%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG052+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 : n006.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 12.17s 8.37s
% Output : CNFRefutation 12.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 14
% Syntax : Number of formulae : 45 ( 21 unt; 0 def)
% Number of atoms : 119 ( 55 equ)
% Maximal formula atoms : 25 ( 2 avg)
% Number of connectives : 120 ( 46 ~; 48 |; 15 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEqInit,axiom,
! [X1,X2] :
( ( aVector0(X1)
& aVector0(X2) )
=> ( ( aDimensionOf0(X1) = aDimensionOf0(X2)
& aDimensionOf0(X2) != sz00 )
=> aDimensionOf0(sziznziztdt0(X1)) = aDimensionOf0(sziznziztdt0(X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEqInit) ).
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__1678,hypothesis,
( aVector0(xs)
& aVector0(xt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678) ).
fof(m__1726,hypothesis,
( aVector0(xq)
& xq = sziznziztdt0(xt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1726) ).
fof(m__1678_01,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678_01) ).
fof(m__1692,hypothesis,
aDimensionOf0(xs) != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1692) ).
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/sandbox2/benchmark/theBenchmark.p',m__1652) ).
fof(m__,conjecture,
sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mDimNat,axiom,
! [X1] :
( aVector0(X1)
=> aNaturalNumber0(aDimensionOf0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDimNat) ).
fof(m__1709,hypothesis,
( aVector0(xp)
& xp = sziznziztdt0(xs) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1709) ).
fof(m__1820,hypothesis,
( aScalar0(xE)
& xE = sdtasasdt0(xp,xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1820) ).
fof(m__1783,hypothesis,
( aScalar0(xC)
& xC = sdtasasdt0(xp,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1783) ).
fof(m__1800,hypothesis,
( aScalar0(xD)
& xD = sdtasasdt0(xq,xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1800) ).
fof(mIH,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> iLess0(X1,szszuzczcdt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).
fof(c_0_14,plain,
! [X131,X132] :
( ~ aVector0(X131)
| ~ aVector0(X132)
| aDimensionOf0(X131) != aDimensionOf0(X132)
| aDimensionOf0(X132) = sz00
| aDimensionOf0(sziznziztdt0(X131)) = aDimensionOf0(sziznziztdt0(X132)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEqInit])]) ).
fof(c_0_15,plain,
! [X126,X127,X128,X129] :
( ( aVector0(X127)
| X127 != sziznziztdt0(X126)
| aDimensionOf0(X126) = sz00
| ~ aVector0(X126) )
& ( szszuzczcdt0(aDimensionOf0(X127)) = aDimensionOf0(X126)
| X127 != sziznziztdt0(X126)
| aDimensionOf0(X126) = sz00
| ~ aVector0(X126) )
& ( ~ aNaturalNumber0(X128)
| sdtlbdtrb0(X127,X128) = sdtlbdtrb0(X126,X128)
| X127 != sziznziztdt0(X126)
| aDimensionOf0(X126) = sz00
| ~ aVector0(X126) )
& ( aNaturalNumber0(esk2_2(X126,X129))
| ~ aVector0(X129)
| szszuzczcdt0(aDimensionOf0(X129)) != aDimensionOf0(X126)
| X129 = sziznziztdt0(X126)
| aDimensionOf0(X126) = sz00
| ~ aVector0(X126) )
& ( sdtlbdtrb0(X129,esk2_2(X126,X129)) != sdtlbdtrb0(X126,esk2_2(X126,X129))
| ~ aVector0(X129)
| szszuzczcdt0(aDimensionOf0(X129)) != aDimensionOf0(X126)
| X129 = sziznziztdt0(X126)
| aDimensionOf0(X126) = sz00
| ~ aVector0(X126) ) ),
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_16,plain,
( aDimensionOf0(X2) = sz00
| aDimensionOf0(sziznziztdt0(X1)) = aDimensionOf0(sziznziztdt0(X2))
| ~ aVector0(X1)
| ~ aVector0(X2)
| aDimensionOf0(X1) != aDimensionOf0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_17,hypothesis,
aVector0(xt),
inference(split_conjunct,[status(thm)],[m__1678]) ).
