TSTP Solution File: NUM543+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM543+2 : 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 : n014.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 10:38:34 EDT 2023
% Result : Theorem 1.39s 1.50s
% Output : CNFRefutation 1.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 36
% Syntax : Number of formulae : 69 ( 8 unt; 29 typ; 0 def)
% Number of atoms : 169 ( 29 equ)
% Maximal formula atoms : 23 ( 4 avg)
% Number of connectives : 218 ( 89 ~; 84 |; 31 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 40 ( 25 >; 15 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 4 con; 0-3 aty)
% Number of variables : 59 ( 2 sgn; 26 !; 3 ?; 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,
xS: $i ).
tff(decl_41,type,
esk1_1: $i > $i ).
tff(decl_42,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_43,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_44,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_45,type,
esk5_1: $i > $i ).
tff(decl_46,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_47,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_48,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk10_1: $i > $i ).
fof(m__,conjecture,
? [X1] :
( aElementOf0(X1,szNzAzT0)
& ( ( aSet0(slbdtrb0(X1))
& ! [X2] :
( aElementOf0(X2,slbdtrb0(X1))
<=> ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X1) ) ) )
=> ( ! [X2] :
( aElementOf0(X2,xS)
=> aElementOf0(X2,slbdtrb0(X1)) )
| aSubsetOf0(xS,slbdtrb0(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mDefMax,axiom,
! [X1] :
( ( aSubsetOf0(X1,szNzAzT0)
& isFinite0(X1)
& X1 != slcrc0 )
=> ! [X2] :
( X2 = szmzazxdt0(X1)
<=> ( aElementOf0(X2,X1)
& ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X3,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefMax) ).
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( aSet0(X1)
& ~ ? [X2] : aElementOf0(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
fof(mSuccLess,axiom,
! [X1,X2] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X2,szNzAzT0) )
=> ( sdtlseqdt0(X1,X2)
<=> sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccLess) ).
fof(mSuccNum,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(X1),szNzAzT0)
& szszuzczcdt0(X1) != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNum) ).
fof(m__1986,hypothesis,
( aSet0(xS)
& ! [X1] :
( aElementOf0(X1,xS)
=> aElementOf0(X1,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& isFinite0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1986) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
fof(c_0_7,negated_conjecture,
~ ? [X1] :
( aElementOf0(X1,szNzAzT0)
& ( ( aSet0(slbdtrb0(X1))
& ! [X2] :
( aElementOf0(X2,slbdtrb0(X1))
<=> ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X1) ) ) )
=> ( ! [X2] :
( aElementOf0(X2,xS)
=> aElementOf0(X2,slbdtrb0(X1)) )
| aSubsetOf0(xS,slbdtrb0(X1)) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_8,plain,
! [X89,X90,X91,X92] :
( ( aElementOf0(X90,X89)
| X90 != szmzazxdt0(X89)
| ~ aSubsetOf0(X89,szNzAzT0)
| ~ isFinite0(X89)
| X89 = slcrc0 )
& ( ~ aElementOf0(X91,X89)
| sdtlseqdt0(X91,X90)
| X90 != szmzazxdt0(X89)
| ~ aSubsetOf0(X89,szNzAzT0)
| ~ isFinite0(X89)
| X89 = slcrc0 )
& ( aElementOf0(esk8_2(X89,X92),X89)
| ~ aElementOf0(X92,X89)
| X92 = szmzazxdt0(X89)
| ~ aSubsetOf0(X89,szNzAzT0)
| ~ isFinite0(X89)
| X89 = slcrc0 )
& ( ~ sdtlseqdt0(esk8_2(X89,X92),X92)
| ~ aElementOf0(X92,X89)
| X92 = szmzazxdt0(X89)
| ~ aSubsetOf0(X89,szNzAzT0)
| ~ isFinite0(X89)
| X89 = slcrc0 ) ),
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)],[mDefMax])])])])])]) ).
fof(c_0_9,plain,
! [X7,X8,X9] :
( ( aSet0(X7)
| X7 != slcrc0 )
& ( ~ aElementOf0(X8,X7)
| X7 != slcrc0 )
& ( ~ aSet0(X9)
| aElementOf0(esk1_1(X9),X9)
| X9 = slcrc0 ) ),
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)],[mDefEmp])])])])])]) ).
