%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC029+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 : 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 02:42:41 PM UTC 2026
% Result : Theorem 0.14s 5.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 13 unt; 0 def)
% Number of atoms : 181 ( 89 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 217 ( 81 ~; 78 |; 27 &)
% ( 3 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil = X2
| nil != X1 )
& ( nil = X1
| nil != X2 ) )
| ( neq(X4,nil)
& ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(X6,cons(X5,nil)) != X3
| app(cons(X5,nil),X6) != X4 ) ) ) )
| ( nil = X4
& nil != X3 )
| 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(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(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(ax81,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil = X2
| nil != X1 )
& ( nil = X1
| nil != X2 ) )
| ( neq(X4,nil)
& ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(X6,cons(X5,nil)) != X3
| app(cons(X5,nil),X6) != X4 ) ) ) )
| ( nil = X4
& nil != X3 )
| 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 = X2
| nil != X1 )
& ( nil = X1
| nil != X2 ) )
| ( neq(X4,nil)
& ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(X6,cons(X5,nil)) != X3
| app(cons(X5,nil),X6) != X4 ) ) ) )
| ( nil = X4
& nil != X3 )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_8,negated_conjecture,
( ( nil != esk1_0
| nil != esk2_0 )
& ( nil != esk1_0
| nil = esk1_0 )
& ( nil = esk2_0
| nil != esk2_0 )
& ( nil = esk2_0
| nil = esk1_0 )
& ( ~ neq(esk4_0,nil)
| app(esk6_0,cons(esk5_0,nil)) = esk3_0 )
& ( ~ neq(esk4_0,nil)
| app(cons(esk5_0,nil),esk6_0) = esk4_0 )
& ( ~ neq(esk4_0,nil)
| ssList(esk6_0) )
& ( ~ neq(esk4_0,nil)
| ssItem(esk5_0) )
& ( nil != esk4_0
| nil = esk3_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(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).
cnf(c_0_9,negated_conjecture,
( nil = esk2_0
| nil = esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_10,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_12,negated_conjecture,
( nil != esk4_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,
( esk1_0 = nil
| esk4_0 = nil ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_15,plain,
! [X20,X21] :
( ( ~ ssList(X20)
| ~ ssList(X21)
| neq(X20,X21)
| X20 = X21 )
& ( ~ ssList(X20)
| ~ ssList(X21)
| X20 != X21
| ~ neq(X20,X21) ) ),
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_11])])])])]) ).
cnf(c_0_16,negated_conjecture,
( nil != esk1_0
| nil != esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
esk1_0 = nil,
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
fof(c_0_18,plain,
! [X39,X40] :
( ( ~ ssList(X39)
| ~ ssList(X40)
| nil = app(X39,X40)
| nil != X39
| nil != X40 )
& ( ~ ssList(X39)
| ~ ssList(X40)
| nil != app(X39,X40)
| nil = X39 )
& ( ~ ssList(X39)
| ~ ssList(X40)
| nil != app(X39,X40)
| nil = X40 ) ),
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_19,negated_conjecture,
( ~ neq(esk4_0,nil)
| app(esk6_0,cons(esk5_0,nil)) = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,negated_conjecture,
( ~ neq(esk4_0,nil)
| ssList(esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_23,negated_conjecture,
ssList(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_24,negated_conjecture,
esk4_0 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_10])]) ).
cnf(c_0_25,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != app(X1,X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,negated_conjecture,
( ~ neq(esk4_0,nil)
| app(esk6_0,cons(esk5_0,nil)) = nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_13]),c_0_17]) ).
cnf(c_0_27,negated_conjecture,
ssList(esk6_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23])]),c_0_24]) ).
cnf(c_0_28,negated_conjecture,
( ~ neq(esk4_0,nil)
| ~ ssList(cons(esk5_0,nil))
| esk6_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
fof(c_0_29,plain,
! [X42,X43] :
( ssList(cons(X43,X42))
| ~ ssItem(X43)
| ~ ssList(X42) ),
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_8]) ).
cnf(c_0_31,negated_conjecture,
( ~ ssList(cons(esk5_0,nil))
| esk6_0 = nil ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_21]),c_0_22]),c_0_23])]),c_0_24]) ).
cnf(c_0_32,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_33,negated_conjecture,
ssItem(esk5_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_21]),c_0_22]),c_0_23])]),c_0_24]) ).
fof(c_0_34,plain,
! [X34,X35] :
( cons(X35,X34) = app(cons(X35,nil),X34)
| ~ ssItem(X35)
| ~ ssList(X34) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
cnf(c_0_35,negated_conjecture,
( ~ neq(esk4_0,nil)
| app(cons(esk5_0,nil),esk6_0) = esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_36,negated_conjecture,
esk6_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_22]),c_0_33])]) ).
cnf(c_0_37,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_38,negated_conjecture,
( ~ neq(esk4_0,nil)
| app(cons(esk5_0,nil),nil) = esk4_0 ),
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
( ~ neq(esk4_0,nil)
| cons(esk5_0,nil) = esk4_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_22]),c_0_33])]) ).
cnf(c_0_40,negated_conjecture,
cons(esk5_0,nil) = esk4_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_21]),c_0_22]),c_0_23])]),c_0_24]) ).
cnf(c_0_41,negated_conjecture,
( ~ neq(esk4_0,nil)
| app(nil,esk4_0) = nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_36]),c_0_40]) ).
