%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG049+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 : n010.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 0.13s 0.62s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 42 ( 18 unt; 0 def)
% Number of atoms : 129 ( 35 equ)
% Maximal formula atoms : 25 ( 3 avg)
% Number of connectives : 150 ( 63 ~; 56 |; 16 &)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mPosMon,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> ( ( sdtlseqdt0(sz0z00,X2)
& sdtlseqdt0(sz0z00,X1) )
=> ( sdtlseqdt0(sz0z00,sdtasdt0(X1,X2))
& sdtlseqdt0(sz0z00,sdtpldt0(X1,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPosMon) ).
fof(m__1568,hypothesis,
sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1568) ).
fof(m__1590,hypothesis,
( sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
& sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1590) ).
fof(mMulSc,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> aScalar0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).
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/sandbox/benchmark/theBenchmark.p',mDefInit) ).
fof(mScPr,axiom,
! [X1,X2] :
( ( aVector0(X2)
& aVector0(X1) )
=> ( aDimensionOf0(X1) = aDimensionOf0(X2)
=> aScalar0(sdtasasdt0(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScPr) ).
fof(m__1542_01,hypothesis,
aDimensionOf0(xs) != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1542_01) ).
fof(m__1542,hypothesis,
aVector0(xs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1542) ).
fof(mElmSc,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aVector0(X1) )
=> aScalar0(sdtlbdtrb0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mElmSc) ).
fof(mDimNat,axiom,
! [X1] :
( aVector0(X1)
=> aNaturalNumber0(aDimensionOf0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDimNat) ).
fof(c_0_11,negated_conjecture,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_12,negated_conjecture,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_13,plain,
! [X53,X54] :
( ( ~ aScalar0(X54)
| ~ aScalar0(X53)
| ~ sdtlseqdt0(sz0z00,X54)
| ~ sdtlseqdt0(sz0z00,X53)
| sdtlseqdt0(sz0z00,sdtasdt0(X53,X54)) )
& ( ~ aScalar0(X54)
| ~ aScalar0(X53)
| ~ sdtlseqdt0(sz0z00,X54)
| ~ sdtlseqdt0(sz0z00,X53)
| sdtlseqdt0(sz0z00,sdtpldt0(X53,X54)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPosMon])])])]) ).
fof(c_0_14,negated_conjecture,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(fof_nnf,[status(thm)],[c_0_12]) ).
cnf(c_0_15,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(sz0z00,X1)
| sdtlseqdt0(sz0z00,sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,hypothesis,
sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(split_conjunct,[status(thm)],[m__1568]) ).
cnf(c_0_17,hypothesis,
sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(split_conjunct,[status(thm)],[m__1590]) ).
cnf(c_0_18,hypothesis,
sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))),
inference(split_conjunct,[status(thm)],[m__1590]) ).
cnf(c_0_19,negated_conjecture,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_20,plain,
! [X17,X18] :
( aScalar0(sdtasdt0(X17,X18))
| ~ aScalar0(X18)
| ~ aScalar0(X17) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulSc])])]) ).
fof(c_0_21,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]) ).
cnf(c_0_22,hypothesis,
( ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18])]),c_0_19]) ).
cnf(c_0_23,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| aScalar0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_24,plain,
! [X69,X70] :
( aScalar0(sdtasasdt0(X69,X70))
| aDimensionOf0(X69) != aDimensionOf0(X70)
| ~ aVector0(X70)
| ~ aVector0(X69) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScPr])])]) ).
