%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COM018+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:11:28 PM UTC 2026
% Result : Theorem 0.19s 0.46s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 6 unt; 0 def)
% Number of atoms : 222 ( 23 equ)
% Maximal formula atoms : 96 ( 13 avg)
% Number of connectives : 295 ( 89 ~; 132 |; 69 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 34 ( 1 sgn 18 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
? [X1] :
( aNormalFormOfIn0(X1,xw,xR)
| ( ~ ? [X2] : aReductOfIn0(X2,X1,xR)
& ( sdtmndtasgtdt0(xw,xR,X1)
| sdtmndtplgtdt0(xw,xR,X1)
| ? [X2] :
( sdtmndtplgtdt0(X2,xR,X1)
& aReductOfIn0(X2,xw,xR)
& aElement0(X2) )
| aReductOfIn0(X1,xw,xR)
| xw = X1 )
& aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mTermNF,axiom,
! [X1] :
( ( isTerminating0(X1)
& aRewritingSystem0(X1) )
=> ! [X2] :
( aElement0(X2)
=> ? [X3] : aNormalFormOfIn0(X3,X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTermNF) ).
fof(m__656_01,hypothesis,
( isTerminating0(xR)
& ! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> ( ( sdtmndtplgtdt0(X1,xR,X2)
| ? [X3] :
( sdtmndtplgtdt0(X3,xR,X2)
& aReductOfIn0(X3,X1,xR)
& aElement0(X3) )
| aReductOfIn0(X2,X1,xR) )
=> iLess0(X2,X1) ) )
& isLocallyConfluent0(xR)
& ! [X1,X2,X3] :
( ( aReductOfIn0(X3,X1,xR)
& aReductOfIn0(X2,X1,xR)
& aElement0(X3)
& aElement0(X2)
& aElement0(X1) )
=> ? [X4] :
( sdtmndtasgtdt0(X3,xR,X4)
& ( ( sdtmndtplgtdt0(X3,xR,X4)
& ( ? [X5] :
( sdtmndtplgtdt0(X5,xR,X4)
& aReductOfIn0(X5,X3,xR)
& aElement0(X5) )
| aReductOfIn0(X4,X3,xR) ) )
| X3 = X4 )
& sdtmndtasgtdt0(X2,xR,X4)
& ( ( sdtmndtplgtdt0(X2,xR,X4)
& ( ? [X5] :
( sdtmndtplgtdt0(X5,xR,X4)
& aReductOfIn0(X5,X2,xR)
& aElement0(X5) )
| aReductOfIn0(X4,X2,xR) ) )
| X2 = X4 )
& aElement0(X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656_01) ).
fof(m__799,hypothesis,
( sdtmndtasgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(xv,xR,xw)
& ( ? [X1] :
( sdtmndtplgtdt0(X1,xR,xw)
& aReductOfIn0(X1,xv,xR)
& aElement0(X1) )
| aReductOfIn0(xw,xv,xR) ) )
| xv = xw )
& sdtmndtasgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(xu,xR,xw)
& ( ? [X1] :
( sdtmndtplgtdt0(X1,xR,xw)
& aReductOfIn0(X1,xu,xR)
& aElement0(X1) )
| aReductOfIn0(xw,xu,xR) ) )
| xu = xw )
& aElement0(xw) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__799) ).
fof(m__656,hypothesis,
aRewritingSystem0(xR),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656) ).
fof(c_0_5,negated_conjecture,
~ ? [X1] :
( aNormalFormOfIn0(X1,xw,xR)
| ( ~ ? [X2] : aReductOfIn0(X2,X1,xR)
& ( sdtmndtasgtdt0(xw,xR,X1)
| sdtmndtplgtdt0(xw,xR,X1)
| ? [X2] :
( sdtmndtplgtdt0(X2,xR,X1)
& aReductOfIn0(X2,xw,xR)
& aElement0(X2) )
| aReductOfIn0(X1,xw,xR)
| xw = X1 )
& aElement0(X1) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_6,negated_conjecture,
! [X29,X30,X32] :
( ~ aNormalFormOfIn0(X32,xw,xR)
& ( aReductOfIn0(esk13_1(X29),X29,xR)
| ~ aElement0(X29)
| ~ sdtmndtasgtdt0(xw,xR,X29) )
& ( aReductOfIn0(esk13_1(X29),X29,xR)
| ~ aElement0(X29)
| ~ sdtmndtplgtdt0(xw,xR,X29) )
& ( aReductOfIn0(esk13_1(X29),X29,xR)
| ~ aElement0(X29)
| ~ sdtmndtplgtdt0(X30,xR,X29)
| ~ aReductOfIn0(X30,xw,xR)
| ~ aElement0(X30) )
& ( aReductOfIn0(esk13_1(X29),X29,xR)
| ~ aElement0(X29)
| ~ aReductOfIn0(X29,xw,xR) )
& ( aReductOfIn0(esk13_1(X29),X29,xR)
| ~ aElement0(X29)
| xw != X29 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])])])]) ).
