%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG052+2 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n018.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 05:05:08 PM UTC 2026
% Result : Theorem 1.33s 1.74s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 40 ( 16 unt; 0 def)
% Number of atoms : 93 ( 37 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 87 ( 34 ~; 27 |; 17 &)
% ( 0 <=>; 9 =>; 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 : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__1652,hypothesis,
! [X1,X2] :
( ( aVector0(X1)
& aVector0(X2) )
=> ( 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/sandbox/benchmark/theBenchmark.p',m__1652) ).
fof(m__1726,hypothesis,
( aVector0(xq)
& szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt)
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(xq,X1) = sdtlbdtrb0(xt,X1) )
& xq = sziznziztdt0(xt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1726) ).
fof(m__1709,hypothesis,
( aVector0(xp)
& szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs)
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(xp,X1) = sdtlbdtrb0(xs,X1) )
& xp = sziznziztdt0(xs) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1709) ).
fof(m__,conjecture,
sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mIH,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> iLess0(X1,szszuzczcdt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH) ).
fof(m__1820,hypothesis,
( aScalar0(xE)
& xE = sdtasasdt0(xp,xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1820) ).
fof(m__1783,hypothesis,
( aScalar0(xC)
& xC = sdtasasdt0(xp,xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1783) ).
fof(m__1800,hypothesis,
( aScalar0(xD)
& xD = sdtasasdt0(xq,xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1800) ).
fof(mSuccEqu,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( szszuzczcdt0(X1) = szszuzczcdt0(X2)
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccEqu) ).
fof(m__1678_01,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1678_01) ).
fof(mDimNat,axiom,
! [X1] :
( aVector0(X1)
=> aNaturalNumber0(aDimensionOf0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDimNat) ).
fof(c_0_11,hypothesis,
! [X142,X143] :
( ~ aVector0(X142)
| ~ aVector0(X143)
| aDimensionOf0(X142) != aDimensionOf0(X143)
| ~ iLess0(aDimensionOf0(X142),aDimensionOf0(xs))
| sdtlseqdt0(sdtasdt0(sdtasasdt0(X142,X143),sdtasasdt0(X142,X143)),sdtasdt0(sdtasasdt0(X142,X142),sdtasasdt0(X143,X143))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1652])]) ).
fof(c_0_12,hypothesis,
! [X145] :
( aVector0(xq)
& szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt)
& ( ~ aNaturalNumber0(X145)
| sdtlbdtrb0(xq,X145) = sdtlbdtrb0(xt,X145) )
& xq = sziznziztdt0(xt) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1726])])]) ).
fof(c_0_13,hypothesis,
! [X144] :
( aVector0(xp)
& szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs)
& ( ~ aNaturalNumber0(X144)
| sdtlbdtrb0(xp,X144) = sdtlbdtrb0(xs,X144) )
& xp = sziznziztdt0(xs) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1709])])]) ).
fof(c_0_14,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
fof(c_0_15,plain,
! [X83] :
( ~ aNaturalNumber0(X83)
| iLess0(X83,szszuzczcdt0(X83)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIH])]) ).
cnf(c_0_16,hypothesis,
( sdtlseqdt0(sdtasdt0(sdtasasdt0(X1,X2),sdtasasdt0(X1,X2)),sdtasdt0(sdtasasdt0(X1,X1),sdtasasdt0(X2,X2)))
| ~ aVector0(X1)
| ~ aVector0(X2)
| aDimensionOf0(X1) != aDimensionOf0(X2)
| ~ iLess0(aDimensionOf0(X1),aDimensionOf0(xs)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,hypothesis,
xE = sdtasasdt0(xp,xq),
inference(split_conjunct,[status(thm)],[m__1820]) ).
cnf(c_0_18,hypothesis,
xC = sdtasasdt0(xp,xp),
inference(split_conjunct,[status(thm)],[m__1783]) ).
cnf(c_0_19,hypothesis,
xD = sdtasasdt0(xq,xq),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_20,hypothesis,
aVector0(xq),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,hypothesis,
aVector0(xp),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
( iLess0(X1,szszuzczcdt0(X1))
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,hypothesis,
szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_25,plain,
! [X81,X82] :
( ~ aNaturalNumber0(X81)
| ~ aNaturalNumber0(X82)
| szszuzczcdt0(X81) != szszuzczcdt0(X82)
| X81 = X82 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSuccEqu])]) ).
cnf(c_0_26,hypothesis,
szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_27,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(split_conjunct,[status(thm)],[m__1678_01]) ).
cnf(c_0_28,hypothesis,
( aDimensionOf0(xp) != aDimensionOf0(xq)
| ~ iLess0(aDimensionOf0(xp),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(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19]),c_0_20]),c_0_21])]),c_0_22]) ).
cnf(c_0_29,hypothesis,
( iLess0(aDimensionOf0(xp),aDimensionOf0(xs))
| ~ aNaturalNumber0(aDimensionOf0(xp)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_30,plain,
! [X125] :
( ~ aVector0(X125)
| aNaturalNumber0(aDimensionOf0(X125)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDimNat])]) ).
cnf(c_0_31,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| szszuzczcdt0(X1) != szszuzczcdt0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,hypothesis,
szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xs),
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,hypothesis,
( aDimensionOf0(xp) != aDimensionOf0(xq)
| ~ aNaturalNumber0(aDimensionOf0(xp)) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
( aNaturalNumber0(aDimensionOf0(X1))
| ~ aVector0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,hypothesis,
( X1 = aDimensionOf0(xq)
| szszuzczcdt0(X1) != aDimensionOf0(xs)
| ~ aNaturalNumber0(aDimensionOf0(xq))
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,hypothesis,
aDimensionOf0(xp) != aDimensionOf0(xq),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_21])]) ).
cnf(c_0_37,hypothesis,
( ~ aNaturalNumber0(aDimensionOf0(xq))
| ~ aNaturalNumber0(aDimensionOf0(xp)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_24]),c_0_36]) ).
cnf(c_0_38,hypothesis,
~ aNaturalNumber0(aDimensionOf0(xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_34]),c_0_21])]) ).
cnf(c_0_39,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_34]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG052+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n018.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 01:48:47 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.33/1.74 % Version : CSE_E---1.7
% 1.33/1.74 % Problem : theBenchmark.p
% 1.33/1.74 % SZS status Theorem for theBenchmark.p
% 1.33/1.74 % SZS output start CNFRefutation
% See solution above
% 1.33/1.74 % Total time : 1.372s
%------------------------------------------------------------------------------