%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG123+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 : 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 0.11s 0.46s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 42 ( 22 unt; 0 def)
% Number of atoms : 118 ( 19 equ)
% Maximal formula atoms : 29 ( 2 avg)
% Number of connectives : 123 ( 47 ~; 42 |; 24 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 24 !; 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(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__2174,hypothesis,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2174) ).
fof(m__2273,hypothesis,
( ! [X1] :
( ( X1 != sz00
& aElementOf0(X1,xI) )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2273) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(m__2690,hypothesis,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2690) ).
fof(m__,conjecture,
aElementOf0(xr,xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__2718,hypothesis,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2718) ).
fof(m__2091,hypothesis,
( aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(m__2666,hypothesis,
( ( iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
| xr = sz00 )
& xb = sdtpldt0(sdtasdt0(xq,xu),xr)
& aElement0(xr)
& aElement0(xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2666) ).
fof(m__2699,hypothesis,
aElementOf0(xb,xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2699) ).
fof(c_0_12,plain,
! [X50,X51,X52,X53,X54] :
( ( aIdeal0(X54)
| ~ aSet0(X54)
| ~ aElementOf0(sdtpldt0(esk13_1(X54),esk14_1(X54)),X54)
| ~ aElementOf0(sdtasdt0(esk15_1(X54),esk13_1(X54)),X54) )
& ( aIdeal0(X54)
| ~ aSet0(X54)
| ~ aElementOf0(sdtpldt0(esk13_1(X54),esk14_1(X54)),X54)
| aElement0(esk15_1(X54)) )
& ( aIdeal0(X54)
| ~ aSet0(X54)
| aElementOf0(esk14_1(X54),X54)
| ~ aElementOf0(sdtasdt0(esk15_1(X54),esk13_1(X54)),X54) )
& ( aIdeal0(X54)
| ~ aSet0(X54)
| aElementOf0(esk14_1(X54),X54)
| aElement0(esk15_1(X54)) )
& ( aIdeal0(X54)
| ~ aSet0(X54)
| aElementOf0(esk13_1(X54),X54) )
& ( ~ aIdeal0(X50)
| ~ aElementOf0(X51,X50)
| aElementOf0(sdtasdt0(X53,X51),X50)
| ~ aElement0(X53) )
& ( ~ aIdeal0(X50)
| ~ aElementOf0(X51,X50)
| aElementOf0(sdtpldt0(X51,X52),X50)
| ~ aElementOf0(X52,X50) )
& ( ~ aIdeal0(X50)
| aSet0(X50) ) ),
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,
! [X92,X93] :
( aElement0(X93)
| ~ aElementOf0(X93,X92)
| ~ aSet0(X92) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])]) ).
cnf(c_0_14,plain,
( ~ aIdeal0(X1)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[m__2174]) ).
fof(c_0_16,hypothesis,
( ! [X1] :
( ( X1 != sz00
& aElementOf0(X1,xI) )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI) ),
inference(fof_simplification,[status(thm)],[m__2273]) ).
fof(c_0_17,plain,
! [X69,X70] :
( sdtpldt0(X69,X70) = sdtpldt0(X70,X69)
| ~ aElement0(X70)
| ~ aElement0(X69) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])])]) ).
cnf(c_0_18,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,hypothesis,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(split_conjunct,[status(thm)],[m__2690]) ).
cnf(c_0_20,hypothesis,
aSet0(xI),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_21,hypothesis,
! [X8] :
( ( ~ iLess0(sbrdtbr0(X8),sbrdtbr0(xu))
| X8 = sz00
| ~ aElementOf0(X8,xI) )
& xu != sz00
& aElementOf0(xu,xI) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
fof(c_0_22,negated_conjecture,
~ aElementOf0(xr,xI),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_23,hypothesis,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
inference(split_conjunct,[status(thm)],[m__2718]) ).
cnf(c_0_24,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,hypothesis,
aElement0(smndt0(sdtasdt0(xq,xu))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_26,hypothesis,
aElement0(xb),
inference(split_conjunct,[status(thm)],[m__2091]) ).
fof(c_0_27,plain,
! [X79,X80] :
( sdtasdt0(X79,X80) = sdtasdt0(X80,X79)
| ~ aElement0(X80)
| ~ aElement0(X79) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
cnf(c_0_28,hypothesis,
aElementOf0(xu,xI),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_29,negated_conjecture,
~ aElementOf0(xr,xI),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
cnf(c_0_30,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_31,hypothesis,
sdtpldt0(xb,smndt0(sdtasdt0(xq,xu))) = xr,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26])]) ).
cnf(c_0_32,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,hypothesis,
aElement0(xq),
inference(split_conjunct,[status(thm)],[m__2666]) ).
cnf(c_0_34,hypothesis,
aElement0(xu),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_28]),c_0_20])]) ).
fof(c_0_35,negated_conjecture,
~ aElementOf0(xr,xI),
inference(fof_nnf,[status(thm)],[c_0_29]) ).
cnf(c_0_36,hypothesis,
( ~ aElementOf0(X2,xI)
| ~ aElementOf0(X1,xI)
| aElementOf0(sdtpldt0(X1,X2),xI) ),
inference(spm,[status(thm)],[c_0_30,c_0_15]) ).
cnf(c_0_37,hypothesis,
sdtpldt0(xb,smndt0(sdtasdt0(xu,xq))) = xr,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_34])]) ).
