%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG091+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 : 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 02:05:48 PM UTC 2026
% Result : Theorem 0.13s 5.95s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 15 unt; 0 def)
% Number of atoms : 145 ( 21 equ)
% Maximal formula atoms : 52 ( 4 avg)
% Number of connectives : 188 ( 74 ~; 81 |; 26 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 9 con; 0-4 aty)
% Number of variables : 40 ( 0 sgn 23 !; 2 ?)
% 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(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/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).
fof(m__870,hypothesis,
( aIdeal0(xJ)
& aIdeal0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__870) ).
fof(m__,conjecture,
( aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ))
& aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__1021,hypothesis,
( aElementOf0(sdtasdt0(xz,xl),xJ)
& aElementOf0(sdtasdt0(xz,xk),xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1021) ).
fof(m__1098,hypothesis,
sdtasdt0(xz,xx) = sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1098) ).
fof(m__994,hypothesis,
( aElementOf0(sdtpldt0(xl,xn),xJ)
& aElementOf0(sdtpldt0(xk,xm),xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__994) ).
fof(m__1061,hypothesis,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1061) ).
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])])])])])])]) ).
fof(c_0_9,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])])])])])])]) ).
cnf(c_0_10,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]) ).
cnf(c_0_11,plain,
( ~ aIdeal0(X1)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,hypothesis,
aIdeal0(xJ),
inference(split_conjunct,[status(thm)],[m__870]) ).
fof(c_0_13,negated_conjecture,
~ ( aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ))
& aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ)) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_14,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_10])]) ).
cnf(c_0_15,hypothesis,
aElementOf0(sdtasdt0(xz,xl),xJ),
inference(split_conjunct,[status(thm)],[m__1021]) ).
cnf(c_0_16,hypothesis,
aSet0(xJ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[m__870]) ).
fof(c_0_18,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ))
| ~ aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ)) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])]) ).
cnf(c_0_19,hypothesis,
( ~ aSet0(X2)
| ~ aElementOf0(X1,X2)
| aElementOf0(sdtpldt0(X1,sdtasdt0(xz,xl)),sdtpldt1(X2,xJ)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).
cnf(c_0_20,hypothesis,
aElementOf0(sdtasdt0(xz,xk),xI),
inference(split_conjunct,[status(thm)],[m__1021]) ).
cnf(c_0_21,hypothesis,
sdtasdt0(xz,xx) = sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),
inference(split_conjunct,[status(thm)],[m__1098]) ).
cnf(c_0_22,hypothesis,
aSet0(xI),
inference(spm,[status(thm)],[c_0_11,c_0_17]) ).
cnf(c_0_23,hypothesis,
aElementOf0(sdtpldt0(xl,xn),xJ),
inference(split_conjunct,[status(thm)],[m__994]) ).
cnf(c_0_24,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ))
| ~ aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,hypothesis,
aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22])]) ).
cnf(c_0_26,hypothesis,
( ~ aSet0(X2)
| ~ aElementOf0(X1,X2)
| aElementOf0(sdtpldt0(X1,sdtpldt0(xl,xn)),sdtpldt1(X2,xJ)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_23]),c_0_16])]) ).
cnf(c_0_27,hypothesis,
aElementOf0(sdtpldt0(xk,xm),xI),
inference(split_conjunct,[status(thm)],[m__994]) ).
cnf(c_0_28,hypothesis,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(split_conjunct,[status(thm)],[m__1061]) ).
cnf(c_0_29,negated_conjecture,
~ aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).
cnf(c_0_30,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_22])]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG091+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/5.36 % Computer : n012.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Mon Sep 21 04:18:59 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/5.40 Running first-order theorem proving
% 0.13/5.40 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
% 0.13/5.95 % Version: 3.5.1
% 0.13/5.95 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.13/5.95 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/5.95 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.13/5.95 % Starting new_bool_3 with 300s (1) cores
% 0.13/5.95 % Starting new_bool_1 with 300s (1) cores
% 0.13/5.95 % Starting sh5l with 300s (1) cores
% 0.13/5.95 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 1546364 completed with status 0
% 0.13/5.95 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.13/5.95 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.13/5.95 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/5.95 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.13/5.95 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/5.95 % No SInE strategy applied
% 0.13/5.95 % Search class: FGHSF-FFMM32-SFFFFFNN
% 0.13/5.95 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/5.95 % Starting SubtermCWHack with 136s (1) cores
% 0.13/5.95 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.13/5.95 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2SI with 136s (1) cores
% 0.13/5.95 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 136s (1) cores
% 0.13/5.95 % Starting G-E--_107_C48_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 0.13/5.95 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2SI with pid 1546371 completed with status 0
% 0.13/5.95 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2SI
% 0.13/5.95 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.13/5.95 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/5.95 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.13/5.95 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/5.95 % No SInE strategy applied
% 0.13/5.95 % Search class: FGHSF-FFMM32-SFFFFFNN
% 0.13/5.95 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/5.95 % Starting SubtermCWHack with 136s (1) cores
% 0.13/5.95 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.13/5.95 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2SI with 136s (1) cores
% 0.13/5.95 % Preprocessing time : 0.002 s
% 0.13/5.95 % Presaturation interreduction done
% 0.13/5.95
% 0.13/5.95 % Proof found!