cnf(c_0_42,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != app(X2,X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_43,negated_conjecture,
app(nil,esk4_0) = nil,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_21]),c_0_22]),c_0_23])]),c_0_24]) ).
cnf(c_0_44,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_42,c_0_43]),c_0_22]),c_0_23])]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC029+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/5.37 % Computer : n007.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Mon Sep 21 07:48:12 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 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
% 0.14/5.45 % Version: 3.5.1
% 0.14/5.45 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/5.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/5.45 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.45 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.45 % Starting sh5l with 300s (1) cores
% 0.14/5.45 % new_bool_3 with pid 568484 completed with status 0
% 0.14/5.45 % Result found by new_bool_3
% 0.14/5.45 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/5.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/5.45 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/5.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/5.45 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.14/5.45 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.14/5.45 % Starting SubtermCWHack with 28s (1) cores
% 0.14/5.45 % SubtermCWHack with pid 568487 completed with status 0
% 0.14/5.45 % Result found by SubtermCWHack
% 0.14/5.45 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/5.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/5.45 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/5.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/5.45 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.14/5.45 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.14/5.45 % Starting SubtermCWHack with 28s (1) cores
% 0.14/5.45 % Preprocessing time : 0.002 s
% 0.14/5.45
% 0.14/5.45 % Proof found!
% 0.14/5.45 % SZS status Theorem
% 0.14/5.45 % SZS output start CNFRefutation
% See solution above
% 0.14/5.45 % Parsed axioms : 96
% 0.14/5.45 % Removed by relevancy pruning/SinE : 77
% 0.14/5.45 % Initial clauses : 42
% 0.14/5.45 % Removed in clause preprocessing : 2
% 0.14/5.45 % Initial clauses in saturation : 40
% 0.14/5.45 % Processed clauses : 64
% 0.14/5.45 % ...of these trivial : 0
% 0.14/5.45 % ...subsumed : 7
% 0.14/5.45 % ...remaining for further processing : 57
% 0.14/5.45 % Other redundant clauses eliminated : 6
% 0.14/5.45 % Clauses deleted for lack of memory : 0
% 0.14/5.45 % Backward-subsumed : 3
% 0.14/5.45 % Backward-rewritten : 15
% 0.14/5.45 % Generated clauses : 74
% 0.14/5.45 % ...of the previous two non-redundant : 54
% 0.14/5.45 % ...aggressively subsumed : 0
% 0.14/5.45 % Contextual simplify-reflections : 1
% 0.14/5.45 % Paramodulations : 68
% 0.14/5.45 % Factorizations : 0
% 0.14/5.45 % NegExts : 0
% 0.14/5.45 % Equation resolutions : 7
% 0.14/5.45 % Disequality decompositions : 0
% 0.14/5.45 % Total rewrite steps : 112
% 0.14/5.45 % ...of those cached : 100
% 0.14/5.45 % Propositional unsat checks : 0
% 0.14/5.45 % Propositional check models : 0
% 0.14/5.45 % Propositional check unsatisfiable : 0
% 0.14/5.45 % Propositional clauses : 0
% 0.14/5.45 % Propositional clauses after purity: 0
% 0.14/5.45 % Propositional unsat core size : 0
% 0.14/5.45 % Propositional preprocessing time : 0.000
% 0.14/5.45 % Propositional encoding time : 0.000
% 0.14/5.45 % Propositional solver time : 0.000
% 0.14/5.45 % Success case prop preproc time : 0.000
% 0.14/5.45 % Success case prop encoding time : 0.000
% 0.14/5.45 % Success case prop solver time : 0.000
% 0.14/5.45 % Current number of processed clauses : 36
% 0.14/5.45 % Positive orientable unit clauses : 13
% 0.14/5.45 % Positive unorientable unit clauses: 0
% 0.14/5.45 % Negative unit clauses : 2
% 0.14/5.45 % Non-unit-clauses : 21
% 0.14/5.45 % Current number of unprocessed clauses: 26
% 0.14/5.45 % ...number of literals in the above : 107
% 0.14/5.45 % Current number of archived formulas : 0
% 0.14/5.45 % Current number of archived clauses : 18
% 0.14/5.45 % Clause-clause subsumption calls (NU) : 48
% 0.14/5.45 % Rec. Clause-clause subsumption calls : 29
% 0.14/5.45 % Non-unit clause-clause subsumptions : 3
% 0.14/5.45 % Unit Clause-clause subsumption calls : 12
% 0.14/5.45 % Rewrite failures with RHS unbound : 0
% 0.14/5.45 % BW rewrite match attempts : 9
% 0.14/5.45 % BW rewrite match successes : 9
% 0.14/5.45 % Condensation attempts : 0
% 0.14/5.45 % Condensation successes : 0
% 0.14/5.45 % Termbank termtop insertions : 4938
% 0.14/5.45 % Search garbage collected termcells : 1391
% 0.14/5.45
% 0.14/5.45 % -------------------------------------------------
% 0.14/5.45 % User time : 0.007 s
% 0.14/5.45 % System time : 0.004 s
% 0.14/5.45 % Total time : 0.011 s
% 0.14/5.45 % Maximum resident set size: 3760 pages
% 0.14/5.45
% 0.14/5.45 % -------------------------------------------------
% 0.14/5.45 % User time : 0.012 s
% 0.14/5.45 % System time : 0.007 s
% 0.14/5.45 % Total time : 0.019 s
% 0.14/5.45 % Maximum resident set size: 4608 pages
% 0.14/5.45 % E exiting
%------------------------------------------------------------------------------