TSTP Solution File: NUM609+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM609+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n015.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 10:39:13 EDT 2023
% Result : Theorem 0.20s 0.70s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 75
% Syntax : Number of formulae : 103 ( 18 unt; 64 typ; 0 def)
% Number of atoms : 154 ( 29 equ)
% Maximal formula atoms : 54 ( 3 avg)
% Number of connectives : 195 ( 80 ~; 87 |; 18 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 89 ( 48 >; 41 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 55 ( 55 usr; 16 con; 0-4 aty)
% Number of variables : 47 ( 0 sgn; 25 !; 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,
esk1_1: $i > $i ).
tff(decl_62,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_63,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_64,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_65,type,
esk5_1: $i > $i ).
tff(decl_66,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_67,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_68,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_69,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_70,type,
esk10_1: $i > $i ).
tff(decl_71,type,
esk11_3: ( $i * $i * $i ) > $i ).
tff(decl_72,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_73,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_74,type,
esk14_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_75,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_76,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_77,type,
esk17_3: ( $i * $i * $i ) > $i ).
tff(decl_78,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_79,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_80,type,
esk20_3: ( $i * $i * $i ) > $i ).
tff(decl_81,type,
esk21_3: ( $i * $i * $i ) > $i ).
tff(decl_82,type,
esk22_1: $i > $i ).
tff(decl_83,type,
esk23_1: $i > $i ).
tff(decl_84,type,
esk24_1: $i > $i ).
tff(decl_85,type,
esk25_1: $i > $i ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(mDefCons,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aElement0(X2) )
=> ! [X3] :
( X3 = sdtpldt0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aElement0(X4)
& ( aElementOf0(X4,X1)
| X4 = X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefCons) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(mConsDiff,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> sdtpldt0(sdtmndt0(X1,X2),X2) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mConsDiff) ).
fof(m__5164,hypothesis,
( aSet0(xP)
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5164) ).
fof(m__5147,hypothesis,
xp = szmzizndt0(xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5147) ).
fof(m__5093,hypothesis,
( aSubsetOf0(xQ,xO)
& xQ != slcrc0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5093) ).
fof(m__4891,hypothesis,
( aSet0(xO)
& xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4891) ).
fof(m__5173,hypothesis,
aElementOf0(xp,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5173) ).
fof(m__5182,hypothesis,
aElementOf0(xp,xO),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5182) ).
fof(m__,conjecture,
aSubsetOf0(xP,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(c_0_11,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])])])])])]) ).
fof(c_0_12,plain,
! [X28,X29,X30,X31,X32,X33] :
( ( aSet0(X30)
| X30 != sdtpldt0(X28,X29)
| ~ aSet0(X28)
| ~ aElement0(X29) )
& ( aElement0(X31)
| ~ aElementOf0(X31,X30)
| X30 != sdtpldt0(X28,X29)
| ~ aSet0(X28)
| ~ aElement0(X29) )
& ( aElementOf0(X31,X28)
| X31 = X29
| ~ aElementOf0(X31,X30)
| X30 != sdtpldt0(X28,X29)
| ~ aSet0(X28)
| ~ aElement0(X29) )
& ( ~ aElementOf0(X32,X28)
| ~ aElement0(X32)
| aElementOf0(X32,X30)
| X30 != sdtpldt0(X28,X29)
| ~ aSet0(X28)
| ~ aElement0(X29) )
& ( X32 != X29
| ~ aElement0(X32)
| aElementOf0(X32,X30)
| X30 != sdtpldt0(X28,X29)
| ~ aSet0(X28)
| ~ aElement0(X29) )
& ( ~ aElementOf0(esk3_3(X28,X29,X33),X28)
| ~ aElement0(esk3_3(X28,X29,X33))
| ~ aElementOf0(esk3_3(X28,X29,X33),X33)
| ~ aSet0(X33)
| X33 = sdtpldt0(X28,X29)
| ~ aSet0(X28)
| ~ aElement0(X29) )
& ( esk3_3(X28,X29,X33) != X29
| ~ aElement0(esk3_3(X28,X29,X33))
| ~ aElementOf0(esk3_3(X28,X29,X33),X33)
| ~ aSet0(X33)
| X33 = sdtpldt0(X28,X29)
| ~ aSet0(X28)
| ~ aElement0(X29) )
& ( aElement0(esk3_3(X28,X29,X33))
| aElementOf0(esk3_3(X28,X29,X33),X33)
| ~ aSet0(X33)
| X33 = sdtpldt0(X28,X29)
| ~ aSet0(X28)
| ~ aElement0(X29) )
& ( aElementOf0(esk3_3(X28,X29,X33),X28)
| esk3_3(X28,X29,X33) = X29
| aElementOf0(esk3_3(X28,X29,X33),X33)
| ~ aSet0(X33)
| X33 = sdtpldt0(X28,X29)
| ~ aSet0(X28)
| ~ aElement0(X29) ) ),
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)],[mDefCons])])])])])]) ).
