%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG081+2 : 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 : n019.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 05:05:16 PM UTC 2026
% Result : Theorem 1.29s 1.72s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 14 unt; 0 def)
% Number of atoms : 223 ( 123 equ)
% Maximal formula atoms : 75 ( 7 avg)
% Number of connectives : 225 ( 31 ~; 59 |; 123 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 53 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 18 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 14 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( aDimensionOf0(xs) != sz00
=> ? [X1] :
( aVector0(X1)
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(xs)
& ! [X2] :
( aNaturalNumber0(X2)
=> sdtlbdtrb0(X1,X2) = sdtlbdtrb0(xs,X2) )
& X1 = sziznziztdt0(xs)
& ? [X2] :
( aVector0(X2)
& szszuzczcdt0(aDimensionOf0(X2)) = aDimensionOf0(xt)
& ! [X3] :
( aNaturalNumber0(X3)
=> sdtlbdtrb0(X2,X3) = sdtlbdtrb0(xt,X3) )
& X2 = sziznziztdt0(xt)
& ? [X3] :
( aScalar0(X3)
& X3 = sdtlbdtrb0(xs,aDimensionOf0(xs))
& ? [X4] :
( aScalar0(X4)
& X4 = sdtlbdtrb0(xt,aDimensionOf0(xt))
& ? [X5] :
( aScalar0(X5)
& X5 = sdtasasdt0(X1,X1)
& ? [X6] :
( aScalar0(X6)
& X6 = sdtasasdt0(X2,X2)
& ? [X7] :
( aScalar0(X7)
& X7 = sdtasasdt0(X1,X2)
& ? [X8] :
( aScalar0(X8)
& X8 = sdtasdt0(X3,X3)
& ? [X9] :
( aScalar0(X9)
& X9 = sdtasdt0(X4,X4)
& ? [X10] :
( aScalar0(X10)
& X10 = sdtasdt0(X3,X4)
& ? [X11] :
( aScalar0(X11)
& X11 = sdtasdt0(X5,X9)
& ? [X12] :
( aScalar0(X12)
& X12 = sdtasdt0(X7,X10)
& ? [X13] :
( aScalar0(X13)
& X13 = sdtasdt0(X8,X6)
& ? [X14] :
( aScalar0(X14)
& X14 = sdtasdt0(X11,X13)
& sdtlseqdt0(sdtasdt0(X7,X7),sdtasdt0(X5,X6))
& sdtlseqdt0(sdtpldt0(X12,X12),sdtpldt0(X11,X13))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X7,X10),sdtpldt0(X7,X10)),sdtasdt0(sdtpldt0(X5,X8),sdtpldt0(X6,X9)))
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mDefSPZ,axiom,
! [X1,X2] :
( ( aVector0(X1)
& aVector0(X2) )
=> ( ( aDimensionOf0(X1) = aDimensionOf0(X2)
& aDimensionOf0(X2) = sz00 )
=> sdtasasdt0(X1,X2) = sz0z00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSPZ) ).
fof(m__1678_01,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678_01) ).
fof(m__1678,hypothesis,
( aVector0(xs)
& aVector0(xt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678) ).
fof(mScZero,axiom,
! [X1] :
( aScalar0(X1)
=> ( sdtpldt0(X1,sz0z00) = X1
& sdtpldt0(sz0z00,X1) = X1
& sdtasdt0(X1,sz0z00) = sz0z00
& sdtasdt0(sz0z00,X1) = sz0z00
& sdtpldt0(X1,smndt0(X1)) = sz0z00
& sdtpldt0(smndt0(X1),X1) = sz0z00
& smndt0(smndt0(X1)) = X1
& smndt0(sz0z00) = sz0z00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScZero) ).
fof(mSZeroSc,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).
fof(mSqPos,axiom,
! [X1] :
( aScalar0(X1)
=> sdtlseqdt0(sz0z00,sdtasdt0(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSqPos) ).