cnf(c_0_18,hypothesis,
xq = sziznziztdt0(xt),
inference(split_conjunct,[status(thm)],[m__1726]) ).
cnf(c_0_19,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(split_conjunct,[status(thm)],[m__1678_01]) ).
cnf(c_0_20,hypothesis,
aDimensionOf0(xs) != sz00,
inference(split_conjunct,[status(thm)],[m__1692]) ).
fof(c_0_21,hypothesis,
! [X140,X141] :
( ~ aVector0(X140)
| ~ aVector0(X141)
| aDimensionOf0(X140) != aDimensionOf0(X141)
| ~ iLess0(aDimensionOf0(X140),aDimensionOf0(xs))
| sdtlseqdt0(sdtasdt0(sdtasasdt0(X140,X141),sdtasasdt0(X140,X141)),sdtasdt0(sdtasasdt0(X140,X140),sdtasasdt0(X141,X141))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1652])]) ).
fof(c_0_22,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_23,plain,
( szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X2)
| aDimensionOf0(X2) = sz00
| X1 != sziznziztdt0(X2)
| ~ aVector0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_24,plain,
! [X123] :
( ~ aVector0(X123)
| aNaturalNumber0(aDimensionOf0(X123)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDimNat])]) ).
cnf(c_0_25,hypothesis,
( aDimensionOf0(sziznziztdt0(X1)) = aDimensionOf0(xq)
| aDimensionOf0(X1) != aDimensionOf0(xs)
| ~ aVector0(X1) ),
inference(sr,[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_19]),c_0_20]) ).
cnf(c_0_26,hypothesis,
xp = sziznziztdt0(xs),
inference(split_conjunct,[status(thm)],[m__1709]) ).
cnf(c_0_27,hypothesis,
aVector0(xs),
inference(split_conjunct,[status(thm)],[m__1678]) ).
cnf(c_0_28,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_21]) ).
cnf(c_0_29,hypothesis,
xE = sdtasasdt0(xp,xq),
inference(split_conjunct,[status(thm)],[m__1820]) ).
cnf(c_0_30,hypothesis,
xC = sdtasasdt0(xp,xp),
inference(split_conjunct,[status(thm)],[m__1783]) ).
cnf(c_0_31,hypothesis,
xD = sdtasasdt0(xq,xq),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_32,hypothesis,
aVector0(xq),
inference(split_conjunct,[status(thm)],[m__1726]) ).
cnf(c_0_33,hypothesis,
aVector0(xp),
inference(split_conjunct,[status(thm)],[m__1709]) ).
cnf(c_0_34,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_35,plain,
! [X81] :
( ~ aNaturalNumber0(X81)
| iLess0(X81,szszuzczcdt0(X81)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIH])]) ).
cnf(c_0_36,plain,
( szszuzczcdt0(aDimensionOf0(sziznziztdt0(X1))) = aDimensionOf0(X1)
| aDimensionOf0(X1) = sz00
| ~ aVector0(X1) ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_37,plain,
( aNaturalNumber0(aDimensionOf0(X1))
| ~ aVector0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_38,hypothesis,
aDimensionOf0(xp) = aDimensionOf0(xq),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_39,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_28,c_0_29]),c_0_30]),c_0_31]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_40,plain,
( iLess0(X1,szszuzczcdt0(X1))
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_41,hypothesis,
szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xs),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_17]),c_0_18]),c_0_19]),c_0_19]),c_0_20]) ).
cnf(c_0_42,hypothesis,
aNaturalNumber0(aDimensionOf0(xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_33])]) ).
cnf(c_0_43,hypothesis,
~ iLess0(aDimensionOf0(xq),aDimensionOf0(xs)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_38]),c_0_38])]) ).
cnf(c_0_44,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG052+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 : n006.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 01:48:46 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 12.17/8.37 % Version : CSE_E---1.7
% 12.17/8.37 % Problem : theBenchmark.p
% 12.17/8.37 % SZS status Theorem for theBenchmark.p
% 12.17/8.37 % SZS output start CNFRefutation
% See solution above
% 12.27/8.42 % Total time : 6.383s
%------------------------------------------------------------------------------