%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG121+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 02:05:56 PM UTC 2026
% Result : Theorem 0.15s 5.61s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 11 unt; 0 def)
% Number of atoms : 166 ( 38 equ)
% Maximal formula atoms : 52 ( 5 avg)
% Number of connectives : 226 ( 92 ~; 98 |; 27 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 4 con; 0-4 aty)
% Number of variables : 55 ( 0 sgn 30 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefSSum,axiom,
! [X1,X2] :
( ( aSet0(X2)
& aSet0(X1) )
=> ! [X3] :
( X3 = sdtpldt1(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ? [X5,X6] :
( sdtpldt0(X5,X6) = X4
& aElementOf0(X6,X2)
& aElementOf0(X5,X1) ) )
& aSet0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSSum) ).
fof(mAddZero,axiom,
! [X1] :
( aElement0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(mDefPrIdeal,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( X2 = slsdtgt0(X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4] :
( sdtasdt0(X1,X4) = X3
& aElement0(X4) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrIdeal) ).
fof(m__2174,hypothesis,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).
fof(m__2203,hypothesis,
( aElementOf0(xb,slsdtgt0(xb))
& aElementOf0(sz00,slsdtgt0(xb))
& aElementOf0(xa,slsdtgt0(xa))
& aElementOf0(sz00,slsdtgt0(xa)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2203) ).
fof(m__,conjecture,
aElementOf0(xb,xI),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__2091,hypothesis,
( aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).
fof(c_0_8,plain,
! [X40,X41,X42,X43,X46,X47,X48,X49,X51,X52] :
( ( ~ aSet0(X41)
| ~ aSet0(X40)
| X49 = sdtpldt1(X40,X41)
| ~ aSet0(X49)
| aElementOf0(esk5_3(X40,X41,X49),X49)
| sdtpldt0(esk6_3(X40,X41,X49),esk7_3(X40,X41,X49)) = esk5_3(X40,X41,X49) )
& ( ~ aSet0(X41)
| ~ aSet0(X40)
| X49 = sdtpldt1(X40,X41)
| ~ aSet0(X49)
| aElementOf0(esk5_3(X40,X41,X49),X49)
| aElementOf0(esk7_3(X40,X41,X49),X41) )
& ( ~ aSet0(X41)
| ~ aSet0(X40)
| X49 = sdtpldt1(X40,X41)
| ~ aSet0(X49)
| aElementOf0(esk5_3(X40,X41,X49),X49)
| aElementOf0(esk6_3(X40,X41,X49),X40) )
& ( ~ aSet0(X41)
| ~ aSet0(X40)
| X49 = sdtpldt1(X40,X41)
| ~ aSet0(X49)
| sdtpldt0(X51,X52) != esk5_3(X40,X41,X49)
| ~ aElementOf0(X52,X41)
| ~ aElementOf0(X51,X40)
| ~ aElementOf0(esk5_3(X40,X41,X49),X49) )
& ( ~ aSet0(X41)
| ~ aSet0(X40)
| X42 != sdtpldt1(X40,X41)
| aElementOf0(X46,X42)
| sdtpldt0(X47,X48) != X46
| ~ aElementOf0(X48,X41)
| ~ aElementOf0(X47,X40) )
& ( ~ aSet0(X41)
| ~ aSet0(X40)
| X42 != sdtpldt1(X40,X41)
| ~ aElementOf0(X43,X42)
| sdtpldt0(esk3_4(X40,X41,X42,X43),esk4_4(X40,X41,X42,X43)) = X43 )
& ( ~ aSet0(X41)
| ~ aSet0(X40)
| X42 != sdtpldt1(X40,X41)
| ~ aElementOf0(X43,X42)
| aElementOf0(esk4_4(X40,X41,X42,X43),X41) )
& ( ~ aSet0(X41)
| ~ aSet0(X40)
| X42 != sdtpldt1(X40,X41)
| ~ aElementOf0(X43,X42)
| aElementOf0(esk3_4(X40,X41,X42,X43),X40) )
& ( ~ aSet0(X41)
| ~ aSet0(X40)
| X42 != sdtpldt1(X40,X41)
| aSet0(X42) ) ),
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)],[mDefSSum])])])])])])]) ).
cnf(c_0_9,plain,
( ~ aSet0(X4)
| ~ aSet0(X2)
| X6 != sdtpldt1(X2,X4)
| sdtpldt0(X1,X3) != X5
| ~ aElementOf0(X3,X4)
| ~ aElementOf0(X1,X2)
| aElementOf0(X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_10,plain,
! [X18] :
( ( ~ aElement0(X18)
| X18 = sdtpldt0(sz00,X18) )
& ( ~ aElement0(X18)
| sdtpldt0(X18,sz00) = X18 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])])]) ).
fof(c_0_11,plain,
! [X34,X35] :
( aElement0(X35)
| ~ aElementOf0(X35,X34)
| ~ aSet0(X34) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])]) ).
