%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : RNG047+1 : 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 02:06:10 PM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 11 unt; 0 def)
% Number of atoms : 135 ( 70 equ)
% Maximal formula atoms : 25 ( 3 avg)
% Number of connectives : 150 ( 57 ~; 57 |; 21 &)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 22 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mNatExtr,axiom,
! [X1] :
( ( X1 != sz00
& aNaturalNumber0(X1) )
=> ? [X2] :
( X1 = szszuzczcdt0(X2)
& aNaturalNumber0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatExtr) ).
fof(mSuccNat,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( szszuzczcdt0(X1) != sz00
& aNaturalNumber0(szszuzczcdt0(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNat) ).
fof(mDefInit,axiom,
! [X1] :
( aVector0(X1)
=> ( aDimensionOf0(X1) != sz00
=> ! [X2] :
( X2 = sziznziztdt0(X1)
<=> ( ! [X3] :
( aNaturalNumber0(X3)
=> sdtlbdtrb0(X2,X3) = sdtlbdtrb0(X1,X3) )
& szszuzczcdt0(aDimensionOf0(X2)) = aDimensionOf0(X1)
& aVector0(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefInit) ).
fof(mSuccEqu,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( szszuzczcdt0(X1) = szszuzczcdt0(X2)
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccEqu) ).
fof(mDimNat,axiom,
! [X1] :
( aVector0(X1)
=> aNaturalNumber0(aDimensionOf0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDimNat) ).
fof(m__1329_01,hypothesis,
( aDimensionOf0(xt) != sz00
& aDimensionOf0(xs) = aDimensionOf0(xt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1329_01) ).
fof(m__,conjecture,
aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__1329,hypothesis,
( aVector0(xt)
& aVector0(xs) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1329) ).
fof(c_0_8,plain,
! [X1] :
( ( X1 != sz00
& aNaturalNumber0(X1) )
=> ? [X2] :
( X1 = szszuzczcdt0(X2)
& aNaturalNumber0(X2) ) ),
inference(fof_simplification,[status(thm)],[mNatExtr]) ).
fof(c_0_9,plain,
! [X1] :
( aNaturalNumber0(X1)
=> ( szszuzczcdt0(X1) != sz00
& aNaturalNumber0(szszuzczcdt0(X1)) ) ),
inference(fof_simplification,[status(thm)],[mSuccNat]) ).
fof(c_0_10,plain,
! [X1] :
( aVector0(X1)
=> ( aDimensionOf0(X1) != sz00
=> ! [X2] :
( X2 = sziznziztdt0(X1)
<=> ( ! [X3] :
( aNaturalNumber0(X3)
=> sdtlbdtrb0(X2,X3) = sdtlbdtrb0(X1,X3) )
& szszuzczcdt0(aDimensionOf0(X2)) = aDimensionOf0(X1)
& aVector0(X2) ) ) ) ),
inference(fof_simplification,[status(thm)],[mDefInit]) ).
fof(c_0_11,plain,
! [X16,X17] :
( X16 = X17
| szszuzczcdt0(X16) != szszuzczcdt0(X17)
| ~ aNaturalNumber0(X17)
| ~ aNaturalNumber0(X16) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSuccEqu])])]) ).
fof(c_0_12,plain,
! [X8] :
( ( X8 = sz00
| ~ aNaturalNumber0(X8)
| X8 = szszuzczcdt0(esk1_1(X8)) )
& ( X8 = sz00
| ~ aNaturalNumber0(X8)
| aNaturalNumber0(esk1_1(X8)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])]) ).
fof(c_0_13,plain,
! [X7] :
( ( ~ aNaturalNumber0(X7)
| szszuzczcdt0(X7) != sz00 )
& ( ~ aNaturalNumber0(X7)
| aNaturalNumber0(szszuzczcdt0(X7)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
fof(c_0_14,plain,
! [X10,X11,X12,X13] :
( ( ~ aVector0(X10)
| aDimensionOf0(X10) = sz00
| X13 = sziznziztdt0(X10)
| szszuzczcdt0(aDimensionOf0(X13)) != aDimensionOf0(X10)
| ~ aVector0(X13)
| sdtlbdtrb0(X13,esk2_2(X10,X13)) != sdtlbdtrb0(X10,esk2_2(X10,X13)) )
& ( ~ aVector0(X10)
| aDimensionOf0(X10) = sz00
| X13 = sziznziztdt0(X10)
| szszuzczcdt0(aDimensionOf0(X13)) != aDimensionOf0(X10)
| ~ aVector0(X13)
| aNaturalNumber0(esk2_2(X10,X13)) )
& ( ~ aVector0(X10)
| aDimensionOf0(X10) = sz00
| X11 != sziznziztdt0(X10)
| sdtlbdtrb0(X11,X12) = sdtlbdtrb0(X10,X12)
| ~ aNaturalNumber0(X12) )
& ( ~ aVector0(X10)
| aDimensionOf0(X10) = sz00
| X11 != sziznziztdt0(X10)
| szszuzczcdt0(aDimensionOf0(X11)) = aDimensionOf0(X10) )
& ( ~ aVector0(X10)
| aDimensionOf0(X10) = sz00
| X11 != sziznziztdt0(X10)
| aVector0(X11) ) ),
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)],[c_0_10])])])])])])]) ).
