%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC003+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 : 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 02:42:34 PM UTC 2026
% Result : Theorem 0.36s 0.48s
% Output : CNFRefutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 13 unt; 0 def)
% Number of atoms : 209 ( 54 equ)
% Maximal formula atoms : 54 ( 5 avg)
% Number of connectives : 263 ( 92 ~; 89 |; 49 &)
% ( 2 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 41 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( ? [X11] :
( geq(X11,X8)
& memberP(X4,X11)
& X8 != X11
& ssItem(X11) )
| app(X9,X10) != X3
| app(app(X9,cons(X8,nil)),X10) != X4 ) ) ) )
| ? [X5] :
( ? [X6] :
( ? [X7] :
( neq(X6,nil)
& app(X5,X7) = X1
& app(app(X5,X6),X7) = X2
& ssList(X7) )
& ssList(X6) )
& ssList(X5) )
| ~ neq(X2,nil) ) )
| 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(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( ? [X11] :
( geq(X11,X8)
& memberP(X4,X11)
& X8 != X11
& ssItem(X11) )
| app(X9,X10) != X3
| app(app(X9,cons(X8,nil)),X10) != X4 ) ) ) )
| ? [X5] :
( ? [X6] :
( ? [X7] :
( neq(X6,nil)
& app(X5,X7) = X1
& app(app(X5,X6),X7) = X2
& ssList(X7) )
& ssList(X6) )
& ssList(X5) )
| ~ neq(X2,nil) ) )
| 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)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( ? [X11] :
( geq(X11,X8)
& memberP(X4,X11)
& X8 != X11
& ssItem(X11) )
| app(X9,X10) != X3
| app(app(X9,cons(X8,nil)),X10) != X4 ) ) ) )
| ? [X5] :
( ? [X6] :
( ? [X7] :
( neq(X6,nil)
& app(X5,X7) = X1
& app(app(X5,X6),X7) = X2
& ssList(X7) )
& ssList(X6) )
& ssList(X5) )
| ~ neq(X2,nil) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_7,negated_conjecture,
! [X16,X17,X18,X22] :
( ( ~ geq(X22,esk5_0)
| ~ memberP(esk4_0,X22)
| esk5_0 = X22
| ~ ssItem(X22)
| ~ neq(esk4_0,nil) )
& ( ~ geq(X22,esk5_0)
| ~ memberP(esk4_0,X22)
| esk5_0 = X22
| ~ ssItem(X22)
| neq(esk2_0,nil) )
& ( app(esk6_0,esk7_0) = esk3_0
| ~ neq(esk4_0,nil) )
& ( app(esk6_0,esk7_0) = esk3_0
| neq(esk2_0,nil) )
& ( app(app(esk6_0,cons(esk5_0,nil)),esk7_0) = esk4_0
| ~ neq(esk4_0,nil) )
& ( app(app(esk6_0,cons(esk5_0,nil)),esk7_0) = esk4_0
| neq(esk2_0,nil) )
& ( ssList(esk7_0)
| ~ neq(esk4_0,nil) )
& ( ssList(esk7_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(X17,nil)
| app(X16,X18) != esk1_0
| app(app(X16,X17),X18) != esk2_0
| ~ ssList(X18)
| ~ ssList(X17)
| ~ ssList(X16)
| ~ neq(esk4_0,nil) )
& ( ~ neq(X17,nil)
| app(X16,X18) != esk1_0
| app(app(X16,X17),X18) != esk2_0
| ~ ssList(X18)
| ~ ssList(X17)
| ~ ssList(X16)
| 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(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])])]) ).
cnf(c_0_8,negated_conjecture,
( neq(esk2_0,nil)
| neq(esk2_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_9,negated_conjecture,
neq(esk2_0,nil),
inference(cn,[status(thm)],[c_0_8]) ).
