%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC371+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 : n007.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 02:44:07 PM UTC 2026
% Result : Theorem 0.17s 0.49s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 11 unt; 0 def)
% Number of atoms : 125 ( 34 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 148 ( 49 ~; 45 |; 32 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 31 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( nil = X3
& nil != X4 )
| segmentP(X2,X1)
| ! [X5] :
( ssList(X5)
=> ( ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( leq(X8,X6)
& app(X9,cons(X8,nil)) = X3
& ssList(X9) )
& ssItem(X8) )
& app(cons(X6,nil),X7) = X5
& ssList(X7) )
& ssItem(X6) )
| ~ totalorderedP(X3)
| app(X3,X5) != X4 ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax56,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( segmentP(X1,X2)
=> segmentP(app(app(X3,X1),X4),X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax56) ).
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(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( nil = X3
& nil != X4 )
| segmentP(X2,X1)
| ! [X5] :
( ssList(X5)
=> ( ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( leq(X8,X6)
& app(X9,cons(X8,nil)) = X3
& ssList(X9) )
& ssItem(X8) )
& app(cons(X6,nil),X7) = X5
& ssList(X7) )
& ssItem(X6) )
| ~ totalorderedP(X3)
| app(X3,X5) != X4 ) )
| 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)
=> ( ( nil = X3
& nil != X4 )
| segmentP(X2,X1)
| ! [X5] :
( ssList(X5)
=> ( ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( leq(X8,X6)
& app(X9,cons(X8,nil)) = X3
& ssList(X9) )
& ssItem(X8) )
& app(cons(X6,nil),X7) = X5
& ssList(X7) )
& ssItem(X6) )
| ~ totalorderedP(X3)
| app(X3,X5) != X4 ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_7,plain,
! [X36,X37,X38,X39] :
( segmentP(app(app(X38,X36),X39),X37)
| ~ segmentP(X36,X37)
| ~ ssList(X39)
| ~ ssList(X38)
| ~ ssList(X37)
| ~ ssList(X36) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax56])])])]) ).
fof(c_0_8,plain,
! [X60] :
( app(nil,X60) = X60
| ~ ssList(X60) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
fof(c_0_9,negated_conjecture,
! [X15,X16,X17,X18] :
( ( nil != esk3_0
| nil = esk4_0 )
& ~ segmentP(esk2_0,esk1_0)
& ( ~ leq(X17,X15)
| app(X18,cons(X17,nil)) != esk3_0
| ~ ssList(X18)
| ~ ssItem(X17)
| app(cons(X15,nil),X16) != esk5_0
| ~ ssList(X16)
| ~ ssItem(X15) )
& totalorderedP(esk3_0)
& app(esk3_0,esk5_0) = esk4_0
& ssList(esk5_0)
& esk1_0 = esk3_0
& esk2_0 = esk4_0
& ssList(esk4_0)
& ssList(esk3_0)
& ssList(esk2_0)
& ssList(esk1_0) ),
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_10,plain,
( ~ segmentP(X1,X2)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| segmentP(app(app(X3,X1),X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_13,negated_conjecture,
~ segmentP(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ segmentP(X1,X3)
| segmentP(app(X1,X2),X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]) ).
cnf(c_0_17,negated_conjecture,
app(esk3_0,esk5_0) = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,negated_conjecture,
ssList(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,negated_conjecture,
ssList(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,negated_conjecture,
~ segmentP(esk4_0,esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_21,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk3_0,X1)
| segmentP(esk4_0,X1) ),
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])]) ).
fof(c_0_22,plain,
! [X35] :
( segmentP(X35,X35)
| ~ ssList(X35) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])])]) ).
cnf(c_0_23,negated_conjecture,
~ segmentP(esk3_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_19])]) ).
cnf(c_0_24,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC371+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n007.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 21 08:17:21 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 0.17/0.49 % Version: 3.5.1
% 0.17/0.49 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.49 % Starting new_bool_1 with 300s (1) cores
% 0.17/0.49 % Starting sh5l with 300s (1) cores
% 0.17/0.49 % new_bool_3 with pid 627620 completed with status 0
% 0.17/0.49 % Result found by new_bool_3
% 0.17/0.49 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.49 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/0.49 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.49 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.17/0.49 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.49 % Starting SubtermCWHack with 31s (1) cores
% 0.17/0.49 % SubtermCWHack with pid 627623 completed with status 0
% 0.17/0.49 % Result found by SubtermCWHack
% 0.17/0.49 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.49 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/0.49 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.49 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.17/0.49 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.49 % Starting SubtermCWHack with 31s (1) cores
% 0.17/0.49 % Preprocessing time : 0.002 s
% 0.17/0.49
% 0.17/0.49 % Proof found!
