%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC106+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 : n017.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 02:43:01 PM UTC 2026
% Result : Theorem 0.14s 5.66s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 14 unt; 0 def)
% Number of atoms : 173 ( 38 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 212 ( 79 ~; 73 |; 27 &)
% ( 3 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 39 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( ( rearsegP(X2,X1)
& neq(X1,nil) )
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(X6,cons(X5,nil)) != X4
| cons(X5,nil) != X3 ) ) )
| ~ neq(X2,nil) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X1,X2)
<=> ? [X3] :
( app(X3,X2) = X1
& ssList(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax6) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
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(c_0_6,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( ( rearsegP(X2,X1)
& neq(X1,nil) )
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(X6,cons(X5,nil)) != X4
| cons(X5,nil) != X3 ) ) )
| ~ neq(X2,nil) ) )
| 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)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( ( rearsegP(X2,X1)
& neq(X1,nil) )
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(X6,cons(X5,nil)) != X4
| cons(X5,nil) != X3 ) ) )
| ~ neq(X2,nil) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_8,negated_conjecture,
( ( ~ rearsegP(esk2_0,esk1_0)
| ~ neq(esk1_0,nil)
| ~ neq(esk4_0,nil) )
& ( ~ rearsegP(esk2_0,esk1_0)
| ~ neq(esk1_0,nil)
| neq(esk2_0,nil) )
& ( app(esk6_0,cons(esk5_0,nil)) = esk4_0
| ~ neq(esk4_0,nil) )
& ( app(esk6_0,cons(esk5_0,nil)) = esk4_0
| neq(esk2_0,nil) )
& ( cons(esk5_0,nil) = esk3_0
| ~ neq(esk4_0,nil) )
& ( cons(esk5_0,nil) = esk3_0
| neq(esk2_0,nil) )
& ( ssList(esk6_0)
| ~ neq(esk4_0,nil) )
& ( ssList(esk6_0)
| neq(esk2_0,nil) )
& ( ssItem(esk5_0)
| ~ neq(esk4_0,nil) )
& ( ssItem(esk5_0)
| neq(esk2_0,nil) )
& ( neq(esk2_0,nil)
| ~ neq(esk4_0,nil) )
& ( neq(esk2_0,nil)
| neq(esk2_0,nil) )
& 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(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).
cnf(c_0_9,negated_conjecture,
( neq(esk2_0,nil)
| neq(esk2_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_10,plain,
! [X22,X23,X25] :
( ( ~ ssList(X22)
| ~ ssList(X23)
| rearsegP(X22,X23)
| app(X25,X23) != X22
| ~ ssList(X25) )
& ( ~ ssList(X22)
| ~ ssList(X23)
| ~ rearsegP(X22,X23)
| app(esk9_2(X22,X23),X23) = X22 )
& ( ~ ssList(X22)
| ~ ssList(X23)
| ~ rearsegP(X22,X23)
| ssList(esk9_2(X22,X23)) ) ),
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)],[ax6])])])])])]) ).
fof(c_0_11,plain,
! [X37,X38] :
( ssList(app(X37,X38))
| ~ ssList(X38)
| ~ ssList(X37) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
cnf(c_0_12,negated_conjecture,
( ~ neq(esk4_0,nil)
| cons(esk5_0,nil) = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
neq(esk2_0,nil),
inference(cn,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| app(X1,X2) != X3
| ~ ssList(X1)
| rearsegP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
( ~ neq(esk4_0,nil)
| app(esk6_0,cons(esk5_0,nil)) = esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,negated_conjecture,
cons(esk5_0,nil) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]) ).
cnf(c_0_20,negated_conjecture,
( ~ neq(esk4_0,nil)
| ssList(esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_21,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
cnf(c_0_22,negated_conjecture,
( ~ rearsegP(esk2_0,esk1_0)
| ~ neq(esk1_0,nil)
| ~ neq(esk4_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_23,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| rearsegP(app(X1,X2),X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_16]),c_0_17]) ).
cnf(c_0_24,negated_conjecture,
app(esk6_0,esk1_0) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_14]),c_0_14]),c_0_15])]) ).
cnf(c_0_25,negated_conjecture,
ssList(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_26,negated_conjecture,
ssList(esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_14]),c_0_15])]) ).
fof(c_0_27,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
fof(c_0_28,plain,
! [X20,X21] :
( nil != cons(X21,X20)
| ~ ssItem(X21)
| ~ ssList(X20) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])]) ).
cnf(c_0_29,negated_conjecture,
( ~ neq(esk4_0,nil)
| ssItem(esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_30,negated_conjecture,
( ~ neq(esk1_0,nil)
| ~ rearsegP(esk2_0,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_14]),c_0_15])]) ).
cnf(c_0_31,negated_conjecture,
rearsegP(esk2_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26])]) ).
fof(c_0_32,plain,
! [X15,X16] :
( ( ~ ssList(X15)
| ~ ssList(X16)
| neq(X15,X16)
| X15 = X16 )
& ( ~ ssList(X15)
| ~ ssList(X16)
| X15 != X16
| ~ neq(X15,X16) ) ),
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_27])])])])]) ).
cnf(c_0_33,plain,
( nil != cons(X2,X1)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_35,negated_conjecture,
ssItem(esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_14]),c_0_15])]) ).
cnf(c_0_36,negated_conjecture,
~ neq(esk1_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]) ).
cnf(c_0_37,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,negated_conjecture,
esk1_0 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_19]),c_0_34]),c_0_35])]) ).
