%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC071+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 : 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 02:42:52 PM UTC 2026
% Result : Theorem 0.10s 0.46s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 10 unt; 0 def)
% Number of atoms : 221 ( 72 equ)
% Maximal formula atoms : 48 ( 5 avg)
% Number of connectives : 269 ( 88 ~; 95 |; 49 &)
% ( 2 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 69 ( 0 sgn 46 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ( ? [X10] :
( lt(X10,X6)
& memberP(X8,X10)
& ssItem(X10) )
| ? [X9] :
( lt(X6,X9)
& memberP(X7,X9)
& ssItem(X9) )
| app(app(X7,X3),X8) != X4
| cons(X6,nil) != X3 ) ) ) ) )
| ( nil = X1
& nil = X2 )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
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(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ( ? [X10] :
( lt(X10,X6)
& memberP(X8,X10)
& ssItem(X10) )
| ? [X9] :
( lt(X6,X9)
& memberP(X7,X9)
& ssItem(X9) )
| app(app(X7,X3),X8) != X4
| cons(X6,nil) != X3 ) ) ) ) )
| ( nil = X1
& nil = X2 )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ( ? [X10] :
( lt(X10,X6)
& memberP(X8,X10)
& ssItem(X10) )
| ? [X9] :
( lt(X6,X9)
& memberP(X7,X9)
& ssItem(X9) )
| app(app(X7,X3),X8) != X4
| cons(X6,nil) != X3 ) ) ) ) )
| ( nil = X1
& nil = X2 )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_8,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
fof(c_0_9,negated_conjecture,
! [X15,X19,X20] :
( ( ~ lt(X20,esk5_0)
| ~ memberP(esk7_0,X20)
| ~ ssItem(X20)
| nil = esk3_0 )
& ( ~ lt(X20,esk5_0)
| ~ memberP(esk7_0,X20)
| ~ ssItem(X20)
| nil = esk4_0 )
& ( ~ lt(esk5_0,X19)
| ~ memberP(esk6_0,X19)
| ~ ssItem(X19)
| nil = esk3_0 )
& ( ~ lt(esk5_0,X19)
| ~ memberP(esk6_0,X19)
| ~ ssItem(X19)
| nil = esk4_0 )
& ( app(app(esk6_0,esk3_0),esk7_0) = esk4_0
| nil = esk3_0 )
& ( app(app(esk6_0,esk3_0),esk7_0) = esk4_0
| nil = esk4_0 )
& ( cons(esk5_0,nil) = esk3_0
| nil = esk3_0 )
& ( cons(esk5_0,nil) = esk3_0
| nil = esk4_0 )
& ( ssList(esk7_0)
| nil = esk3_0 )
& ( ssList(esk7_0)
| nil = esk4_0 )
& ( ssList(esk6_0)
| nil = esk3_0 )
& ( ssList(esk6_0)
| nil = esk4_0 )
& ( ssItem(esk5_0)
| nil = esk3_0 )
& ( ssItem(esk5_0)
| nil = esk4_0 )
& ( nil != esk1_0
| nil != esk2_0 )
& ( ~ segmentP(esk1_0,X15)
| ~ segmentP(esk2_0,X15)
| ~ neq(X15,nil)
| ~ ssList(X15) )
& 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_7])])])])])]) ).
fof(c_0_10,plain,
! [X24,X25] :
( nil != cons(X25,X24)
| ~ ssItem(X25)
| ~ ssList(X24) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
cnf(c_0_11,negated_conjecture,
( nil != esk1_0
| nil != esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_15,plain,
( nil != cons(X2,X1)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( cons(esk5_0,nil) = esk3_0
| nil = esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_18,negated_conjecture,
( ssItem(esk5_0)
| nil = esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,negated_conjecture,
( esk4_0 != nil
| esk3_0 != nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
cnf(c_0_20,negated_conjecture,
( ~ segmentP(esk1_0,X1)
| ~ segmentP(esk2_0,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_21,plain,
! [X102,X103] :
( ( ~ ssList(X102)
| ~ ssList(X103)
| neq(X102,X103)
| X102 = X103 )
& ( ~ ssList(X102)
| ~ ssList(X103)
| X102 != X103
| ~ neq(X102,X103) ) ),
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_14])])])])]) ).
fof(c_0_22,plain,
! [X94,X95,X96,X97] :
( segmentP(app(app(X96,X94),X97),X95)
| ~ segmentP(X94,X95)
| ~ ssList(X97)
| ~ ssList(X96)
| ~ ssList(X95)
| ~ ssList(X94) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax56])])])]) ).
cnf(c_0_23,negated_conjecture,
( app(app(esk6_0,esk3_0),esk7_0) = esk4_0
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_24,negated_conjecture,
esk3_0 != nil,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]),c_0_18]),c_0_19]) ).
cnf(c_0_25,negated_conjecture,
( ssList(esk7_0)
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_26,negated_conjecture,
( ssList(esk6_0)
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,negated_conjecture,
( ~ neq(X1,nil)
| ~ ssList(X1)
| ~ segmentP(esk4_0,X1)
| ~ segmentP(esk3_0,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_12]),c_0_13]) ).
cnf(c_0_28,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,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_22]) ).
cnf(c_0_30,negated_conjecture,
app(app(esk6_0,esk3_0),esk7_0) = esk4_0,
inference(sr,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,negated_conjecture,
ssList(esk7_0),
inference(sr,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_32,negated_conjecture,
ssList(esk6_0),
inference(sr,[status(thm)],[c_0_26,c_0_24]) ).