fof(c_0_7,plain,
! [X61,X62] :
( aNormalFormOfIn0(esk17_2(X61,X62),X62,X61)
| ~ aElement0(X62)
| ~ isTerminating0(X61)
| ~ aRewritingSystem0(X61) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mTermNF])])])])]) ).
fof(c_0_8,hypothesis,
! [X6,X7,X8,X12,X13,X14] :
( isTerminating0(xR)
& ( ~ aElement0(X13)
| ~ aElement0(X12)
| iLess0(X13,X12)
| ~ sdtmndtplgtdt0(X12,xR,X13) )
& ( ~ aElement0(X13)
| ~ aElement0(X12)
| iLess0(X13,X12)
| ~ sdtmndtplgtdt0(X14,xR,X13)
| ~ aReductOfIn0(X14,X12,xR)
| ~ aElement0(X14) )
& ( ~ aElement0(X13)
| ~ aElement0(X12)
| iLess0(X13,X12)
| ~ aReductOfIn0(X13,X12,xR) )
& isLocallyConfluent0(xR)
& ( ~ aReductOfIn0(X8,X6,xR)
| ~ aReductOfIn0(X7,X6,xR)
| ~ aElement0(X8)
| ~ aElement0(X7)
| ~ aElement0(X6)
| sdtmndtasgtdt0(X8,xR,esk1_3(X6,X7,X8)) )
& ( ~ aReductOfIn0(X8,X6,xR)
| ~ aReductOfIn0(X7,X6,xR)
| ~ aElement0(X8)
| ~ aElement0(X7)
| ~ aElement0(X6)
| X8 = esk1_3(X6,X7,X8)
| sdtmndtplgtdt0(X8,xR,esk1_3(X6,X7,X8)) )
& ( ~ aReductOfIn0(X8,X6,xR)
| ~ aReductOfIn0(X7,X6,xR)
| ~ aElement0(X8)
| ~ aElement0(X7)
| ~ aElement0(X6)
| X8 = esk1_3(X6,X7,X8)
| aReductOfIn0(esk1_3(X6,X7,X8),X8,xR)
| sdtmndtplgtdt0(esk3_3(X6,X7,X8),xR,esk1_3(X6,X7,X8)) )
& ( ~ aReductOfIn0(X8,X6,xR)
| ~ aReductOfIn0(X7,X6,xR)
| ~ aElement0(X8)
| ~ aElement0(X7)
| ~ aElement0(X6)
| X8 = esk1_3(X6,X7,X8)
| aReductOfIn0(esk1_3(X6,X7,X8),X8,xR)
| aReductOfIn0(esk3_3(X6,X7,X8),X8,xR) )
& ( ~ aReductOfIn0(X8,X6,xR)
| ~ aReductOfIn0(X7,X6,xR)
| ~ aElement0(X8)
| ~ aElement0(X7)
| ~ aElement0(X6)
| X8 = esk1_3(X6,X7,X8)
| aReductOfIn0(esk1_3(X6,X7,X8),X8,xR)
| aElement0(esk3_3(X6,X7,X8)) )
& ( ~ aReductOfIn0(X8,X6,xR)
| ~ aReductOfIn0(X7,X6,xR)
| ~ aElement0(X8)
| ~ aElement0(X7)
| ~ aElement0(X6)
| sdtmndtasgtdt0(X7,xR,esk1_3(X6,X7,X8)) )
& ( ~ aReductOfIn0(X8,X6,xR)
| ~ aReductOfIn0(X7,X6,xR)
| ~ aElement0(X8)
| ~ aElement0(X7)
| ~ aElement0(X6)
| X7 = esk1_3(X6,X7,X8)
| sdtmndtplgtdt0(X7,xR,esk1_3(X6,X7,X8)) )
& ( ~ aReductOfIn0(X8,X6,xR)
| ~ aReductOfIn0(X7,X6,xR)
| ~ aElement0(X8)
| ~ aElement0(X7)
| ~ aElement0(X6)
| X7 = esk1_3(X6,X7,X8)
| aReductOfIn0(esk1_3(X6,X7,X8),X7,xR)
| sdtmndtplgtdt0(esk2_3(X6,X7,X8),xR,esk1_3(X6,X7,X8)) )
& ( ~ aReductOfIn0(X8,X6,xR)
| ~ aReductOfIn0(X7,X6,xR)
| ~ aElement0(X8)
| ~ aElement0(X7)
| ~ aElement0(X6)
| X7 = esk1_3(X6,X7,X8)
| aReductOfIn0(esk1_3(X6,X7,X8),X7,xR)
| aReductOfIn0(esk2_3(X6,X7,X8),X7,xR) )
& ( ~ aReductOfIn0(X8,X6,xR)
| ~ aReductOfIn0(X7,X6,xR)
| ~ aElement0(X8)
| ~ aElement0(X7)
| ~ aElement0(X6)
| X7 = esk1_3(X6,X7,X8)
| aReductOfIn0(esk1_3(X6,X7,X8),X7,xR)
| aElement0(esk2_3(X6,X7,X8)) )
& ( ~ aReductOfIn0(X8,X6,xR)
| ~ aReductOfIn0(X7,X6,xR)
| ~ aElement0(X8)
| ~ aElement0(X7)
| ~ aElement0(X6)
| aElement0(esk1_3(X6,X7,X8)) ) ),
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)],[m__656_01])])])])])]) ).
fof(c_0_9,hypothesis,
( sdtmndtasgtdt0(xv,xR,xw)
& ( xv = xw
| sdtmndtplgtdt0(xv,xR,xw) )
& ( xv = xw
| aReductOfIn0(xw,xv,xR)