fof(c_0_7,negated_conjecture,
~ ( ( aDimensionOf0(xs) != sz00
=> ? [X1] :
( aVector0(X1)
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(xs)
& ! [X2] :
( aNaturalNumber0(X2)
=> sdtlbdtrb0(X1,X2) = sdtlbdtrb0(xs,X2) )
& X1 = sziznziztdt0(xs)
& ? [X2] :
( aVector0(X2)
& szszuzczcdt0(aDimensionOf0(X2)) = aDimensionOf0(xt)
& ! [X3] :
( aNaturalNumber0(X3)
=> sdtlbdtrb0(X2,X3) = sdtlbdtrb0(xt,X3) )
& X2 = sziznziztdt0(xt)
& ? [X3] :
( aScalar0(X3)
& X3 = sdtlbdtrb0(xs,aDimensionOf0(xs))
& ? [X4] :
( aScalar0(X4)
& X4 = sdtlbdtrb0(xt,aDimensionOf0(xt))
& ? [X5] :
( aScalar0(X5)
& X5 = sdtasasdt0(X1,X1)
& ? [X6] :
( aScalar0(X6)
& X6 = sdtasasdt0(X2,X2)
& ? [X7] :
( aScalar0(X7)
& X7 = sdtasasdt0(X1,X2)
& ? [X8] :
( aScalar0(X8)
& X8 = sdtasdt0(X3,X3)
& ? [X9] :
( aScalar0(X9)
& X9 = sdtasdt0(X4,X4)
& ? [X10] :
( aScalar0(X10)
& X10 = sdtasdt0(X3,X4)
& ? [X11] :
( aScalar0(X11)
& X11 = sdtasdt0(X5,X9)
& ? [X12] :
( aScalar0(X12)
& X12 = sdtasdt0(X7,X10)
& ? [X13] :
( aScalar0(X13)
& X13 = sdtasdt0(X8,X6)
& ? [X14] :
( aScalar0(X14)
& X14 = sdtasdt0(X11,X13)
& sdtlseqdt0(sdtasdt0(X7,X7),sdtasdt0(X5,X6))
& sdtlseqdt0(sdtpldt0(X12,X12),sdtpldt0(X11,X13))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X7,X10),sdtpldt0(X7,X10)),sdtasdt0(sdtpldt0(X5,X8),sdtpldt0(X6,X9)))
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_8,negated_conjecture,
! [X169,X171] :
( ( aVector0(esk3_0)
| aDimensionOf0(xs) = sz00 )
& ( szszuzczcdt0(aDimensionOf0(esk3_0)) = aDimensionOf0(xs)
| aDimensionOf0(xs) = sz00 )
& ( ~ aNaturalNumber0(X169)
| sdtlbdtrb0(esk3_0,X169) = sdtlbdtrb0(xs,X169)
| aDimensionOf0(xs) = sz00 )
& ( esk3_0 = sziznziztdt0(xs)
| aDimensionOf0(xs) = sz00 )
& ( aVector0(esk4_0)
| aDimensionOf0(xs) = sz00 )
& ( szszuzczcdt0(aDimensionOf0(esk4_0)) = aDimensionOf0(xt)
| aDimensionOf0(xs) = sz00 )
& ( ~ aNaturalNumber0(X171)
| sdtlbdtrb0(esk4_0,X171) = sdtlbdtrb0(xt,X171)
| aDimensionOf0(xs) = sz00 )
& ( esk4_0 = sziznziztdt0(xt)
| aDimensionOf0(xs) = sz00 )
& ( aScalar0(esk5_0)
| aDimensionOf0(xs) = sz00 )
& ( esk5_0 = sdtlbdtrb0(xs,aDimensionOf0(xs))
| aDimensionOf0(xs) = sz00 )
& ( aScalar0(esk6_0)
| aDimensionOf0(xs) = sz00 )
& ( esk6_0 = sdtlbdtrb0(xt,aDimensionOf0(xt))
| aDimensionOf0(xs) = sz00 )
& ( aScalar0(esk7_0)
| aDimensionOf0(xs) = sz00 )
& ( esk7_0 = sdtasasdt0(esk3_0,esk3_0)
| aDimensionOf0(xs) = sz00 )
& ( aScalar0(esk8_0)
| aDimensionOf0(xs) = sz00 )
& ( esk8_0 = sdtasasdt0(esk4_0,esk4_0)
| aDimensionOf0(xs) = sz00 )
& ( aScalar0(esk9_0)
| aDimensionOf0(xs) = sz00 )
& ( esk9_0 = sdtasasdt0(esk3_0,esk4_0)
| aDimensionOf0(xs) = sz00 )
& ( aScalar0(esk10_0)
| aDimensionOf0(xs) = sz00 )
& ( esk10_0 = sdtasdt0(esk5_0,esk5_0)
| aDimensionOf0(xs) = sz00 )
& ( aScalar0(esk11_0)
| aDimensionOf0(xs) = sz00 )
& ( esk11_0 = sdtasdt0(esk6_0,esk6_0)
| aDimensionOf0(xs) = sz00 )
& ( aScalar0(esk12_0)
| aDimensionOf0(xs) = sz00 )
& ( esk12_0 = sdtasdt0(esk5_0,esk6_0)
| aDimensionOf0(xs) = sz00 )
& ( aScalar0(esk13_0)
| aDimensionOf0(xs) = sz00 )
& ( esk13_0 = sdtasdt0(esk7_0,esk11_0)
| aDimensionOf0(xs) = sz00 )
& ( aScalar0(esk14_0)
| aDimensionOf0(xs) = sz00 )
& ( esk14_0 = sdtasdt0(esk9_0,esk12_0)
| aDimensionOf0(xs) = sz00 )
& ( aScalar0(esk15_0)
| aDimensionOf0(xs) = sz00 )
& ( esk15_0 = sdtasdt0(esk10_0,esk8_0)
| aDimensionOf0(xs) = sz00 )
& ( aScalar0(esk16_0)
| aDimensionOf0(xs) = sz00 )
& ( esk16_0 = sdtasdt0(esk13_0,esk15_0)
| aDimensionOf0(xs) = sz00 )
& ( sdtlseqdt0(sdtasdt0(esk9_0,esk9_0),sdtasdt0(esk7_0,esk8_0))
| aDimensionOf0(xs) = sz00 )
& ( sdtlseqdt0(sdtpldt0(esk14_0,esk14_0),sdtpldt0(esk13_0,esk15_0))
| aDimensionOf0(xs) = sz00 )
& ( sdtlseqdt0(sdtasdt0(sdtpldt0(esk9_0,esk12_0),sdtpldt0(esk9_0,esk12_0)),sdtasdt0(sdtpldt0(esk7_0,esk10_0),sdtpldt0(esk8_0,esk11_0)))
| aDimensionOf0(xs) = sz00 )
& ( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
| aDimensionOf0(xs) = sz00 )
& ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).
