk2
| nil != sk1 ),
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_11,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
cnf(co1_9,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
cnf(clause100,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause100) ).
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_4,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(co1_8,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
cnf(clause86,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(co1_10,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
cnf(clause73,axiom,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
cnf(clause119,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause119) ).
cnf(c_0_16,negated_conjecture,
( nil != sk4
| nil = sk3 ),
inference(fof_simplification,[status(thm)],[co1_7]) ).
cnf(c_0_17,negated_conjecture,
( nil = sk1
| nil = sk2 ),
co1_12 ).
cnf(c_0_18,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_19,negated_conjecture,
( nil != sk2
| nil != sk1 ),
inference(fof_simplification,[status(thm)],[co1_15]) ).
cnf(c_0_20,negated_conjecture,
( nil != sk4
| nil = sk3 ),
c_0_16 ).
cnf(c_0_21,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_22,negated_conjecture,
( sk1 = nil
| sk4 = nil ),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk3 ),
inference(fof_simplification,[status(thm)],[co1_11]) ).
cnf(c_0_24,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk6) ),
inference(fof_simplification,[status(thm)],[co1_9]) ).
cnf(c_0_25,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
inference(fof_simplification,[status(thm)],[clause100]) ).
cnf(c_0_26,negated_conjecture,
( nil != sk2
| nil != sk1 ),
c_0_19 ).
cnf(c_0_27,negated_conjecture,
sk1 = nil,
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_28,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
inference(fof_simplification,[status(thm)],[clause118]) ).
cnf(c_0_29,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk3 ),
c_0_23 ).
cnf(c_0_30,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk6) ),
c_0_24 ).
cnf(c_0_31,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
c_0_25 ).
cnf(c_0_32,negated_conjecture,
ssList(sk4),
co1_4 ).
cnf(c_0_33,axiom,
ssList(nil),
clause8 ).
cnf(c_0_34,negated_conjecture,
sk4 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_18])]) ).
cnf(c_0_35,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X1 ),
c_0_28 ).
cnf(c_0_36,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_21]),c_0_27]) ).
cnf(c_0_37,negated_conjecture,
ssList(sk6),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_38,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(fof_simplification,[status(thm)],[co1_8]) ).
cnf(c_0_39,negated_conjecture,
( ~ ssList(cons(sk5,nil))
| ~ neq(sk4,nil)
| sk6 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).
cnf(c_0_40,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clause86]) ).
cnf(c_0_41,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
c_0_38 ).
cnf(c_0_42,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk4 ),
inference(fof_simplification,[status(thm)],[co1_10]) ).
cnf(c_0_43,negated_conjecture,
( ~ ssList(cons(sk5,nil))
| sk6 = nil ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_31]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_44,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
c_0_40 ).
cnf(c_0_45,negated_conjecture,
ssItem(sk5),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_31]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_46,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_simplification,[status(thm)],[clause73]) ).
cnf(c_0_47,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk4 ),
c_0_42 ).
cnf(c_0_48,negated_conjecture,
sk6 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_33])]) ).
cnf(c_0_49,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
c_0_46 ).
cnf(c_0_50,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),nil) = sk4 ),
inference(rw,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_51,negated_conjecture,
( ~ ssList(cons(sk5,nil))
| ~ neq(sk4,nil)
| cons(sk5,nil) = sk4 ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_52,negated_conjecture,
( ~ ssList(cons(sk5,nil))
| cons(sk5,nil) = sk4 ),
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_31]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_53,negated_conjecture,
( ~ neq(sk4,nil)
| app(nil,cons(sk5,nil)) = nil ),
inference(rw,[status(thm)],[c_0_36,c_0_48]) ).
cnf(c_0_54,negated_conjecture,
cons(sk5,nil) = sk4,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_44]),c_0_45]),c_0_33])]) ).
cnf(c_0_55,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X2 ),
inference(fof_simplification,[status(thm)],[clause119]) ).
cnf(c_0_56,negated_conjecture,
( ~ neq(sk4,nil)
| app(nil,sk4) = nil ),
inference(rw,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_57,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X2 ),
c_0_55 ).
cnf(c_0_58,negated_conjecture,
app(nil,sk4) = nil,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_31]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_59,negated_conjecture,
$false,
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_32]),c_0_33])]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC029-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.57 % Computer : n010.cluster.edu
% 0.12/0.57 % Model : x86_64 x86_64
% 0.12/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.57 % Memory : 8046.5625MB
% 0.12/0.57 % OS : Linux 6.8.0-71-generic
% 0.12/0.57 % CPULimit : 300
% 0.12/0.57 % WCLimit : 300
% 0.12/0.57 % DateTime : Mon Sep 21 07:50:41 UTC 2026
% 0.12/0.58 % CPUTime :
% 0.12/0.58 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.61 Running first-order theorem proving
% 0.12/0.61 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
% 0.15/0.64 % Version: 3.5.1
% 0.15/0.64 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.64 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.64 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.64 % Starting sh5l with 300s (1) cores
% 0.15/0.64 % new_bool_3 with pid 406477 completed with status 0
% 0.15/0.64 % Result found by new_bool_3
% 0.15/0.64 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.64 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.64 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.64 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.64 % Search class: FGHSF-FFMM22-SFFFFFNN
% 0.15/0.64 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.64 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.64 % SubtermCWHack with pid 406480 completed with status 0
% 0.15/0.64 % Result found by SubtermCWHack
% 0.15/0.64 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.64 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.64 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.64 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.64 % Search class: FGHSF-FFMM22-SFFFFFNN
% 0.15/0.64 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.64 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.64 % Preprocessing time : 0.002 s
% 0.15/0.64
% 0.15/0.64 % Proof found!
