%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC110+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 : n013.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 : Theorem 0.25s 0.49s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 12 unt; 0 def)
% Number of atoms : 200 ( 73 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 252 ( 94 ~; 88 |; 39 &)
% ( 3 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 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 : 66 ( 0 sgn 40 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( ( segmentP(X2,X1)
& neq(X1,nil) )
| ~ neq(X2,nil) )
& ( nil = X1
| nil != X2 ) )
| ( nil = X3
& nil != X4 )
| ! [X5] :
( ssList(X5)
=> ( ? [X6] :
( ? [X7] :
( ? [X8] :
( app(X8,cons(X6,nil)) = X3
& ssList(X8) )
& app(cons(X6,nil),X7) = X5
& ssList(X7) )
& ssItem(X6) )
| ~ equalelemsP(X3)
| app(X3,X5) != X4 ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax56) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X1
& nil = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( ( segmentP(X2,X1)
& neq(X1,nil) )
| ~ neq(X2,nil) )
& ( nil = X1
| nil != X2 ) )
| ( nil = X3
& nil != X4 )
| ! [X5] :
( ssList(X5)
=> ( ? [X6] :
( ? [X7] :
( ? [X8] :
( app(X8,cons(X6,nil)) = X3
& ssList(X8) )
& app(cons(X6,nil),X7) = X5
& ssList(X7) )
& ssItem(X6) )
| ~ equalelemsP(X3)
| app(X3,X5) != X4 ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( ( segmentP(X2,X1)
& neq(X1,nil) )
| ~ neq(X2,nil) )
& ( nil = X1
| nil != X2 ) )
| ( nil = X3
& nil != X4 )
| ! [X5] :
( ssList(X5)
=> ( ? [X6] :
( ? [X7] :
( ? [X8] :
( app(X8,cons(X6,nil)) = X3
& ssList(X8) )
& app(cons(X6,nil),X7) = X5
& ssList(X7) )
& ssItem(X6) )
| ~ equalelemsP(X3)
| app(X3,X5) != X4 ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_9,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
fof(c_0_10,negated_conjecture,
! [X14,X15,X16] :
( ( nil != esk1_0
| ~ segmentP(esk2_0,esk1_0)
| ~ neq(esk1_0,nil) )
& ( nil != esk1_0
| neq(esk2_0,nil) )
& ( nil = esk2_0
| ~ segmentP(esk2_0,esk1_0)
| ~ neq(esk1_0,nil) )
& ( nil = esk2_0
| neq(esk2_0,nil) )
& ( nil != esk3_0
| nil = esk4_0 )
& ( app(X16,cons(X14,nil)) != esk3_0
| ~ ssList(X16)
| app(cons(X14,nil),X15) != esk5_0
| ~ ssList(X15)
| ~ ssItem(X14) )
& equalelemsP(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(distribute,[status(thm)],[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_8])])])])])]) ).
fof(c_0_11,plain,
! [X37,X38] :
( ( ~ ssList(X37)
| ~ ssList(X38)
| neq(X37,X38)
| X37 = X38 )
& ( ~ ssList(X37)
| ~ ssList(X38)
| X37 != X38
| ~ neq(X37,X38) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])])]) ).
cnf(c_0_12,negated_conjecture,
( nil != esk3_0
| nil = esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,plain,
! [X29,X30,X31,X32] :
( segmentP(app(app(X31,X29),X32),X30)
| ~ segmentP(X29,X30)
| ~ ssList(X32)
| ~ ssList(X31)
| ~ ssList(X30)
| ~ ssList(X29) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax56])])])]) ).
fof(c_0_16,plain,
! [X49] :
( app(nil,X49) = X49
| ~ ssList(X49) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
cnf(c_0_17,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
( nil != esk1_0
| neq(esk2_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,negated_conjecture,
( esk1_0 != nil
| esk2_0 = nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_20,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_15]) ).
cnf(c_0_21,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_23,negated_conjecture,
app(esk3_0,esk5_0) = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_24,plain,
! [X61,X62] :
( ( ~ ssList(X61)
| ~ ssList(X62)
| nil = app(X61,X62)
| nil != X61
| nil != X62 )
& ( ~ ssList(X61)
| ~ ssList(X62)
| nil != app(X61,X62)
| nil = X61 )
& ( ~ ssList(X61)
| ~ ssList(X62)
| nil != app(X61,X62)
| nil = X62 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])])]) ).
cnf(c_0_25,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_26,negated_conjecture,
( esk1_0 != nil
| neq(nil,nil) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_27,negated_conjecture,
( ~ segmentP(esk2_0,esk1_0)
| ~ neq(esk1_0,nil)
| nil = esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_28,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_29,negated_conjecture,
ssList(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_30,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_20,c_0_21]),c_0_22])]) ).
cnf(c_0_31,negated_conjecture,
app(esk1_0,esk5_0) = esk2_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_14]),c_0_13]) ).
cnf(c_0_32,negated_conjecture,
ssList(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_33,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != app(X1,X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,negated_conjecture,
esk1_0 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_22])]) ).
cnf(c_0_35,negated_conjecture,
( ~ segmentP(esk2_0,esk1_0)
| esk2_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_22]),c_0_29])]),c_0_19]) ).
cnf(c_0_36,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk1_0,X1)
| segmentP(esk2_0,X1) ),
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_29])]) ).
cnf(c_0_37,negated_conjecture,
esk2_0 != nil,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_31]),c_0_32]),c_0_29])]),c_0_34]) ).
