%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG087+1 : 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 : n014.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 02:05:47 PM UTC 2026
% Result : Theorem 9.47s 1.68s
% Output : CNFRefutation 9.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 9 unt; 0 def)
% Number of atoms : 151 ( 25 equ)
% Maximal formula atoms : 52 ( 5 avg)
% Number of connectives : 207 ( 82 ~; 90 |; 28 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-4 aty)
% Number of variables : 55 ( 0 sgn 25 !; 6 ?)
% 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/sandbox/benchmark/theBenchmark.p',mDefSSum) ).
fof(mDefIdeal,axiom,
! [X1] :
( aIdeal0(X1)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> ( ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X2),X1) )
& ! [X3] :
( aElementOf0(X3,X1)
=> aElementOf0(sdtpldt0(X2,X3),X1) ) ) )
& aSet0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).
fof(m__,conjecture,
? [X1,X2] :
( xy = sdtpldt0(X1,X2)
& aElementOf0(X2,xJ)
& aElementOf0(X1,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__870,hypothesis,
( aIdeal0(xJ)
& aIdeal0(xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__870) ).
fof(m__901,hypothesis,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElementOf0(xx,sdtpldt1(xI,xJ)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__901) ).
fof(c_0_5,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])])])])])])]) ).
fof(c_0_6,plain,
! [X62,X63,X64,X65,X66] :
( ( aIdeal0(X66)
| ~ aSet0(X66)
| ~ aElementOf0(sdtpldt0(esk9_1(X66),esk10_1(X66)),X66)
| ~ aElementOf0(sdtasdt0(esk11_1(X66),esk9_1(X66)),X66) )
& ( aIdeal0(X66)
| ~ aSet0(X66)
| ~ aElementOf0(sdtpldt0(esk9_1(X66),esk10_1(X66)),X66)
| aElement0(esk11_1(X66)) )
& ( aIdeal0(X66)
| ~ aSet0(X66)
| aElementOf0(esk10_1(X66),X66)
| ~ aElementOf0(sdtasdt0(esk11_1(X66),esk9_1(X66)),X66) )
& ( aIdeal0(X66)
| ~ aSet0(X66)
| aElementOf0(esk10_1(X66),X66)
| aElement0(esk11_1(X66)) )
& ( aIdeal0(X66)
| ~ aSet0(X66)
| aElementOf0(esk9_1(X66),X66) )
& ( ~ aIdeal0(X62)
| ~ aElementOf0(X63,X62)
| aElementOf0(sdtasdt0(X65,X63),X62)
| ~ aElement0(X65) )
& ( ~ aIdeal0(X62)
| ~ aElementOf0(X63,X62)
| aElementOf0(sdtpldt0(X63,X64),X62)
| ~ aElementOf0(X64,X62) )
& ( ~ aIdeal0(X62)
| aSet0(X62) ) ),
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)],[mDefIdeal])])])])])])]) ).
fof(c_0_7,negated_conjecture,
~ ? [X1,X2] :
( xy = sdtpldt0(X1,X2)
& aElementOf0(X2,xJ)
& aElementOf0(X1,xI) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_8,plain,
( ~ aSet0(X2)
| ~ aSet0(X1)
| X3 != sdtpldt1(X1,X2)
| ~ aElementOf0(X4,X3)
| sdtpldt0(esk3_4(X1,X2,X3,X4),esk4_4(X1,X2,X3,X4)) = X4 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( ~ aIdeal0(X1)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,hypothesis,
aIdeal0(xJ),
inference(split_conjunct,[status(thm)],[m__870]) ).
cnf(c_0_11,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[m__870]) ).
