%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG047+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 : n023.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 1.29s 1.72s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 14 unt; 0 def)
% Number of atoms : 88 ( 42 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 82 ( 27 ~; 23 |; 20 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 14 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDimNat,axiom,
! [X1] :
( aVector0(X1)
=> aNaturalNumber0(aDimensionOf0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDimNat) ).
fof(mNatExtr,axiom,
! [X1] :
( ( aNaturalNumber0(X1)
& X1 != sz00 )
=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = szszuzczcdt0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatExtr) ).
fof(m__1329_01,hypothesis,
( aDimensionOf0(xs) = aDimensionOf0(xt)
& aDimensionOf0(xt) != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1329_01) ).
fof(m__1329,hypothesis,
( aVector0(xs)
& aVector0(xt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1329) ).
fof(m__,conjecture,
( ( aVector0(sziznziztdt0(xs))
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(sziznziztdt0(xs),X1) = sdtlbdtrb0(xs,X1) ) )
=> ( ( aVector0(sziznziztdt0(xt))
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(sziznziztdt0(xt),X1) = sdtlbdtrb0(xt,X1) ) )
=> aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mSuccEqu,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( szszuzczcdt0(X1) = szszuzczcdt0(X2)
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccEqu) ).
fof(c_0_6,plain,
! [X114] :
( ~ aVector0(X114)
| aNaturalNumber0(aDimensionOf0(X114)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDimNat])]) ).
fof(c_0_7,plain,
! [X68] :
( ( aNaturalNumber0(esk1_1(X68))
| ~ aNaturalNumber0(X68)
| X68 = sz00 )
& ( X68 = szszuzczcdt0(esk1_1(X68))
| ~ aNaturalNumber0(X68)
| X68 = sz00 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mNatExtr])])])]) ).
cnf(c_0_8,plain,
( aNaturalNumber0(aDimensionOf0(X1))
| ~ aVector0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(split_conjunct,[status(thm)],[m__1329_01]) ).
cnf(c_0_10,hypothesis,
aVector0(xs),
inference(split_conjunct,[status(thm)],[m__1329]) ).
fof(c_0_11,negated_conjecture,
~ ( ( aVector0(sziznziztdt0(xs))
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(sziznziztdt0(xs),X1) = sdtlbdtrb0(xs,X1) ) )
=> ( ( aVector0(sziznziztdt0(xt))
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(sziznziztdt0(xt),X1) = sdtlbdtrb0(xt,X1) ) )
=> aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_12,plain,
! [X70,X71] :
( ~ aNaturalNumber0(X70)
| ~ aNaturalNumber0(X71)
| szszuzczcdt0(X70) != szszuzczcdt0(X71)
| X70 = X71 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSuccEqu])]) ).
cnf(c_0_13,plain,
( X1 = szszuzczcdt0(esk1_1(X1))
| X1 = sz00
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,hypothesis,
aNaturalNumber0(aDimensionOf0(xt)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10])]) ).
cnf(c_0_15,hypothesis,
aDimensionOf0(xt) != sz00,
inference(split_conjunct,[status(thm)],[m__1329_01]) ).
cnf(c_0_16,plain,
( aNaturalNumber0(esk1_1(X1))
| X1 = sz00
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_17,negated_conjecture,
! [X122,X123] :
( aVector0(sziznziztdt0(xs))
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& ( ~ aNaturalNumber0(X122)
| sdtlbdtrb0(sziznziztdt0(xs),X122) = sdtlbdtrb0(xs,X122) )
& aVector0(sziznziztdt0(xt))
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)
& ( ~ aNaturalNumber0(X123)
| sdtlbdtrb0(sziznziztdt0(xt),X123) = sdtlbdtrb0(xt,X123) )
& aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
cnf(c_0_18,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| szszuzczcdt0(X1) != szszuzczcdt0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,hypothesis,
szszuzczcdt0(esk1_1(aDimensionOf0(xt))) = aDimensionOf0(xt),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_20,hypothesis,
aNaturalNumber0(esk1_1(aDimensionOf0(xt))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_14]),c_0_15]) ).
cnf(c_0_21,negated_conjecture,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,hypothesis,
( esk1_1(aDimensionOf0(xt)) = X1
| szszuzczcdt0(X1) != aDimensionOf0(xt)
| ~ aNaturalNumber0(X1) ),
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,negated_conjecture,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xt),
inference(rw,[status(thm)],[c_0_21,c_0_9]) ).
cnf(c_0_24,negated_conjecture,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,negated_conjecture,
( esk1_1(aDimensionOf0(xt)) = aDimensionOf0(sziznziztdt0(xs))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
( esk1_1(aDimensionOf0(xt)) = aDimensionOf0(sziznziztdt0(xt))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt))) ),
inference(spm,[status(thm)],[c_0_22,c_0_24]) ).
cnf(c_0_27,negated_conjecture,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_28,negated_conjecture,
( ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_29,negated_conjecture,
aVector0(sziznziztdt0(xs)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_30,negated_conjecture,
~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_8]),c_0_29])]) ).
cnf(c_0_31,negated_conjecture,
aVector0(sziznziztdt0(xt)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_8]),c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG047+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
% 0.15/0.32 % Computer : n023.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
% 0.15/0.32 % DateTime : Tue May 5 01:48:53 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 : 1.371s
%------------------------------------------------------------------------------