%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC109-1 : 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 : n006.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 02:43:02 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.45s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 19
% Syntax : Number of clauses : 67 ( 15 unt; 13 nHn; 67 RR)
% Number of literals : 162 ( 61 equ; 92 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_23,negated_conjecture,
( nil != sk1
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_23) ).
cnf(clause98,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause98) ).
cnf(clause115,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ neq(X1,X2)
| X1 != X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause115) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
cnf(co1_11,negated_conjecture,
( nil = sk4
| cons(sk5,nil) = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(co1_7,negated_conjecture,
( nil = sk4
| ssItem(sk5) ),
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_18,negated_conjecture,
( nil = sk3
| app(app(sk6,sk3),sk7) = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).
cnf(co1_16,negated_conjecture,
( nil = sk3
| ssList(sk7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
cnf(clause85,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
cnf(co1_15,negated_conjecture,
( nil = sk3
| ssList(sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
cnf(co1_3,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
cnf(clause73,axiom,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause73) ).
cnf(co1_22,negated_conjecture,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil)
| nil = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_22) ).
cnf(clause100,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).
cnf(clause172,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ segmentP(X1,X2)
| segmentP(app(app(X4,X1),X3),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause172) ).
cnf(clause57,axiom,
( ~ ssList(X1)
| segmentP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause57) ).
cnf(c_0_19,negated_conjecture,
( nil != sk1
| neq(sk2,nil) ),
inference(fof_simplification,[status(thm)],[co1_23]) ).
cnf(c_0_20,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
inference(fof_simplification,[status(thm)],[clause98]) ).
cnf(c_0_21,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ neq(X1,X2)
| X1 != X2 ),
inference(fof_simplification,[status(thm)],[clause115]) ).
cnf(c_0_22,negated_conjecture,
( nil != sk1
| neq(sk2,nil) ),
c_0_19 ).
cnf(c_0_23,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_24,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_25,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
c_0_20 ).
cnf(c_0_26,negated_conjecture,
( nil = sk4
| cons(sk5,nil) = sk3 ),
co1_11 ).
cnf(c_0_27,axiom,
ssList(nil),
clause8 ).
cnf(c_0_28,negated_conjecture,
( nil = sk4
| ssItem(sk5) ),
co1_7 ).
cnf(c_0_29,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ neq(X1,X2)
| X1 != X2 ),
c_0_21 ).
cnf(c_0_30,negated_conjecture,
( sk3 != nil
| neq(sk4,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_31,negated_conjecture,
( sk3 != nil
| sk4 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]),c_0_28]) ).
cnf(c_0_32,plain,
( ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_33,negated_conjecture,
( sk3 != nil
| neq(nil,nil) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X2 ),
inference(fof_simplification,[status(thm)],[clause119]) ).
cnf(c_0_35,negated_conjecture,
( nil = sk3
| app(app(sk6,sk3),sk7) = sk4 ),
co1_18 ).
cnf(c_0_36,negated_conjecture,
sk3 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_27])]) ).
cnf(c_0_37,negated_conjecture,
( nil = sk3
| ssList(sk7) ),
co1_16 ).
cnf(c_0_38,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != nil
| nil = X2 ),
c_0_34 ).
cnf(c_0_39,negated_conjecture,
app(app(sk6,sk3),sk7) = sk4,
inference(sr,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
ssList(sk7),
inference(sr,[status(thm)],[c_0_37,c_0_36]) ).
cnf(c_0_41,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
inference(fof_simplification,[status(thm)],[clause85]) ).
cnf(c_0_42,negated_conjecture,
( nil = sk3
| ssList(sk6) ),
co1_15 ).
cnf(c_0_43,negated_conjecture,
( ~ ssList(app(sk6,sk3))
| sk4 != nil
| sk7 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).
cnf(c_0_44,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
c_0_41 ).
