%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC013+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 : n001.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 02:42:36 PM UTC 2026
% Result : Theorem 0.15s 0.62s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 9 unt; 0 def)
% Number of atoms : 200 ( 70 equ)
% Maximal formula atoms : 38 ( 5 avg)
% Number of connectives : 265 ( 101 ~; 95 |; 45 &)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 29 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( ? [X7] :
( ? [X8] :
( neq(nil,X2)
& hd(X2) = X8
& cons(X8,nil) = X7
& ssItem(X8) )
& X1 = X7
& ssList(X7) )
| ? [X5] :
( ? [X6] :
( neq(nil,X4)
& hd(X4) = X6
& cons(X6,nil) = X5
& ssItem(X6) )
& X3 != X5
& 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(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
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) )
& ( ? [X7] :
( ? [X8] :
( neq(nil,X2)
& hd(X2) = X8
& cons(X8,nil) = X7
& ssItem(X8) )
& X1 = X7
& ssList(X7) )
| ? [X5] :
( ? [X6] :
( neq(nil,X4)
& hd(X4) = X6
& cons(X6,nil) = X5
& ssItem(X6) )
& X3 != X5
& 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) )
& ( ? [X7] :
( ? [X8] :
( neq(nil,X2)
& hd(X2) = X8
& cons(X8,nil) = X7
& ssItem(X8) )
& X1 = X7
& ssList(X7) )
| ? [X5] :
( ? [X6] :
( neq(nil,X4)
& hd(X4) = X6
& cons(X6,nil) = X5
& ssItem(X6) )
& X3 != X5
& ssList(X5) )
| ~ neq(X2,nil) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_7,negated_conjecture,
! [X257,X258,X259,X260] :
( ( ~ neq(nil,esk49_0)
| hd(esk49_0) != X260
| cons(X260,nil) != X259
| ~ ssItem(X260)
| esk48_0 != X259
| ~ ssList(X259)
| ~ neq(esk51_0,nil) )
& ( ~ neq(nil,esk49_0)
| hd(esk49_0) != X260
| cons(X260,nil) != X259
| ~ ssItem(X260)
| esk48_0 != X259
| ~ ssList(X259)
| neq(esk49_0,nil) )
& ( ~ neq(nil,esk51_0)
| hd(esk51_0) != X258
| cons(X258,nil) != X257
| ~ ssItem(X258)
| esk50_0 = X257
| ~ ssList(X257)
| ~ neq(esk51_0,nil) )
& ( ~ neq(nil,esk51_0)
| hd(esk51_0) != X258
| cons(X258,nil) != X257
| ~ ssItem(X258)
| esk50_0 = X257
| ~ ssList(X257)
| neq(esk49_0,nil) )
& ( neq(esk49_0,nil)
| ~ neq(esk51_0,nil) )
& ( neq(esk49_0,nil)
| 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)
| neq(esk49_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_9,negated_conjecture,
( ~ neq(nil,esk49_0)
| hd(esk49_0) != X2
| cons(X2,nil) != X1
| ~ ssItem(X2)
| esk48_0 != X1
| ~ ssList(X1)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
neq(esk49_0,nil),
inference(cn,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_13,negated_conjecture,
( ~ neq(nil,esk51_0)
| hd(esk51_0) != X2
| cons(X2,nil) != X1
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ neq(esk51_0,nil)
| esk50_0 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,negated_conjecture,
( ~ ssItem(X1)
| ~ neq(nil,esk49_0)
| ~ ssList(X2)
| esk48_0 != X2
| hd(esk49_0) != X1
| cons(X1,nil) != X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_11])]) ).
fof(c_0_16,plain,
! [X111,X112] :
( ( ~ ssList(X111)
| ~ ssList(X112)
| neq(X111,X112)
| X111 = X112 )
& ( ~ ssList(X111)
| ~ ssList(X112)
| X111 != X112
| ~ neq(X111,X112) ) ),
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_12])])])])]) ).
cnf(c_0_17,negated_conjecture,
( ~ ssItem(X1)
| ~ neq(nil,esk49_0)
| ~ ssList(X2)
| hd(esk49_0) != X1
| cons(X1,nil) != X2 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_10]),c_0_10]),c_0_10]),c_0_11])]),c_0_15]) ).
cnf(c_0_18,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_20,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_21,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| hd(esk49_0) != X1
| cons(X1,nil) != X2
| esk49_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]) ).
fof(c_0_22,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax22]) ).
cnf(c_0_23,negated_conjecture,
( ~ ssItem(hd(esk49_0))
| ~ ssList(X1)
| cons(hd(esk49_0),nil) != X1
| esk49_0 = nil ),
inference(er,[status(thm)],[c_0_21]) ).
fof(c_0_24,plain,
! [X126] :
( ssItem(hd(X126))
| nil = X126
| ~ ssList(X126) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])]) ).
cnf(c_0_25,negated_conjecture,
( ~ ssItem(hd(esk49_0))
| ~ ssList(cons(hd(esk49_0),nil))
| esk49_0 = nil ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_26,plain,
( ~ ssList(X1)
| ssItem(hd(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_27,plain,
! [X113,X114] :
( ssList(cons(X114,X113))
| ~ ssItem(X114)
| ~ ssList(X113) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
cnf(c_0_28,negated_conjecture,
( ~ ssList(cons(hd(esk49_0),nil))
| esk49_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_19])]) ).
cnf(c_0_29,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_30,negated_conjecture,
( ~ ssItem(hd(esk49_0))
| esk49_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_20])]) ).
cnf(c_0_31,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_32,negated_conjecture,
esk49_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_26]),c_0_19])]) ).
cnf(c_0_33,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[c_0_31]) ).