cnf(c_0_15,plain,
( szszuzczcdt0(X1) != szszuzczcdt0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( ~ aNaturalNumber0(X1)
| X1 = sz00
| X1 = szszuzczcdt0(esk1_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( ~ aNaturalNumber0(X1)
| aNaturalNumber0(szszuzczcdt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( ~ aNaturalNumber0(X1)
| szszuzczcdt0(X1) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_19,plain,
! [X6] :
( aNaturalNumber0(aDimensionOf0(X6))
| ~ aVector0(X6) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDimNat])])]) ).
cnf(c_0_20,plain,
( ~ aVector0(X2)
| X1 != sziznziztdt0(X2)
| aDimensionOf0(X2) = sz00
| aVector0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(esk1_1(szszuzczcdt0(X1)))
| esk1_1(szszuzczcdt0(X1)) = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16])]),c_0_17]),c_0_18]) ).
cnf(c_0_22,plain,
( ~ aNaturalNumber0(X1)
| X1 = sz00
| aNaturalNumber0(esk1_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_23,plain,
( ~ aVector0(X2)
| X1 != sziznziztdt0(X2)
| aDimensionOf0(X2) = sz00
| szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,plain,
( ~ aVector0(X1)
| aNaturalNumber0(aDimensionOf0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
( ~ aVector0(X1)
| aVector0(sziznziztdt0(X1))
| aDimensionOf0(X1) = sz00 ),
inference(er,[status(thm)],[c_0_20]) ).
fof(c_0_26,hypothesis,
( aDimensionOf0(xt) != sz00
& aDimensionOf0(xs) = aDimensionOf0(xt) ),
inference(fof_simplification,[status(thm)],[m__1329_01]) ).
fof(c_0_27,negated_conjecture,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_28,plain,
( ~ aNaturalNumber0(X1)
| esk1_1(szszuzczcdt0(X1)) = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_17]),c_0_18]) ).
cnf(c_0_29,plain,
( ~ aVector0(X1)
| aDimensionOf0(X1) = sz00
| szszuzczcdt0(aDimensionOf0(sziznziztdt0(X1))) = aDimensionOf0(X1) ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( ~ aVector0(X1)
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(X1)))
| aDimensionOf0(X1) = sz00 ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_31,hypothesis,
( aDimensionOf0(xt) != sz00
& aDimensionOf0(xs) = aDimensionOf0(xt) ),
inference(fof_nnf,[status(thm)],[c_0_26]) ).
fof(c_0_32,negated_conjecture,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
( ~ aVector0(X1)
| aDimensionOf0(X1) = sz00
| esk1_1(aDimensionOf0(X1)) = aDimensionOf0(sziznziztdt0(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_34,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_35,hypothesis,
aVector0(xs),
inference(split_conjunct,[status(thm)],[m__1329]) ).
cnf(c_0_36,hypothesis,
aDimensionOf0(xt) != sz00,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_37,negated_conjecture,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
inference(fof_nnf,[status(thm)],[c_0_32]) ).
cnf(c_0_38,hypothesis,
esk1_1(aDimensionOf0(xt)) = aDimensionOf0(sziznziztdt0(xs)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]),c_0_36]) ).
cnf(c_0_39,hypothesis,
aVector0(xt),
inference(split_conjunct,[status(thm)],[m__1329]) ).
cnf(c_0_40,negated_conjecture,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_41,hypothesis,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_38]),c_0_39])]),c_0_40]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG047+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n026.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
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 04:17:53 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.45 % Version: 3.5.1
% 0.11/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.45 % Starting sh5l with 300s (1) cores
% 0.11/0.45 % new_bool_3 with pid 1344440 completed with status 0
% 0.11/0.45 % Result found by new_bool_3
% 0.11/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.45 % Search class: FGHSF-FFSS21-SFFFFFNN
% 0.11/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.45 % SubtermCWHack with pid 1344444 completed with status 0
% 0.11/0.45 % Result found by SubtermCWHack
% 0.11/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.45 % Search class: FGHSF-FFSS21-SFFFFFNN
% 0.11/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.45 % Preprocessing time : 0.001 s
% 0.11/0.45
% 0.11/0.45 % Proof found!
