%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG069+2 : 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 : n009.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 02:05:43 PM UTC 2026
% Result : Theorem 2.08s 0.75s
% Output : CNFRefutation 2.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 17 unt; 0 def)
% Number of atoms : 72 ( 15 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 70 ( 30 ~; 25 |; 12 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2580,hypothesis,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,xS)),sdtpldt0(sdtasdt0(xS,xR),sdtasdt0(xS,xS)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2580) ).
fof(m__1949,hypothesis,
( xN = sdtasdt0(xR,xS)
& aScalar0(xN) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1949) ).
fof(mDistr2,axiom,
! [X1,X2,X3,X4] :
( ( aScalar0(X4)
& aScalar0(X3)
& aScalar0(X2)
& aScalar0(X1) )
=> sdtasdt0(sdtpldt0(X1,X2),sdtpldt0(X3,X4)) = sdtpldt0(sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X1,X4)),sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X2,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDistr2) ).
fof(m__1911,hypothesis,
( xP = sdtasdt0(xE,xH)
& aScalar0(xP) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1911) ).
fof(mDistr,axiom,
! [X1,X2,X3] :
( ( aScalar0(X3)
& aScalar0(X2)
& aScalar0(X1) )
=> ( sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3))
& sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDistr) ).
fof(m__,conjecture,
sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__1930,hypothesis,
( xS = sdtasdt0(xF,xD)
& aScalar0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1930) ).
fof(m__1892,hypothesis,
( xR = sdtasdt0(xC,xG)
& aScalar0(xR) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1892) ).
fof(mSumSc,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> aScalar0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSumSc) ).
cnf(c_0_9,hypothesis,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,xS)),sdtpldt0(sdtasdt0(xS,xR),sdtasdt0(xS,xS)))),
inference(split_conjunct,[status(thm)],[m__2580]) ).
cnf(c_0_10,hypothesis,
xN = sdtasdt0(xR,xS),
inference(split_conjunct,[status(thm)],[m__1949]) ).
fof(c_0_11,plain,
! [X27,X28,X29,X30] :
( sdtasdt0(sdtpldt0(X27,X28),sdtpldt0(X29,X30)) = sdtpldt0(sdtpldt0(sdtasdt0(X27,X29),sdtasdt0(X27,X30)),sdtpldt0(sdtasdt0(X28,X29),sdtasdt0(X28,X30)))
| ~ aScalar0(X30)
| ~ aScalar0(X29)
| ~ aScalar0(X28)
| ~ aScalar0(X27) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistr2])])]) ).
cnf(c_0_12,hypothesis,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),xN),sdtpldt0(sdtasdt0(xS,xR),sdtasdt0(xS,xS)))),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
( ~ aScalar0(X4)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(sdtpldt0(X1,X2),sdtpldt0(X3,X4)) = sdtpldt0(sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X1,X4)),sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X2,X4))) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,hypothesis,
aScalar0(xP),
inference(split_conjunct,[status(thm)],[m__1911]) ).
fof(c_0_15,plain,
! [X24,X25,X26] :
( ( ~ aScalar0(X26)
| ~ aScalar0(X25)
| ~ aScalar0(X24)
| sdtasdt0(sdtpldt0(X24,X25),X26) = sdtpldt0(sdtasdt0(X24,X26),sdtasdt0(X25,X26)) )
& ( ~ aScalar0(X26)
| ~ aScalar0(X25)
| ~ aScalar0(X24)
| sdtasdt0(X24,sdtpldt0(X25,X26)) = sdtpldt0(sdtasdt0(X24,X25),sdtasdt0(X24,X26)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistr])])])]) ).
fof(c_0_16,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_17,hypothesis,
sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),xN),sdtpldt0(sdtasdt0(xS,xR),sdtasdt0(xS,xS)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]) ).
cnf(c_0_18,plain,
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,hypothesis,
aScalar0(xS),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_20,hypothesis,
aScalar0(xR),
inference(split_conjunct,[status(thm)],[m__1892]) ).
fof(c_0_21,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
cnf(c_0_22,hypothesis,
sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),xN),sdtasdt0(xS,sdtpldt0(xR,xS)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]) ).
cnf(c_0_23,hypothesis,
( ~ aScalar0(X1)
| sdtpldt0(sdtasdt0(xR,X1),xN) = sdtasdt0(xR,sdtpldt0(X1,xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_10]),c_0_19]),c_0_20])]) ).
fof(c_0_24,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
inference(fof_nnf,[status(thm)],[c_0_21]) ).
cnf(c_0_25,hypothesis,
sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtpldt0(sdtasdt0(xR,sdtpldt0(xR,xS)),sdtasdt0(xS,sdtpldt0(xR,xS)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_20])]) ).
cnf(c_0_26,plain,
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_27,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_28,plain,
! [X15,X16] :
( aScalar0(sdtpldt0(X15,X16))
| ~ aScalar0(X16)
| ~ aScalar0(X15) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSumSc])])]) ).
cnf(c_0_29,hypothesis,
~ aScalar0(sdtpldt0(xR,xS)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_19]),c_0_20])]),c_0_27]) ).