fof(c_0_9,plain,
! [X161,X162] :
( ~ aVector0(X161)
| ~ aVector0(X162)
| aDimensionOf0(X161) != aDimensionOf0(X162)
| aDimensionOf0(X162) != sz00
| sdtasasdt0(X161,X162) = sz0z00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefSPZ])]) ).
cnf(c_0_10,negated_conjecture,
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
| aDimensionOf0(xs) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( sdtasasdt0(X1,X2) = sz0z00
| ~ aVector0(X1)
| ~ aVector0(X2)
| aDimensionOf0(X1) != aDimensionOf0(X2)
| aDimensionOf0(X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
aDimensionOf0(xs) = sz00,
inference(sr,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(split_conjunct,[status(thm)],[m__1678_01]) ).
cnf(c_0_15,hypothesis,
aVector0(xt),
inference(split_conjunct,[status(thm)],[m__1678]) ).
cnf(c_0_16,hypothesis,
aVector0(xs),
inference(split_conjunct,[status(thm)],[m__1678]) ).
fof(c_0_17,plain,
! [X113] :
( ( sdtpldt0(X113,sz0z00) = X113
| ~ aScalar0(X113) )
& ( sdtpldt0(sz0z00,X113) = X113
| ~ aScalar0(X113) )
& ( sdtasdt0(X113,sz0z00) = sz0z00
| ~ aScalar0(X113) )
& ( sdtasdt0(sz0z00,X113) = sz0z00
| ~ aScalar0(X113) )
& ( sdtpldt0(X113,smndt0(X113)) = sz0z00
| ~ aScalar0(X113) )
& ( sdtpldt0(smndt0(X113),X113) = sz0z00
| ~ aScalar0(X113) )
& ( smndt0(smndt0(X113)) = X113
| ~ aScalar0(X113) )
& ( smndt0(sz0z00) = sz0z00
| ~ aScalar0(X113) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScZero])])]) ).
cnf(c_0_18,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sz0z00,sz0z00),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14]),c_0_13]),c_0_14]),c_0_13]),c_0_15]),c_0_16])]) ).
cnf(c_0_19,plain,
( sdtasdt0(X1,sz0z00) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_20,plain,
aScalar0(sz0z00),
inference(split_conjunct,[status(thm)],[mSZeroSc]) ).
fof(c_0_21,plain,
! [X146] :
( ~ aScalar0(X146)
| sdtlseqdt0(sz0z00,sdtasdt0(X146,X146)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSqPos])]) ).
cnf(c_0_22,negated_conjecture,
~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_23,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(X1,X1))
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_24,plain,
( sdtasdt0(sz0z00,X1) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,negated_conjecture,
~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sz0z00)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_12]),c_0_14]),c_0_13]),c_0_15])]) ).
cnf(c_0_26,plain,
sdtlseqdt0(sz0z00,sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_20])]) ).
cnf(c_0_27,negated_conjecture,
~ aScalar0(sdtasasdt0(xs,xs)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_19]),c_0_26])]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_12]),c_0_20]),c_0_13]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG081+2 : 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
% 0.15/0.32 % Computer : n019.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 01:51:29 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.29/1.72 % Version : CSE_E---1.7
% 1.29/1.72 % Problem : theBenchmark.p
% 1.29/1.72 % SZS status Theorem for theBenchmark.p
% 1.29/1.72 % SZS output start CNFRefutation
% See solution above
% 1.29/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------