cnf(c_0_10,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
( ~ neq(X2,nil)
| app(X1,X3) != esk1_0
| app(app(X1,X2),X3) != esk2_0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(esk4_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
neq(esk4_0,nil),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,negated_conjecture,
( ~ neq(esk4_0,nil)
| app(app(esk6_0,cons(esk5_0,nil)),esk7_0) = esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,negated_conjecture,
( ~ neq(esk4_0,nil)
| app(esk6_0,esk7_0) = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,negated_conjecture,
( ~ neq(esk4_0,nil)
| ssList(esk7_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,negated_conjecture,
( ~ neq(esk4_0,nil)
| ssList(esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_18,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_19,negated_conjecture,
( ~ neq(X2,nil)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X1,X3) != esk1_0
| app(app(X1,X2),X3) != esk4_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_10]),c_0_12])]) ).
cnf(c_0_20,negated_conjecture,
app(app(esk6_0,cons(esk5_0,nil)),esk7_0) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_12])]) ).
cnf(c_0_21,negated_conjecture,
app(esk6_0,esk7_0) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_12])]) ).
cnf(c_0_22,negated_conjecture,
ssList(esk7_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_12])]) ).
cnf(c_0_23,negated_conjecture,
ssList(esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_12])]) ).
fof(c_0_24,plain,
! [X25,X26] :
( ( ~ ssList(X25)
| ~ ssList(X26)
| neq(X25,X26)
| X25 = X26 )
& ( ~ ssList(X25)
| ~ ssList(X26)
| X25 != X26
| ~ neq(X25,X26) ) ),
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_18])])])])]) ).
fof(c_0_25,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
cnf(c_0_26,negated_conjecture,
( ~ neq(cons(esk5_0,nil),nil)
| ~ ssList(cons(esk5_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_27,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_29,plain,
! [X75,X76] :
( ssList(cons(X76,X75))
| ~ ssItem(X76)
| ~ ssList(X75) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
cnf(c_0_30,negated_conjecture,
( ~ neq(esk4_0,nil)
| ssItem(esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_31,plain,
! [X30,X31] :
( nil != cons(X31,X30)
| ~ ssItem(X31)
| ~ ssList(X30) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])]) ).
cnf(c_0_32,negated_conjecture,
( ~ ssList(cons(esk5_0,nil))
| cons(esk5_0,nil) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
cnf(c_0_33,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_34,negated_conjecture,
ssItem(esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_12])]) ).
cnf(c_0_35,plain,
( nil != cons(X2,X1)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,negated_conjecture,
cons(esk5_0,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_28]),c_0_34])]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_28]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC003+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n010.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon Sep 21 07:48:55 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 0.36/0.48 % Version: 3.5.1
% 0.36/0.48 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.36/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.36/0.48 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.36/0.48 % Starting new_bool_3 with 300s (1) cores
% 0.36/0.48 % Starting new_bool_1 with 300s (1) cores
% 0.36/0.48 % Starting sh5l with 300s (1) cores
% 0.36/0.48 % new_bool_1 with pid 402336 completed with status 0
% 0.36/0.48 % Result found by new_bool_1
% 0.36/0.48 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.36/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.36/0.48 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.36/0.48 % Starting new_bool_3 with 300s (1) cores
% 0.36/0.48 % Starting new_bool_1 with 300s (1) cores
% 0.36/0.48 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.36/0.48 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.36/0.48 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.36/0.48 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.36/0.48 % Starting SubtermCWHack with 31s (1) cores
% 0.36/0.48 % SubtermCWHack with pid 402338 completed with status 0
% 0.36/0.48 % Result found by SubtermCWHack
% 0.36/0.48 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.36/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.36/0.48 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.36/0.48 % Starting new_bool_3 with 300s (1) cores
% 0.36/0.48 % Starting new_bool_1 with 300s (1) cores
% 0.36/0.48 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.36/0.48 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.36/0.48 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.36/0.48 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.36/0.48 % Starting SubtermCWHack with 31s (1) cores
% 0.36/0.48 % Preprocessing time : 0.002 s
% 0.36/0.48
% 0.36/0.48 % Proof found!
