%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG047+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 : n004.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 05:05:06 PM UTC 2026
% Result : Theorem 1.28s 1.72s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 14 unt; 0 def)
% Number of atoms : 87 ( 47 equ)
% Maximal formula atoms : 25 ( 2 avg)
% Number of connectives : 93 ( 37 ~; 40 |; 9 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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 : 25 ( 0 sgn 13 !; 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(m__1329,hypothesis,
( aVector0(xs)
& aVector0(xt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1329) ).
fof(m__1329_01,hypothesis,
( aDimensionOf0(xs) = aDimensionOf0(xt)
& aDimensionOf0(xt) != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1329_01) ).
fof(mDimNat,axiom,
! [X1] :
( aVector0(X1)
=> aNaturalNumber0(aDimensionOf0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDimNat) ).
fof(mSuccEqu,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( szszuzczcdt0(X1) = szszuzczcdt0(X2)
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccEqu) ).
fof(m__,conjecture,
aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(c_0_6,plain,
! [X115,X116,X117,X118] :
( ( aVector0(X116)
| X116 != sziznziztdt0(X115)
| aDimensionOf0(X115) = sz00
| ~ aVector0(X115) )
& ( szszuzczcdt0(aDimensionOf0(X116)) = aDimensionOf0(X115)
| X116 != sziznziztdt0(X115)
| aDimensionOf0(X115) = sz00
| ~ aVector0(X115) )
& ( ~ aNaturalNumber0(X117)
| sdtlbdtrb0(X116,X117) = sdtlbdtrb0(X115,X117)
| X116 != sziznziztdt0(X115)
| aDimensionOf0(X115) = sz00
| ~ aVector0(X115) )
& ( aNaturalNumber0(esk2_2(X115,X118))
| ~ aVector0(X118)
| szszuzczcdt0(aDimensionOf0(X118)) != aDimensionOf0(X115)
| X118 = sziznziztdt0(X115)
| aDimensionOf0(X115) = sz00
| ~ aVector0(X115) )
& ( sdtlbdtrb0(X118,esk2_2(X115,X118)) != sdtlbdtrb0(X115,esk2_2(X115,X118))
| ~ aVector0(X118)
| szszuzczcdt0(aDimensionOf0(X118)) != aDimensionOf0(X115)
| X118 = sziznziztdt0(X115)
| aDimensionOf0(X115) = sz00
| ~ aVector0(X115) ) ),
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])])])])])]) ).
cnf(c_0_7,plain,
( aVector0(X1)
| aDimensionOf0(X2) = sz00
| X1 != sziznziztdt0(X2)
| ~ aVector0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_8,hypothesis,
aVector0(xt),
inference(split_conjunct,[status(thm)],[m__1329]) ).
cnf(c_0_9,hypothesis,
aDimensionOf0(xt) != sz00,
inference(split_conjunct,[status(thm)],[m__1329_01]) ).
cnf(c_0_10,plain,
( szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X2)
| aDimensionOf0(X2) = sz00
| X1 != sziznziztdt0(X2)
| ~ aVector0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,plain,
! [X112] :
( ~ aVector0(X112)
| aNaturalNumber0(aDimensionOf0(X112)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDimNat])]) ).
cnf(c_0_12,hypothesis,
( aVector0(X1)
| X1 != sziznziztdt0(xt) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).
cnf(c_0_13,hypothesis,
aVector0(xs),
inference(split_conjunct,[status(thm)],[m__1329]) ).
cnf(c_0_14,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(split_conjunct,[status(thm)],[m__1329_01]) ).
fof(c_0_15,plain,
! [X68,X69] :
( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X69)
| szszuzczcdt0(X68) != szszuzczcdt0(X69)
| X68 = X69 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSuccEqu])]) ).
cnf(c_0_16,hypothesis,
( szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(xt)
| X1 != sziznziztdt0(xt) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_8]),c_0_9]) ).
cnf(c_0_17,plain,
( aNaturalNumber0(aDimensionOf0(X1))
| ~ aVector0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,hypothesis,
aVector0(sziznziztdt0(xt)),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_19,hypothesis,
( aVector0(X1)
| X1 != sziznziztdt0(xs) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_13]),c_0_14]),c_0_9]) ).
cnf(c_0_20,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| szszuzczcdt0(X1) != szszuzczcdt0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,hypothesis,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_22,hypothesis,
aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt))),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,hypothesis,
( szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(xt)
| X1 != sziznziztdt0(xs) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_13]),c_0_14]),c_0_14]),c_0_9]) ).
cnf(c_0_24,hypothesis,
aVector0(sziznziztdt0(xs)),
inference(er,[status(thm)],[c_0_19]) ).
fof(c_0_25,negated_conjecture,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_26,hypothesis,
( aDimensionOf0(sziznziztdt0(xt)) = X1
| szszuzczcdt0(X1) != aDimensionOf0(xt)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_27,hypothesis,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xt),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_28,hypothesis,
aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))),
inference(spm,[status(thm)],[c_0_17,c_0_24]) ).
cnf(c_0_29,negated_conjecture,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG047+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
% 0.15/0.33 % Computer : n004.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 01:48:02 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.28/1.72 % Version : CSE_E---1.7
% 1.28/1.72 % Problem : theBenchmark.p
% 1.28/1.72 % SZS status Theorem for theBenchmark.p
% 1.28/1.72 % SZS output start CNFRefutation
% See solution above
% 1.28/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------