cnf(c_0_39,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_36,c_0_37]),c_0_34]),c_0_25])]),c_0_38]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC106+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/5.58 % Computer : n017.cluster.edu
% 0.11/5.58 % Model : x86_64 x86_64
% 0.11/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.58 % Memory : 8046.5625MB
% 0.11/5.58 % OS : Linux 6.8.0-71-generic
% 0.11/5.58 % CPULimit : 300
% 0.11/5.58 % WCLimit : 300
% 0.11/5.58 % DateTime : Mon Sep 21 07:51:32 UTC 2026
% 0.11/5.58 % CPUTime :
% 0.11/5.58 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/5.62 Running first-order theorem proving
% 0.14/5.63 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
% 0.14/5.66 % Version: 3.5.1
% 0.14/5.66 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/5.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/5.66 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.66 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.66 % Starting sh5l with 300s (1) cores
% 0.14/5.66 % new_bool_3 with pid 1827678 completed with status 0
% 0.14/5.66 % Result found by new_bool_3
% 0.14/5.66 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/5.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/5.66 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.66 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/5.66 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/5.66 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.14/5.66 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.14/5.66 % Starting SubtermCWHack with 28s (1) cores
% 0.14/5.66 % SubtermCWHack with pid 1827681 completed with status 0
% 0.14/5.66 % Result found by SubtermCWHack
% 0.14/5.66 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/5.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/5.66 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.66 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/5.66 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/5.66 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.14/5.66 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.14/5.66 % Starting SubtermCWHack with 28s (1) cores
% 0.14/5.66 % Preprocessing time : 0.002 s
% 0.14/5.66
% 0.14/5.66 % Proof found!
% 0.14/5.66 % SZS status Theorem
% 0.14/5.66 % SZS output start CNFRefutation
% See solution above
% 0.14/5.66 % Parsed axioms : 96
% 0.14/5.66 % Removed by relevancy pruning/SinE : 70
% 0.14/5.66 % Initial clauses : 55
% 0.14/5.66 % Removed in clause preprocessing : 0
% 0.14/5.66 % Initial clauses in saturation : 55
% 0.14/5.66 % Processed clauses : 142
% 0.14/5.66 % ...of these trivial : 7
% 0.14/5.66 % ...subsumed : 37
% 0.14/5.66 % ...remaining for further processing : 98
% 0.14/5.66 % Other redundant clauses eliminated : 24
% 0.14/5.66 % Clauses deleted for lack of memory : 0
% 0.14/5.66 % Backward-subsumed : 3
% 0.14/5.66 % Backward-rewritten : 9
% 0.14/5.66 % Generated clauses : 201
% 0.14/5.66 % ...of the previous two non-redundant : 139
% 0.14/5.66 % ...aggressively subsumed : 0
% 0.14/5.66 % Contextual simplify-reflections : 1
% 0.14/5.66 % Paramodulations : 174
% 0.14/5.66 % Factorizations : 0
% 0.14/5.66 % NegExts : 0
% 0.14/5.66 % Equation resolutions : 28
% 0.14/5.66 % Disequality decompositions : 0
% 0.14/5.66 % Total rewrite steps : 252
% 0.14/5.66 % ...of those cached : 234
% 0.14/5.66 % Propositional unsat checks : 0
% 0.14/5.66 % Propositional check models : 0
% 0.14/5.66 % Propositional check unsatisfiable : 0
% 0.14/5.66 % Propositional clauses : 0
% 0.14/5.66 % Propositional clauses after purity: 0
% 0.14/5.66 % Propositional unsat core size : 0
% 0.14/5.66 % Propositional preprocessing time : 0.000
% 0.14/5.66 % Propositional encoding time : 0.000
% 0.14/5.66 % Propositional solver time : 0.000
% 0.14/5.66 % Success case prop preproc time : 0.000
% 0.14/5.66 % Success case prop encoding time : 0.000
% 0.14/5.66 % Success case prop solver time : 0.000
% 0.14/5.66 % Current number of processed clauses : 81
% 0.14/5.66 % Positive orientable unit clauses : 22
% 0.14/5.66 % Positive unorientable unit clauses: 0
% 0.14/5.66 % Negative unit clauses : 5
% 0.14/5.66 % Non-unit-clauses : 54
% 0.14/5.66 % Current number of unprocessed clauses: 52
% 0.14/5.66 % ...number of literals in the above : 238
% 0.14/5.66 % Current number of archived formulas : 0
% 0.14/5.66 % Current number of archived clauses : 12
% 0.14/5.66 % Clause-clause subsumption calls (NU) : 534
% 0.14/5.66 % Rec. Clause-clause subsumption calls : 312
% 0.14/5.66 % Non-unit clause-clause subsumptions : 28
% 0.14/5.66 % Unit Clause-clause subsumption calls : 67
% 0.14/5.66 % Rewrite failures with RHS unbound : 0
% 0.14/5.66 % BW rewrite match attempts : 7
% 0.14/5.66 % BW rewrite match successes : 7
% 0.14/5.66 % Condensation attempts : 0
% 0.14/5.66 % Condensation successes : 0
% 0.14/5.66 % Termbank termtop insertions : 7646
% 0.14/5.66 % Search garbage collected termcells : 1527
% 0.14/5.66
% 0.14/5.66 % -------------------------------------------------
% 0.14/5.66 % User time : 0.011 s
% 0.14/5.66 % System time : 0.005 s
% 0.14/5.66 % Total time : 0.016 s
% 0.14/5.66 % Maximum resident set size: 3760 pages
% 0.14/5.66
% 0.14/5.66 % -------------------------------------------------
% 0.14/5.66 % User time : 0.012 s
% 0.14/5.66 % System time : 0.009 s
% 0.14/5.66 % Total time : 0.021 s
% 0.14/5.66 % Maximum resident set size: 4608 pages
% 0.14/5.66 % E exiting
%------------------------------------------------------------------------------