%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG123+4 : 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 : n015.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 0.12s 0.60s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 14 unt; 0 def)
% Number of atoms : 123 ( 28 equ)
% Maximal formula atoms : 33 ( 3 avg)
% Number of connectives : 125 ( 34 ~; 32 |; 50 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 29 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__2690,hypothesis,
( aElementOf0(smndt0(sdtasdt0(xq,xu)),xI)
& ? [X1,X2] :
( sdtpldt0(X1,X2) = smndt0(sdtasdt0(xq,xu))
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2690) ).
fof(m__2174,hypothesis,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X1] :
( aElementOf0(X1,xI)
<=> ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) )
& ! [X1] :
( aElementOf0(X1,slsdtgt0(xb))
<=> ? [X2] :
( sdtasdt0(xb,X2) = X1
& aElement0(X2) ) )
& ! [X1] :
( aElementOf0(X1,slsdtgt0(xa))
<=> ? [X2] :
( sdtasdt0(xa,X2) = X1
& aElement0(X2) ) )
& aIdeal0(xI)
& ! [X1] :
( aElementOf0(X1,xI)
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),xI) )
& ! [X2] :
( aElementOf0(X2,xI)
=> aElementOf0(sdtpldt0(X1,X2),xI) ) ) )
& aSet0(xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2174) ).
fof(m__2718,hypothesis,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2718) ).
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__2699,hypothesis,
( aElementOf0(xb,xI)
& ? [X1,X2] :
( sdtpldt0(X1,X2) = xb
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
& ? [X1,X2] :
( sdtpldt0(X1,X2) = xb
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2699) ).
fof(m__,conjecture,
( aElementOf0(xr,xI)
| ? [X1,X2] :
( sdtpldt0(X1,X2) = xr
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__2091,hypothesis,
( aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).
fof(c_0_8,plain,
! [X9,X10] :
( aElement0(X10)
| ~ aElementOf0(X10,X9)
| ~ aSet0(X9) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])]) ).
fof(c_0_9,hypothesis,
( aElementOf0(smndt0(sdtasdt0(xq,xu)),xI)
& sdtpldt0(esk29_0,esk30_0) = smndt0(sdtasdt0(xq,xu))
& aElementOf0(esk30_0,slsdtgt0(xb))
& aElementOf0(esk29_0,slsdtgt0(xa)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2690])]) ).
fof(c_0_10,hypothesis,
! [X48,X49,X50,X51,X53,X54,X55,X57,X58,X59,X62,X63,X64] :
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ( aElementOf0(X62,xI)
| sdtpldt0(X63,X64) != X62
| ~ aElementOf0(X64,slsdtgt0(xb))
| ~ aElementOf0(X63,slsdtgt0(xa)) )
& ( ~ aElementOf0(X59,xI)
| sdtpldt0(esk16_1(X59),esk17_1(X59)) = X59 )
& ( ~ aElementOf0(X59,xI)
| aElementOf0(esk17_1(X59),slsdtgt0(xb)) )
& ( ~ aElementOf0(X59,xI)
| aElementOf0(esk16_1(X59),slsdtgt0(xa)) )
& ( aElementOf0(X57,slsdtgt0(xb))
| sdtasdt0(xb,X58) != X57
| ~ aElement0(X58) )
& ( ~ aElementOf0(X55,slsdtgt0(xb))
| sdtasdt0(xb,esk15_1(X55)) = X55 )
& ( ~ aElementOf0(X55,slsdtgt0(xb))
| aElement0(esk15_1(X55)) )
& ( aElementOf0(X53,slsdtgt0(xa))
| sdtasdt0(xa,X54) != X53
| ~ aElement0(X54) )
& ( ~ aElementOf0(X51,slsdtgt0(xa))
| sdtasdt0(xa,esk14_1(X51)) = X51 )
& ( ~ aElementOf0(X51,slsdtgt0(xa))
| aElement0(esk14_1(X51)) )
& aIdeal0(xI)
& ( ~ aElementOf0(X48,xI)
| aElementOf0(sdtasdt0(X50,X48),xI)
| ~ aElement0(X50) )
& ( ~ aElementOf0(X48,xI)
| aElementOf0(sdtpldt0(X48,X49),xI)
| ~ aElementOf0(X49,xI) )
& aSet0(xI) ),
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)],[m__2174])])])])])])]) ).
