TSTP Solution File: NUM574+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM574+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n027.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 : Thu Aug 31 10:38:52 EDT 2023
% Result : Theorem 0.21s 0.61s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 66
% Syntax : Number of formulae : 99 ( 12 unt; 55 typ; 0 def)
% Number of atoms : 136 ( 26 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 146 ( 54 ~; 55 |; 23 &)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 85 ( 44 >; 41 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 46 ( 46 usr; 11 con; 0-4 aty)
% Number of variables : 33 ( 0 sgn; 20 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
aSet0: $i > $o ).
tff(decl_23,type,
aElement0: $i > $o ).
tff(decl_24,type,
aElementOf0: ( $i * $i ) > $o ).
tff(decl_25,type,
isFinite0: $i > $o ).
tff(decl_26,type,
slcrc0: $i ).
tff(decl_27,type,
isCountable0: $i > $o ).
tff(decl_28,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(decl_29,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(decl_30,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(decl_31,type,
szNzAzT0: $i ).
tff(decl_32,type,
sz00: $i ).
tff(decl_33,type,
szszuzczcdt0: $i > $i ).
tff(decl_34,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(decl_35,type,
iLess0: ( $i * $i ) > $o ).
tff(decl_36,type,
sbrdtbr0: $i > $i ).
tff(decl_37,type,
szmzizndt0: $i > $i ).
tff(decl_38,type,
szmzazxdt0: $i > $i ).
tff(decl_39,type,
slbdtrb0: $i > $i ).
tff(decl_40,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(decl_41,type,
aFunction0: $i > $o ).
tff(decl_42,type,
szDzozmdt0: $i > $i ).
tff(decl_43,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(decl_44,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(decl_45,type,
sdtlcdtrc0: ( $i * $i ) > $i ).
tff(decl_46,type,
sdtexdt0: ( $i * $i ) > $i ).
tff(decl_47,type,
szDzizrdt0: $i > $i ).
tff(decl_48,type,
xT: $i ).
tff(decl_49,type,
xK: $i ).
tff(decl_50,type,
xS: $i ).
tff(decl_51,type,
xc: $i ).
tff(decl_52,type,
xk: $i ).
tff(decl_53,type,
xN: $i ).
tff(decl_54,type,
xj: $i ).
tff(decl_55,type,
xi: $i ).
tff(decl_56,type,
esk1_1: $i > $i ).
tff(decl_57,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_58,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_59,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_60,type,
esk5_1: $i > $i ).
tff(decl_61,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_62,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_63,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_64,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_65,type,
esk10_1: $i > $i ).
tff(decl_66,type,
esk11_3: ( $i * $i * $i ) > $i ).
tff(decl_67,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_68,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_69,type,
esk14_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_70,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_71,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_72,type,
esk17_3: ( $i * $i * $i ) > $i ).
tff(decl_73,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_74,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_75,type,
esk20_3: ( $i * $i * $i ) > $i ).
tff(decl_76,type,
esk21_3: ( $i * $i * $i ) > $i ).
fof(m__3786_02,hypothesis,
( ( sdtlseqdt0(xj,xi)
& ? [X1] :
( aElementOf0(X1,szNzAzT0)
& szszuzczcdt0(X1) = xi ) )
=> ( sdtlseqdt0(xj,xi)
=> aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3786_02) ).
fof(m__,conjecture,
( sdtlseqdt0(xj,xi)
=> aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mNatExtra,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( X1 = sz00
| ? [X2] :
( aElementOf0(X2,szNzAzT0)
& X1 = szszuzczcdt0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatExtra) ).
fof(mLessASymm,axiom,
! [X1,X2] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X2,szNzAzT0) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessASymm) ).
fof(m__3786,hypothesis,
( aElementOf0(xj,szNzAzT0)
& aElementOf0(xi,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3786) ).
fof(mZeroLess,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> sdtlseqdt0(sz00,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroLess) ).
fof(m__3623,hypothesis,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( ( aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X1)) )
=> ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X1))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3623) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(mSubRefl,axiom,
! [X1] :
( aSet0(X1)
=> aSubsetOf0(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
fof(m__3435,hypothesis,
( aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
fof(mNATSet,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(c_0_11,hypothesis,
! [X178] :
( ~ sdtlseqdt0(xj,xi)
| ~ aElementOf0(X178,szNzAzT0)
| szszuzczcdt0(X178) != xi
| ~ sdtlseqdt0(xj,xi)
| aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3786_02])])]) ).
fof(c_0_12,negated_conjecture,
~ ( sdtlseqdt0(xj,xi)
=> aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_13,hypothesis,
( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
| ~ sdtlseqdt0(xj,xi)
| ~ aElementOf0(X1,szNzAzT0)
| szszuzczcdt0(X1) != xi
| ~ sdtlseqdt0(xj,xi) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_14,negated_conjecture,
( sdtlseqdt0(xj,xi)
& ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ),
inference(fof_nnf,[status(thm)],[c_0_12]) ).