% 0.15/0.64 % SZS status Unsatisfiable
% 0.15/0.64 % SZS output start CNFRefutation
% See solution above
% 0.15/0.64 % Parsed axioms : 200
% 0.15/0.64 % Removed by relevancy pruning/SinE : 164
% 0.15/0.64 % Initial clauses : 36
% 0.15/0.64 % Removed in clause preprocessing : 2
% 0.15/0.64 % Initial clauses in saturation : 34
% 0.15/0.64 % Processed clauses : 46
% 0.15/0.64 % ...of these trivial : 0
% 0.15/0.64 % ...subsumed : 2
% 0.15/0.64 % ...remaining for further processing : 44
% 0.15/0.64 % Other redundant clauses eliminated : 4
% 0.15/0.64 % Clauses deleted for lack of memory : 0
% 0.15/0.64 % Backward-subsumed : 3
% 0.15/0.64 % Backward-rewritten : 14
% 0.15/0.64 % Generated clauses : 42
% 0.15/0.64 % ...of the previous two non-redundant : 33
% 0.15/0.64 % ...aggressively subsumed : 0
% 0.15/0.64 % Contextual simplify-reflections : 1
% 0.15/0.64 % Paramodulations : 39
% 0.15/0.64 % Factorizations : 0
% 0.15/0.64 % NegExts : 0
% 0.15/0.64 % Equation resolutions : 4
% 0.15/0.64 % Disequality decompositions : 0
% 0.15/0.64 % Total rewrite steps : 72
% 0.15/0.64 % ...of those cached : 61
% 0.15/0.64 % Propositional unsat checks : 0
% 0.15/0.64 % Propositional check models : 0
% 0.15/0.64 % Propositional check unsatisfiable : 0
% 0.15/0.64 % Propositional clauses : 0
% 0.15/0.64 % Propositional clauses after purity: 0
% 0.15/0.64 % Propositional unsat core size : 0
% 0.15/0.64 % Propositional preprocessing time : 0.000
% 0.15/0.64 % Propositional encoding time : 0.000
% 0.15/0.64 % Propositional solver time : 0.000
% 0.15/0.64 % Success case prop preproc time : 0.000
% 0.15/0.64 % Success case prop encoding time : 0.000
% 0.15/0.64 % Success case prop solver time : 0.000
% 0.15/0.64 % Current number of processed clauses : 24
% 0.15/0.64 % Positive orientable unit clauses : 10
% 0.15/0.64 % Positive unorientable unit clauses: 0
% 0.15/0.64 % Negative unit clauses : 1
% 0.15/0.64 % Non-unit-clauses : 13
% 0.15/0.64 % Current number of unprocessed clauses: 18
% 0.15/0.64 % ...number of literals in the above : 73
% 0.15/0.64 % Current number of archived formulas : 0
% 0.15/0.64 % Current number of archived clauses : 17
% 0.15/0.64 % Clause-clause subsumption calls (NU) : 60
% 0.15/0.64 % Rec. Clause-clause subsumption calls : 39
% 0.15/0.64 % Non-unit clause-clause subsumptions : 3
% 0.15/0.64 % Unit Clause-clause subsumption calls : 3
% 0.15/0.64 % Rewrite failures with RHS unbound : 0
% 0.15/0.64 % BW rewrite match attempts : 8
% 0.15/0.64 % BW rewrite match successes : 8
% 0.15/0.64 % Condensation attempts : 0
% 0.15/0.64 % Condensation successes : 0
% 0.15/0.64 % Termbank termtop insertions : 3411
% 0.15/0.64 % Search garbage collected termcells : 930
% 0.15/0.64
% 0.15/0.64 % -------------------------------------------------
% 0.15/0.64 % User time : 0.004 s
% 0.15/0.64 % System time : 0.005 s
% 0.15/0.64 % Total time : 0.009 s
% 0.15/0.64 % Maximum resident set size: 3812 pages
% 0.15/0.64
% 0.15/0.64 % -------------------------------------------------
% 0.15/0.64 % User time : 0.009 s
% 0.15/0.64 % System time : 0.010 s
% 0.15/0.64 % Total time : 0.018 s
% 0.15/0.64 % Maximum resident set size: 4864 pages
% 0.15/0.64 % E exiting
%------------------------------------------------------------------------------