% 0.36/0.48 % SZS status Theorem
% 0.36/0.48 % SZS output start CNFRefutation
% See solution above
% 0.36/0.48 % Parsed axioms : 96
% 0.36/0.48 % Removed by relevancy pruning/SinE : 60
% 0.36/0.48 % Initial clauses : 76
% 0.36/0.48 % Removed in clause preprocessing : 0
% 0.36/0.48 % Initial clauses in saturation : 76
% 0.36/0.48 % Processed clauses : 212
% 0.36/0.48 % ...of these trivial : 9
% 0.36/0.48 % ...subsumed : 77
% 0.36/0.48 % ...remaining for further processing : 126
% 0.36/0.48 % Other redundant clauses eliminated : 16
% 0.36/0.48 % Clauses deleted for lack of memory : 0
% 0.36/0.48 % Backward-subsumed : 7
% 0.36/0.48 % Backward-rewritten : 6
% 0.36/0.48 % Generated clauses : 493
% 0.36/0.48 % ...of the previous two non-redundant : 385
% 0.36/0.48 % ...aggressively subsumed : 0
% 0.36/0.48 % Contextual simplify-reflections : 5
% 0.36/0.48 % Paramodulations : 474
% 0.36/0.48 % Factorizations : 0
% 0.36/0.48 % NegExts : 0
% 0.36/0.48 % Equation resolutions : 20
% 0.36/0.48 % Disequality decompositions : 0
% 0.36/0.48 % Total rewrite steps : 490
% 0.36/0.48 % ...of those cached : 477
% 0.36/0.48 % Propositional unsat checks : 0
% 0.36/0.48 % Propositional check models : 0
% 0.36/0.48 % Propositional check unsatisfiable : 0
% 0.36/0.48 % Propositional clauses : 0
% 0.36/0.48 % Propositional clauses after purity: 0
% 0.36/0.48 % Propositional unsat core size : 0
% 0.36/0.48 % Propositional preprocessing time : 0.000
% 0.36/0.48 % Propositional encoding time : 0.000
% 0.36/0.48 % Propositional solver time : 0.000
% 0.36/0.48 % Success case prop preproc time : 0.000
% 0.36/0.48 % Success case prop encoding time : 0.000
% 0.36/0.48 % Success case prop solver time : 0.000
% 0.36/0.48 % Current number of processed clauses : 107
% 0.36/0.48 % Positive orientable unit clauses : 16
% 0.36/0.48 % Positive unorientable unit clauses: 0
% 0.36/0.48 % Negative unit clauses : 1
% 0.36/0.48 % Non-unit-clauses : 90
% 0.36/0.48 % Current number of unprocessed clauses: 242
% 0.36/0.48 % ...number of literals in the above : 1125
% 0.36/0.48 % Current number of archived formulas : 0
% 0.36/0.48 % Current number of archived clauses : 13
% 0.36/0.48 % Clause-clause subsumption calls (NU) : 1124
% 0.36/0.48 % Rec. Clause-clause subsumption calls : 617
% 0.36/0.48 % Non-unit clause-clause subsumptions : 89
% 0.36/0.48 % Unit Clause-clause subsumption calls : 3
% 0.36/0.48 % Rewrite failures with RHS unbound : 0
% 0.36/0.48 % BW rewrite match attempts : 3
% 0.36/0.48 % BW rewrite match successes : 3
% 0.36/0.48 % Condensation attempts : 0
% 0.36/0.48 % Condensation successes : 0
% 0.36/0.48 % Termbank termtop insertions : 14380
% 0.36/0.48 % Search garbage collected termcells : 2030
% 0.36/0.48
% 0.36/0.48 % -------------------------------------------------
% 0.36/0.48 % User time : 0.021 s
% 0.36/0.48 % System time : 0.002 s
% 0.36/0.48 % Total time : 0.023 s
% 0.36/0.48 % Maximum resident set size: 3764 pages
% 0.36/0.48
% 0.36/0.48 % -------------------------------------------------
% 0.36/0.48 % User time : 0.025 s
% 0.36/0.48 % System time : 0.007 s
% 0.36/0.48 % Total time : 0.032 s
% 0.36/0.48 % Maximum resident set size: 4608 pages
% 0.36/0.48 % E exiting
%------------------------------------------------------------------------------