TSTP Solution File: NUM556+3 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM556+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 : n019.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 10:38:40 EDT 2023
% Result : Theorem 0.19s 0.63s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 55
% Syntax : Number of formulae : 103 ( 22 unt; 42 typ; 0 def)
% Number of atoms : 198 ( 41 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 209 ( 72 ~; 66 |; 52 &)
% ( 4 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 48 ( 30 >; 18 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 34 ( 34 usr; 12 con; 0-3 aty)
% Number of variables : 47 ( 0 sgn; 33 !; 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,
xk: $i ).
tff(decl_42,type,
xS: $i ).
tff(decl_43,type,
xT: $i ).
tff(decl_44,type,
xx: $i ).
tff(decl_45,type,
xQ: $i ).
tff(decl_46,type,
xy: $i ).
tff(decl_47,type,
xP: $i ).
tff(decl_48,type,
esk1_1: $i > $i ).
tff(decl_49,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_51,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_52,type,
esk5_1: $i > $i ).
tff(decl_53,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_56,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_57,type,
esk10_1: $i > $i ).
tff(decl_58,type,
esk11_3: ( $i * $i * $i ) > $i ).
tff(decl_59,type,
esk12_1: $i > $i ).
tff(decl_60,type,
esk13_1: $i > $i ).
tff(decl_61,type,
esk14_1: $i > $i ).
tff(decl_62,type,
esk15_0: $i ).
tff(decl_63,type,
esk16_0: $i ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__2357,hypothesis,
( aSet0(sdtmndt0(xQ,xy))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(xQ,xy))
<=> ( aElement0(X1)
& aElementOf0(X1,xQ)
& X1 != xy ) )
& aSet0(xP)
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( aElement0(X1)
& ( aElementOf0(X1,sdtmndt0(xQ,xy))
| X1 = xx ) ) )
& xP = sdtpldt0(sdtmndt0(xQ,xy),xx) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2357) ).
fof(m__2256,hypothesis,
aElementOf0(xx,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2256) ).
fof(m__2202_02,hypothesis,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).
fof(mDiffCons,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aSet0(X2) )
=> ( ~ aElementOf0(X1,X2)
=> sdtmndt0(sdtpldt0(X2,X1),X1) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDiffCons) ).
fof(m__2411,hypothesis,
( ~ aElementOf0(xx,sdtmndt0(xQ,xy))
& aSet0(sdtmndt0(xQ,xy))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(xQ,xy))
<=> ( aElement0(X1)
& aElementOf0(X1,xQ)
& X1 != xy ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2411) ).
fof(mFConsSet,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( ( aSet0(X2)
& isFinite0(X2) )
=> isFinite0(sdtpldt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFConsSet) ).
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__2270,hypothesis,
( aSet0(xQ)
& ! [X1] :
( aElementOf0(X1,xQ)
=> aElementOf0(X1,xS) )
& aSubsetOf0(xQ,xS)
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2270) ).
fof(mFDiffSet,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( ( aSet0(X2)
& isFinite0(X2) )
=> isFinite0(sdtmndt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFDiffSet) ).
fof(m__,conjecture,
( ( ! [X1] :
( aElementOf0(X1,xP)
=> aElementOf0(X1,xS) )
| aSubsetOf0(xP,xS) )
& sbrdtbr0(xP) = xk ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__2304,hypothesis,
( aElement0(xy)
& aElementOf0(xy,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2304) ).
fof(m__2291,hypothesis,
( aSet0(xQ)
& isFinite0(xQ)
& sbrdtbr0(xQ) = xk ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2291) ).