cnf(c_0_11,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,hypothesis,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,hypothesis,
aSet0(xI),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,hypothesis,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
inference(split_conjunct,[status(thm)],[m__2718]) ).
cnf(c_0_15,hypothesis,
sdtpldt0(esk29_0,esk30_0) = smndt0(sdtasdt0(xq,xu)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_16,plain,
! [X89,X90] :
( sdtpldt0(X89,X90) = sdtpldt0(X90,X89)
| ~ aElement0(X90)
| ~ aElement0(X89) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])])]) ).
cnf(c_0_17,hypothesis,
aElement0(smndt0(sdtasdt0(xq,xu))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).
fof(c_0_18,hypothesis,
( aElementOf0(xb,xI)
& ? [X1,X2] :
( sdtpldt0(X1,X2) = xb
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) ),
inference(fof_simplification,[status(thm)],[m__2699]) ).
fof(c_0_19,negated_conjecture,
~ ( aElementOf0(xr,xI)
| ? [X1,X2] :
( sdtpldt0(X1,X2) = xr
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_20,hypothesis,
sdtpldt0(sdtpldt0(esk29_0,esk30_0),xb) = xr,
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,hypothesis,
aElement0(sdtpldt0(esk29_0,esk30_0)),
inference(rw,[status(thm)],[c_0_17,c_0_15]) ).
cnf(c_0_23,hypothesis,
aElement0(xb),
inference(split_conjunct,[status(thm)],[m__2091]) ).
fof(c_0_24,hypothesis,
( aElementOf0(xb,xI)
& sdtpldt0(esk31_0,esk32_0) = xb
& aElementOf0(esk32_0,slsdtgt0(xb))
& aElementOf0(esk31_0,slsdtgt0(xa)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_18])]) ).
fof(c_0_25,negated_conjecture,
! [X7,X8] :
( ~ aElementOf0(xr,xI)
& ( sdtpldt0(X7,X8) != xr
| ~ aElementOf0(X8,slsdtgt0(xb))
| ~ aElementOf0(X7,slsdtgt0(xa)) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])]) ).
cnf(c_0_26,hypothesis,
( ~ aElementOf0(X2,xI)
| ~ aElementOf0(X1,xI)
| aElementOf0(sdtpldt0(X2,X1),xI) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_27,hypothesis,
sdtpldt0(xb,sdtpldt0(esk29_0,esk30_0)) = xr,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_28,hypothesis,
aElementOf0(xb,xI),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,hypothesis,
aElementOf0(sdtpldt0(esk29_0,esk30_0),xI),
inference(rw,[status(thm)],[c_0_12,c_0_15]) ).
cnf(c_0_30,negated_conjecture,
~ aElementOf0(xr,xI),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,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_29])]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG123+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.52 % Computer : n015.cluster.edu
% 0.09/0.52 % Model : x86_64 x86_64
% 0.09/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.52 % Memory : 8046.5625MB
% 0.09/0.52 % OS : Linux 6.8.0-71-generic
% 0.09/0.52 % CPULimit : 300
% 0.09/0.52 % WCLimit : 300
% 0.09/0.52 % DateTime : Mon Sep 21 04:25:06 UTC 2026
% 0.09/0.52 % CPUTime :
% 0.09/0.52 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.56 Running first-order theorem proving
% 0.12/0.56 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
% 0.12/0.59 % Version: 3.5.1
% 0.12/0.59 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.12/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.59 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.12/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.59 % Starting sh5l with 300s (1) cores
% 0.12/0.59 % sh5l with pid 549499 completed with status 0
% 0.12/0.59 % Result found by sh5l
% 0.12/0.59 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.12/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.59 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.12/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.59 % Starting sh5l with 300s (1) cores
% 0.12/0.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.12/0.59 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.12/0.59 % Search class: FGHSF-FSLM31-MFFFFFNN
% 0.12/0.59 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.59 % Starting SubtermCWHack with 28s (1) cores
% 0.12/0.59 % SubtermCWHack with pid 549503 completed with status 0
% 0.12/0.59 % Result found by SubtermCWHack
% 0.12/0.60 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.12/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.60 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.12/0.60 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.60 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.60 % Starting sh5l with 300s (1) cores
% 0.12/0.60 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.12/0.60 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.12/0.60 % Search class: FGHSF-FSLM31-MFFFFFNN
% 0.12/0.60 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.60 % Starting SubtermCWHack with 28s (1) cores
% 0.12/0.60 % Preprocessing time : 0.002 s
% 0.12/0.60
% 0.12/0.60 % Proof found!
