%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC392+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 : n015.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 02:44:13 PM UTC 2026
% Result : Theorem 0.22s 5.67s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 19 unt; 0 def)
% Number of atoms : 179 ( 56 equ)
% Maximal formula atoms : 31 ( 4 avg)
% Number of connectives : 213 ( 76 ~; 78 |; 33 &)
% ( 2 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 31 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X6] :
( ssItem(X6)
=> ( ? [X7] :
( leq(X7,X6)
& memberP(X4,X7)
& X6 != X7
& ssItem(X7) )
| ~ memberP(X4,X6)
| cons(X6,nil) != X3 ) ) )
| ! [X5] :
( ssItem(X5)
=> ( memberP(X2,X5)
| ~ memberP(X1,X5) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(ax37,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(cons(X2,X3),X1)
<=> ( memberP(X3,X1)
| X1 = X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(ax4,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( cons(X2,nil) = X1
& ssItem(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax39,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax39) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X6] :
( ssItem(X6)
=> ( ? [X7] :
( leq(X7,X6)
& memberP(X4,X7)
& X6 != X7
& ssItem(X7) )
| ~ memberP(X4,X6)
| cons(X6,nil) != X3 ) ) )
| ! [X5] :
( ssItem(X5)
=> ( memberP(X2,X5)
| ~ memberP(X1,X5) ) )
| 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 != X3
| nil != X4 )
& ! [X6] :
( ssItem(X6)
=> ( ? [X7] :
( leq(X7,X6)
& memberP(X4,X7)
& X6 != X7
& ssItem(X7) )
| ~ memberP(X4,X6)
| cons(X6,nil) != X3 ) ) )
| ! [X5] :
( ssItem(X5)
=> ( memberP(X2,X5)
| ~ memberP(X1,X5) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_8,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
fof(c_0_9,plain,
! [X155,X156,X157] :
( ( ~ ssItem(X155)
| ~ ssItem(X156)
| ~ ssList(X157)
| memberP(cons(X156,X157),X155)
| ~ memberP(X157,X155) )
& ( ~ ssItem(X155)
| ~ ssItem(X156)
| ~ ssList(X157)
| memberP(cons(X156,X157),X155)
| X155 != X156 )
& ( ~ ssItem(X155)
| ~ ssItem(X156)
| ~ ssList(X157)
| memberP(X157,X155)
| X155 = X156
| ~ memberP(cons(X156,X157),X155) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])])]) ).
fof(c_0_10,negated_conjecture,
! [X258] :
( ( ~ leq(X258,esk53_0)
| ~ memberP(esk51_0,X258)
| esk53_0 = X258
| ~ ssItem(X258)
| nil = esk50_0 )
& ( ~ leq(X258,esk53_0)
| ~ memberP(esk51_0,X258)
| esk53_0 = X258
| ~ ssItem(X258)
| nil = esk51_0 )
& ( memberP(esk51_0,esk53_0)
| nil = esk50_0 )
& ( memberP(esk51_0,esk53_0)
| nil = esk51_0 )
& ( cons(esk53_0,nil) = esk50_0
| nil = esk50_0 )
& ( cons(esk53_0,nil) = esk50_0
| nil = esk51_0 )
& ( ssItem(esk53_0)
| nil = esk50_0 )
& ( ssItem(esk53_0)
| nil = esk51_0 )
& ~ memberP(esk49_0,esk52_0)
& memberP(esk48_0,esk52_0)
& ssItem(esk52_0)
& 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_7])])])])])]) ).
fof(c_0_11,plain,
! [X158] :
( ~ memberP(nil,X158)
| ~ ssItem(X158) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_12,plain,
! [X18,X20] :
( ( ~ ssList(X18)
| singletonP(X18)
| cons(X20,nil) != X18
| ~ ssItem(X20) )
& ( ~ ssList(X18)
| ~ singletonP(X18)
| cons(esk5_1(X18),nil) = X18 )
& ( ~ ssList(X18)
| ~ singletonP(X18)
| ssItem(esk5_1(X18)) ) ),
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)],[ax4])])])])])]) ).