cnf(c_0_45,negated_conjecture,
ssList(sk6),
inference(sr,[status(thm)],[c_0_42,c_0_36]) ).
cnf(c_0_46,negated_conjecture,
ssList(sk3),
co1_3 ).
cnf(c_0_47,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_simplification,[status(thm)],[clause73]) ).
cnf(c_0_48,negated_conjecture,
( sk4 != nil
| sk7 = 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_46])]) ).
cnf(c_0_49,negated_conjecture,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil)
| nil = sk2 ),
inference(fof_simplification,[status(thm)],[co1_22]) ).
cnf(c_0_50,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
c_0_47 ).
cnf(c_0_51,negated_conjecture,
( sk4 != nil
| app(app(sk6,sk3),nil) = sk4 ),
inference(spm,[status(thm)],[c_0_39,c_0_48]) ).
cnf(c_0_52,negated_conjecture,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil)
| nil = sk2 ),
c_0_49 ).
cnf(c_0_53,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
inference(fof_simplification,[status(thm)],[clause100]) ).
cnf(c_0_54,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ segmentP(X1,X2)
| segmentP(app(app(X4,X1),X3),X2) ),
inference(fof_simplification,[status(thm)],[clause172]) ).
cnf(c_0_55,negated_conjecture,
( ~ ssList(app(sk6,sk3))
| sk4 != nil
| app(sk6,sk3) = sk4 ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_56,negated_conjecture,
( ~ segmentP(sk4,sk3)
| ~ neq(sk3,nil)
| sk4 = nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_23]),c_0_23]),c_0_24]),c_0_24]) ).
cnf(c_0_57,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
c_0_53 ).
cnf(c_0_58,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ segmentP(X1,X2)
| segmentP(app(app(X4,X1),X3),X2) ),
c_0_54 ).
cnf(c_0_59,negated_conjecture,
( sk4 != nil
| app(sk6,sk3) = sk4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_44]),c_0_45]),c_0_46])]) ).
cnf(c_0_60,negated_conjecture,
( ~ segmentP(sk4,sk3)
| sk4 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_46]),c_0_27])]),c_0_31]) ).
cnf(c_0_61,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(sk3,X1)
| segmentP(sk4,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_39]),c_0_45]),c_0_40]),c_0_46])]) ).
cnf(c_0_62,negated_conjecture,
sk4 != nil,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_59]),c_0_46]),c_0_45])]),c_0_36]) ).
cnf(c_0_63,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(fof_simplification,[status(thm)],[clause57]) ).
cnf(c_0_64,negated_conjecture,
~ segmentP(sk3,sk3),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_46])]),c_0_62]) ).
cnf(c_0_65,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
c_0_63 ).
cnf(c_0_66,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_46])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC109-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 07:55:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.45 % Version: 3.5.1
% 0.10/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.10/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.10/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.45 % Starting sh5l with 300s (1) cores
% 0.10/0.45 % new_bool_3 with pid 2362466 completed with status 0
% 0.10/0.45 % Result found by new_bool_3
% 0.10/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.10/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.10/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.45 % Search class: FGHSF-FFMM22-SFFFFFNN
% 0.10/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.45 % SubtermCWHack with pid 2362470 completed with status 0
% 0.10/0.45 % Result found by SubtermCWHack
% 0.10/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.10/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.10/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.45 % Search class: FGHSF-FFMM22-SFFFFFNN
% 0.10/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.45 % Preprocessing time : 0.001 s
% 0.10/0.45
% 0.10/0.45 % Proof found!
