%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG052+2 : 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 : n026.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 02:05:38 PM UTC 2026
% Result : Theorem 0.19s 0.53s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 48 ( 26 unt; 0 def)
% Number of atoms : 104 ( 46 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 89 ( 33 ~; 24 |; 21 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEqInit,axiom,
! [X1,X2] :
( ( aVector0(X2)
& aVector0(X1) )
=> ( ( aDimensionOf0(X2) != sz00
& aDimensionOf0(X1) = aDimensionOf0(X2) )
=> aDimensionOf0(sziznziztdt0(X1)) = aDimensionOf0(sziznziztdt0(X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEqInit) ).
fof(m__1692,hypothesis,
aDimensionOf0(xs) != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1692) ).
fof(m__1726,hypothesis,
( xq = sziznziztdt0(xt)
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(xq,X1) = sdtlbdtrb0(xt,X1) )
& szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt)
& aVector0(xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1726) ).
fof(m__,conjecture,
sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__1678_01,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678_01) ).
fof(m__1678,hypothesis,
( aVector0(xt)
& aVector0(xs) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678) ).
fof(m__1709,hypothesis,
( xp = sziznziztdt0(xs)
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(xp,X1) = sdtlbdtrb0(xs,X1) )
& szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs)
& aVector0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1709) ).
fof(mDimNat,axiom,
! [X1] :
( aVector0(X1)
=> aNaturalNumber0(aDimensionOf0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDimNat) ).
fof(m__1652,hypothesis,
! [X1,X2] :
( ( aVector0(X2)
& aVector0(X1) )
=> ( aDimensionOf0(X1) = aDimensionOf0(X2)
=> ( iLess0(aDimensionOf0(X1),aDimensionOf0(xs))
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(X1,X2),sdtasasdt0(X1,X2)),sdtasdt0(sdtasasdt0(X1,X1),sdtasasdt0(X2,X2))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1652) ).
fof(mIH,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> iLess0(X1,szszuzczcdt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).
fof(m__1820,hypothesis,
( xE = sdtasasdt0(xp,xq)
& aScalar0(xE) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1820) ).
fof(m__1783,hypothesis,
( xC = sdtasasdt0(xp,xp)
& aScalar0(xC) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1783) ).
fof(m__1800,hypothesis,
( xD = sdtasasdt0(xq,xq)
& aScalar0(xD) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1800) ).
fof(c_0_13,plain,
! [X1,X2] :
( ( aVector0(X2)
& aVector0(X1) )
=> ( ( aDimensionOf0(X2) != sz00
& aDimensionOf0(X1) = aDimensionOf0(X2) )
=> aDimensionOf0(sziznziztdt0(X1)) = aDimensionOf0(sziznziztdt0(X2)) ) ),
inference(fof_simplification,[status(thm)],[mEqInit]) ).
fof(c_0_14,hypothesis,
aDimensionOf0(xs) != sz00,
inference(fof_simplification,[status(thm)],[m__1692]) ).
fof(c_0_15,plain,
! [X67,X68] :
( aDimensionOf0(sziznziztdt0(X67)) = aDimensionOf0(sziznziztdt0(X68))
| aDimensionOf0(X68) = sz00
| aDimensionOf0(X67) != aDimensionOf0(X68)
| ~ aVector0(X68)
| ~ aVector0(X67) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_16,hypothesis,
! [X79] :
( xq = sziznziztdt0(xt)
& ( sdtlbdtrb0(xq,X79) = sdtlbdtrb0(xt,X79)
| ~ aNaturalNumber0(X79) )
& szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt)
& aVector0(xq) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1726])])])]) ).
fof(c_0_17,hypothesis,
aDimensionOf0(xs) != sz00,
inference(fof_nnf,[status(thm)],[c_0_14]) ).
fof(c_0_18,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_19,plain,
( aDimensionOf0(X1) != aDimensionOf0(X2)
| ~ aVector0(X2)
| ~ aVector0(X1)
| aDimensionOf0(sziznziztdt0(X1)) = aDimensionOf0(sziznziztdt0(X2))
| aDimensionOf0(X2) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(split_conjunct,[status(thm)],[m__1678_01]) ).
cnf(c_0_21,hypothesis,
xq = sziznziztdt0(xt),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,hypothesis,
aVector0(xt),
inference(split_conjunct,[status(thm)],[m__1678]) ).
cnf(c_0_23,hypothesis,
aDimensionOf0(xs) != sz00,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_24,hypothesis,
! [X78] :
( xp = sziznziztdt0(xs)
& ( sdtlbdtrb0(xp,X78) = sdtlbdtrb0(xs,X78)
| ~ aNaturalNumber0(X78) )
& szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs)
& aVector0(xp) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1709])])])]) ).