% 0.12/0.60 % SZS status Theorem
% 0.12/0.60 % SZS output start CNFRefutation
% See solution above
% 0.12/0.60 % Parsed axioms : 55
% 0.12/0.60 % Removed by relevancy pruning/SinE : 0
% 0.12/0.60 % Initial clauses : 212
% 0.12/0.60 % Removed in clause preprocessing : 4
% 0.12/0.60 % Initial clauses in saturation : 208
% 0.12/0.60 % Processed clauses : 294
% 0.12/0.60 % ...of these trivial : 7
% 0.12/0.60 % ...subsumed : 75
% 0.12/0.60 % ...remaining for further processing : 212
% 0.12/0.60 % Other redundant clauses eliminated : 11
% 0.12/0.60 % Clauses deleted for lack of memory : 0
% 0.12/0.60 % Backward-subsumed : 6
% 0.12/0.60 % Backward-rewritten : 21
% 0.12/0.60 % Generated clauses : 356
% 0.12/0.60 % ...of the previous two non-redundant : 204
% 0.12/0.60 % ...aggressively subsumed : 0
% 0.12/0.60 % Contextual simplify-reflections : 2
% 0.12/0.60 % Paramodulations : 345
% 0.12/0.60 % Factorizations : 0
% 0.12/0.60 % NegExts : 0
% 0.12/0.60 % Equation resolutions : 11
% 0.12/0.60 % Disequality decompositions : 0
% 0.12/0.60 % Total rewrite steps : 435
% 0.12/0.60 % ...of those cached : 381
% 0.12/0.60 % Propositional unsat checks : 0
% 0.12/0.60 % Propositional check models : 0
% 0.12/0.60 % Propositional check unsatisfiable : 0
% 0.12/0.60 % Propositional clauses : 0
% 0.12/0.60 % Propositional clauses after purity: 0
% 0.12/0.60 % Propositional unsat core size : 0
% 0.12/0.60 % Propositional preprocessing time : 0.000
% 0.12/0.60 % Propositional encoding time : 0.000
% 0.12/0.60 % Propositional solver time : 0.000
% 0.12/0.60 % Success case prop preproc time : 0.000
% 0.12/0.60 % Success case prop encoding time : 0.000
% 0.12/0.60 % Success case prop solver time : 0.000
% 0.12/0.60 % Current number of processed clauses : 178
% 0.12/0.60 % Positive orientable unit clauses : 78
% 0.12/0.60 % Positive unorientable unit clauses: 0
% 0.12/0.60 % Negative unit clauses : 11
% 0.12/0.60 % Non-unit-clauses : 89
% 0.12/0.60 % Current number of unprocessed clauses: 114
% 0.12/0.60 % ...number of literals in the above : 504
% 0.12/0.60 % Current number of archived formulas : 0
% 0.12/0.60 % Current number of archived clauses : 27
% 0.12/0.60 % Clause-clause subsumption calls (NU) : 1553
% 0.12/0.60 % Rec. Clause-clause subsumption calls : 1410
% 0.12/0.60 % Non-unit clause-clause subsumptions : 69
% 0.12/0.60 % Unit Clause-clause subsumption calls : 146
% 0.12/0.60 % Rewrite failures with RHS unbound : 0
% 0.12/0.60 % BW rewrite match attempts : 17
% 0.12/0.60 % BW rewrite match successes : 17
% 0.12/0.60 % Condensation attempts : 0
% 0.12/0.60 % Condensation successes : 0
% 0.12/0.60 % Termbank termtop insertions : 16095
% 0.12/0.60 % Search garbage collected termcells : 2727
% 0.12/0.60
% 0.12/0.60 % -------------------------------------------------
% 0.12/0.60 % User time : 0.020 s
% 0.12/0.60 % System time : 0.001 s
% 0.12/0.60 % Total time : 0.021 s
% 0.12/0.60 % Maximum resident set size: 4232 pages
% 0.12/0.60
% 0.12/0.60 % -------------------------------------------------
% 0.12/0.60 % User time : 0.023 s
% 0.12/0.60 % System time : 0.002 s
% 0.12/0.60 % Total time : 0.025 s
% 0.12/0.60 % Maximum resident set size: 4608 pages
% 0.12/0.60 % E exiting
%------------------------------------------------------------------------------