% 0.17/0.49 % SZS status Theorem
% 0.17/0.49 % SZS output start CNFRefutation
% See solution above
% 0.17/0.49 % Parsed axioms : 96
% 0.17/0.49 % Removed by relevancy pruning/SinE : 49
% 0.17/0.49 % Initial clauses : 84
% 0.17/0.49 % Removed in clause preprocessing : 1
% 0.17/0.49 % Initial clauses in saturation : 83
% 0.17/0.49 % Processed clauses : 471
% 0.17/0.49 % ...of these trivial : 35
% 0.17/0.49 % ...subsumed : 163
% 0.17/0.49 % ...remaining for further processing : 273
% 0.17/0.49 % Other redundant clauses eliminated : 37
% 0.17/0.49 % Clauses deleted for lack of memory : 0
% 0.17/0.49 % Backward-subsumed : 66
% 0.17/0.49 % Backward-rewritten : 4
% 0.17/0.49 % Generated clauses : 1716
% 0.17/0.49 % ...of the previous two non-redundant : 1358
% 0.17/0.49 % ...aggressively subsumed : 0
% 0.17/0.49 % Contextual simplify-reflections : 32
% 0.17/0.49 % Paramodulations : 1666
% 0.17/0.49 % Factorizations : 0
% 0.17/0.49 % NegExts : 0
% 0.17/0.49 % Equation resolutions : 42
% 0.17/0.49 % Disequality decompositions : 0
% 0.17/0.49 % Total rewrite steps : 1336
% 0.17/0.49 % ...of those cached : 1312
% 0.17/0.49 % Propositional unsat checks : 0
% 0.17/0.49 % Propositional check models : 0
% 0.17/0.49 % Propositional check unsatisfiable : 0
% 0.17/0.49 % Propositional clauses : 0
% 0.17/0.49 % Propositional clauses after purity: 0
% 0.17/0.49 % Propositional unsat core size : 0
% 0.17/0.50 % Propositional preprocessing time : 0.000
% 0.17/0.50 % Propositional encoding time : 0.000
% 0.17/0.50 % Propositional solver time : 0.000
% 0.17/0.50 % Success case prop preproc time : 0.000
% 0.17/0.50 % Success case prop encoding time : 0.000
% 0.17/0.50 % Success case prop solver time : 0.000
% 0.17/0.50 % Current number of processed clauses : 188
% 0.17/0.50 % Positive orientable unit clauses : 26
% 0.17/0.50 % Positive unorientable unit clauses: 0
% 0.17/0.50 % Negative unit clauses : 7
% 0.17/0.50 % Non-unit-clauses : 155
% 0.17/0.50 % Current number of unprocessed clauses: 920
% 0.17/0.50 % ...number of literals in the above : 4902
% 0.17/0.50 % Current number of archived formulas : 0
% 0.17/0.50 % Current number of archived clauses : 79
% 0.17/0.50 % Clause-clause subsumption calls (NU) : 4272
% 0.17/0.50 % Rec. Clause-clause subsumption calls : 2123
% 0.17/0.50 % Non-unit clause-clause subsumptions : 216
% 0.17/0.50 % Unit Clause-clause subsumption calls : 305
% 0.17/0.50 % Rewrite failures with RHS unbound : 0
% 0.17/0.50 % BW rewrite match attempts : 7
% 0.17/0.50 % BW rewrite match successes : 7
% 0.17/0.50 % Condensation attempts : 0
% 0.17/0.50 % Condensation successes : 0
% 0.17/0.50 % Termbank termtop insertions : 35982
% 0.17/0.50 % Search garbage collected termcells : 2180
% 0.17/0.50
% 0.17/0.50 % -------------------------------------------------
% 0.17/0.50 % User time : 0.040 s
% 0.17/0.50 % System time : 0.008 s
% 0.17/0.50 % Total time : 0.048 s
% 0.17/0.50 % Maximum resident set size: 3964 pages
% 0.17/0.50
% 0.17/0.50 % -------------------------------------------------
% 0.17/0.50 % User time : 0.044 s
% 0.17/0.50 % System time : 0.013 s
% 0.17/0.50 % Total time : 0.057 s
% 0.17/0.50 % Maximum resident set size: 4864 pages
% 0.17/0.50 % E exiting
%------------------------------------------------------------------------------