fof(c_0_13,plain,
! [X5,X6] :
( ~ aSet0(X5)
| ~ aElementOf0(X6,X5)
| aElement0(X6) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
fof(c_0_14,hypothesis,
! [X138,X139] :
( aSet0(sdtmndt0(xQ,xy))
& ( aElement0(X138)
| ~ aElementOf0(X138,sdtmndt0(xQ,xy)) )
& ( aElementOf0(X138,xQ)
| ~ aElementOf0(X138,sdtmndt0(xQ,xy)) )
& ( X138 != xy
| ~ aElementOf0(X138,sdtmndt0(xQ,xy)) )
& ( ~ aElement0(X138)
| ~ aElementOf0(X138,xQ)
| X138 = xy
| aElementOf0(X138,sdtmndt0(xQ,xy)) )
& aSet0(xP)
& ( aElement0(X139)
| ~ aElementOf0(X139,xP) )
& ( aElementOf0(X139,sdtmndt0(xQ,xy))
| X139 = xx
| ~ aElementOf0(X139,xP) )
& ( ~ aElementOf0(X139,sdtmndt0(xQ,xy))
| ~ aElement0(X139)
| aElementOf0(X139,xP) )
& ( X139 != xx
| ~ aElement0(X139)
| aElementOf0(X139,xP) )
& xP = sdtpldt0(sdtmndt0(xQ,xy),xx) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2357])])])]) ).
cnf(c_0_15,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,hypothesis,
aElementOf0(xx,xS),
inference(split_conjunct,[status(thm)],[m__2256]) ).
cnf(c_0_17,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[m__2202_02]) ).
fof(c_0_18,plain,
! [X1,X2] :
( ( aElement0(X1)
& aSet0(X2) )
=> ( ~ aElementOf0(X1,X2)
=> sdtmndt0(sdtpldt0(X2,X1),X1) = X2 ) ),
inference(fof_simplification,[status(thm)],[mDiffCons]) ).
fof(c_0_19,hypothesis,
( ~ aElementOf0(xx,sdtmndt0(xQ,xy))
& aSet0(sdtmndt0(xQ,xy))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(xQ,xy))
<=> ( aElement0(X1)
& aElementOf0(X1,xQ)
& X1 != xy ) ) ),
inference(fof_simplification,[status(thm)],[m__2411]) ).
fof(c_0_20,plain,
! [X48,X49] :
( ~ aElement0(X48)
| ~ aSet0(X49)
| ~ isFinite0(X49)
| isFinite0(sdtpldt0(X49,X48)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mFConsSet])])]) ).
fof(c_0_21,plain,
! [X77,X78] :
( ~ aSet0(X77)
| ~ isFinite0(X77)
| ~ aElementOf0(X78,X77)
| szszuzczcdt0(sbrdtbr0(sdtmndt0(X77,X78))) = sbrdtbr0(X77) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardDiff])])]) ).
cnf(c_0_22,hypothesis,
( aElementOf0(X1,xP)
| X1 != xx
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,hypothesis,
aElement0(xx),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
fof(c_0_24,plain,
! [X42,X43] :
( ~ aElement0(X42)
| ~ aSet0(X43)
| aElementOf0(X42,X43)
| sdtmndt0(sdtpldt0(X43,X42),X42) = X43 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])]) ).
fof(c_0_25,hypothesis,
! [X140] :
( ~ aElementOf0(xx,sdtmndt0(xQ,xy))
& aSet0(sdtmndt0(xQ,xy))
& ( aElement0(X140)
| ~ aElementOf0(X140,sdtmndt0(xQ,xy)) )
& ( aElementOf0(X140,xQ)
| ~ aElementOf0(X140,sdtmndt0(xQ,xy)) )
& ( X140 != xy
| ~ aElementOf0(X140,sdtmndt0(xQ,xy)) )
& ( ~ aElement0(X140)
| ~ aElementOf0(X140,xQ)
| X140 = xy
| aElementOf0(X140,sdtmndt0(xQ,xy)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])]) ).
fof(c_0_26,hypothesis,
! [X137] :
( aSet0(xQ)
& ( ~ aElementOf0(X137,xQ)
| aElementOf0(X137,xS) )
& aSubsetOf0(xQ,xS)
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2270])])]) ).
cnf(c_0_27,plain,
( isFinite0(sdtpldt0(X2,X1))
| ~ aElement0(X1)
| ~ aSet0(X2)
| ~ isFinite0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,hypothesis,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_29,hypothesis,
aSet0(sdtmndt0(xQ,xy)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_30,plain,
! [X50,X51] :
( ~ aElement0(X50)
| ~ aSet0(X51)
| ~ isFinite0(X51)
| isFinite0(sdtmndt0(X51,X50)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mFDiffSet])])]) ).