cnf(c_0_30,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| aScalar0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_31,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_19]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG069+2 : 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 : n009.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 04:17:44 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 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
% 2.08/0.75 % Version: 3.5.1
% 2.08/0.75 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.08/0.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.08/0.75 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.08/0.75 % Starting new_bool_3 with 300s (1) cores
% 2.08/0.75 % Starting new_bool_1 with 300s (1) cores
% 2.08/0.75 % Starting sh5l with 300s (1) cores
% 2.08/0.75 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 827456 completed with status 0
% 2.08/0.75 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 2.08/0.75 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.08/0.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.08/0.75 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.08/0.75 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.08/0.75 % No SInE strategy applied
% 2.08/0.75 % Search class: FGHSF-FFMM21-MFFFFFNN
% 2.08/0.75 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.08/0.75 % Starting SubtermCWHack with 136s (1) cores
% 2.08/0.75 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 2.08/0.75 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 2.08/0.75 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 2.08/0.75 % Starting new_bool_3 with 136s (1) cores
% 2.08/0.75 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 827464 completed with status 0
% 2.08/0.75 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 2.08/0.75 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.08/0.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.08/0.75 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.08/0.75 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.08/0.75 % No SInE strategy applied
% 2.08/0.75 % Search class: FGHSF-FFMM21-MFFFFFNN
% 2.08/0.75 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.08/0.75 % Starting SubtermCWHack with 136s (1) cores
% 2.08/0.75 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 2.08/0.75 % Preprocessing time : 0.002 s
% 2.08/0.75 % Presaturation interreduction done
% 2.08/0.75
% 2.08/0.75 % Proof found!
% 2.08/0.75 % SZS status Theorem
% 2.08/0.75 % SZS output start CNFRefutation
% See solution above
% 2.08/0.75 % Parsed axioms : 62
% 2.08/0.75 % Removed by relevancy pruning/SinE : 0
% 2.08/0.75 % Initial clauses : 100
% 2.08/0.75 % Removed in clause preprocessing : 5
% 2.08/0.75 % Initial clauses in saturation : 95
% 2.08/0.75 % Processed clauses : 1950
% 2.08/0.75 % ...of these trivial : 82
% 2.08/0.75 % ...subsumed : 837
% 2.08/0.75 % ...remaining for further processing : 1031
% 2.08/0.75 % Other redundant clauses eliminated : 6
% 2.08/0.75 % Clauses deleted for lack of memory : 0
% 2.08/0.75 % Backward-subsumed : 11
% 2.08/0.75 % Backward-rewritten : 29
% 2.08/0.75 % Generated clauses : 12547
% 2.08/0.75 % ...of the previous two non-redundant : 10742
% 2.08/0.75 % ...aggressively subsumed : 0
% 2.08/0.75 % Contextual simplify-reflections : 63
% 2.08/0.75 % Paramodulations : 12534
% 2.08/0.75 % Factorizations : 0
% 2.08/0.75 % NegExts : 0
% 2.08/0.75 % Equation resolutions : 13
% 2.08/0.75 % Disequality decompositions : 0
% 2.08/0.75 % Total rewrite steps : 16498
% 2.08/0.75 % ...of those cached : 16287
% 2.08/0.75 % Propositional unsat checks : 0
% 2.08/0.75 % Propositional check models : 0
% 2.08/0.75 % Propositional check unsatisfiable : 0
% 2.08/0.75 % Propositional clauses : 0
% 2.08/0.75 % Propositional clauses after purity: 0
% 2.08/0.75 % Propositional unsat core size : 0
% 2.08/0.75 % Propositional preprocessing time : 0.000
% 2.08/0.75 % Propositional encoding time : 0.000
% 2.08/0.75 % Propositional solver time : 0.000
% 2.08/0.75 % Success case prop preproc time : 0.000
% 2.08/0.75 % Success case prop encoding time : 0.000
% 2.08/0.75 % Success case prop solver time : 0.000
% 2.08/0.75 % Current number of processed clauses : 893
% 2.08/0.75 % Positive orientable unit clauses : 228
% 2.08/0.75 % Positive unorientable unit clauses: 0
% 2.08/0.75 % Negative unit clauses : 3
% 2.08/0.75 % Non-unit-clauses : 662
% 2.08/0.75 % Current number of unprocessed clauses: 8912
% 2.08/0.75 % ...number of literals in the above : 39321
% 2.08/0.75 % Current number of archived formulas : 0
% 2.08/0.75 % Current number of archived clauses : 135
% 2.08/0.75 % Clause-clause subsumption calls (NU) : 69606
% 2.08/0.75 % Rec. Clause-clause subsumption calls : 23015
% 2.08/0.75 % Non-unit clause-clause subsumptions : 898
% 2.08/0.75 % Unit Clause-clause subsumption calls : 2895
% 2.08/0.75 % Rewrite failures with RHS unbound : 0
% 2.08/0.75 % BW rewrite match attempts : 23
% 2.08/0.75 % BW rewrite match successes : 20
% 2.08/0.75 % Condensation attempts : 0
% 2.08/0.75 % Condensation successes : 0
% 2.08/0.75 % Termbank termtop insertions : 250469
% 2.08/0.75 % Search garbage collected termcells : 888
% 2.08/0.75
% 2.08/0.75 % -------------------------------------------------
% 2.08/0.75 % User time : 0.294 s
% 2.08/0.75 % System time : 0.014 s
% 2.08/0.75 % Total time : 0.308 s
% 2.08/0.75 % Maximum resident set size: 3452 pages
% 2.08/0.75
% 2.08/0.75 % -------------------------------------------------
% 2.08/0.75 % User time : 1.309 s
% 2.08/0.75 % System time : 0.080 s
% 2.08/0.75 % Total time : 1.389 s
% 2.08/0.75 % Maximum resident set size: 4608 pages
% 2.08/0.75 % E exiting
%------------------------------------------------------------------------------