% 0.13/5.95 % SZS status Theorem
% 0.13/5.95 % SZS output start CNFRefutation
% See solution above
% 0.13/5.95 % Parsed axioms : 33
% 0.13/5.95 % Removed by relevancy pruning/SinE : 0
% 0.13/5.95 % Initial clauses : 72
% 0.13/5.95 % Removed in clause preprocessing : 2
% 0.13/5.95 % Initial clauses in saturation : 70
% 0.13/5.95 % Processed clauses : 1535
% 0.13/5.95 % ...of these trivial : 102
% 0.13/5.95 % ...subsumed : 44
% 0.13/5.95 % ...remaining for further processing : 1389
% 0.13/5.95 % Other redundant clauses eliminated : 10
% 0.13/5.95 % Clauses deleted for lack of memory : 0
% 0.13/5.95 % Backward-subsumed : 0
% 0.13/5.95 % Backward-rewritten : 64
% 0.13/5.95 % Generated clauses : 59625
% 0.13/5.95 % ...of the previous two non-redundant : 58201
% 0.13/5.95 % ...aggressively subsumed : 0
% 0.13/5.95 % Contextual simplify-reflections : 0
% 0.13/5.95 % Paramodulations : 59616
% 0.13/5.95 % Factorizations : 0
% 0.13/5.95 % NegExts : 0
% 0.13/5.95 % Equation resolutions : 10
% 0.13/5.95 % Disequality decompositions : 0
% 0.13/5.95 % Total rewrite steps : 7577
% 0.13/5.95 % ...of those cached : 6975
% 0.13/5.95 % Propositional unsat checks : 0
% 0.13/5.95 % Propositional check models : 0
% 0.13/5.95 % Propositional check unsatisfiable : 0
% 0.13/5.95 % Propositional clauses : 0
% 0.13/5.95 % Propositional clauses after purity: 0
% 0.13/5.95 % Propositional unsat core size : 0
% 0.13/5.95 % Propositional preprocessing time : 0.000
% 0.13/5.95 % Propositional encoding time : 0.000
% 0.13/5.95 % Propositional solver time : 0.000
% 0.13/5.95 % Success case prop preproc time : 0.000
% 0.13/5.95 % Success case prop encoding time : 0.000
% 0.13/5.95 % Success case prop solver time : 0.000
% 0.13/5.95 % Current number of processed clauses : 1246
% 0.13/5.95 % Positive orientable unit clauses : 833
% 0.13/5.95 % Positive unorientable unit clauses: 0
% 0.13/5.95 % Negative unit clauses : 2
% 0.13/5.95 % Non-unit-clauses : 411
% 0.13/5.95 % Current number of unprocessed clauses: 56654
% 0.13/5.95 % ...number of literals in the above : 101013
% 0.13/5.95 % Current number of archived formulas : 0
% 0.13/5.95 % Current number of archived clauses : 134
% 0.13/5.95 % Clause-clause subsumption calls (NU) : 11643
% 0.13/5.95 % Rec. Clause-clause subsumption calls : 9392
% 0.13/5.95 % Non-unit clause-clause subsumptions : 44
% 0.13/5.95 % Unit Clause-clause subsumption calls : 5306
% 0.13/5.95 % Rewrite failures with RHS unbound : 0
% 0.13/5.95 % BW rewrite match attempts : 522
% 0.13/5.95 % BW rewrite match successes : 38
% 0.13/5.95 % Condensation attempts : 0
% 0.13/5.95 % Condensation successes : 0
% 0.13/5.95 % Termbank termtop insertions : 904832
% 0.13/5.95 % Search garbage collected termcells : 1014
% 0.13/5.95
% 0.13/5.95 % -------------------------------------------------
% 0.13/5.95 % User time : 0.455 s
% 0.13/5.95 % System time : 0.044 s
% 0.13/5.95 % Total time : 0.499 s
% 0.13/5.95 % Maximum resident set size: 3672 pages
% 0.13/5.95
% 0.13/5.95 % -------------------------------------------------
% 0.13/5.95 % User time : 1.877 s
% 0.13/5.95 % System time : 0.175 s
% 0.13/5.95 % Total time : 2.052 s
% 0.13/5.95 % Maximum resident set size: 4608 pages
% 0.13/5.95 % E exiting
%------------------------------------------------------------------------------