cnf(c_0_13,plain,
( ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X3)
| memberP(X2,X3)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( cons(esk53_0,nil) = esk50_0
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_16,negated_conjecture,
( ssItem(esk53_0)
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
memberP(esk48_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_20,plain,
( ~ ssList(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| singletonP(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_22,negated_conjecture,
~ memberP(esk49_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_23,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_24,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(esk50_0,X1)
| esk53_0 = X1
| esk50_0 = nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]),c_0_16]),c_0_17]) ).
cnf(c_0_25,negated_conjecture,
memberP(esk50_0,esk52_0),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_27,plain,
~ singletonP(nil),
inference(fof_simplification,[status(thm)],[ax39]) ).
cnf(c_0_28,plain,
( ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| singletonP(cons(X1,nil)) ),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_29,negated_conjecture,
( cons(esk53_0,nil) = esk50_0
| nil = esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_30,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_31,negated_conjecture,
( ssItem(esk53_0)
| nil = esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_32,negated_conjecture,
~ memberP(esk51_0,esk52_0),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_33,negated_conjecture,
( esk50_0 = nil
| esk52_0 = esk53_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_34,negated_conjecture,
( memberP(esk51_0,esk53_0)
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_35,plain,
~ singletonP(nil),
inference(fof_nnf,[status(thm)],[c_0_27]) ).
cnf(c_0_36,negated_conjecture,
( singletonP(esk50_0)
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]),c_0_31]) ).
cnf(c_0_37,negated_conjecture,
esk50_0 = nil,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_38,plain,
~ singletonP(nil),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_39,negated_conjecture,
esk51_0 = nil,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_40,negated_conjecture,
~ memberP(nil,esk52_0),
inference(rw,[status(thm)],[c_0_32,c_0_39]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_37]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC392+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/5.44 % Computer : n015.cluster.edu
% 0.18/5.44 % Model : x86_64 x86_64
% 0.18/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.44 % Memory : 8046.5625MB
% 0.18/5.44 % OS : Linux 6.8.0-71-generic
% 0.18/5.44 % CPULimit : 300
% 0.18/5.44 % WCLimit : 300
% 0.18/5.44 % DateTime : Mon Sep 21 08:24:11 UTC 2026
% 0.18/5.45 % CPUTime :
% 0.18/5.45 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/5.50 Running first-order theorem proving
% 0.22/5.50 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
% 0.22/5.67 % Version: 3.5.1
% 0.22/5.67 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/5.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/5.67 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/5.67 % Starting new_bool_3 with 300s (1) cores
% 0.22/5.67 % Starting new_bool_1 with 300s (1) cores
% 0.22/5.67 % Starting sh5l with 300s (1) cores
% 0.22/5.67 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1026016 completed with status 0
% 0.22/5.67 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.22/5.67 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/5.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/5.67 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/5.67 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/5.67 % No SInE strategy applied
% 0.22/5.67 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.22/5.67 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/5.67 % Starting SubtermCWHack with 136s (1) cores
% 0.22/5.67 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.22/5.67 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.22/5.67 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 0.22/5.67 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 0.22/5.67 % G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with pid 1026027 completed with status 0
% 0.22/5.67 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y
% 0.22/5.67 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/5.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/5.67 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/5.67 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/5.67 % No SInE strategy applied
% 0.22/5.67 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.22/5.67 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/5.67 % Starting SubtermCWHack with 136s (1) cores
% 0.22/5.67 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.22/5.67 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.22/5.67 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 0.22/5.67 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 0.22/5.67 % Preprocessing time : 0.006 s
% 0.22/5.67 % Presaturation interreduction done
% 0.22/5.67
% 0.22/5.67 % Proof found!
