%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC415+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 : n012.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 02:44:19 PM UTC 2026
% Result : Theorem 0.07s 11.02s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 10 unt; 0 def)
% Number of atoms : 151 ( 49 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 189 ( 69 ~; 65 |; 33 &)
% ( 2 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 37 ( 0 sgn 23 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( ? [X6] :
( neq(nil,X2)
& X1 = X6
& tl(X2) = X6
& ssList(X6) )
| ? [X5] :
( neq(nil,X4)
& tl(X4) = X5
& X3 != X5
& ssList(X5) )
| ~ neq(X2,nil) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( ? [X6] :
( neq(nil,X2)
& X1 = X6
& tl(X2) = X6
& ssList(X6) )
| ? [X5] :
( neq(nil,X4)
& tl(X4) = X5
& X3 != X5
& ssList(X5) )
| ~ neq(X2,nil) ) )
| 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)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( ? [X6] :
( neq(nil,X2)
& X1 = X6
& tl(X2) = X6
& ssList(X6) )
| ? [X5] :
( neq(nil,X4)
& tl(X4) = X5
& X3 != X5
& ssList(X5) )
| ~ neq(X2,nil) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_6,negated_conjecture,
! [X11,X12] :
( ( ~ neq(nil,esk2_0)
| esk1_0 != X12
| tl(esk2_0) != X12
| ~ ssList(X12)
| ~ neq(esk4_0,nil) )
& ( ~ neq(nil,esk2_0)
| esk1_0 != X12
| tl(esk2_0) != X12
| ~ ssList(X12)
| neq(esk2_0,nil) )
& ( ~ neq(nil,esk4_0)
| tl(esk4_0) != X11
| esk3_0 = X11
| ~ ssList(X11)
| ~ neq(esk4_0,nil) )
& ( ~ neq(nil,esk4_0)
| tl(esk4_0) != X11
| esk3_0 = X11
| ~ ssList(X11)
| neq(esk2_0,nil) )
& ( neq(esk2_0,nil)
| ~ neq(esk4_0,nil) )
& ( neq(esk2_0,nil)
| neq(esk2_0,nil) )
& 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])])])])])]) ).
cnf(c_0_7,negated_conjecture,
( neq(esk2_0,nil)
| neq(esk2_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_8,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax24]) ).
cnf(c_0_9,negated_conjecture,
( ~ neq(nil,esk4_0)
| tl(esk4_0) != X1
| ~ ssList(X1)
| ~ neq(esk4_0,nil)
| esk3_0 = X1 ),
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]) ).
cnf(c_0_12,negated_conjecture,
neq(esk2_0,nil),
inference(cn,[status(thm)],[c_0_7]) ).
fof(c_0_13,plain,
! [X22] :
( ssList(tl(X22))
| nil = X22
| ~ ssList(X22) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_14,negated_conjecture,
( ~ neq(nil,esk2_0)
| esk1_0 != X1
| tl(esk2_0) != X1
| ~ ssList(X1)
| ~ neq(esk4_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,negated_conjecture,
( ~ neq(nil,esk2_0)
| ~ ssList(tl(esk2_0))
| tl(esk2_0) = esk1_0 ),
inference(er,[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_9,c_0_10]),c_0_11]),c_0_11]),c_0_11]),c_0_12])])]) ).
cnf(c_0_16,plain,
( ~ ssList(X1)
| ssList(tl(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
ssList(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_18,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_19,negated_conjecture,
( ~ neq(nil,esk2_0)
| ~ ssList(tl(esk2_0)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_11]),c_0_12])])]),c_0_15]) ).
cnf(c_0_20,negated_conjecture,
( ~ neq(nil,esk2_0)
| esk2_0 = nil
| tl(esk2_0) = esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
cnf(c_0_21,negated_conjecture,
ssList(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_22,plain,
! [X15,X16] :
( ( ~ ssList(X15)
| ~ ssList(X16)
| neq(X15,X16)
| X15 = X16 )
& ( ~ ssList(X15)
| ~ ssList(X16)
| X15 != X16
| ~ neq(X15,X16) ) ),
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_18])])])])]) ).
cnf(c_0_23,negated_conjecture,
( ~ neq(nil,esk2_0)
| esk2_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_24,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_25,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_26,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,negated_conjecture,
esk2_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_17]),c_0_25])]) ).