cnf(c_0_12,plain,
( ~ aSet0(X3)
| ~ aSet0(X4)
| ~ aElementOf0(X1,X3)
| ~ aElementOf0(X2,X4)
| aElementOf0(sdtpldt0(X1,X2),sdtpldt1(X3,X4)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_9])]) ).
cnf(c_0_13,plain,
( ~ aElement0(X1)
| X1 = sdtpldt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,plain,
! [X105,X106,X107,X109,X110,X111,X113] :
( ( ~ aElement0(X105)
| X111 = slsdtgt0(X105)
| ~ aSet0(X111)
| aElementOf0(esk19_2(X105,X111),X111)
| sdtasdt0(X105,esk20_2(X105,X111)) = esk19_2(X105,X111) )
& ( ~ aElement0(X105)
| X111 = slsdtgt0(X105)
| ~ aSet0(X111)
| aElementOf0(esk19_2(X105,X111),X111)
| aElement0(esk20_2(X105,X111)) )
& ( ~ aElement0(X105)
| X111 = slsdtgt0(X105)
| ~ aSet0(X111)
| sdtasdt0(X105,X113) != esk19_2(X105,X111)
| ~ aElement0(X113)
| ~ aElementOf0(esk19_2(X105,X111),X111) )
& ( ~ aElement0(X105)
| X106 != slsdtgt0(X105)
| aElementOf0(X109,X106)
| sdtasdt0(X105,X110) != X109
| ~ aElement0(X110) )
& ( ~ aElement0(X105)
| X106 != slsdtgt0(X105)
| ~ aElementOf0(X107,X106)
| sdtasdt0(X105,esk18_3(X105,X106,X107)) = X107 )
& ( ~ aElement0(X105)
| X106 != slsdtgt0(X105)
| ~ aElementOf0(X107,X106)
| aElement0(esk18_3(X105,X106,X107)) )
& ( ~ aElement0(X105)
| X106 != slsdtgt0(X105)
| aSet0(X106) ) ),
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)],[mDefPrIdeal])])])])])])]) ).
cnf(c_0_16,plain,
( ~ aSet0(X2)
| ~ aSet0(X3)
| ~ aElementOf0(X1,X3)
| ~ aElementOf0(sz00,X2)
| aElementOf0(X1,sdtpldt1(X2,X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_17,hypothesis,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(split_conjunct,[status(thm)],[m__2174]) ).
cnf(c_0_18,hypothesis,
aElementOf0(sz00,slsdtgt0(xa)),
inference(split_conjunct,[status(thm)],[m__2203]) ).
cnf(c_0_19,plain,
( ~ aElement0(X2)
| X1 != slsdtgt0(X2)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_20,negated_conjecture,
~ aElementOf0(xb,xI),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_21,hypothesis,
( ~ aSet0(slsdtgt0(xa))
| ~ aSet0(slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xb))
| aElementOf0(X1,xI) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
cnf(c_0_22,plain,
( ~ aElement0(X1)
| aSet0(slsdtgt0(X1)) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_23,hypothesis,
aElement0(xb),
inference(split_conjunct,[status(thm)],[m__2091]) ).
fof(c_0_24,negated_conjecture,
~ aElementOf0(xb,xI),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
cnf(c_0_25,hypothesis,
( ~ aSet0(slsdtgt0(xa))
| ~ aElementOf0(X1,slsdtgt0(xb))
| aElementOf0(X1,xI) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_26,hypothesis,
aElement0(xa),
inference(split_conjunct,[status(thm)],[m__2091]) ).
fof(c_0_27,negated_conjecture,
~ aElementOf0(xb,xI),
inference(fof_nnf,[status(thm)],[c_0_24]) ).
cnf(c_0_28,hypothesis,
( ~ aElementOf0(X1,slsdtgt0(xb))
| aElementOf0(X1,xI) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_22]),c_0_26])]) ).
cnf(c_0_29,hypothesis,
aElementOf0(xb,slsdtgt0(xb)),
inference(split_conjunct,[status(thm)],[m__2203]) ).
cnf(c_0_30,negated_conjecture,
~ aElementOf0(xb,xI),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG121+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/5.37 % Computer : n004.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 04:21:26 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/5.42 Running first-order theorem proving
% 0.15/5.42 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
% 0.15/5.61 % Version: 3.5.1
% 0.15/5.61 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/5.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.61 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/5.61 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.61 % Starting new_bool_1 with 300s (1) cores
% 0.15/5.61 % Starting sh5l with 300s (1) cores
% 0.15/5.61 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2232531 completed with status 0
% 0.15/5.61 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.15/5.61 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/5.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.61 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/5.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/5.61 % No SInE strategy applied
% 0.15/5.61 % Search class: FGHSF-FSMM32-MFFFFFNN
% 0.15/5.61 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/5.61 % Starting SubtermCWHack with 136s (1) cores
% 0.15/5.61 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.15/5.61 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 0.15/5.61 % Starting new_bool_3 with 136s (1) cores
% 0.15/5.61 % Starting new_bool_1 with 136s (1) cores
% 0.15/5.61 % G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with pid 2232540 completed with status 0
% 0.15/5.61 % Result found by G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N
% 0.15/5.61 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/5.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.61 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/5.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/5.61 % No SInE strategy applied
% 0.15/5.61 % Search class: FGHSF-FSMM32-MFFFFFNN
% 0.15/5.61 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/5.61 % Starting SubtermCWHack with 136s (1) cores
% 0.15/5.61 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.15/5.61 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 0.15/5.61 % Preprocessing time : 0.003 s
% 0.15/5.61 % Presaturation interreduction done
% 0.15/5.61
% 0.15/5.61 % Proof found!