cnf(c_0_34,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[c_0_11,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC013+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.53 % Computer : n001.cluster.edu
% 0.13/0.53 % Model : x86_64 x86_64
% 0.13/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.53 % Memory : 8046.5625MB
% 0.13/0.53 % OS : Linux 6.8.0-71-generic
% 0.13/0.53 % CPULimit : 300
% 0.13/0.53 % WCLimit : 300
% 0.13/0.53 % DateTime : Mon Sep 21 07:54:47 UTC 2026
% 0.13/0.53 % CPUTime :
% 0.13/0.53 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.57 Running first-order theorem proving
% 0.15/0.57 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
% 0.15/0.62 % Version: 3.5.1
% 0.15/0.62 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.62 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.62 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.62 % Starting sh5l with 300s (1) cores
% 0.15/0.62 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2605718 completed with status 0
% 0.15/0.62 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.15/0.62 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.62 % No SInE strategy applied
% 0.15/0.62 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.15/0.62 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.62 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.15/0.62 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.15/0.62 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 0.15/0.62 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 0.15/0.62 % G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with pid 2605727 completed with status 0
% 0.15/0.62 % Result found by G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d
% 0.15/0.62 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.62 % No SInE strategy applied
% 0.15/0.62 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.15/0.62 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.62 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.15/0.62 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.15/0.62 % Preprocessing time : 0.002 s
% 0.15/0.62
% 0.15/0.62 % Proof found!
% 0.15/0.62 % SZS status Theorem
% 0.15/0.62 % SZS output start CNFRefutation
% See solution above
% 0.15/0.62 % Parsed axioms : 96
% 0.15/0.62 % Removed by relevancy pruning/SinE : 0
% 0.15/0.62 % Initial clauses : 202
% 0.15/0.62 % Removed in clause preprocessing : 2
% 0.15/0.62 % Initial clauses in saturation : 200
% 0.15/0.62 % Processed clauses : 245
% 0.15/0.62 % ...of these trivial : 5
% 0.15/0.62 % ...subsumed : 16
% 0.15/0.62 % ...remaining for further processing : 224
% 0.15/0.62 % Other redundant clauses eliminated : 63
% 0.15/0.62 % Clauses deleted for lack of memory : 0
% 0.15/0.62 % Backward-subsumed : 3
% 0.15/0.62 % Backward-rewritten : 11
% 0.15/0.62 % Generated clauses : 592
% 0.15/0.62 % ...of the previous two non-redundant : 487
% 0.15/0.62 % ...aggressively subsumed : 0
% 0.15/0.62 % Contextual simplify-reflections : 4
% 0.15/0.62 % Paramodulations : 503
% 0.15/0.62 % Factorizations : 0
% 0.15/0.62 % NegExts : 0
% 0.15/0.62 % Equation resolutions : 89
% 0.15/0.62 % Disequality decompositions : 0
% 0.15/0.62 % Total rewrite steps : 214
% 0.15/0.62 % ...of those cached : 202
% 0.15/0.62 % Propositional unsat checks : 0
% 0.15/0.62 % Propositional check models : 0
% 0.15/0.62 % Propositional check unsatisfiable : 0
% 0.15/0.62 % Propositional clauses : 0
% 0.15/0.62 % Propositional clauses after purity: 0
% 0.15/0.62 % Propositional unsat core size : 0
% 0.15/0.62 % Propositional preprocessing time : 0.000
% 0.15/0.62 % Propositional encoding time : 0.000
% 0.15/0.62 % Propositional solver time : 0.000
% 0.15/0.62 % Success case prop preproc time : 0.000
% 0.15/0.62 % Success case prop encoding time : 0.000
% 0.15/0.62 % Success case prop solver time : 0.000
% 0.15/0.62 % Current number of processed clauses : 204
% 0.15/0.62 % Positive orientable unit clauses : 23
% 0.15/0.62 % Positive unorientable unit clauses: 0
% 0.15/0.62 % Negative unit clauses : 2
% 0.15/0.62 % Non-unit-clauses : 179
% 0.15/0.62 % Current number of unprocessed clauses: 435
% 0.15/0.62 % ...number of literals in the above : 3037
% 0.15/0.62 % Current number of archived formulas : 0
% 0.15/0.62 % Current number of archived clauses : 14
% 0.15/0.62 % Clause-clause subsumption calls (NU) : 7357
% 0.15/0.62 % Rec. Clause-clause subsumption calls : 1886
% 0.15/0.62 % Non-unit clause-clause subsumptions : 23
% 0.15/0.62 % Unit Clause-clause subsumption calls : 69
% 0.15/0.62 % Rewrite failures with RHS unbound : 0
% 0.15/0.62 % BW rewrite match attempts : 3
% 0.15/0.62 % BW rewrite match successes : 3
% 0.15/0.62 % Condensation attempts : 0
% 0.15/0.62 % Condensation successes : 0
% 0.15/0.62 % Termbank termtop insertions : 30086
% 0.15/0.62 % Search garbage collected termcells : 4373
% 0.15/0.62
% 0.15/0.62 % -------------------------------------------------
% 0.15/0.62 % User time : 0.024 s
% 0.15/0.62 % System time : 0.009 s
% 0.15/0.62 % Total time : 0.033 s
% 0.15/0.62 % Maximum resident set size: 4272 pages
% 0.15/0.62
% 0.15/0.62 % -------------------------------------------------
% 0.15/0.62 % User time : 0.089 s
% 0.15/0.62 % System time : 0.023 s
% 0.15/0.62 % Total time : 0.113 s
% 0.15/0.62 % Maximum resident set size: 4608 pages
% 0.15/0.62 % E exiting
%------------------------------------------------------------------------------