TSTP Solution File: NUM612+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM612+3 : 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 : n002.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 10:39:17 EDT 2023
% Result : Theorem 4.27s 4.36s
% Output : CNFRefutation 4.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 101
% Syntax : Number of formulae : 131 ( 15 unt; 92 typ; 0 def)
% Number of atoms : 114 ( 22 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 115 ( 40 ~; 34 |; 30 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 141 ( 74 >; 67 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-2 aty)
% Number of functors : 79 ( 79 usr; 18 con; 0-4 aty)
% Number of variables : 27 ( 0 sgn; 20 !; 0 ?; 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,
xC: $i ).
tff(decl_55,type,
xe: $i ).
tff(decl_56,type,
xd: $i ).
tff(decl_57,type,
xO: $i ).
tff(decl_58,type,
xQ: $i ).
tff(decl_59,type,
xp: $i ).
tff(decl_60,type,
xP: $i ).
tff(decl_61,type,
epred1_1: $i > $o ).
tff(decl_62,type,
epred2_1: $i > $o ).
tff(decl_63,type,
epred3_1: $i > $o ).
tff(decl_64,type,
epred4_1: $i > $o ).
tff(decl_65,type,
esk1_1: $i > $i ).
tff(decl_66,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_67,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_68,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_69,type,
esk5_1: $i > $i ).
tff(decl_70,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_71,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_72,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_73,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_74,type,
esk10_1: $i > $i ).
tff(decl_75,type,
esk11_3: ( $i * $i * $i ) > $i ).
tff(decl_76,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_77,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_78,type,
esk14_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_79,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_80,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_81,type,
esk17_3: ( $i * $i * $i ) > $i ).
tff(decl_82,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_83,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_84,type,
esk20_1: $i > $i ).
tff(decl_85,type,
esk21_1: $i > $i ).
tff(decl_86,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_87,type,
esk23_3: ( $i * $i * $i ) > $i ).
tff(decl_88,type,
esk24_3: ( $i * $i * $i ) > $i ).
tff(decl_89,type,
esk25_3: ( $i * $i * $i ) > $i ).
tff(decl_90,type,
esk26_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_91,type,
esk27_3: ( $i * $i * $i ) > $i ).
tff(decl_92,type,
esk28_3: ( $i * $i * $i ) > $i ).
tff(decl_93,type,
esk29_3: ( $i * $i * $i ) > $i ).
tff(decl_94,type,
esk30_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_95,type,
esk31_1: $i > $i ).
tff(decl_96,type,
esk32_2: ( $i * $i ) > $i ).
tff(decl_97,type,
esk33_2: ( $i * $i ) > $i ).
tff(decl_98,type,
esk34_1: $i > $i ).
tff(decl_99,type,
esk35_2: ( $i * $i ) > $i ).
tff(decl_100,type,
esk36_2: ( $i * $i ) > $i ).
tff(decl_101,type,
esk37_1: $i > $i ).
tff(decl_102,type,
esk38_1: $i > $i ).
tff(decl_103,type,
esk39_1: $i > $i ).
tff(decl_104,type,
esk40_0: $i ).
tff(decl_105,type,
esk41_0: $i ).
tff(decl_106,type,
esk42_2: ( $i * $i ) > $i ).
tff(decl_107,type,
esk43_2: ( $i * $i ) > $i ).
tff(decl_108,type,
esk44_2: ( $i * $i ) > $i ).
tff(decl_109,type,
esk45_2: ( $i * $i ) > $i ).
tff(decl_110,type,
esk46_3: ( $i * $i * $i ) > $i ).
tff(decl_111,type,
esk47_1: $i > $i ).
tff(decl_112,type,
esk48_1: $i > $i ).
tff(decl_113,type,
esk49_2: ( $i * $i ) > $i ).
fof(mCardNum,axiom,
! [X1] :
( aSet0(X1)
=> ( aElementOf0(sbrdtbr0(X1),szNzAzT0)
<=> isFinite0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardNum) ).
fof(m__5078,hypothesis,
( aSet0(xQ)
& ! [X1] :
( aElementOf0(X1,xQ)
=> aElementOf0(X1,xO) )
& aSubsetOf0(xQ,xO)
& sbrdtbr0(xQ) = xK
& aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5078) ).
fof(m__,conjecture,
( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ)
& aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__5164,hypothesis,
( aSet0(xP)
& ! [X1] :
( aElementOf0(X1,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),X1) )
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( aElement0(X1)
& aElementOf0(X1,xQ)
& X1 != szmzizndt0(xQ) ) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5164) ).
fof(m__5147,hypothesis,
( aElementOf0(xp,xQ)
& ! [X1] :
( aElementOf0(X1,xQ)
=> sdtlseqdt0(xp,X1) )
& xp = szmzizndt0(xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5147) ).
fof(mSubFSet,axiom,
! [X1] :
( ( aSet0(X1)
& isFinite0(X1) )
=> ! [X2] :
( aSubsetOf0(X2,X1)
=> isFinite0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubFSet) ).
fof(m__3418,hypothesis,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).
fof(mCardDiff,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( ( isFinite0(X1)
& aElementOf0(X2,X1) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardDiff) ).