| sdtmndtplgtdt0(esk12_0,xR,xw) )
& ( xv = xw
| aReductOfIn0(xw,xv,xR)
| aReductOfIn0(esk12_0,xv,xR) )
& ( xv = xw
| aReductOfIn0(xw,xv,xR)
| aElement0(esk12_0) )
& sdtmndtasgtdt0(xu,xR,xw)
& ( xu = xw
| sdtmndtplgtdt0(xu,xR,xw) )
& ( xu = xw
| aReductOfIn0(xw,xu,xR)
| sdtmndtplgtdt0(esk11_0,xR,xw) )
& ( xu = xw
| aReductOfIn0(xw,xu,xR)
| aReductOfIn0(esk11_0,xu,xR) )
& ( xu = xw
| aReductOfIn0(xw,xu,xR)
| aElement0(esk11_0) )
& aElement0(xw) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__799])])]) ).
cnf(c_0_10,negated_conjecture,
~ aNormalFormOfIn0(X1,xw,xR),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( ~ aElement0(X2)
| ~ isTerminating0(X1)
| ~ aRewritingSystem0(X1)
| aNormalFormOfIn0(esk17_2(X1,X2),X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,hypothesis,
isTerminating0(xR),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,hypothesis,
aRewritingSystem0(xR),
inference(split_conjunct,[status(thm)],[m__656]) ).
cnf(c_0_14,hypothesis,
aElement0(xw),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM018+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n006.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 21 14:14:28 UTC 2026
% 0.15/0.38 % CPUTime :
% 0.15/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 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
% 0.19/0.46 % Version: 3.5.1
% 0.19/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.19/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.19/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.19/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.19/0.46 % Starting sh5l with 300s (1) cores
% 0.19/0.46 % new_bool_1 with pid 3049861 completed with status 0
% 0.19/0.46 % Result found by new_bool_1
% 0.19/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.19/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.19/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.19/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.19/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.19/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.46 % Search class: FGHSF-FSLM32-SFFFFFNN
% 0.19/0.46 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.46 % Starting SubtermCWHack with 28s (1) cores
% 0.19/0.46 % SubtermCWHack with pid 3049865 completed with status 0
% 0.19/0.46 % Result found by SubtermCWHack
% 0.19/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.19/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.19/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.19/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.19/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.19/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.46 % Search class: FGHSF-FSLM32-SFFFFFNN
% 0.19/0.46 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.46 % Starting SubtermCWHack with 28s (1) cores
% 0.19/0.46 % Preprocessing time : 0.004 s
% 0.19/0.46
% 0.19/0.46 % Proof found!