cnf(c_0_12,plain,
( ~ aSet0(X2)
| ~ aSet0(X1)
| X3 != sdtpldt1(X1,X2)
| ~ aElementOf0(X4,X3)
| aElementOf0(esk4_4(X1,X2,X3,X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,plain,
( ~ aSet0(X2)
| ~ aSet0(X1)
| X3 != sdtpldt1(X1,X2)
| ~ aElementOf0(X4,X3)
| aElementOf0(esk3_4(X1,X2,X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_14,negated_conjecture,
! [X70,X71] :
( xy != sdtpldt0(X70,X71)
| ~ aElementOf0(X71,xJ)
| ~ aElementOf0(X70,xI) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_15,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(X3,sdtpldt1(X1,X2))
| sdtpldt0(esk3_4(X1,X2,sdtpldt1(X1,X2),X3),esk4_4(X1,X2,sdtpldt1(X1,X2),X3)) = X3 ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_16,hypothesis,
aElementOf0(xy,sdtpldt1(xI,xJ)),
inference(split_conjunct,[status(thm)],[m__901]) ).
cnf(c_0_17,hypothesis,
aSet0(xJ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_18,hypothesis,
aSet0(xI),
inference(spm,[status(thm)],[c_0_9,c_0_11]) ).
cnf(c_0_19,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(X3,sdtpldt1(X1,X2))
| aElementOf0(esk4_4(X1,X2,sdtpldt1(X1,X2),X3),X2) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(X3,sdtpldt1(X1,X2))
| aElementOf0(esk3_4(X1,X2,sdtpldt1(X1,X2),X3),X1) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_21,negated_conjecture,
( xy != sdtpldt0(X1,X2)
| ~ aElementOf0(X2,xJ)
| ~ aElementOf0(X1,xI) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,hypothesis,
sdtpldt0(esk3_4(xI,xJ,sdtpldt1(xI,xJ),xy),esk4_4(xI,xJ,sdtpldt1(xI,xJ),xy)) = xy,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18])]) ).
cnf(c_0_23,hypothesis,
aElementOf0(esk4_4(xI,xJ,sdtpldt1(xI,xJ),xy),xJ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_16]),c_0_17]),c_0_18])]) ).
cnf(c_0_24,hypothesis,
aElementOf0(esk3_4(xI,xJ,sdtpldt1(xI,xJ),xy),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_16]),c_0_17]),c_0_18])]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG087+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n014.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 04:18:51 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 9.47/1.68 % Version: 3.5.1
% 9.47/1.68 % Preprocessing class: FSMSSMSMSSSNFFN.
% 9.47/1.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.47/1.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 9.47/1.68 % Starting new_bool_3 with 300s (1) cores
% 9.47/1.68 % Starting new_bool_1 with 300s (1) cores
% 9.47/1.68 % Starting sh5l with 300s (1) cores
% 9.47/1.68 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 3121085 completed with status 0
% 9.47/1.68 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 9.47/1.68 % Preprocessing class: FSMSSMSMSSSNFFN.
% 9.47/1.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.47/1.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 9.47/1.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 9.47/1.68 % No SInE strategy applied
% 9.47/1.68 % Search class: FGHSF-FFMM32-SFFFFFNN
% 9.47/1.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 9.47/1.68 % Starting SubtermCWHack with 136s (1) cores
% 9.47/1.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 9.47/1.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2SI with 136s (1) cores
% 9.47/1.68 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 136s (1) cores
% 9.47/1.68 % Starting G-E--_107_C48_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 9.47/1.68 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2SI with pid 3121094 completed with status 0
% 9.47/1.68 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2SI
% 9.47/1.68 % Preprocessing class: FSMSSMSMSSSNFFN.
% 9.47/1.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.47/1.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 9.47/1.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 9.47/1.68 % No SInE strategy applied
% 9.47/1.68 % Search class: FGHSF-FFMM32-SFFFFFNN
% 9.47/1.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 9.47/1.68 % Starting SubtermCWHack with 136s (1) cores
% 9.47/1.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 9.47/1.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2SI with 136s (1) cores
% 9.47/1.68 % Preprocessing time : 0.002 s
% 9.47/1.68 % Presaturation interreduction done
% 9.47/1.68
% 9.47/1.68 % Proof found!
