%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG049+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:05:07 PM UTC 2026
% Result : Theorem 1.55s 1.80s
% Output : CNFRefutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 44 ( 16 unt; 0 def)
% Number of atoms : 136 ( 37 equ)
% Maximal formula atoms : 25 ( 3 avg)
% Number of connectives : 156 ( 64 ~; 64 |; 16 &)
% ( 1 <=>; 11 =>; 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 : 43 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefInit,axiom,
! [X1] :
( aVector0(X1)
=> ( aDimensionOf0(X1) != sz00
=> ! [X2] :
( X2 = sziznziztdt0(X1)
<=> ( aVector0(X2)
& szszuzczcdt0(aDimensionOf0(X2)) = aDimensionOf0(X1)
& ! [X3] :
( aNaturalNumber0(X3)
=> sdtlbdtrb0(X2,X3) = sdtlbdtrb0(X1,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefInit) ).
fof(mPosMon,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> ( ( sdtlseqdt0(sz0z00,X1)
& sdtlseqdt0(sz0z00,X2) )
=> ( sdtlseqdt0(sz0z00,sdtpldt0(X1,X2))
& sdtlseqdt0(sz0z00,sdtasdt0(X1,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPosMon) ).
fof(m__,conjecture,
sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
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/sandbox2/benchmark/theBenchmark.p',m__1568) ).
fof(m__1590,hypothesis,
( sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
& sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1590) ).
fof(mMulSc,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> aScalar0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
fof(mSuccNat,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( aNaturalNumber0(szszuzczcdt0(X1))
& szszuzczcdt0(X1) != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNat) ).
fof(m__1542,hypothesis,
aVector0(xs),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1542) ).
fof(m__1542_01,hypothesis,
aDimensionOf0(xs) != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1542_01) ).
fof(mScPr,axiom,
! [X1,X2] :
( ( aVector0(X1)
& aVector0(X2) )
=> ( aDimensionOf0(X1) = aDimensionOf0(X2)
=> aScalar0(sdtasasdt0(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScPr) ).
fof(mDimNat,axiom,
! [X1] :
( aVector0(X1)
=> aNaturalNumber0(aDimensionOf0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDimNat) ).
fof(mElmSc,axiom,
! [X1,X2] :
( ( aVector0(X1)
& aNaturalNumber0(X2) )
=> aScalar0(sdtlbdtrb0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSc) ).
fof(c_0_12,plain,
! [X124,X125,X126,X127] :
( ( aVector0(X125)
| X125 != sziznziztdt0(X124)
| aDimensionOf0(X124) = sz00
| ~ aVector0(X124) )
& ( szszuzczcdt0(aDimensionOf0(X125)) = aDimensionOf0(X124)
| X125 != sziznziztdt0(X124)
| aDimensionOf0(X124) = sz00
| ~ aVector0(X124) )
& ( ~ aNaturalNumber0(X126)
| sdtlbdtrb0(X125,X126) = sdtlbdtrb0(X124,X126)
| X125 != sziznziztdt0(X124)
| aDimensionOf0(X124) = sz00
| ~ aVector0(X124) )
& ( aNaturalNumber0(esk2_2(X124,X127))
| ~ aVector0(X127)
| szszuzczcdt0(aDimensionOf0(X127)) != aDimensionOf0(X124)
| X127 = sziznziztdt0(X124)
| aDimensionOf0(X124) = sz00
| ~ aVector0(X124) )
& ( sdtlbdtrb0(X127,esk2_2(X124,X127)) != sdtlbdtrb0(X124,esk2_2(X124,X127))
| ~ aVector0(X127)
| szszuzczcdt0(aDimensionOf0(X127)) != aDimensionOf0(X124)
| X127 = sziznziztdt0(X124)
| aDimensionOf0(X124) = sz00
| ~ aVector0(X124) ) ),
inference(distribute,[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)],[mDefInit])])])])])]) ).
