%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC025+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 02:42:40 PM UTC 2026
% Result : Theorem 0.15s 1.08s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 8 unt; 0 def)
% Number of atoms : 162 ( 57 equ)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 204 ( 77 ~; 78 |; 30 &)
% ( 1 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 24 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil = X2
| nil != X1 )
& ( nil = X1
| nil != X2 ) )
| ? [X5] :
( ( ( memberP(X4,X5)
& ~ memberP(X3,X5) )
| ( memberP(X3,X5)
& ~ memberP(X4,X5) ) )
& ssItem(X5) )
| ~ duplicatefreeP(X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(ax20,axiom,
! [X1] :
( ssList(X1)
=> ( ? [X2] :
( ? [X3] :
( cons(X3,X2) = X1
& ssItem(X3) )
& ssList(X2) )
| nil = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax20) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil = X2
| nil != X1 )
& ( nil = X1
| nil != X2 ) )
| ? [X5] :
( ( ( memberP(X4,X5)
& ~ memberP(X3,X5) )
| ( memberP(X3,X5)
& ~ memberP(X4,X5) ) )
& ssItem(X5) )
| ~ duplicatefreeP(X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil = X2
| nil != X1 )
& ( nil = X1
| nil != X2 ) )
| ? [X5] :
( ( ( memberP(X4,X5)
& ~ memberP(X3,X5) )
| ( memberP(X3,X5)
& ~ memberP(X4,X5) ) )
& ssItem(X5) )
| ~ duplicatefreeP(X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_6,negated_conjecture,
! [X11] :
( ( nil != esk1_0
| nil != esk2_0 )
& ( nil != esk1_0
| nil = esk1_0 )
& ( nil = esk2_0
| nil != esk2_0 )
& ( nil = esk2_0
| nil = esk1_0 )
& ( ~ ssItem(X11)
| ~ memberP(esk4_0,X11)
| memberP(esk3_0,X11) )
& ( ~ ssItem(X11)
| ~ memberP(esk3_0,X11)
| memberP(esk4_0,X11) )
& duplicatefreeP(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(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])])]) ).
fof(c_0_7,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
fof(c_0_8,plain,
! [X26,X27,X28] :
( ( ~ ssItem(X26)
| ~ ssItem(X27)
| ~ ssList(X28)
| memberP(cons(X27,X28),X26)
| ~ memberP(X28,X26) )
& ( ~ ssItem(X26)
| ~ ssItem(X27)
| ~ ssList(X28)
| memberP(cons(X27,X28),X26)
| X26 != X27 )
& ( ~ ssItem(X26)
| ~ ssItem(X27)
| ~ ssList(X28)
| memberP(X28,X26)
| X26 = X27
| ~ memberP(cons(X27,X28),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)],[ax37])])])])]) ).
cnf(c_0_9,negated_conjecture,
( nil = esk2_0
| nil = esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_12,plain,
! [X29] :
( ~ memberP(nil,X29)
| ~ ssItem(X29) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_13,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_14,plain,
! [X12] :
( ( ~ ssList(X12)
| nil = X12
| cons(esk6_1(X12),esk5_1(X12)) = X12 )
& ( ~ ssList(X12)
| nil = X12
| ssItem(esk6_1(X12)) )
& ( ~ ssList(X12)
| nil = X12
| ssList(esk5_1(X12)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])])]) ).
cnf(c_0_15,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(esk3_0,X1)
| memberP(esk4_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,negated_conjecture,
( esk3_0 = nil
| esk4_0 = nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_17,plain,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| memberP(cons(X1,X2),X1) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( ~ ssList(X1)
| nil = X1
| cons(esk6_1(X1),esk5_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(esk6_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( ~ ssList(X1)
| nil = X1
| ssList(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(esk3_0,X1)
| esk3_0 = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_23,plain,
( ~ ssList(X1)
| memberP(X1,esk6_1(X1))
| nil = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21]) ).
cnf(c_0_24,negated_conjecture,
ssList(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_25,negated_conjecture,
( ~ ssItem(esk6_1(esk3_0))
| esk3_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_26,negated_conjecture,
( nil != esk1_0
| nil != esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_27,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(esk4_0,X1)
| memberP(esk3_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_28,negated_conjecture,
esk3_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_20]),c_0_24])]) ).
cnf(c_0_29,negated_conjecture,
( esk4_0 != nil
| esk3_0 != nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_10]),c_0_11]) ).
cnf(c_0_30,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(esk4_0,X1) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_17]) ).
cnf(c_0_31,negated_conjecture,
ssList(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_32,negated_conjecture,
esk4_0 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_28])]) ).