% 0.10/0.45 % SZS status Unsatisfiable
% 0.10/0.45 % SZS output start CNFRefutation
% See solution above
% 0.10/0.45 % Parsed axioms : 209
% 0.10/0.45 % Removed by relevancy pruning/SinE : 137
% 0.10/0.45 % Initial clauses : 72
% 0.10/0.45 % Removed in clause preprocessing : 0
% 0.10/0.45 % Initial clauses in saturation : 72
% 0.10/0.45 % Processed clauses : 223
% 0.10/0.45 % ...of these trivial : 2
% 0.10/0.45 % ...subsumed : 67
% 0.10/0.45 % ...remaining for further processing : 154
% 0.10/0.45 % Other redundant clauses eliminated : 13
% 0.10/0.45 % Clauses deleted for lack of memory : 0
% 0.10/0.45 % Backward-subsumed : 22
% 0.10/0.45 % Backward-rewritten : 3
% 0.10/0.45 % Generated clauses : 582
% 0.10/0.45 % ...of the previous two non-redundant : 416
% 0.10/0.45 % ...aggressively subsumed : 0
% 0.10/0.45 % Contextual simplify-reflections : 3
% 0.10/0.45 % Paramodulations : 560
% 0.10/0.45 % Factorizations : 0
% 0.10/0.45 % NegExts : 0
% 0.10/0.45 % Equation resolutions : 17
% 0.10/0.45 % Disequality decompositions : 0
% 0.10/0.45 % Total rewrite steps : 635
% 0.10/0.45 % ...of those cached : 617
% 0.10/0.45 % Propositional unsat checks : 0
% 0.10/0.45 % Propositional check models : 0
% 0.10/0.45 % Propositional check unsatisfiable : 0
% 0.10/0.45 % Propositional clauses : 0
% 0.10/0.45 % Propositional clauses after purity: 0
% 0.10/0.45 % Propositional unsat core size : 0
% 0.10/0.45 % Propositional preprocessing time : 0.000
% 0.10/0.45 % Propositional encoding time : 0.000
% 0.10/0.45 % Propositional solver time : 0.000
% 0.10/0.45 % Success case prop preproc time : 0.000
% 0.10/0.45 % Success case prop encoding time : 0.000
% 0.10/0.45 % Success case prop solver time : 0.000
% 0.10/0.45 % Current number of processed clauses : 115
% 0.10/0.45 % Positive orientable unit clauses : 22
% 0.10/0.45 % Positive unorientable unit clauses: 0
% 0.10/0.45 % Negative unit clauses : 7
% 0.10/0.45 % Non-unit-clauses : 86
% 0.10/0.45 % Current number of unprocessed clauses: 237
% 0.10/0.45 % ...number of literals in the above : 1139
% 0.10/0.45 % Current number of archived formulas : 0
% 0.10/0.45 % Current number of archived clauses : 31
% 0.10/0.45 % Clause-clause subsumption calls (NU) : 1791
% 0.10/0.45 % Rec. Clause-clause subsumption calls : 624
% 0.10/0.45 % Non-unit clause-clause subsumptions : 67
% 0.10/0.45 % Unit Clause-clause subsumption calls : 200
% 0.10/0.45 % Rewrite failures with RHS unbound : 0
% 0.10/0.45 % BW rewrite match attempts : 8
% 0.10/0.45 % BW rewrite match successes : 8
% 0.10/0.45 % Condensation attempts : 0
% 0.10/0.45 % Condensation successes : 0
% 0.10/0.45 % Termbank termtop insertions : 13465
% 0.10/0.45 % Search garbage collected termcells : 897
% 0.10/0.45
% 0.10/0.45 % -------------------------------------------------
% 0.10/0.45 % User time : 0.012 s
% 0.10/0.45 % System time : 0.003 s
% 0.10/0.45 % Total time : 0.015 s
% 0.10/0.45 % Maximum resident set size: 4072 pages
% 0.10/0.45
% 0.10/0.45 % -------------------------------------------------
% 0.10/0.45 % User time : 0.015 s
% 0.10/0.45 % System time : 0.009 s
% 0.10/0.45 % Total time : 0.024 s
% 0.10/0.45 % Maximum resident set size: 4864 pages
% 0.10/0.45 % E exiting
%------------------------------------------------------------------------------