fof(c_0_25,plain,
! [X62,X63,X64,X65] :
( ( ~ aVector0(X62)
| aDimensionOf0(X62) = sz00
| X65 = sziznziztdt0(X62)
| szszuzczcdt0(aDimensionOf0(X65)) != aDimensionOf0(X62)
| ~ aVector0(X65)
| sdtlbdtrb0(X65,esk2_2(X62,X65)) != sdtlbdtrb0(X62,esk2_2(X62,X65)) )
& ( ~ aVector0(X62)
| aDimensionOf0(X62) = sz00
| X65 = sziznziztdt0(X62)
| szszuzczcdt0(aDimensionOf0(X65)) != aDimensionOf0(X62)
| ~ aVector0(X65)
| aNaturalNumber0(esk2_2(X62,X65)) )
& ( ~ aVector0(X62)
| aDimensionOf0(X62) = sz00
| X63 != sziznziztdt0(X62)
| sdtlbdtrb0(X63,X64) = sdtlbdtrb0(X62,X64)
| ~ aNaturalNumber0(X64) )
& ( ~ aVector0(X62)
| aDimensionOf0(X62) = sz00
| X63 != sziznziztdt0(X62)
| szszuzczcdt0(aDimensionOf0(X63)) = aDimensionOf0(X62) )
& ( ~ aVector0(X62)
| aDimensionOf0(X62) = sz00
| X63 != sziznziztdt0(X62)
| aVector0(X63) ) ),
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_21])])])])])])]) ).
fof(c_0_26,hypothesis,
aDimensionOf0(xs) != sz00,
inference(fof_simplification,[status(thm)],[m__1542_01]) ).
cnf(c_0_27,hypothesis,
( ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
( aDimensionOf0(X1) != aDimensionOf0(X2)
| ~ aVector0(X2)
| ~ aVector0(X1)
| aScalar0(sdtasasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
( ~ aVector0(X2)
| X1 != sziznziztdt0(X2)
| aDimensionOf0(X2) = sz00
| aVector0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_30,hypothesis,
aDimensionOf0(xs) != sz00,
inference(fof_nnf,[status(thm)],[c_0_26]) ).
cnf(c_0_31,hypothesis,
( ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aVector0(sziznziztdt0(xs)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
( ~ aVector0(X1)
| aVector0(sziznziztdt0(X1))
| aDimensionOf0(X1) = sz00 ),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_33,hypothesis,
aVector0(xs),
inference(split_conjunct,[status(thm)],[m__1542]) ).
cnf(c_0_34,hypothesis,
aDimensionOf0(xs) != sz00,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_35,plain,
! [X60,X61] :
( aScalar0(sdtlbdtrb0(X60,X61))
| ~ aNaturalNumber0(X61)
| ~ aVector0(X60) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mElmSc])])]) ).
cnf(c_0_36,hypothesis,
~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))),
inference(sr,[status(thm)],[inference(cn,[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_37,plain,
( ~ aNaturalNumber0(X2)
| ~ aVector0(X1)
| aScalar0(sdtlbdtrb0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_38,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_39,hypothesis,
~ aNaturalNumber0(aDimensionOf0(xs)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_33])]) ).
cnf(c_0_40,plain,
( ~ aVector0(X1)
| aNaturalNumber0(aDimensionOf0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_41,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG049+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.54 % Computer : n010.cluster.edu
% 0.09/0.54 % Model : x86_64 x86_64
% 0.09/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.54 % Memory : 8046.5625MB
% 0.09/0.54 % OS : Linux 6.8.0-71-generic
% 0.09/0.54 % CPULimit : 300
% 0.09/0.54 % WCLimit : 300
% 0.09/0.54 % DateTime : Mon Sep 21 04:15:41 UTC 2026
% 0.09/0.54 % CPUTime :
% 0.09/0.54 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.59 Running first-order theorem proving
% 0.13/0.59 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
% 0.13/0.62 % Version: 3.5.1
% 0.13/0.62 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/0.62 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.62 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.62 % Starting sh5l with 300s (1) cores
% 0.13/0.62 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 4114 completed with status 0
% 0.13/0.62 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.13/0.62 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/0.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.62 % No SInE strategy applied
% 0.13/0.62 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.13/0.62 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.62 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.13/0.62 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.13/0.62 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 0.13/0.62 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.62 % SAT001_MinMin_p005000_rr_RG with pid 4122 completed with status 0
% 0.13/0.62 % Result found by SAT001_MinMin_p005000_rr_RG
% 0.13/0.62 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/0.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.62 % No SInE strategy applied
% 0.13/0.62 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.13/0.62 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.62 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.13/0.62 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.13/0.62 % Preprocessing time : 0.002 s
% 0.13/0.62 % Presaturation interreduction done
% 0.13/0.62
% 0.13/0.62 % Proof found!