cnf(c_0_33,negated_conjecture,
~ ssItem(esk6_1(esk4_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_23]),c_0_31])]),c_0_32]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_20]),c_0_31])]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC025+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/1.00 % Computer : n010.cluster.edu
% 0.10/1.00 % Model : x86_64 x86_64
% 0.10/1.00 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/1.00 % Memory : 8046.5625MB
% 0.10/1.00 % OS : Linux 6.8.0-71-generic
% 0.10/1.00 % CPULimit : 300
% 0.10/1.00 % WCLimit : 300
% 0.10/1.00 % DateTime : Mon Sep 21 07:50:14 UTC 2026
% 0.10/1.00 % CPUTime :
% 0.10/1.00 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/1.05 Running first-order theorem proving
% 0.15/1.05 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.15/1.08 % Version: 3.5.1
% 0.15/1.08 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/1.08 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/1.08 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/1.08 % Starting new_bool_3 with 300s (1) cores
% 0.15/1.08 % Starting new_bool_1 with 300s (1) cores
% 0.15/1.08 % Starting sh5l with 300s (1) cores
% 0.15/1.08 % new_bool_3 with pid 404803 completed with status 0
% 0.15/1.08 % Result found by new_bool_3
% 0.15/1.08 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/1.08 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/1.08 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/1.08 % Starting new_bool_3 with 300s (1) cores
% 0.15/1.08 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/1.08 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/1.08 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.15/1.08 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/1.08 % Starting SubtermCWHack with 31s (1) cores
% 0.15/1.08 % SubtermCWHack with pid 404806 completed with status 0
% 0.15/1.08 % Result found by SubtermCWHack
% 0.15/1.08 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/1.08 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/1.08 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/1.08 % Starting new_bool_3 with 300s (1) cores
% 0.15/1.08 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/1.08 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/1.08 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.15/1.08 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/1.08 % Starting SubtermCWHack with 31s (1) cores
% 0.15/1.08 % Preprocessing time : 0.002 s
% 0.15/1.08
% 0.15/1.08 % Proof found!
% 0.15/1.08 % SZS status Theorem
% 0.15/1.08 % SZS output start CNFRefutation
% See solution above
% 0.15/1.08 % Parsed axioms : 96
% 0.15/1.08 % Removed by relevancy pruning/SinE : 72
% 0.15/1.08 % Initial clauses : 57
% 0.15/1.08 % Removed in clause preprocessing : 2
% 0.15/1.08 % Initial clauses in saturation : 55
% 0.15/1.08 % Processed clauses : 61
% 0.15/1.08 % ...of these trivial : 0
% 0.15/1.08 % ...subsumed : 6
% 0.15/1.08 % ...remaining for further processing : 55
% 0.15/1.08 % Other redundant clauses eliminated : 5
% 0.15/1.08 % Clauses deleted for lack of memory : 0
% 0.15/1.08 % Backward-subsumed : 0
% 0.15/1.08 % Backward-rewritten : 11
% 0.15/1.08 % Generated clauses : 45
% 0.15/1.08 % ...of the previous two non-redundant : 31
% 0.15/1.08 % ...aggressively subsumed : 0
% 0.15/1.08 % Contextual simplify-reflections : 6
% 0.15/1.08 % Paramodulations : 40
% 0.15/1.08 % Factorizations : 0
% 0.15/1.08 % NegExts : 0
% 0.15/1.08 % Equation resolutions : 6
% 0.15/1.08 % Disequality decompositions : 0
% 0.15/1.08 % Total rewrite steps : 46
% 0.15/1.08 % ...of those cached : 39
% 0.15/1.08 % Propositional unsat checks : 0
% 0.15/1.08 % Propositional check models : 0
% 0.15/1.08 % Propositional check unsatisfiable : 0
% 0.15/1.08 % Propositional clauses : 0
% 0.15/1.08 % Propositional clauses after purity: 0
% 0.15/1.08 % Propositional unsat core size : 0
% 0.15/1.08 % Propositional preprocessing time : 0.000
% 0.15/1.08 % Propositional encoding time : 0.000
% 0.15/1.08 % Propositional solver time : 0.000
% 0.15/1.08 % Success case prop preproc time : 0.000
% 0.15/1.08 % Success case prop encoding time : 0.000
% 0.15/1.08 % Success case prop solver time : 0.000
% 0.15/1.08 % Current number of processed clauses : 42
% 0.15/1.08 % Positive orientable unit clauses : 9
% 0.15/1.08 % Positive unorientable unit clauses: 0
% 0.15/1.08 % Negative unit clauses : 3
% 0.15/1.08 % Non-unit-clauses : 30
% 0.15/1.08 % Current number of unprocessed clauses: 25
% 0.15/1.08 % ...number of literals in the above : 123
% 0.15/1.08 % Current number of archived formulas : 0
% 0.15/1.08 % Current number of archived clauses : 11
% 0.15/1.08 % Clause-clause subsumption calls (NU) : 119
% 0.15/1.08 % Rec. Clause-clause subsumption calls : 46
% 0.15/1.08 % Non-unit clause-clause subsumptions : 12
% 0.15/1.08 % Unit Clause-clause subsumption calls : 27
% 0.15/1.08 % Rewrite failures with RHS unbound : 0
% 0.15/1.08 % BW rewrite match attempts : 3
% 0.15/1.08 % BW rewrite match successes : 3
% 0.15/1.08 % Condensation attempts : 0
% 0.15/1.08 % Condensation successes : 0
% 0.15/1.08 % Termbank termtop insertions : 5984
% 0.15/1.08 % Search garbage collected termcells : 1679
% 0.15/1.08
% 0.15/1.08 % -------------------------------------------------
% 0.15/1.08 % User time : 0.007 s
% 0.15/1.08 % System time : 0.006 s
% 0.15/1.08 % Total time : 0.013 s
% 0.15/1.08 % Maximum resident set size: 3760 pages
% 0.15/1.08
% 0.15/1.08 % -------------------------------------------------
% 0.15/1.08 % User time : 0.013 s
% 0.15/1.08 % System time : 0.013 s
% 0.15/1.08 % Total time : 0.026 s
% 0.15/1.08 % Maximum resident set size: 4608 pages
% 0.15/1.08 % E exiting
%------------------------------------------------------------------------------