fof(c_0_25,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_26,plain,
! [X59] :
( aNaturalNumber0(aDimensionOf0(X59))
| ~ aVector0(X59) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDimNat])])]) ).
cnf(c_0_27,hypothesis,
( ~ aVector0(X1)
| aDimensionOf0(X1) != aDimensionOf0(xs)
| aDimensionOf0(sziznziztdt0(X1)) = aDimensionOf0(xq) ),
inference(sr,[status(thm)],[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])]),c_0_23]) ).
cnf(c_0_28,hypothesis,
xp = sziznziztdt0(xs),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,hypothesis,
aVector0(xs),
inference(split_conjunct,[status(thm)],[m__1678]) ).
fof(c_0_30,hypothesis,
! [X76,X77] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(X76,X77),sdtasasdt0(X76,X77)),sdtasdt0(sdtasasdt0(X76,X76),sdtasasdt0(X77,X77)))
| ~ iLess0(aDimensionOf0(X76),aDimensionOf0(xs))
| aDimensionOf0(X76) != aDimensionOf0(X77)
| ~ aVector0(X77)
| ~ aVector0(X76) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1652])])]) ).
fof(c_0_31,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
inference(fof_nnf,[status(thm)],[c_0_25]) ).
fof(c_0_32,plain,
! [X13] :
( iLess0(X13,szszuzczcdt0(X13))
| ~ aNaturalNumber0(X13) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIH])])]) ).
cnf(c_0_33,hypothesis,
szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_34,plain,
( ~ aVector0(X1)
| aNaturalNumber0(aDimensionOf0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,hypothesis,
aDimensionOf0(xp) = aDimensionOf0(xq),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
cnf(c_0_36,hypothesis,
aVector0(xp),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_37,hypothesis,
( ~ iLess0(aDimensionOf0(X1),aDimensionOf0(xs))
| aDimensionOf0(X1) != aDimensionOf0(X2)
| ~ aVector0(X2)
| ~ aVector0(X1)
| sdtlseqdt0(sdtasdt0(sdtasasdt0(X1,X2),sdtasasdt0(X1,X2)),sdtasdt0(sdtasasdt0(X1,X1),sdtasasdt0(X2,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_38,hypothesis,
xE = sdtasasdt0(xp,xq),
inference(split_conjunct,[status(thm)],[m__1820]) ).
cnf(c_0_39,hypothesis,
xC = sdtasasdt0(xp,xp),
inference(split_conjunct,[status(thm)],[m__1783]) ).
cnf(c_0_40,hypothesis,
xD = sdtasasdt0(xq,xq),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_41,hypothesis,
aVector0(xq),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_42,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_43,plain,
( ~ aNaturalNumber0(X1)
| iLess0(X1,szszuzczcdt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_44,hypothesis,
szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xs),
inference(rw,[status(thm)],[c_0_33,c_0_20]) ).
cnf(c_0_45,hypothesis,
aNaturalNumber0(aDimensionOf0(xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_46,hypothesis,
~ iLess0(aDimensionOf0(xq),aDimensionOf0(xs)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_40]),c_0_35]),c_0_41]),c_0_36]),c_0_35])]),c_0_42]) ).
cnf(c_0_47,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]),c_0_46]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG052+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 04:18:21 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.44 Running first-order theorem proving
% 0.09/0.44 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
% 0.19/0.53 % Version: 3.5.1
% 0.19/0.53 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.19/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.53 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.19/0.53 % Starting new_bool_3 with 300s (1) cores
% 0.19/0.53 % Starting new_bool_1 with 300s (1) cores
% 0.19/0.53 % Starting sh5l with 300s (1) cores
% 0.19/0.53 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1345967 completed with status 0
% 0.19/0.53 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.19/0.53 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.19/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.53 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.19/0.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/0.53 % No SInE strategy applied
% 0.19/0.53 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.19/0.53 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.53 % Starting SubtermCWHack with 136s (1) cores
% 0.19/0.53 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.19/0.53 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.19/0.53 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 0.19/0.53 % Starting new_bool_3 with 136s (1) cores
% 0.19/0.53 % SAT001_MinMin_p005000_rr_RG with pid 1345973 completed with status 0
% 0.19/0.53 % Result found by SAT001_MinMin_p005000_rr_RG
% 0.19/0.53 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.19/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.53 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.19/0.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/0.53 % No SInE strategy applied
% 0.19/0.53 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.19/0.53 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.53 % Starting SubtermCWHack with 136s (1) cores
% 0.19/0.53 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.19/0.53 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.19/0.53 % Preprocessing time : 0.004 s
% 0.19/0.53 % Presaturation interreduction done
% 0.19/0.53
% 0.19/0.53 % Proof found!