% 0.22/5.67 % SZS status Theorem
% 0.22/5.67 % SZS output start CNFRefutation
% See solution above
% 0.22/5.67 % Parsed axioms : 96
% 0.22/5.67 % Removed by relevancy pruning/SinE : 0
% 0.22/5.67 % Initial clauses : 207
% 0.22/5.67 % Removed in clause preprocessing : 2
% 0.22/5.67 % Initial clauses in saturation : 205
% 0.22/5.67 % Processed clauses : 513
% 0.22/5.67 % ...of these trivial : 3
% 0.22/5.67 % ...subsumed : 46
% 0.22/5.67 % ...remaining for further processing : 463
% 0.22/5.67 % Other redundant clauses eliminated : 71
% 0.22/5.67 % Clauses deleted for lack of memory : 0
% 0.22/5.67 % Backward-subsumed : 1
% 0.22/5.67 % Backward-rewritten : 46
% 0.22/5.67 % Generated clauses : 908
% 0.22/5.67 % ...of the previous two non-redundant : 769
% 0.22/5.67 % ...aggressively subsumed : 0
% 0.22/5.67 % Contextual simplify-reflections : 30
% 0.22/5.67 % Paramodulations : 834
% 0.22/5.67 % Factorizations : 0
% 0.22/5.67 % NegExts : 0
% 0.22/5.67 % Equation resolutions : 76
% 0.22/5.67 % Disequality decompositions : 0
% 0.22/5.67 % Total rewrite steps : 387
% 0.22/5.67 % ...of those cached : 367
% 0.22/5.67 % Propositional unsat checks : 0
% 0.22/5.67 % Propositional check models : 0
% 0.22/5.67 % Propositional check unsatisfiable : 0
% 0.22/5.67 % Propositional clauses : 0
% 0.22/5.67 % Propositional clauses after purity: 0
% 0.22/5.67 % Propositional unsat core size : 0
% 0.22/5.67 % Propositional preprocessing time : 0.000
% 0.22/5.67 % Propositional encoding time : 0.000
% 0.22/5.67 % Propositional solver time : 0.000
% 0.22/5.67 % Success case prop preproc time : 0.000
% 0.22/5.67 % Success case prop encoding time : 0.000
% 0.22/5.67 % Success case prop solver time : 0.000
% 0.22/5.67 % Current number of processed clauses : 194
% 0.22/5.67 % Positive orientable unit clauses : 21
% 0.22/5.67 % Positive unorientable unit clauses: 0
% 0.22/5.67 % Negative unit clauses : 3
% 0.22/5.67 % Non-unit-clauses : 170
% 0.22/5.67 % Current number of unprocessed clauses: 660
% 0.22/5.67 % ...number of literals in the above : 4672
% 0.22/5.67 % Current number of archived formulas : 0
% 0.22/5.67 % Current number of archived clauses : 246
% 0.22/5.67 % Clause-clause subsumption calls (NU) : 19823
% 0.22/5.67 % Rec. Clause-clause subsumption calls : 4722
% 0.22/5.67 % Non-unit clause-clause subsumptions : 75
% 0.22/5.67 % Unit Clause-clause subsumption calls : 91
% 0.22/5.67 % Rewrite failures with RHS unbound : 0
% 0.22/5.67 % BW rewrite match attempts : 4
% 0.22/5.67 % BW rewrite match successes : 4
% 0.22/5.67 % Condensation attempts : 0
% 0.22/5.67 % Condensation successes : 0
% 0.22/5.67 % Termbank termtop insertions : 37591
% 0.22/5.67 % Search garbage collected termcells : 4353
% 0.22/5.67
% 0.22/5.67 % -------------------------------------------------
% 0.22/5.67 % User time : 0.105 s
% 0.22/5.67 % System time : 0.008 s
% 0.22/5.67 % Total time : 0.113 s
% 0.22/5.67 % Maximum resident set size: 4272 pages
% 0.22/5.67
% 0.22/5.67 % -------------------------------------------------
% 0.22/5.67 % User time : 0.393 s
% 0.22/5.67 % System time : 0.033 s
% 0.22/5.67 % Total time : 0.426 s
% 0.22/5.67 % Maximum resident set size: 4608 pages
% 0.22/5.67 % E exiting
%------------------------------------------------------------------------------