fof(c_0_31,negated_conjecture,
~ ( ( ! [X1] :
( aElementOf0(X1,xP)
=> aElementOf0(X1,xS) )
| aSubsetOf0(xP,xS) )
& sbrdtbr0(xP) = xk ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_32,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1)
| ~ aSet0(X1)
| ~ isFinite0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_33,hypothesis,
aElementOf0(xx,xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_22]),c_0_23])]) ).
cnf(c_0_34,hypothesis,
aSet0(xP),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_35,plain,
( aElementOf0(X1,X2)
| sdtmndt0(sdtpldt0(X2,X1),X1) = X2
| ~ aElement0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_36,hypothesis,
~ aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_37,hypothesis,
aElementOf0(xy,xQ),
inference(split_conjunct,[status(thm)],[m__2304]) ).
cnf(c_0_38,hypothesis,
sbrdtbr0(xQ) = xk,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_39,hypothesis,
isFinite0(xQ),
inference(split_conjunct,[status(thm)],[m__2291]) ).
cnf(c_0_40,hypothesis,
aSet0(xQ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_41,hypothesis,
( isFinite0(xP)
| ~ isFinite0(sdtmndt0(xQ,xy)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]),c_0_23])]) ).
cnf(c_0_42,plain,
( isFinite0(sdtmndt0(X2,X1))
| ~ aElement0(X1)
| ~ aSet0(X2)
| ~ isFinite0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_43,hypothesis,
aElement0(xy),
inference(split_conjunct,[status(thm)],[m__2304]) ).
fof(c_0_44,negated_conjecture,
( ( aElementOf0(esk16_0,xP)
| sbrdtbr0(xP) != xk )
& ( ~ aElementOf0(esk16_0,xS)
| sbrdtbr0(xP) != xk )
& ( ~ aSubsetOf0(xP,xS)
| sbrdtbr0(xP) != xk ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])]) ).
cnf(c_0_45,hypothesis,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xP,xx))) = sbrdtbr0(xP)
| ~ isFinite0(xP) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).
cnf(c_0_46,hypothesis,
sdtmndt0(xP,xx) = sdtmndt0(xQ,xy),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_28]),c_0_29])]),c_0_36]),c_0_23])]) ).
cnf(c_0_47,hypothesis,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = xk,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_37]),c_0_38]),c_0_39]),c_0_40])]) ).
cnf(c_0_48,hypothesis,
isFinite0(xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_39]),c_0_43]),c_0_40])]) ).
cnf(c_0_49,negated_conjecture,
( aElementOf0(esk16_0,xP)
| sbrdtbr0(xP) != xk ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_50,hypothesis,
sbrdtbr0(xP) = xk,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_48])]) ).
cnf(c_0_51,hypothesis,
( aElementOf0(X1,sdtmndt0(xQ,xy))
| X1 = xx
| ~ aElementOf0(X1,xP) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_52,negated_conjecture,
aElementOf0(esk16_0,xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]) ).
cnf(c_0_53,hypothesis,
( aElementOf0(X1,xQ)
| ~ aElementOf0(X1,sdtmndt0(xQ,xy)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_54,hypothesis,
( esk16_0 = xx
| aElementOf0(esk16_0,sdtmndt0(xQ,xy)) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_55,negated_conjecture,
( ~ aElementOf0(esk16_0,xS)
| sbrdtbr0(xP) != xk ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_56,hypothesis,
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,xQ) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_57,hypothesis,
( esk16_0 = xx
| aElementOf0(esk16_0,xQ) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_58,negated_conjecture,
~ aElementOf0(esk16_0,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_50])]) ).
cnf(c_0_59,hypothesis,
esk16_0 = xx,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]) ).
cnf(c_0_60,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM556+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 10:16:13 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 0.19/0.63 % Version : CSE_E---1.5
% 0.19/0.63 % Problem : theBenchmark.p
% 0.19/0.63 % Proof found
% 0.19/0.63 % SZS status Theorem for theBenchmark.p
% 0.19/0.63 % SZS output start Proof
% See solution above
% 0.19/0.64 % Total time : 0.077000 s
% 0.19/0.64 % SZS output end Proof
% 0.19/0.64 % Total time : 0.082000 s
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