%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG098+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 : n019.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 02:05:50 PM UTC 2026
% Result : Theorem 221.66s 32.79s
% Output : CNFRefutation 221.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 45 ( 21 unt; 0 def)
% Number of atoms : 127 ( 14 equ)
% Maximal formula atoms : 29 ( 2 avg)
% Number of connectives : 137 ( 55 ~; 54 |; 19 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(mAMDistr,axiom,
! [X1,X2,X3] :
( ( aElement0(X3)
& aElement0(X2)
& aElement0(X1) )
=> ( sdtasdt0(sdtpldt0(X2,X3),X1) = sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
& sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
fof(mMulMnOne,axiom,
! [X1] :
( aElement0(X1)
=> ( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
& sdtasdt0(smndt0(sz10),X1) = smndt0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulMnOne) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__1205,hypothesis,
( aIdeal0(xJ)
& aIdeal0(xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1205) ).
fof(m__,conjecture,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__1294,hypothesis,
( sdtpldt0(xa,xb) = sz10
& aElementOf0(xb,xJ)
& aElementOf0(xa,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1294) ).
fof(m__1374,hypothesis,
sdtpldt0(xw,smndt0(xx)) = sdtpldt0(sdtasdt0(xy,xa),sdtpldt0(sdtasdt0(xx,xb),smndt0(xx))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1374) ).
fof(m__1393,hypothesis,
aElementOf0(sdtasdt0(xx,sdtpldt0(xb,smndt0(sz10))),xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1393) ).
fof(m__1217,hypothesis,
( aElement0(xy)
& aElement0(xx) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1217) ).
fof(mSortsU,axiom,
! [X1] :
( aElement0(X1)
=> aElement0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsU) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(c_0_12,plain,
! [X8,X9,X10,X11,X12] :
( ( aIdeal0(X12)
| ~ aSet0(X12)
| ~ aElementOf0(sdtpldt0(esk1_1(X12),esk2_1(X12)),X12)
| ~ aElementOf0(sdtasdt0(esk3_1(X12),esk1_1(X12)),X12) )
& ( aIdeal0(X12)
| ~ aSet0(X12)
| ~ aElementOf0(sdtpldt0(esk1_1(X12),esk2_1(X12)),X12)
| aElement0(esk3_1(X12)) )
& ( aIdeal0(X12)
| ~ aSet0(X12)
| aElementOf0(esk2_1(X12),X12)
| ~ aElementOf0(sdtasdt0(esk3_1(X12),esk1_1(X12)),X12) )
& ( aIdeal0(X12)
| ~ aSet0(X12)
| aElementOf0(esk2_1(X12),X12)
| aElement0(esk3_1(X12)) )
& ( aIdeal0(X12)
| ~ aSet0(X12)
| aElementOf0(esk1_1(X12),X12) )
& ( ~ aIdeal0(X8)
| ~ aElementOf0(X9,X8)
| aElementOf0(sdtasdt0(X11,X9),X8)
| ~ aElement0(X11) )
& ( ~ aIdeal0(X8)
| ~ aElementOf0(X9,X8)
| aElementOf0(sdtpldt0(X9,X10),X8)
| ~ aElementOf0(X10,X8) )
& ( ~ aIdeal0(X8)
| aSet0(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(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefIdeal])])])])])])]) ).
fof(c_0_13,plain,
! [X43,X44,X45] :
( ( ~ aElement0(X45)
| ~ aElement0(X44)
| ~ aElement0(X43)
| sdtasdt0(sdtpldt0(X44,X45),X43) = sdtpldt0(sdtasdt0(X44,X43),sdtasdt0(X45,X43)) )
& ( ~ aElement0(X45)
| ~ aElement0(X44)
| ~ aElement0(X43)
| sdtasdt0(X43,sdtpldt0(X44,X45)) = sdtpldt0(sdtasdt0(X43,X44),sdtasdt0(X43,X45)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])])]) ).
fof(c_0_14,plain,
! [X35] :
( ( ~ aElement0(X35)
| smndt0(X35) = sdtasdt0(X35,smndt0(sz10)) )
& ( ~ aElement0(X35)
| sdtasdt0(smndt0(sz10),X35) = smndt0(X35) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMnOne])])])]) ).
fof(c_0_15,plain,
! [X56,X57] :
( aElement0(X57)
| ~ aElementOf0(X57,X56)
| ~ aSet0(X56) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])]) ).
cnf(c_0_16,plain,
( ~ aIdeal0(X1)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,hypothesis,
aIdeal0(xJ),
inference(split_conjunct,[status(thm)],[m__1205]) ).
fof(c_0_18,negated_conjecture,
~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_19,plain,
( ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( ~ aElement0(X1)
| smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,hypothesis,
aElementOf0(xb,xJ),
inference(split_conjunct,[status(thm)],[m__1294]) ).