fof(c_0_38,plain,
! [X28] :
( segmentP(X28,X28)
| ~ ssList(X28) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])])]) ).
cnf(c_0_39,negated_conjecture,
~ segmentP(esk1_0,esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_29])]),c_0_37]) ).
cnf(c_0_40,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC110+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n013.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 21 07:55:22 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.25/0.49 % Version: 3.5.1
% 0.25/0.49 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.25/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.25/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.49 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.49 % Starting sh5l with 300s (1) cores
% 0.25/0.49 % new_bool_1 with pid 311096 completed with status 0
% 0.25/0.49 % Result found by new_bool_1
% 0.25/0.49 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.25/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.25/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.49 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.49 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.25/0.49 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.25/0.49 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.25/0.49 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.49 % Starting SubtermCWHack with 31s (1) cores
% 0.25/0.49 % SubtermCWHack with pid 311104 completed with status 0
% 0.25/0.49 % Result found by SubtermCWHack
% 0.25/0.49 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.25/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.25/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.49 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.49 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.25/0.49 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.25/0.49 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.25/0.49 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.49 % Starting SubtermCWHack with 31s (1) cores
% 0.25/0.49 % Preprocessing time : 0.003 s
% 0.25/0.49
% 0.25/0.49 % Proof found!
% 0.25/0.49 % SZS status Theorem
% 0.25/0.49 % SZS output start CNFRefutation
% See solution above
% 0.25/0.49 % Parsed axioms : 96
% 0.25/0.49 % Removed by relevancy pruning/SinE : 67
% 0.25/0.49 % Initial clauses : 62
% 0.25/0.49 % Removed in clause preprocessing : 0
% 0.25/0.49 % Initial clauses in saturation : 62
% 0.25/0.49 % Processed clauses : 236
% 0.25/0.49 % ...of these trivial : 7
% 0.25/0.49 % ...subsumed : 80
% 0.25/0.49 % ...remaining for further processing : 149
% 0.25/0.49 % Other redundant clauses eliminated : 20
% 0.25/0.49 % Clauses deleted for lack of memory : 0
% 0.25/0.49 % Backward-subsumed : 19
% 0.25/0.49 % Backward-rewritten : 3
% 0.25/0.49 % Generated clauses : 600
% 0.25/0.49 % ...of the previous two non-redundant : 484
% 0.25/0.49 % ...aggressively subsumed : 0
% 0.25/0.49 % Contextual simplify-reflections : 3
% 0.25/0.49 % Paramodulations : 576
% 0.25/0.49 % Factorizations : 0
% 0.25/0.49 % NegExts : 0
% 0.25/0.49 % Equation resolutions : 24
% 0.25/0.49 % Disequality decompositions : 0
% 0.25/0.49 % Total rewrite steps : 518
% 0.25/0.49 % ...of those cached : 505
% 0.25/0.49 % Propositional unsat checks : 0
% 0.25/0.49 % Propositional check models : 0
% 0.25/0.49 % Propositional check unsatisfiable : 0
% 0.25/0.49 % Propositional clauses : 0
% 0.25/0.49 % Propositional clauses after purity: 0
% 0.25/0.49 % Propositional unsat core size : 0
% 0.25/0.49 % Propositional preprocessing time : 0.000
% 0.25/0.49 % Propositional encoding time : 0.000
% 0.25/0.49 % Propositional solver time : 0.000
% 0.25/0.49 % Success case prop preproc time : 0.000
% 0.25/0.49 % Success case prop encoding time : 0.000
% 0.25/0.49 % Success case prop solver time : 0.000
% 0.25/0.49 % Current number of processed clauses : 120
% 0.25/0.49 % Positive orientable unit clauses : 18
% 0.25/0.49 % Positive unorientable unit clauses: 0
% 0.25/0.49 % Negative unit clauses : 9
% 0.25/0.49 % Non-unit-clauses : 93
% 0.25/0.49 % Current number of unprocessed clauses: 306
% 0.25/0.49 % ...number of literals in the above : 1627
% 0.25/0.49 % Current number of archived formulas : 0
% 0.25/0.49 % Current number of archived clauses : 23
% 0.25/0.49 % Clause-clause subsumption calls (NU) : 1488
% 0.25/0.49 % Rec. Clause-clause subsumption calls : 648
% 0.25/0.49 % Non-unit clause-clause subsumptions : 69
% 0.25/0.49 % Unit Clause-clause subsumption calls : 102
% 0.25/0.49 % Rewrite failures with RHS unbound : 0
% 0.25/0.49 % BW rewrite match attempts : 2
% 0.25/0.49 % BW rewrite match successes : 2
% 0.25/0.49 % Condensation attempts : 0
% 0.25/0.49 % Condensation successes : 0
% 0.25/0.49 % Termbank termtop insertions : 15445
% 0.25/0.49 % Search garbage collected termcells : 1787
% 0.25/0.49
% 0.25/0.49 % -------------------------------------------------
% 0.25/0.49 % User time : 0.031 s
% 0.25/0.49 % System time : 0.007 s
% 0.25/0.49 % Total time : 0.038 s
% 0.25/0.49 % Maximum resident set size: 3760 pages
% 0.25/0.49
% 0.25/0.49 % -------------------------------------------------
% 0.25/0.49 % User time : 0.035 s
% 0.25/0.49 % System time : 0.013 s
% 0.25/0.49 % Total time : 0.047 s
% 0.25/0.49 % Maximum resident set size: 4608 pages
% 0.25/0.49 % E exiting
%------------------------------------------------------------------------------