cnf(c_0_38,hypothesis,
aElementOf0(xb,xI),
inference(split_conjunct,[status(thm)],[m__2699]) ).
cnf(c_0_39,hypothesis,
aElementOf0(smndt0(sdtasdt0(xu,xq)),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_32]),c_0_33]),c_0_34])]) ).
cnf(c_0_40,negated_conjecture,
~ aElementOf0(xr,xI),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_41,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_39])]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG123+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n004.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 04:21:52 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.46 % Version: 3.5.1
% 0.11/0.46 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.11/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.46 % Starting sh5l with 300s (1) cores
% 0.11/0.46 % new_bool_3 with pid 2233990 completed with status 0
% 0.11/0.46 % Result found by new_bool_3
% 0.11/0.46 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.11/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.46 % Search class: FGHSF-FFMM32-MFFFFFNN
% 0.11/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.46 % SubtermCWHack with pid 2233993 completed with status 0
% 0.11/0.46 % Result found by SubtermCWHack
% 0.11/0.46 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.11/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.46 % Search class: FGHSF-FFMM32-MFFFFFNN
% 0.11/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.46 % Preprocessing time : 0.003 s
% 0.11/0.46
% 0.11/0.46 % Proof found!
% 0.11/0.46 % SZS status Theorem
% 0.11/0.46 % SZS output start CNFRefutation
% See solution above
% 0.11/0.46 % Parsed axioms : 55
% 0.11/0.46 % Removed by relevancy pruning/SinE : 5
% 0.11/0.46 % Initial clauses : 105
% 0.11/0.46 % Removed in clause preprocessing : 4
% 0.11/0.46 % Initial clauses in saturation : 101
% 0.11/0.46 % Processed clauses : 166
% 0.11/0.46 % ...of these trivial : 8
% 0.11/0.46 % ...subsumed : 45
% 0.11/0.46 % ...remaining for further processing : 113
% 0.11/0.46 % Other redundant clauses eliminated : 6
% 0.11/0.46 % Clauses deleted for lack of memory : 0
% 0.11/0.46 % Backward-subsumed : 1
% 0.11/0.46 % Backward-rewritten : 3
% 0.11/0.46 % Generated clauses : 221
% 0.11/0.46 % ...of the previous two non-redundant : 148
% 0.11/0.46 % ...aggressively subsumed : 0
% 0.11/0.46 % Contextual simplify-reflections : 0
% 0.11/0.46 % Paramodulations : 216
% 0.11/0.46 % Factorizations : 0
% 0.11/0.46 % NegExts : 0
% 0.11/0.46 % Equation resolutions : 6
% 0.11/0.46 % Disequality decompositions : 0
% 0.11/0.46 % Total rewrite steps : 183
% 0.11/0.46 % ...of those cached : 159
% 0.11/0.46 % Propositional unsat checks : 0
% 0.11/0.46 % Propositional check models : 0
% 0.11/0.46 % Propositional check unsatisfiable : 0
% 0.11/0.46 % Propositional clauses : 0
% 0.11/0.46 % Propositional clauses after purity: 0
% 0.11/0.46 % Propositional unsat core size : 0
% 0.11/0.46 % Propositional preprocessing time : 0.000
% 0.11/0.46 % Propositional encoding time : 0.000
% 0.11/0.46 % Propositional solver time : 0.000
% 0.11/0.46 % Success case prop preproc time : 0.000
% 0.11/0.46 % Success case prop encoding time : 0.000
% 0.11/0.46 % Success case prop solver time : 0.000
% 0.11/0.46 % Current number of processed clauses : 105
% 0.11/0.46 % Positive orientable unit clauses : 42
% 0.11/0.46 % Positive unorientable unit clauses: 0
% 0.11/0.46 % Negative unit clauses : 7
% 0.11/0.46 % Non-unit-clauses : 56
% 0.11/0.46 % Current number of unprocessed clauses: 57
% 0.11/0.46 % ...number of literals in the above : 273
% 0.11/0.46 % Current number of archived formulas : 0
% 0.11/0.46 % Current number of archived clauses : 4
% 0.11/0.46 % Clause-clause subsumption calls (NU) : 786
% 0.11/0.46 % Rec. Clause-clause subsumption calls : 569
% 0.11/0.46 % Non-unit clause-clause subsumptions : 44
% 0.11/0.46 % Unit Clause-clause subsumption calls : 18
% 0.11/0.46 % Rewrite failures with RHS unbound : 0
% 0.11/0.46 % BW rewrite match attempts : 7
% 0.11/0.46 % BW rewrite match successes : 3
% 0.11/0.46 % Condensation attempts : 0
% 0.11/0.46 % Condensation successes : 0
% 0.11/0.46 % Termbank termtop insertions : 9387
% 0.11/0.46 % Search garbage collected termcells : 1562
% 0.11/0.46
% 0.11/0.46 % -------------------------------------------------
% 0.11/0.46 % User time : 0.015 s
% 0.11/0.46 % System time : 0.001 s
% 0.11/0.46 % Total time : 0.016 s
% 0.11/0.46 % Maximum resident set size: 3956 pages
% 0.11/0.46
% 0.11/0.46 % -------------------------------------------------
% 0.11/0.46 % User time : 0.016 s
% 0.11/0.46 % System time : 0.006 s
% 0.11/0.46 % Total time : 0.023 s
% 0.11/0.46 % Maximum resident set size: 4864 pages
% 0.11/0.46 % E exiting
%------------------------------------------------------------------------------