% 0.15/5.61 % SZS status Theorem
% 0.15/5.61 % SZS output start CNFRefutation
% See solution above
% 0.15/5.61 % Parsed axioms : 53
% 0.15/5.61 % Removed by relevancy pruning/SinE : 0
% 0.15/5.61 % Initial clauses : 121
% 0.15/5.61 % Removed in clause preprocessing : 4
% 0.15/5.61 % Initial clauses in saturation : 117
% 0.15/5.61 % Processed clauses : 1555
% 0.15/5.61 % ...of these trivial : 31
% 0.15/5.61 % ...subsumed : 753
% 0.15/5.61 % ...remaining for further processing : 771
% 0.15/5.61 % Other redundant clauses eliminated : 20
% 0.15/5.61 % Clauses deleted for lack of memory : 0
% 0.15/5.61 % Backward-subsumed : 70
% 0.15/5.61 % Backward-rewritten : 20
% 0.15/5.61 % Generated clauses : 5403
% 0.15/5.61 % ...of the previous two non-redundant : 4300
% 0.15/5.61 % ...aggressively subsumed : 0
% 0.15/5.61 % Contextual simplify-reflections : 71
% 0.15/5.61 % Paramodulations : 5385
% 0.15/5.61 % Factorizations : 0
% 0.15/5.61 % NegExts : 0
% 0.15/5.61 % Equation resolutions : 20
% 0.15/5.61 % Disequality decompositions : 0
% 0.15/5.61 % Total rewrite steps : 3978
% 0.15/5.61 % ...of those cached : 3912
% 0.15/5.61 % Propositional unsat checks : 0
% 0.15/5.61 % Propositional check models : 0
% 0.15/5.61 % Propositional check unsatisfiable : 0
% 0.15/5.61 % Propositional clauses : 0
% 0.15/5.61 % Propositional clauses after purity: 0
% 0.15/5.61 % Propositional unsat core size : 0
% 0.15/5.61 % Propositional preprocessing time : 0.000
% 0.15/5.61 % Propositional encoding time : 0.000
% 0.15/5.61 % Propositional solver time : 0.000
% 0.15/5.61 % Success case prop preproc time : 0.000
% 0.15/5.61 % Success case prop encoding time : 0.000
% 0.15/5.61 % Success case prop solver time : 0.000
% 0.15/5.61 % Current number of processed clauses : 550
% 0.15/5.61 % Positive orientable unit clauses : 84
% 0.15/5.61 % Positive unorientable unit clauses: 0
% 0.15/5.61 % Negative unit clauses : 10
% 0.15/5.61 % Non-unit-clauses : 456
% 0.15/5.61 % Current number of unprocessed clauses: 2911
% 0.15/5.61 % ...number of literals in the above : 15689
% 0.15/5.61 % Current number of archived formulas : 0
% 0.15/5.61 % Current number of archived clauses : 207
% 0.15/5.61 % Clause-clause subsumption calls (NU) : 21818
% 0.15/5.61 % Rec. Clause-clause subsumption calls : 12108
% 0.15/5.61 % Non-unit clause-clause subsumptions : 882
% 0.15/5.61 % Unit Clause-clause subsumption calls : 868
% 0.15/5.61 % Rewrite failures with RHS unbound : 0
% 0.15/5.61 % BW rewrite match attempts : 20
% 0.15/5.61 % BW rewrite match successes : 17
% 0.15/5.61 % Condensation attempts : 0
% 0.15/5.61 % Condensation successes : 0
% 0.15/5.61 % Termbank termtop insertions : 95209
% 0.15/5.61 % Search garbage collected termcells : 1911
% 0.15/5.61
% 0.15/5.61 % -------------------------------------------------
% 0.15/5.61 % User time : 0.154 s
% 0.15/5.61 % System time : 0.014 s
% 0.15/5.61 % Total time : 0.168 s
% 0.15/5.61 % Maximum resident set size: 3700 pages
% 0.15/5.61
% 0.15/5.61 % -------------------------------------------------
% 0.15/5.61 % User time : 0.762 s
% 0.15/5.61 % System time : 0.052 s
% 0.15/5.61 % Total time : 0.814 s
% 0.15/5.61 % Maximum resident set size: 4864 pages
% 0.15/5.61 % E exiting
%------------------------------------------------------------------------------