cnf(c_0_33,negated_conjecture,
ssList(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_34,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk4_0,X1)
| ~ segmentP(esk3_0,X1)
| X1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_17])]) ).
cnf(c_0_35,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32]),c_0_33])]) ).
fof(c_0_36,plain,
! [X93] :
( segmentP(X93,X93)
| ~ ssList(X93) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])])]) ).
cnf(c_0_37,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk3_0,X1)
| X1 = nil ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_33])]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC071+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 : n010.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 07:53:55 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
% 0.10/0.41 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
% 0.10/0.46 % Version: 3.5.1
% 0.10/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.46 % Starting sh5l with 300s (1) cores
% 0.10/0.46 % new_bool_1 with pid 411751 completed with status 0
% 0.10/0.46 % Result found by new_bool_1
% 0.10/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.46 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.10/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.46 % SubtermCWHack with pid 411753 completed with status 0
% 0.10/0.46 % Result found by SubtermCWHack
% 0.10/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.46 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.10/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.46 % Preprocessing time : 0.002 s
% 0.10/0.46
% 0.10/0.46 % Proof found!
% 0.10/0.46 % SZS status Theorem
% 0.10/0.46 % SZS output start CNFRefutation
% See solution above
% 0.10/0.46 % Parsed axioms : 96
% 0.10/0.46 % Removed by relevancy pruning/SinE : 57
% 0.10/0.46 % Initial clauses : 82
% 0.10/0.46 % Removed in clause preprocessing : 0
% 0.10/0.46 % Initial clauses in saturation : 82
% 0.10/0.46 % Processed clauses : 233
% 0.10/0.46 % ...of these trivial : 4
% 0.10/0.46 % ...subsumed : 64
% 0.10/0.46 % ...remaining for further processing : 165
% 0.10/0.46 % Other redundant clauses eliminated : 19
% 0.10/0.46 % Clauses deleted for lack of memory : 0
% 0.10/0.46 % Backward-subsumed : 18
% 0.10/0.46 % Backward-rewritten : 7
% 0.10/0.46 % Generated clauses : 586
% 0.10/0.46 % ...of the previous two non-redundant : 419
% 0.10/0.46 % ...aggressively subsumed : 0
% 0.10/0.46 % Contextual simplify-reflections : 7
% 0.10/0.46 % Paramodulations : 560
% 0.10/0.46 % Factorizations : 0
% 0.10/0.46 % NegExts : 0
% 0.10/0.46 % Equation resolutions : 23
% 0.10/0.46 % Disequality decompositions : 0
% 0.10/0.46 % Total rewrite steps : 644
% 0.10/0.46 % ...of those cached : 624
% 0.10/0.46 % Propositional unsat checks : 0
% 0.10/0.46 % Propositional check models : 0
% 0.10/0.46 % Propositional check unsatisfiable : 0
% 0.10/0.46 % Propositional clauses : 0
% 0.10/0.46 % Propositional clauses after purity: 0
% 0.10/0.46 % Propositional unsat core size : 0
% 0.10/0.46 % Propositional preprocessing time : 0.000
% 0.10/0.46 % Propositional encoding time : 0.000
% 0.10/0.46 % Propositional solver time : 0.000
% 0.10/0.46 % Success case prop preproc time : 0.000
% 0.10/0.46 % Success case prop encoding time : 0.000
% 0.10/0.46 % Success case prop solver time : 0.000
% 0.10/0.46 % Current number of processed clauses : 128
% 0.10/0.46 % Positive orientable unit clauses : 25
% 0.10/0.46 % Positive unorientable unit clauses: 0
% 0.10/0.46 % Negative unit clauses : 7
% 0.10/0.46 % Non-unit-clauses : 96
% 0.10/0.46 % Current number of unprocessed clauses: 237
% 0.10/0.46 % ...number of literals in the above : 1157
% 0.10/0.46 % Current number of archived formulas : 0
% 0.10/0.46 % Current number of archived clauses : 29
% 0.10/0.46 % Clause-clause subsumption calls (NU) : 1709
% 0.10/0.46 % Rec. Clause-clause subsumption calls : 608
% 0.10/0.46 % Non-unit clause-clause subsumptions : 67
% 0.10/0.46 % Unit Clause-clause subsumption calls : 94
% 0.10/0.46 % Rewrite failures with RHS unbound : 0
% 0.10/0.46 % BW rewrite match attempts : 9
% 0.10/0.46 % BW rewrite match successes : 9
% 0.10/0.46 % Condensation attempts : 0
% 0.10/0.46 % Condensation successes : 0
% 0.10/0.46 % Termbank termtop insertions : 16734
% 0.10/0.46 % Search garbage collected termcells : 2161
% 0.10/0.46
% 0.10/0.46 % -------------------------------------------------
% 0.10/0.46 % User time : 0.021 s
% 0.10/0.46 % System time : 0.003 s
% 0.10/0.46 % Total time : 0.023 s
% 0.10/0.46 % Maximum resident set size: 3764 pages
% 0.10/0.46
% 0.10/0.46 % -------------------------------------------------
% 0.10/0.46 % User time : 0.024 s
% 0.10/0.46 % System time : 0.007 s
% 0.10/0.46 % Total time : 0.031 s
% 0.10/0.46 % Maximum resident set size: 4864 pages
% 0.10/0.46 % E exiting
%------------------------------------------------------------------------------