%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC419+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 : n008.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 02:44:20 PM UTC 2026
% Result : Theorem 0.22s 0.63s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 15 unt; 0 def)
% Number of atoms : 136 ( 51 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 164 ( 63 ~; 55 |; 30 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 4 ( 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 : 49 ( 0 sgn 29 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ( neq(X4,nil)
& ! [X8] :
( ssItem(X8)
=> ! [X9] :
( app(X9,cons(X8,nil)) != X3
| app(cons(X8,nil),X9) != X4
| ~ ssList(X9) ) ) )
| ( nil = X4
& nil != X3 )
| ? [X5] :
( ? [X6] :
( ? [X7] :
( app(app(X7,cons(X5,nil)),X6) = X1
& app(app(X6,cons(X5,nil)),X7) = X2
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
| ~ neq(X2,nil)
| X1 != X3
| X2 != X4
| ~ ssList(X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
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] :
( ( neq(X4,nil)
& ! [X8] :
( ssItem(X8)
=> ! [X9] :
( app(X9,cons(X8,nil)) != X3
| app(cons(X8,nil),X9) != X4
| ~ ssList(X9) ) ) )
| ( nil = X4
& nil != X3 )
| ? [X5] :
( ? [X6] :
( ? [X7] :
( app(app(X7,cons(X5,nil)),X6) = X1
& app(app(X6,cons(X5,nil)),X7) = X2
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
| ~ neq(X2,nil)
| X1 != X3
| X2 != X4
| ~ ssList(X4) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ( neq(X4,nil)
& ! [X8] :
( ssItem(X8)
=> ! [X9] :
( app(X9,cons(X8,nil)) != X3
| app(cons(X8,nil),X9) != X4
| ~ ssList(X9) ) ) )
| ( nil = X4
& nil != X3 )
| ? [X5] :
( ? [X6] :
( ? [X7] :
( app(app(X7,cons(X5,nil)),X6) = X1
& app(app(X6,cons(X5,nil)),X7) = X2
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
| ~ neq(X2,nil)
| X1 != X3
| X2 != X4
| ~ ssList(X4) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_7,negated_conjecture,
! [X258,X259,X260] :
( ( ~ neq(esk51_0,nil)
| app(esk53_0,cons(esk52_0,nil)) = esk50_0 )
& ( ~ neq(esk51_0,nil)
| app(cons(esk52_0,nil),esk53_0) = esk51_0 )
& ( ~ neq(esk51_0,nil)
| ssList(esk53_0) )
& ( ~ neq(esk51_0,nil)
| ssItem(esk52_0) )
& ( nil != esk51_0
| nil = esk50_0 )
& ( app(app(X260,cons(X258,nil)),X259) != esk48_0
| app(app(X259,cons(X258,nil)),X260) != esk49_0
| ~ ssList(X260)
| ~ ssList(X259)
| ~ ssItem(X258) )
& neq(esk49_0,nil)
& esk48_0 = esk50_0
& esk49_0 = esk51_0
& ssList(esk51_0)
& ssList(esk50_0)
& ssList(esk49_0)
& ssList(esk48_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(esk49_0,nil),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_9,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,negated_conjecture,
( app(app(X3,cons(X1,nil)),X2) != esk48_0
| app(app(X2,cons(X1,nil)),X3) != esk49_0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
( ~ neq(esk51_0,nil)
| app(esk53_0,cons(esk52_0,nil)) = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
neq(esk51_0,nil),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( ~ neq(esk51_0,nil)
| ssList(esk53_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,negated_conjecture,
( ~ neq(esk51_0,nil)
| ssItem(esk52_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,negated_conjecture,
( ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| app(app(X3,cons(X2,nil)),X1) != esk51_0
| app(app(X1,cons(X2,nil)),X3) != esk50_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_9]) ).
cnf(c_0_17,negated_conjecture,
app(esk53_0,cons(esk52_0,nil)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13])]) ).
cnf(c_0_18,negated_conjecture,
ssList(esk53_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_13])]) ).
cnf(c_0_19,negated_conjecture,
ssItem(esk52_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_13])]) ).
fof(c_0_20,plain,
! [X230] :
( app(X230,nil) = X230
| ~ ssList(X230) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
cnf(c_0_21,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,negated_conjecture,
( ~ ssList(X1)
| app(esk50_0,X1) != esk50_0
| app(app(X1,cons(esk52_0,nil)),esk53_0) != esk51_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19])]) ).
cnf(c_0_23,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_25,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_21,c_0_11]) ).
fof(c_0_26,plain,
! [X138] :
( app(nil,X138) = X138
| ~ ssList(X138) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
cnf(c_0_27,negated_conjecture,
( ~ neq(esk51_0,nil)
| app(cons(esk52_0,nil),esk53_0) = esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_28,negated_conjecture,
app(app(nil,cons(esk52_0,nil)),esk53_0) != esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]) ).
cnf(c_0_29,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_30,negated_conjecture,
app(cons(esk52_0,nil),esk53_0) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_13])]) ).