cnf(c_0_23,hypothesis,
aSet0(xJ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_24,negated_conjecture,
~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( ~ aIdeal0(X2)
| ~ aElementOf0(X3,X2)
| ~ aElementOf0(X1,X2)
| aElementOf0(sdtpldt0(X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_26,hypothesis,
sdtpldt0(xw,smndt0(xx)) = sdtpldt0(sdtasdt0(xy,xa),sdtpldt0(sdtasdt0(xx,xb),smndt0(xx))),
inference(split_conjunct,[status(thm)],[m__1374]) ).
cnf(c_0_27,hypothesis,
aElementOf0(sdtasdt0(xx,sdtpldt0(xb,smndt0(sz10))),xI),
inference(split_conjunct,[status(thm)],[m__1393]) ).
cnf(c_0_28,plain,
( ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(smndt0(sz10))
| sdtpldt0(sdtasdt0(X1,X2),smndt0(X1)) = sdtasdt0(X1,sdtpldt0(X2,smndt0(sz10))) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_29,hypothesis,
aElement0(xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_30,hypothesis,
aElement0(xx),
inference(split_conjunct,[status(thm)],[m__1217]) ).
fof(c_0_31,negated_conjecture,
~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(fof_nnf,[status(thm)],[c_0_24]) ).
cnf(c_0_32,hypothesis,
( ~ aElementOf0(sdtasdt0(xy,xa),X1)
| ~ aElementOf0(sdtpldt0(sdtasdt0(xx,xb),smndt0(xx)),X1)
| ~ aIdeal0(X1)
| aElementOf0(sdtpldt0(xw,smndt0(xx)),X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,hypothesis,
( ~ aElement0(smndt0(sz10))
| aElementOf0(sdtpldt0(sdtasdt0(xx,xb),smndt0(xx)),xI) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30])]) ).
cnf(c_0_34,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[m__1205]) ).
cnf(c_0_35,negated_conjecture,
~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,hypothesis,
( ~ aElement0(smndt0(sz10))
| ~ aElementOf0(sdtasdt0(xy,xa),xI) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]),c_0_35]) ).
cnf(c_0_37,plain,
( ~ aIdeal0(X3)
| ~ aElementOf0(X2,X3)
| ~ aElement0(X1)
| aElementOf0(sdtasdt0(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_38,hypothesis,
aElementOf0(xa,xI),
inference(split_conjunct,[status(thm)],[m__1294]) ).
cnf(c_0_39,hypothesis,
aElement0(xy),
inference(split_conjunct,[status(thm)],[m__1217]) ).
fof(c_0_40,plain,
! [X53] :
( aElement0(smndt0(X53))
| ~ aElement0(X53) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsU])])]) ).
cnf(c_0_41,hypothesis,
~ aElement0(smndt0(sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_34]),c_0_38]),c_0_39])]) ).
cnf(c_0_42,plain,
( ~ aElement0(X1)
| aElement0(smndt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_43,plain,
aElement0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_44,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG098+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n019.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 04:19:50 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 221.66/32.79 % Version: 3.5.1
% 221.66/32.79 % Preprocessing class: FSMSSMSMSSSNFFN.
% 221.66/32.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 221.66/32.79 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 221.66/32.79 % Starting new_bool_3 with 300s (1) cores
% 221.66/32.79 % Starting new_bool_1 with 300s (1) cores
% 221.66/32.79 % Starting sh5l with 300s (1) cores
% 221.66/32.79 % new_bool_3 with pid 1670487 completed with status 0
% 221.66/32.79 % Result found by new_bool_3
% 221.66/32.79 % Preprocessing class: FSMSSMSMSSSNFFN.
% 221.66/32.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 221.66/32.79 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 221.66/32.79 % Starting new_bool_3 with 300s (1) cores
% 221.66/32.79 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 221.66/32.79 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 221.66/32.79 % Search class: FGUSF-FFMM32-MFFFFFNN
% 221.66/32.79 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 221.66/32.79 % Starting SubtermCWHack with 31s (1) cores
% 221.66/32.79 % SubtermCWHack with pid 1670490 completed with status 8
% 221.66/32.79 % Starting SAT001_MinMin_p005000_rr_RG with 181s (1) cores
% 221.66/32.79 % SAT001_MinMin_p005000_rr_RG with pid 1670542 completed with status 0
% 221.66/32.79 % Result found by SAT001_MinMin_p005000_rr_RG
% 221.66/32.79 % Preprocessing class: FSMSSMSMSSSNFFN.