cnf(c_0_28,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_29,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[c_0_12,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC415+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.03/10.98 % Computer : n012.cluster.edu
% 0.03/10.98 % Model : x86_64 x86_64
% 0.03/10.98 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/10.98 % Memory : 8046.5625MB
% 0.03/10.98 % OS : Linux 6.8.0-71-generic
% 0.03/10.98 % CPULimit : 300
% 0.03/10.98 % WCLimit : 300
% 0.03/10.98 % DateTime : Mon Sep 21 08:22:50 UTC 2026
% 0.03/10.98 % CPUTime :
% 0.03/10.98 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.03/11.00 Running first-order theorem proving
% 0.03/11.00 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
% 0.07/11.02 % Version: 3.5.1
% 0.07/11.02 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.07/11.02 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/11.02 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.07/11.02 % Starting new_bool_3 with 300s (1) cores
% 0.07/11.02 % Starting new_bool_1 with 300s (1) cores
% 0.07/11.02 % Starting sh5l with 300s (1) cores
% 0.07/11.02 % new_bool_3 with pid 1975867 completed with status 0
% 0.07/11.02 % Result found by new_bool_3
% 0.07/11.02 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.07/11.02 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/11.02 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.07/11.02 % Starting new_bool_3 with 300s (1) cores
% 0.07/11.02 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.07/11.02 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.07/11.02 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.07/11.02 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/11.02 % Starting SubtermCWHack with 28s (1) cores
% 0.07/11.02 % SubtermCWHack with pid 1975870 completed with status 0
% 0.07/11.02 % Result found by SubtermCWHack
% 0.07/11.02 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.07/11.02 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/11.02 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.07/11.02 % Starting new_bool_3 with 300s (1) cores
% 0.07/11.02 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.07/11.02 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.07/11.02 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.07/11.02 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/11.02 % Starting SubtermCWHack with 28s (1) cores
% 0.07/11.02 % Preprocessing time : 0.001 s
% 0.07/11.02
% 0.07/11.02 % Proof found!
% 0.07/11.02 % SZS status Theorem
% 0.07/11.02 % SZS output start CNFRefutation
% See solution above
% 0.07/11.02 % Parsed axioms : 96
% 0.07/11.02 % Removed by relevancy pruning/SinE : 67
% 0.07/11.02 % Initial clauses : 51
% 0.07/11.02 % Removed in clause preprocessing : 0
% 0.07/11.02 % Initial clauses in saturation : 51
% 0.07/11.02 % Processed clauses : 61
% 0.07/11.02 % ...of these trivial : 3
% 0.07/11.02 % ...subsumed : 4
% 0.07/11.02 % ...remaining for further processing : 54
% 0.07/11.02 % Other redundant clauses eliminated : 8
% 0.07/11.02 % Clauses deleted for lack of memory : 0
% 0.07/11.02 % Backward-subsumed : 5
% 0.07/11.02 % Backward-rewritten : 8
% 0.07/11.02 % Generated clauses : 53
% 0.07/11.02 % ...of the previous two non-redundant : 38
% 0.07/11.02 % ...aggressively subsumed : 0
% 0.07/11.02 % Contextual simplify-reflections : 1
% 0.07/11.02 % Paramodulations : 45
% 0.07/11.02 % Factorizations : 0
% 0.07/11.02 % NegExts : 0
% 0.07/11.02 % Equation resolutions : 9
% 0.07/11.02 % Disequality decompositions : 0
% 0.07/11.02 % Total rewrite steps : 53
% 0.07/11.02 % ...of those cached : 46
% 0.07/11.02 % Propositional unsat checks : 0
% 0.07/11.02 % Propositional check models : 0
% 0.07/11.02 % Propositional check unsatisfiable : 0
% 0.07/11.02 % Propositional clauses : 0
% 0.07/11.02 % Propositional clauses after purity: 0
% 0.07/11.02 % Propositional unsat core size : 0
% 0.07/11.02 % Propositional preprocessing time : 0.000
% 0.07/11.02 % Propositional encoding time : 0.000
% 0.07/11.02 % Propositional solver time : 0.000
% 0.07/11.02 % Success case prop preproc time : 0.000
% 0.07/11.02 % Success case prop encoding time : 0.000
% 0.07/11.02 % Success case prop solver time : 0.000
% 0.07/11.02 % Current number of processed clauses : 36
% 0.07/11.02 % Positive orientable unit clauses : 8
% 0.07/11.02 % Positive unorientable unit clauses: 0
% 0.07/11.02 % Negative unit clauses : 1
% 0.07/11.02 % Non-unit-clauses : 27
% 0.07/11.02 % Current number of unprocessed clauses: 26
% 0.07/11.02 % ...number of literals in the above : 135
% 0.07/11.02 % Current number of archived formulas : 0
% 0.07/11.02 % Current number of archived clauses : 13
% 0.07/11.02 % Clause-clause subsumption calls (NU) : 154
% 0.07/11.02 % Rec. Clause-clause subsumption calls : 99
% 0.07/11.02 % Non-unit clause-clause subsumptions : 10
% 0.07/11.02 % Unit Clause-clause subsumption calls : 17
% 0.07/11.02 % Rewrite failures with RHS unbound : 0
% 0.07/11.02 % BW rewrite match attempts : 3
% 0.07/11.02 % BW rewrite match successes : 3
% 0.07/11.02 % Condensation attempts : 0
% 0.07/11.02 % Condensation successes : 0
% 0.07/11.02 % Termbank termtop insertions : 5834
% 0.07/11.02 % Search garbage collected termcells : 1521
% 0.07/11.02
% 0.07/11.02 % -------------------------------------------------
% 0.07/11.02 % User time : 0.004 s
% 0.07/11.02 % System time : 0.002 s
% 0.07/11.02 % Total time : 0.007 s
% 0.07/11.02 % Maximum resident set size: 3760 pages
% 0.07/11.02
% 0.07/11.02 % -------------------------------------------------
% 0.07/11.02 % User time : 0.007 s
% 0.07/11.02 % System time : 0.005 s
% 0.07/11.02 % Total time : 0.011 s
% 0.07/11.02 % Maximum resident set size: 4864 pages
% 0.07/11.02 % E exiting
%------------------------------------------------------------------------------