fof(c_0_31,plain,
! [X114,X115] :
( ssList(cons(X115,X114))
| ~ ssItem(X115)
| ~ ssList(X114) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
cnf(c_0_32,negated_conjecture,
~ ssList(cons(esk52_0,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
cnf(c_0_33,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_24]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC419+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n008.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 08:23:54 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.47 Running first-order theorem proving
% 0.16/0.47 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
% 0.22/0.63 % Version: 3.5.1
% 0.22/0.63 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/0.63 % Starting new_bool_3 with 300s (1) cores
% 0.22/0.63 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.63 % Starting sh5l with 300s (1) cores
% 0.22/0.63 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 573394 completed with status 0
% 0.22/0.63 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.22/0.63 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/0.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.63 % No SInE strategy applied
% 0.22/0.63 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.22/0.63 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.63 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.22/0.63 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.22/0.63 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 0.22/0.63 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 0.22/0.63 % G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with pid 573403 completed with status 0
% 0.22/0.63 % Result found by G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S
% 0.22/0.63 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/0.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.63 % No SInE strategy applied
% 0.22/0.63 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.22/0.63 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.63 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.22/0.63 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.22/0.63 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 0.22/0.63 % Preprocessing time : 0.008 s
% 0.22/0.63 % Presaturation interreduction done
% 0.22/0.63
% 0.22/0.63 % Proof found!
% 0.22/0.63 % SZS status Theorem
% 0.22/0.63 % SZS output start CNFRefutation
% See solution above
% 0.22/0.63 % Parsed axioms : 96
% 0.22/0.63 % Removed by relevancy pruning/SinE : 0
% 0.22/0.63 % Initial clauses : 203
% 0.22/0.63 % Removed in clause preprocessing : 2
% 0.22/0.63 % Initial clauses in saturation : 201
% 0.22/0.63 % Processed clauses : 443
% 0.22/0.63 % ...of these trivial : 2
% 0.22/0.63 % ...subsumed : 9
% 0.22/0.63 % ...remaining for further processing : 432
% 0.22/0.63 % Other redundant clauses eliminated : 59
% 0.22/0.63 % Clauses deleted for lack of memory : 0
% 0.22/0.63 % Backward-subsumed : 2
% 0.22/0.63 % Backward-rewritten : 0
% 0.22/0.63 % Generated clauses : 729
% 0.22/0.63 % ...of the previous two non-redundant : 625
% 0.22/0.63 % ...aggressively subsumed : 0
% 0.22/0.63 % Contextual simplify-reflections : 2
% 0.22/0.63 % Paramodulations : 667
% 0.22/0.63 % Factorizations : 0
% 0.22/0.63 % NegExts : 0
% 0.22/0.63 % Equation resolutions : 64
% 0.22/0.63 % Disequality decompositions : 0
% 0.22/0.63 % Total rewrite steps : 373
% 0.22/0.63 % ...of those cached : 351
% 0.22/0.63 % Propositional unsat checks : 0
% 0.22/0.63 % Propositional check models : 0
% 0.22/0.63 % Propositional check unsatisfiable : 0
% 0.22/0.63 % Propositional clauses : 0
% 0.22/0.63 % Propositional clauses after purity: 0
% 0.22/0.63 % Propositional unsat core size : 0
% 0.22/0.63 % Propositional preprocessing time : 0.000
% 0.22/0.63 % Propositional encoding time : 0.000
% 0.22/0.63 % Propositional solver time : 0.000
% 0.22/0.63 % Success case prop preproc time : 0.000
% 0.22/0.63 % Success case prop encoding time : 0.000
% 0.22/0.63 % Success case prop solver time : 0.000
% 0.22/0.63 % Current number of processed clauses : 212
% 0.22/0.63 % Positive orientable unit clauses : 32
% 0.22/0.63 % Positive unorientable unit clauses: 0
% 0.22/0.63 % Negative unit clauses : 6
% 0.22/0.63 % Non-unit-clauses : 174
% 0.22/0.63 % Current number of unprocessed clauses: 578
% 0.22/0.63 % ...number of literals in the above : 3701
% 0.22/0.63 % Current number of archived formulas : 0
% 0.22/0.63 % Current number of archived clauses : 197
% 0.22/0.63 % Clause-clause subsumption calls (NU) : 16554
% 0.22/0.63 % Rec. Clause-clause subsumption calls : 3763
% 0.22/0.63 % Non-unit clause-clause subsumptions : 6
% 0.22/0.63 % Unit Clause-clause subsumption calls : 254
% 0.22/0.63 % Rewrite failures with RHS unbound : 0
% 0.22/0.63 % BW rewrite match attempts : 0
% 0.22/0.63 % BW rewrite match successes : 0
% 0.22/0.63 % Condensation attempts : 0
% 0.22/0.63 % Condensation successes : 0
% 0.22/0.63 % Termbank termtop insertions : 35080
% 0.22/0.63 % Search garbage collected termcells : 4344
% 0.22/0.63
% 0.22/0.63 % -------------------------------------------------
% 0.22/0.63 % User time : 0.066 s
% 0.22/0.63 % System time : 0.010 s
% 0.22/0.63 % Total time : 0.076 s
% 0.22/0.63 % Maximum resident set size: 4272 pages
% 0.22/0.63
% 0.22/0.63 % -------------------------------------------------
% 0.22/0.63 % User time : 0.276 s
% 0.22/0.63 % System time : 0.034 s
% 0.22/0.63 % Total time : 0.310 s
% 0.22/0.63 % Maximum resident set size: 4608 pages
% 0.22/0.63 % E exiting
%------------------------------------------------------------------------------