fof(c_0_13,plain,
! [X7,X8] :
( ~ aSet0(X7)
| ~ aElementOf0(X8,X7)
| aElement0(X8) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
fof(c_0_14,plain,
! [X42,X43] :
( ~ aSet0(X42)
| ~ aElementOf0(X43,X42)
| sdtpldt0(sdtmndt0(X42,X43),X43) = X42 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mConsDiff])])]) ).
cnf(c_0_15,hypothesis,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(split_conjunct,[status(thm)],[m__5164]) ).
cnf(c_0_16,hypothesis,
xp = szmzizndt0(xQ),
inference(split_conjunct,[status(thm)],[m__5147]) ).
cnf(c_0_17,plain,
( aSet0(X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,hypothesis,
aSubsetOf0(xQ,xO),
inference(split_conjunct,[status(thm)],[m__5093]) ).
cnf(c_0_19,hypothesis,
aSet0(xO),
inference(split_conjunct,[status(thm)],[m__4891]) ).
cnf(c_0_20,plain,
( aElementOf0(X1,X3)
| ~ aElementOf0(X1,X2)
| ~ aElement0(X1)
| X3 != sdtpldt0(X2,X4)
| ~ aSet0(X2)
| ~ aElement0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,plain,
( sdtpldt0(sdtmndt0(X1,X2),X2) = X1
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,hypothesis,
aElementOf0(xp,xQ),
inference(split_conjunct,[status(thm)],[m__5173]) ).
cnf(c_0_24,hypothesis,
sdtmndt0(xQ,xp) = xP,
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_25,hypothesis,
aSet0(xQ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
cnf(c_0_26,hypothesis,
aElementOf0(xp,xO),
inference(split_conjunct,[status(thm)],[m__5182]) ).
cnf(c_0_27,plain,
( aElementOf0(X1,X2)
| X2 != sdtpldt0(X3,X4)
| ~ aElementOf0(X1,X3)
| ~ aElement0(X4)
| ~ aSet0(X3) ),
inference(csr,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,hypothesis,
sdtpldt0(xP,xp) = xQ,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]) ).
cnf(c_0_29,hypothesis,
aElement0(xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_26]),c_0_19])]) ).
cnf(c_0_30,hypothesis,
aSet0(xP),
inference(split_conjunct,[status(thm)],[m__5164]) ).
cnf(c_0_31,hypothesis,
( aElementOf0(X1,X2)
| X2 != xQ
| ~ aElementOf0(X1,xP) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30])]) ).
cnf(c_0_32,hypothesis,
( aElementOf0(X1,xQ)
| ~ aElementOf0(X1,xP) ),
inference(er,[status(thm)],[c_0_31]) ).
cnf(c_0_33,plain,
( aElementOf0(esk2_2(X1,X2),X2)
| aSubsetOf0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_34,negated_conjecture,
~ aSubsetOf0(xP,xQ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_35,plain,
( aSubsetOf0(X2,X1)
| ~ aElementOf0(esk2_2(X1,X2),X1)
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_36,hypothesis,
( aSubsetOf0(xP,X1)
| aElementOf0(esk2_2(X1,xP),xQ)
| ~ aSet0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_30])]) ).
cnf(c_0_37,negated_conjecture,
~ aSubsetOf0(xP,xQ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_38,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_30]),c_0_25])]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM609+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n015.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 18:10:52 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.20/0.70 % Version : CSE_E---1.5
% 0.20/0.70 % Problem : theBenchmark.p
% 0.20/0.70 % Proof found
% 0.20/0.70 % SZS status Theorem for theBenchmark.p
% 0.20/0.70 % SZS output start Proof
% See solution above
% 0.20/0.71 % Total time : 0.110000 s
% 0.20/0.71 % SZS output end Proof
% 0.20/0.71 % Total time : 0.114000 s
%------------------------------------------------------------------------------