fof(m__5195,hypothesis,
( ! [X1] :
( aElementOf0(X1,xP)
=> aElementOf0(X1,xQ) )
& aSubsetOf0(xP,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5195) ).
fof(c_0_9,plain,
! [X76] :
( ( ~ aElementOf0(sbrdtbr0(X76),szNzAzT0)
| isFinite0(X76)
| ~ aSet0(X76) )
& ( ~ isFinite0(X76)
| aElementOf0(sbrdtbr0(X76),szNzAzT0)
| ~ aSet0(X76) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardNum])])]) ).
fof(c_0_10,hypothesis,
! [X246] :
( aSet0(xQ)
& ( ~ aElementOf0(X246,xQ)
| aElementOf0(X246,xO) )
& aSubsetOf0(xQ,xO)
& sbrdtbr0(xQ) = xK
& aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__5078])])]) ).
fof(c_0_11,negated_conjecture,
~ ( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ)
& aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_12,hypothesis,
! [X253,X254] :
( aSet0(xP)
& ( ~ aElementOf0(X253,xQ)
| sdtlseqdt0(szmzizndt0(xQ),X253) )
& ( aElement0(X254)
| ~ aElementOf0(X254,xP) )
& ( aElementOf0(X254,xQ)
| ~ aElementOf0(X254,xP) )
& ( X254 != szmzizndt0(xQ)
| ~ aElementOf0(X254,xP) )
& ( ~ aElement0(X254)
| ~ aElementOf0(X254,xQ)
| X254 = szmzizndt0(xQ)
| aElementOf0(X254,xP) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__5164])])])]) ).
fof(c_0_13,hypothesis,
! [X252] :
( aElementOf0(xp,xQ)
& ( ~ aElementOf0(X252,xQ)
| sdtlseqdt0(xp,X252) )
& xp = szmzizndt0(xQ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__5147])])]) ).
fof(c_0_14,plain,
! [X21,X22] :
( ~ aSet0(X21)
| ~ isFinite0(X21)
| ~ aSubsetOf0(X22,X21)
| isFinite0(X22) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubFSet])])]) ).
cnf(c_0_15,plain,
( isFinite0(X1)
| ~ aElementOf0(sbrdtbr0(X1),szNzAzT0)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,hypothesis,
sbrdtbr0(xQ) = xK,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,hypothesis,
aElementOf0(xK,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3418]) ).
cnf(c_0_18,hypothesis,
aSet0(xQ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_19,negated_conjecture,
( szszuzczcdt0(sbrdtbr0(xP)) != sbrdtbr0(xQ)
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(fof_nnf,[status(thm)],[c_0_11]) ).
fof(c_0_20,plain,
! [X80,X81] :
( ~ aSet0(X80)
| ~ isFinite0(X80)
| ~ aElementOf0(X81,X80)
| szszuzczcdt0(sbrdtbr0(sdtmndt0(X80,X81))) = sbrdtbr0(X80) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardDiff])])]) ).
cnf(c_0_21,hypothesis,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_22,hypothesis,
xp = szmzizndt0(xQ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_23,plain,
( isFinite0(X2)
| ~ aSet0(X1)
| ~ isFinite0(X1)
| ~ aSubsetOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,hypothesis,
isFinite0(xQ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18])]) ).
fof(c_0_25,hypothesis,
! [X256] :
( ( ~ aElementOf0(X256,xP)
| aElementOf0(X256,xQ) )
& aSubsetOf0(xP,xQ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__5195])])]) ).
cnf(c_0_26,negated_conjecture,
( szszuzczcdt0(sbrdtbr0(xP)) != sbrdtbr0(xQ)
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1)
| ~ aSet0(X1)
| ~ isFinite0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,hypothesis,
sdtmndt0(xQ,xp) = xP,
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,hypothesis,
aElementOf0(xp,xQ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_30,hypothesis,
( isFinite0(X1)
| ~ aSubsetOf0(X1,xQ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_18])]) ).
cnf(c_0_31,hypothesis,
aSubsetOf0(xP,xQ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,negated_conjecture,
( szszuzczcdt0(sbrdtbr0(xP)) != xK
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(rw,[status(thm)],[c_0_26,c_0_16]) ).
cnf(c_0_33,hypothesis,
szszuzczcdt0(sbrdtbr0(xP)) = xK,
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_27,c_0_28]),c_0_16]),c_0_24]),c_0_29]),c_0_18])]) ).
cnf(c_0_34,plain,
( aElementOf0(sbrdtbr0(X1),szNzAzT0)
| ~ isFinite0(X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_35,hypothesis,
isFinite0(xP),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,hypothesis,
aSet0(xP),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_37,negated_conjecture,
~ aElementOf0(sbrdtbr0(xP),szNzAzT0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]) ).
cnf(c_0_38,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM612+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 10:51:17 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 4.27/4.36 % Version : CSE_E---1.5
% 4.27/4.36 % Problem : theBenchmark.p
% 4.27/4.36 % Proof found
% 4.27/4.36 % SZS status Theorem for theBenchmark.p
% 4.27/4.36 % SZS output start Proof
% See solution above
% 4.27/4.37 % Total time : 3.778000 s
% 4.27/4.37 % SZS output end Proof
% 4.27/4.37 % Total time : 3.788000 s
%------------------------------------------------------------------------------