% 221.66/32.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 221.66/32.79 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 221.66/32.79 % Starting new_bool_3 with 300s (1) cores
% 221.66/32.79 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 221.66/32.79 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 221.66/32.79 % Search class: FGUSF-FFMM32-MFFFFFNN
% 221.66/32.79 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 221.66/32.79 % Starting SubtermCWHack with 31s (1) cores
% 221.66/32.79 % SubtermCWHack with pid 1670490 completed with status 8
% 221.66/32.79 % Starting SAT001_MinMin_p005000_rr_RG with 181s (1) cores
% 221.66/32.79 % Preprocessing time : 0.003 s
% 221.66/32.79 % Presaturation interreduction done
% 221.66/32.79
% 221.66/32.79 % Proof found!
% 221.66/32.79 % SZS status Theorem
% 221.66/32.79 % SZS output start CNFRefutation
% See solution above
% 221.66/32.80 % Parsed axioms : 35
% 221.66/32.80 % Removed by relevancy pruning/SinE : 3
% 221.66/32.80 % Initial clauses : 60
% 221.66/32.80 % Removed in clause preprocessing : 2
% 221.66/32.80 % Initial clauses in saturation : 58
% 221.66/32.80 % Processed clauses : 1258
% 221.66/32.80 % ...of these trivial : 28
% 221.66/32.80 % ...subsumed : 697
% 221.66/32.80 % ...remaining for further processing : 533
% 221.66/32.80 % Other redundant clauses eliminated : 6
% 221.66/32.80 % Clauses deleted for lack of memory : 0
% 221.66/32.80 % Backward-subsumed : 80
% 221.66/32.80 % Backward-rewritten : 16
% 221.66/32.80 % Generated clauses : 7741
% 221.66/32.80 % ...of the previous two non-redundant : 6245
% 221.66/32.80 % ...aggressively subsumed : 0
% 221.66/32.80 % Contextual simplify-reflections : 49
% 221.66/32.80 % Paramodulations : 7736
% 221.66/32.80 % Factorizations : 0
% 221.66/32.80 % NegExts : 0
% 221.66/32.80 % Equation resolutions : 6
% 221.66/32.80 % Disequality decompositions : 0
% 221.66/32.80 % Total rewrite steps : 7895
% 221.66/32.80 % ...of those cached : 7825
% 221.66/32.80 % Propositional unsat checks : 0
% 221.66/32.80 % Propositional check models : 0
% 221.66/32.80 % Propositional check unsatisfiable : 0
% 221.66/32.80 % Propositional clauses : 0
% 221.66/32.80 % Propositional clauses after purity: 0
% 221.66/32.80 % Propositional unsat core size : 0
% 221.66/32.80 % Propositional preprocessing time : 0.000
% 221.66/32.80 % Propositional encoding time : 0.000
% 221.66/32.80 % Propositional solver time : 0.000
% 221.66/32.80 % Success case prop preproc time : 0.000
% 221.66/32.80 % Success case prop encoding time : 0.000
% 221.66/32.80 % Success case prop solver time : 0.000
% 221.66/32.80 % Current number of processed clauses : 374
% 221.66/32.80 % Positive orientable unit clauses : 67
% 221.66/32.80 % Positive unorientable unit clauses: 0
% 221.66/32.80 % Negative unit clauses : 5
% 221.66/32.80 % Non-unit-clauses : 302
% 221.66/32.80 % Current number of unprocessed clauses: 4921
% 221.66/32.80 % ...number of literals in the above : 24538
% 221.66/32.80 % Current number of archived formulas : 0
% 221.66/32.80 % Current number of archived clauses : 154
% 221.66/32.80 % Clause-clause subsumption calls (NU) : 20771
% 221.66/32.80 % Rec. Clause-clause subsumption calls : 12996
% 221.66/32.80 % Non-unit clause-clause subsumptions : 789
% 221.66/32.80 % Unit Clause-clause subsumption calls : 971
% 221.66/32.80 % Rewrite failures with RHS unbound : 0
% 221.66/32.80 % BW rewrite match attempts : 12
% 221.66/32.80 % BW rewrite match successes : 11
% 221.66/32.80 % Condensation attempts : 0
% 221.66/32.80 % Condensation successes : 0
% 221.66/32.80 % Termbank termtop insertions : 133865
% 221.66/32.80 % Search garbage collected termcells : 871
% 221.66/32.80
% 221.66/32.80 % -------------------------------------------------
% 221.66/32.80 % User time : 30.359 s
% 221.66/32.80 % System time : 1.079 s
% 221.66/32.80 % Total time : 31.439 s
% 221.66/32.80 % Maximum resident set size: 3676 pages
% 221.66/32.80
% 221.66/32.80 % -------------------------------------------------
% 221.66/32.80 % User time : 30.363 s
% 221.66/32.80 % System time : 1.086 s
% 221.66/32.80 % Total time : 31.448 s
% 221.66/32.80 % Maximum resident set size: 4608 pages
% 221.66/32.80 % E exiting
%------------------------------------------------------------------------------