fof(c_0_13,plain,
! [X116,X117] :
( ( sdtlseqdt0(sz0z00,sdtpldt0(X116,X117))
| ~ sdtlseqdt0(sz0z00,X116)
| ~ sdtlseqdt0(sz0z00,X117)
| ~ aScalar0(X116)
| ~ aScalar0(X117) )
& ( sdtlseqdt0(sz0z00,sdtasdt0(X116,X117))
| ~ sdtlseqdt0(sz0z00,X116)
| ~ sdtlseqdt0(sz0z00,X117)
| ~ aScalar0(X116)
| ~ aScalar0(X117) ) ),
inference(distribute,[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_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_15,plain,
( szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X2)
| aDimensionOf0(X2) = sz00
| X1 != sziznziztdt0(X2)
| ~ aVector0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( sdtlseqdt0(sz0z00,sdtpldt0(X1,X2))
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,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_18,hypothesis,
sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(split_conjunct,[status(thm)],[m__1590]) ).
cnf(c_0_19,hypothesis,
sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))),
inference(split_conjunct,[status(thm)],[m__1590]) ).
cnf(c_0_20,negated_conjecture,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_21,plain,
! [X82,X83] :
( ~ aScalar0(X82)
| ~ aScalar0(X83)
| aScalar0(sdtasdt0(X82,X83)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulSc])]) ).
cnf(c_0_22,plain,
( aVector0(X1)
| aDimensionOf0(X2) = sz00
| X1 != sziznziztdt0(X2)
| ~ aVector0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_23,plain,
! [X74] :
( ( aNaturalNumber0(szszuzczcdt0(X74))
| ~ aNaturalNumber0(X74) )
& ( szszuzczcdt0(X74) != sz00
| ~ aNaturalNumber0(X74) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSuccNat])])]) ).
cnf(c_0_24,plain,
( szszuzczcdt0(aDimensionOf0(sziznziztdt0(X1))) = aDimensionOf0(X1)
| aDimensionOf0(X1) = sz00
| ~ aVector0(X1) ),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_25,hypothesis,
aVector0(xs),
inference(split_conjunct,[status(thm)],[m__1542]) ).
cnf(c_0_26,hypothesis,
aDimensionOf0(xs) != sz00,
inference(split_conjunct,[status(thm)],[m__1542_01]) ).
cnf(c_0_27,hypothesis,
( ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19])]),c_0_20]) ).
cnf(c_0_28,plain,
( aScalar0(sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_29,plain,
! [X131,X132] :
( ~ aVector0(X131)
| ~ aVector0(X132)
| aDimensionOf0(X131) != aDimensionOf0(X132)
| aScalar0(sdtasasdt0(X131,X132)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScPr])]) ).
cnf(c_0_30,plain,
( aDimensionOf0(X1) = sz00
| aVector0(sziznziztdt0(X1))
| ~ aVector0(X1) ),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_31,plain,
( aNaturalNumber0(szszuzczcdt0(X1))
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,hypothesis,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
fof(c_0_33,plain,
! [X121] :
( ~ aVector0(X121)
| aNaturalNumber0(aDimensionOf0(X121)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDimNat])]) ).
cnf(c_0_34,hypothesis,
( ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,plain,
( aScalar0(sdtasasdt0(X1,X2))
| ~ aVector0(X1)
| ~ aVector0(X2)
| aDimensionOf0(X1) != aDimensionOf0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,hypothesis,
aVector0(sziznziztdt0(xs)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_25]),c_0_26]) ).
fof(c_0_37,plain,
! [X122,X123] :
( ~ aVector0(X122)
| ~ aNaturalNumber0(X123)
| aScalar0(sdtlbdtrb0(X122,X123)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mElmSc])]) ).
cnf(c_0_38,hypothesis,
( aNaturalNumber0(aDimensionOf0(xs))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_39,plain,
( aNaturalNumber0(aDimensionOf0(X1))
| ~ aVector0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,hypothesis,
~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_41,plain,
( aScalar0(sdtlbdtrb0(X1,X2))
| ~ aVector0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_42,hypothesis,
aNaturalNumber0(aDimensionOf0(xs)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_36])]) ).
cnf(c_0_43,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_25]),c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG049+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.32 % Computer : n001.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue May 5 01:48:48 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.55/1.80 % Version : CSE_E---1.7
% 1.55/1.80 % Problem : theBenchmark.p
% 1.55/1.80 % SZS status Theorem for theBenchmark.p
% 1.55/1.80 % SZS output start CNFRefutation
% See solution above
% 1.55/1.80 % Total time : 1.371s
%------------------------------------------------------------------------------