% 0.11/0.45 % SZS status Theorem
% 0.11/0.45 % SZS output start CNFRefutation
% See solution above
% 0.11/0.45 % Parsed axioms : 35
% 0.11/0.45 % Removed by relevancy pruning/SinE : 22
% 0.11/0.45 % Initial clauses : 21
% 0.11/0.45 % Removed in clause preprocessing : 3
% 0.11/0.45 % Initial clauses in saturation : 18
% 0.11/0.45 % Processed clauses : 28
% 0.11/0.45 % ...of these trivial : 1
% 0.11/0.45 % ...subsumed : 2
% 0.11/0.45 % ...remaining for further processing : 25
% 0.11/0.45 % Other redundant clauses eliminated : 5
% 0.11/0.45 % Clauses deleted for lack of memory : 0
% 0.11/0.45 % Backward-subsumed : 1
% 0.11/0.45 % Backward-rewritten : 0
% 0.11/0.45 % Generated clauses : 28
% 0.11/0.45 % ...of the previous two non-redundant : 20
% 0.11/0.45 % ...aggressively subsumed : 0
% 0.11/0.45 % Contextual simplify-reflections : 5
% 0.11/0.45 % Paramodulations : 22
% 0.11/0.45 % Factorizations : 0
% 0.11/0.45 % NegExts : 0
% 0.11/0.45 % Equation resolutions : 6
% 0.11/0.45 % Disequality decompositions : 0
% 0.11/0.45 % Total rewrite steps : 6
% 0.11/0.45 % ...of those cached : 2
% 0.11/0.45 % Propositional unsat checks : 0
% 0.11/0.45 % Propositional check models : 0
% 0.11/0.45 % Propositional check unsatisfiable : 0
% 0.11/0.45 % Propositional clauses : 0
% 0.11/0.45 % Propositional clauses after purity: 0
% 0.11/0.45 % Propositional unsat core size : 0
% 0.11/0.45 % Propositional preprocessing time : 0.000
% 0.11/0.45 % Propositional encoding time : 0.000
% 0.11/0.45 % Propositional solver time : 0.000
% 0.11/0.45 % Success case prop preproc time : 0.000
% 0.11/0.45 % Success case prop encoding time : 0.000
% 0.11/0.45 % Success case prop solver time : 0.000
% 0.11/0.45 % Current number of processed clauses : 21
% 0.11/0.45 % Positive orientable unit clauses : 6
% 0.11/0.45 % Positive unorientable unit clauses: 0
% 0.11/0.45 % Negative unit clauses : 2
% 0.11/0.45 % Non-unit-clauses : 13
% 0.11/0.45 % Current number of unprocessed clauses: 8
% 0.11/0.45 % ...number of literals in the above : 42
% 0.11/0.45 % Current number of archived formulas : 0
% 0.11/0.45 % Current number of archived clauses : 1
% 0.11/0.45 % Clause-clause subsumption calls (NU) : 47
% 0.11/0.45 % Rec. Clause-clause subsumption calls : 23
% 0.11/0.45 % Non-unit clause-clause subsumptions : 8
% 0.11/0.45 % Unit Clause-clause subsumption calls : 0
% 0.11/0.45 % Rewrite failures with RHS unbound : 0
% 0.11/0.45 % BW rewrite match attempts : 0
% 0.11/0.45 % BW rewrite match successes : 0
% 0.11/0.45 % Condensation attempts : 0
% 0.11/0.45 % Condensation successes : 0
% 0.11/0.45 % Termbank termtop insertions : 1974
% 0.11/0.45 % Search garbage collected termcells : 472
% 0.11/0.45
% 0.11/0.45 % -------------------------------------------------
% 0.11/0.45 % User time : 0.005 s
% 0.11/0.45 % System time : 0.003 s
% 0.11/0.45 % Total time : 0.008 s
% 0.11/0.45 % Maximum resident set size: 3672 pages
% 0.11/0.45
% 0.11/0.45 % -------------------------------------------------
% 0.11/0.45 % User time : 0.007 s
% 0.11/0.45 % System time : 0.008 s
% 0.11/0.45 % Total time : 0.015 s
% 0.11/0.45 % Maximum resident set size: 4864 pages
% 0.11/0.45 % E exiting
%------------------------------------------------------------------------------