% 0.19/0.53 % SZS status Theorem
% 0.19/0.53 % SZS output start CNFRefutation
% See solution above
% 0.19/0.53 % Parsed axioms : 56
% 0.19/0.53 % Removed by relevancy pruning/SinE : 0
% 0.19/0.53 % Initial clauses : 94
% 0.19/0.53 % Removed in clause preprocessing : 5
% 0.19/0.53 % Initial clauses in saturation : 89
% 0.19/0.53 % Processed clauses : 270
% 0.19/0.53 % ...of these trivial : 3
% 0.19/0.53 % ...subsumed : 19
% 0.19/0.53 % ...remaining for further processing : 247
% 0.19/0.53 % Other redundant clauses eliminated : 5
% 0.19/0.53 % Clauses deleted for lack of memory : 0
% 0.19/0.53 % Backward-subsumed : 1
% 0.19/0.53 % Backward-rewritten : 3
% 0.19/0.53 % Generated clauses : 621
% 0.19/0.53 % ...of the previous two non-redundant : 535
% 0.19/0.53 % ...aggressively subsumed : 0
% 0.19/0.53 % Contextual simplify-reflections : 1
% 0.19/0.53 % Paramodulations : 612
% 0.19/0.53 % Factorizations : 0
% 0.19/0.53 % NegExts : 0
% 0.19/0.53 % Equation resolutions : 9
% 0.19/0.53 % Disequality decompositions : 0
% 0.19/0.53 % Total rewrite steps : 655
% 0.19/0.53 % ...of those cached : 616
% 0.19/0.53 % Propositional unsat checks : 0
% 0.19/0.53 % Propositional check models : 0
% 0.19/0.53 % Propositional check unsatisfiable : 0
% 0.19/0.53 % Propositional clauses : 0
% 0.19/0.53 % Propositional clauses after purity: 0
% 0.19/0.53 % Propositional unsat core size : 0
% 0.19/0.53 % Propositional preprocessing time : 0.000
% 0.19/0.53 % Propositional encoding time : 0.000
% 0.19/0.53 % Propositional solver time : 0.000
% 0.19/0.53 % Success case prop preproc time : 0.000
% 0.19/0.53 % Success case prop encoding time : 0.000
% 0.19/0.53 % Success case prop solver time : 0.000
% 0.19/0.53 % Current number of processed clauses : 151
% 0.19/0.53 % Positive orientable unit clauses : 49
% 0.19/0.53 % Positive unorientable unit clauses: 0
% 0.19/0.53 % Negative unit clauses : 3
% 0.19/0.53 % Non-unit-clauses : 99
% 0.19/0.53 % Current number of unprocessed clauses: 429
% 0.19/0.53 % ...number of literals in the above : 1915
% 0.19/0.53 % Current number of archived formulas : 0
% 0.19/0.53 % Current number of archived clauses : 93
% 0.19/0.53 % Clause-clause subsumption calls (NU) : 2546
% 0.19/0.53 % Rec. Clause-clause subsumption calls : 898
% 0.19/0.53 % Non-unit clause-clause subsumptions : 16
% 0.19/0.53 % Unit Clause-clause subsumption calls : 34
% 0.19/0.53 % Rewrite failures with RHS unbound : 0
% 0.19/0.53 % BW rewrite match attempts : 2
% 0.19/0.53 % BW rewrite match successes : 2
% 0.19/0.53 % Condensation attempts : 0
% 0.19/0.53 % Condensation successes : 0
% 0.19/0.53 % Termbank termtop insertions : 16986
% 0.19/0.53 % Search garbage collected termcells : 913
% 0.19/0.53
% 0.19/0.53 % -------------------------------------------------
% 0.19/0.53 % User time : 0.044 s
% 0.19/0.53 % System time : 0.011 s
% 0.19/0.53 % Total time : 0.055 s
% 0.19/0.53 % Maximum resident set size: 3700 pages
% 0.19/0.53
% 0.19/0.53 % -------------------------------------------------
% 0.19/0.53 % User time : 0.131 s
% 0.19/0.53 % System time : 0.033 s
% 0.19/0.53 % Total time : 0.164 s
% 0.19/0.53 % Maximum resident set size: 4608 pages
% 0.19/0.53 % E exiting
%------------------------------------------------------------------------------