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 % SZS output start CNFRefutation
% See solution above
% 0.19/0.46 % Parsed axioms : 23
% 0.19/0.46 % Removed by relevancy pruning/SinE : 1
% 0.19/0.46 % Initial clauses : 368
% 0.19/0.46 % Removed in clause preprocessing : 4
% 0.19/0.46 % Initial clauses in saturation : 364
% 0.19/0.46 % Processed clauses : 66
% 0.19/0.46 % ...of these trivial : 0
% 0.19/0.46 % ...subsumed : 8
% 0.19/0.46 % ...remaining for further processing : 58
% 0.19/0.46 % Other redundant clauses eliminated : 2
% 0.19/0.46 % Clauses deleted for lack of memory : 0
% 0.19/0.46 % Backward-subsumed : 0
% 0.19/0.46 % Backward-rewritten : 0
% 0.19/0.46 % Generated clauses : 22
% 0.19/0.46 % ...of the previous two non-redundant : 12
% 0.19/0.46 % ...aggressively subsumed : 0
% 0.19/0.46 % Contextual simplify-reflections : 0
% 0.19/0.46 % Paramodulations : 20
% 0.19/0.46 % Factorizations : 0
% 0.19/0.46 % NegExts : 0
% 0.19/0.46 % Equation resolutions : 2
% 0.19/0.46 % Disequality decompositions : 0
% 0.19/0.46 % Total rewrite steps : 42
% 0.19/0.46 % ...of those cached : 34
% 0.19/0.46 % Propositional unsat checks : 0
% 0.19/0.46 % Propositional check models : 0
% 0.19/0.46 % Propositional check unsatisfiable : 0
% 0.19/0.46 % Propositional clauses : 0
% 0.19/0.46 % Propositional clauses after purity: 0
% 0.19/0.46 % Propositional unsat core size : 0
% 0.19/0.46 % Propositional preprocessing time : 0.000
% 0.19/0.46 % Propositional encoding time : 0.000
% 0.19/0.46 % Propositional solver time : 0.000
% 0.19/0.46 % Success case prop preproc time : 0.000
% 0.19/0.46 % Success case prop encoding time : 0.000
% 0.19/0.46 % Success case prop solver time : 0.000
% 0.19/0.46 % Current number of processed clauses : 56
% 0.19/0.46 % Positive orientable unit clauses : 19
% 0.19/0.46 % Positive unorientable unit clauses: 0
% 0.19/0.46 % Negative unit clauses : 1
% 0.19/0.46 % Non-unit-clauses : 36
% 0.19/0.46 % Current number of unprocessed clauses: 310
% 0.19/0.46 % ...number of literals in the above : 2707
% 0.19/0.46 % Current number of archived formulas : 0
% 0.19/0.46 % Current number of archived clauses : 0
% 0.19/0.46 % Clause-clause subsumption calls (NU) : 88
% 0.19/0.46 % Rec. Clause-clause subsumption calls : 61
% 0.19/0.46 % Non-unit clause-clause subsumptions : 8
% 0.19/0.46 % Unit Clause-clause subsumption calls : 4
% 0.19/0.46 % Rewrite failures with RHS unbound : 0
% 0.19/0.46 % BW rewrite match attempts : 3
% 0.19/0.46 % BW rewrite match successes : 0
% 0.19/0.46 % Condensation attempts : 0
% 0.19/0.46 % Condensation successes : 0
% 0.19/0.46 % Termbank termtop insertions : 21095
% 0.19/0.46 % Search garbage collected termcells : 2239
% 0.19/0.46
% 0.19/0.46 % -------------------------------------------------
% 0.19/0.46 % User time : 0.018 s
% 0.19/0.46 % System time : 0.005 s
% 0.19/0.46 % Total time : 0.023 s
% 0.19/0.46 % Maximum resident set size: 4452 pages
% 0.19/0.46
% 0.19/0.46 % -------------------------------------------------
% 0.19/0.46 % User time : 0.019 s
% 0.19/0.46 % System time : 0.008 s
% 0.19/0.46 % Total time : 0.027 s
% 0.19/0.46 % Maximum resident set size: 4608 pages
% 0.19/0.46 % E exiting
%------------------------------------------------------------------------------