cnf(c_0_15,hypothesis,
( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
| szszuzczcdt0(X1) != xi
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(xj,xi) ),
inference(cn,[status(thm)],[c_0_13]) ).
cnf(c_0_16,negated_conjecture,
sdtlseqdt0(xj,xi),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_17,negated_conjecture,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_18,plain,
! [X57] :
( ( aElementOf0(esk5_1(X57),szNzAzT0)
| X57 = sz00
| ~ aElementOf0(X57,szNzAzT0) )
& ( X57 = szszuzczcdt0(esk5_1(X57))
| X57 = sz00
| ~ aElementOf0(X57,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mNatExtra])])])]) ).
fof(c_0_19,plain,
! [X66,X67] :
( ~ aElementOf0(X66,szNzAzT0)
| ~ aElementOf0(X67,szNzAzT0)
| ~ sdtlseqdt0(X66,X67)
| ~ sdtlseqdt0(X67,X66)
| X66 = X67 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLessASymm])]) ).
cnf(c_0_20,hypothesis,
( szszuzczcdt0(X1) != xi
| ~ aElementOf0(X1,szNzAzT0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]),c_0_17]) ).
cnf(c_0_21,plain,
( X1 = szszuzczcdt0(esk5_1(X1))
| X1 = sz00
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,hypothesis,
aElementOf0(xi,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3786]) ).
cnf(c_0_23,plain,
( X1 = X2
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,hypothesis,
aElementOf0(xj,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3786]) ).
cnf(c_0_25,hypothesis,
( xi = sz00
| ~ aElementOf0(esk5_1(xi),szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21])]),c_0_22])]) ).
cnf(c_0_26,plain,
( aElementOf0(esk5_1(X1),szNzAzT0)
| X1 = sz00
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,negated_conjecture,
( xj = xi
| ~ sdtlseqdt0(xi,xj) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_16]),c_0_24]),c_0_22])]) ).
cnf(c_0_28,hypothesis,
xi = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_22])]) ).
fof(c_0_29,plain,
! [X60] :
( ~ aElementOf0(X60,szNzAzT0)
| sdtlseqdt0(sz00,X60) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroLess])]) ).
cnf(c_0_30,negated_conjecture,
( xj = sz00
| ~ sdtlseqdt0(sz00,xj) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_28]) ).
cnf(c_0_31,plain,
( sdtlseqdt0(sz00,X1)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_32,hypothesis,
! [X174] :
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X174)),sdtmndt0(sdtlpdtrp0(xN,X174),szmzizndt0(sdtlpdtrp0(xN,X174))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X174),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X174))
| ~ aElementOf0(X174,szNzAzT0) )
& ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X174)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X174),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X174))
| ~ aElementOf0(X174,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3623])])])]) ).
fof(c_0_33,plain,
! [X15,X16,X17,X18] :
( ( aSet0(X16)
| ~ aSubsetOf0(X16,X15)
| ~ aSet0(X15) )
& ( ~ aElementOf0(X17,X16)
| aElementOf0(X17,X15)
| ~ aSubsetOf0(X16,X15)
| ~ aSet0(X15) )
& ( aElementOf0(esk2_2(X15,X18),X18)
| ~ aSet0(X18)
| aSubsetOf0(X18,X15)
| ~ aSet0(X15) )
& ( ~ aElementOf0(esk2_2(X15,X18),X15)
| ~ aSet0(X18)
| aSubsetOf0(X18,X15)
| ~ aSet0(X15) ) ),
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)],[mDefSub])])])])])]) ).
cnf(c_0_34,negated_conjecture,
xj = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_24])]) ).
cnf(c_0_35,hypothesis,
sdtlpdtrp0(xN,sz00) = xS,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_36,plain,
! [X22] :
( ~ aSet0(X22)
| aSubsetOf0(X22,X22) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubRefl])]) ).
cnf(c_0_37,plain,
( aSet0(X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,hypothesis,
aSubsetOf0(xS,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3435]) ).
cnf(c_0_39,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
cnf(c_0_40,negated_conjecture,
~ aSubsetOf0(xS,xS),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_34]),c_0_28]),c_0_35]),c_0_35]) ).
cnf(c_0_41,plain,
( aSubsetOf0(X1,X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_42,hypothesis,
aSet0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM574+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 15:40:19 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.56 start to proof: theBenchmark
% 0.21/0.61 % Version : CSE_E---1.5
% 0.21/0.61 % Problem : theBenchmark.p
% 0.21/0.61 % Proof found
% 0.21/0.61 % SZS status Theorem for theBenchmark.p
% 0.21/0.61 % SZS output start Proof
% See solution above
% 0.21/0.61 % Total time : 0.035000 s
% 0.21/0.61 % SZS output end Proof
% 0.21/0.61 % Total time : 0.040000 s
%------------------------------------------------------------------------------