% 9.47/1.68 % SZS status Theorem
% 9.47/1.68 % SZS output start CNFRefutation
% See solution above
% 9.47/1.68 % Parsed axioms : 28
% 9.47/1.68 % Removed by relevancy pruning/SinE : 0
% 9.47/1.68 % Initial clauses : 63
% 9.47/1.68 % Removed in clause preprocessing : 2
% 9.47/1.68 % Initial clauses in saturation : 61
% 9.47/1.68 % Processed clauses : 2195
% 9.47/1.68 % ...of these trivial : 285
% 9.47/1.68 % ...subsumed : 215
% 9.47/1.68 % ...remaining for further processing : 1695
% 9.47/1.68 % Other redundant clauses eliminated : 10
% 9.47/1.68 % Clauses deleted for lack of memory : 0
% 9.47/1.68 % Backward-subsumed : 14
% 9.47/1.68 % Backward-rewritten : 120
% 9.47/1.68 % Generated clauses : 110374
% 9.47/1.68 % ...of the previous two non-redundant : 107541
% 9.47/1.68 % ...aggressively subsumed : 0
% 9.47/1.68 % Contextual simplify-reflections : 0
% 9.47/1.68 % Paramodulations : 110365
% 9.47/1.68 % Factorizations : 0
% 9.47/1.68 % NegExts : 0
% 9.47/1.68 % Equation resolutions : 10
% 9.47/1.68 % Disequality decompositions : 0
% 9.47/1.68 % Total rewrite steps : 11956
% 9.47/1.68 % ...of those cached : 11456
% 9.47/1.68 % Propositional unsat checks : 0
% 9.47/1.68 % Propositional check models : 0
% 9.47/1.68 % Propositional check unsatisfiable : 0
% 9.47/1.68 % Propositional clauses : 0
% 9.47/1.68 % Propositional clauses after purity: 0
% 9.47/1.68 % Propositional unsat core size : 0
% 9.47/1.68 % Propositional preprocessing time : 0.000
% 9.47/1.68 % Propositional encoding time : 0.000
% 9.47/1.68 % Propositional solver time : 0.000
% 9.47/1.68 % Success case prop preproc time : 0.000
% 9.47/1.68 % Success case prop encoding time : 0.000
% 9.47/1.68 % Success case prop solver time : 0.000
% 9.47/1.68 % Current number of processed clauses : 1491
% 9.47/1.68 % Positive orientable unit clauses : 710
% 9.47/1.68 % Positive unorientable unit clauses: 0
% 9.47/1.68 % Negative unit clauses : 8
% 9.47/1.68 % Non-unit-clauses : 773
% 9.47/1.68 % Current number of unprocessed clauses: 105447
% 9.47/1.68 % ...number of literals in the above : 193849
% 9.47/1.68 % Current number of archived formulas : 0
% 9.47/1.68 % Current number of archived clauses : 195
% 9.47/1.68 % Clause-clause subsumption calls (NU) : 69312
% 9.47/1.68 % Rec. Clause-clause subsumption calls : 43109
% 9.47/1.68 % Non-unit clause-clause subsumptions : 115
% 9.47/1.68 % Unit Clause-clause subsumption calls : 11626
% 9.47/1.68 % Rewrite failures with RHS unbound : 0
% 9.47/1.68 % BW rewrite match attempts : 2264
% 9.47/1.68 % BW rewrite match successes : 64
% 9.47/1.68 % Condensation attempts : 0
% 9.47/1.68 % Condensation successes : 0
% 9.47/1.68 % Termbank termtop insertions : 2062014
% 9.47/1.68 % Search garbage collected termcells : 1038
% 9.47/1.68
% 9.47/1.68 % -------------------------------------------------
% 9.47/1.68 % User time : 1.128 s
% 9.47/1.68 % System time : 0.086 s
% 9.47/1.68 % Total time : 1.214 s
% 9.47/1.68 % Maximum resident set size: 3664 pages
% 9.47/1.68
% 9.47/1.68 % -------------------------------------------------
% 9.47/1.68 % User time : 5.728 s
% 9.47/1.68 % System time : 0.390 s
% 9.47/1.68 % Total time : 6.118 s
% 9.47/1.68 % Maximum resident set size: 4608 pages
% 9.47/1.68 % E exiting
%------------------------------------------------------------------------------