% 0.13/0.62 % SZS status Theorem
% 0.13/0.62 % SZS output start CNFRefutation
% See solution above
% 0.13/0.62 % Parsed axioms : 42
% 0.13/0.62 % Removed by relevancy pruning/SinE : 0
% 0.13/0.62 % Initial clauses : 62
% 0.13/0.62 % Removed in clause preprocessing : 5
% 0.13/0.62 % Initial clauses in saturation : 57
% 0.13/0.62 % Processed clauses : 124
% 0.13/0.62 % ...of these trivial : 1
% 0.13/0.62 % ...subsumed : 5
% 0.13/0.62 % ...remaining for further processing : 118
% 0.13/0.62 % Other redundant clauses eliminated : 5
% 0.13/0.62 % Clauses deleted for lack of memory : 0
% 0.13/0.62 % Backward-subsumed : 2
% 0.13/0.62 % Backward-rewritten : 1
% 0.13/0.62 % Generated clauses : 143
% 0.13/0.62 % ...of the previous two non-redundant : 104
% 0.13/0.62 % ...aggressively subsumed : 0
% 0.13/0.62 % Contextual simplify-reflections : 0
% 0.13/0.62 % Paramodulations : 137
% 0.13/0.62 % Factorizations : 0
% 0.13/0.62 % NegExts : 0
% 0.13/0.62 % Equation resolutions : 6
% 0.13/0.62 % Disequality decompositions : 0
% 0.13/0.62 % Total rewrite steps : 107
% 0.13/0.62 % ...of those cached : 99
% 0.13/0.62 % Propositional unsat checks : 0
% 0.13/0.62 % Propositional check models : 0
% 0.13/0.62 % Propositional check unsatisfiable : 0
% 0.13/0.62 % Propositional clauses : 0
% 0.13/0.62 % Propositional clauses after purity: 0
% 0.13/0.62 % Propositional unsat core size : 0
% 0.13/0.62 % Propositional preprocessing time : 0.000
% 0.13/0.62 % Propositional encoding time : 0.000
% 0.13/0.62 % Propositional solver time : 0.000
% 0.13/0.62 % Success case prop preproc time : 0.000
% 0.13/0.62 % Success case prop encoding time : 0.000
% 0.13/0.62 % Success case prop solver time : 0.000
% 0.13/0.62 % Current number of processed clauses : 55
% 0.13/0.62 % Positive orientable unit clauses : 10
% 0.13/0.62 % Positive unorientable unit clauses: 0
% 0.13/0.62 % Negative unit clauses : 4
% 0.13/0.62 % Non-unit-clauses : 41
% 0.13/0.62 % Current number of unprocessed clauses: 94
% 0.13/0.62 % ...number of literals in the above : 410
% 0.13/0.62 % Current number of archived formulas : 0
% 0.13/0.62 % Current number of archived clauses : 60
% 0.13/0.62 % Clause-clause subsumption calls (NU) : 554
% 0.13/0.62 % Rec. Clause-clause subsumption calls : 225
% 0.13/0.62 % Non-unit clause-clause subsumptions : 4
% 0.13/0.62 % Unit Clause-clause subsumption calls : 3
% 0.13/0.62 % Rewrite failures with RHS unbound : 0
% 0.13/0.62 % BW rewrite match attempts : 1
% 0.13/0.62 % BW rewrite match successes : 1
% 0.13/0.62 % Condensation attempts : 0
% 0.13/0.62 % Condensation successes : 0
% 0.13/0.62 % Termbank termtop insertions : 7845
% 0.13/0.62 % Search garbage collected termcells : 854
% 0.13/0.62
% 0.13/0.62 % -------------------------------------------------
% 0.13/0.62 % User time : 0.015 s
% 0.13/0.62 % System time : 0.005 s
% 0.13/0.62 % Total time : 0.019 s
% 0.13/0.62 % Maximum resident set size: 3680 pages
% 0.13/0.62
% 0.13/0.62 % -------------------------------------------------
% 0.13/0.62 % User time : 0.057 s
% 0.13/0.62 % System time : 0.018 s
% 0.13/0.62 % Total time : 0.076 s
% 0.13/0.62 % Maximum resident set size: 4864 pages
% 0.13/0.62 % E exiting
%------------------------------------------------------------------------------