fof(c_0_10,negated_conjecture,
! [X108,X109,X110] :
( ( aSet0(slbdtrb0(X108))
| ~ aElementOf0(X108,szNzAzT0) )
& ( aElementOf0(X109,szNzAzT0)
| ~ aElementOf0(X109,slbdtrb0(X108))
| ~ aElementOf0(X108,szNzAzT0) )
& ( sdtlseqdt0(szszuzczcdt0(X109),X108)
| ~ aElementOf0(X109,slbdtrb0(X108))
| ~ aElementOf0(X108,szNzAzT0) )
& ( ~ aElementOf0(X110,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X110),X108)
| aElementOf0(X110,slbdtrb0(X108))
| ~ aElementOf0(X108,szNzAzT0) )
& ( aElementOf0(esk10_1(X108),xS)
| ~ aElementOf0(X108,szNzAzT0) )
& ( ~ aElementOf0(esk10_1(X108),slbdtrb0(X108))
| ~ aElementOf0(X108,szNzAzT0) )
& ( ~ aSubsetOf0(xS,slbdtrb0(X108))
| ~ aElementOf0(X108,szNzAzT0) ) ),
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)],[c_0_7])])])])])]) ).
fof(c_0_11,plain,
! [X60,X61] :
( ( ~ sdtlseqdt0(X60,X61)
| sdtlseqdt0(szszuzczcdt0(X60),szszuzczcdt0(X61))
| ~ aElementOf0(X60,szNzAzT0)
| ~ aElementOf0(X61,szNzAzT0) )
& ( ~ sdtlseqdt0(szszuzczcdt0(X60),szszuzczcdt0(X61))
| sdtlseqdt0(X60,X61)
| ~ aElementOf0(X60,szNzAzT0)
| ~ aElementOf0(X61,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSuccLess])])]) ).
fof(c_0_12,plain,
! [X52] :
( ( aElementOf0(szszuzczcdt0(X52),szNzAzT0)
| ~ aElementOf0(X52,szNzAzT0) )
& ( szszuzczcdt0(X52) != sz00
| ~ aElementOf0(X52,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSuccNum])])]) ).
cnf(c_0_13,plain,
( sdtlseqdt0(X1,X3)
| X2 = slcrc0
| ~ aElementOf0(X1,X2)
| X3 != szmzazxdt0(X2)
| ~ aSubsetOf0(X2,szNzAzT0)
| ~ isFinite0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( ~ aElementOf0(X1,X2)
| X2 != slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_15,hypothesis,
! [X107] :
( aSet0(xS)
& ( ~ aElementOf0(X107,xS)
| aElementOf0(X107,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& isFinite0(xS) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1986])])]) ).
cnf(c_0_16,negated_conjecture,
( aElementOf0(esk10_1(X1),xS)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
( aElementOf0(X1,slbdtrb0(X2))
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X1),X2)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
( sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
( aElementOf0(szszuzczcdt0(X1),szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( sdtlseqdt0(X1,X2)
| X2 != szmzazxdt0(X3)
| ~ aSubsetOf0(X3,szNzAzT0)
| ~ isFinite0(X3)
| ~ aElementOf0(X1,X3) ),
inference(csr,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_21,hypothesis,
aSubsetOf0(xS,szNzAzT0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,hypothesis,
isFinite0(xS),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,negated_conjecture,
( xS != slcrc0
| ~ aElementOf0(X1,szNzAzT0) ),
inference(spm,[status(thm)],[c_0_14,c_0_16]) ).
cnf(c_0_24,plain,
aElementOf0(sz00,szNzAzT0),
inference(split_conjunct,[status(thm)],[mZeroNum]) ).
cnf(c_0_25,negated_conjecture,
( ~ aElementOf0(esk10_1(X1),slbdtrb0(X1))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_26,negated_conjecture,
( aElementOf0(X1,slbdtrb0(szszuzczcdt0(X2)))
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_27,hypothesis,
( sdtlseqdt0(X1,X2)
| X2 != szmzazxdt0(xS)
| ~ aElementOf0(X1,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_28,plain,
( aElementOf0(X1,X2)
| X2 = slcrc0
| X1 != szmzazxdt0(X2)
| ~ aSubsetOf0(X2,szNzAzT0)
| ~ isFinite0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_29,negated_conjecture,
xS != slcrc0,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,negated_conjecture,
( ~ sdtlseqdt0(esk10_1(szszuzczcdt0(X1)),X1)
| ~ aElementOf0(esk10_1(szszuzczcdt0(X1)),szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_19]) ).
cnf(c_0_31,negated_conjecture,
( sdtlseqdt0(esk10_1(X1),X2)
| X2 != szmzazxdt0(xS)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(spm,[status(thm)],[c_0_27,c_0_16]) ).
cnf(c_0_32,hypothesis,
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_33,hypothesis,
( aElementOf0(X1,xS)
| X1 != szmzazxdt0(xS) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_21]),c_0_22])]),c_0_29]) ).
cnf(c_0_34,negated_conjecture,
( X1 != szmzazxdt0(xS)
| ~ aElementOf0(esk10_1(szszuzczcdt0(X1)),szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_19]) ).
cnf(c_0_35,hypothesis,
( aElementOf0(esk10_1(X1),szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(spm,[status(thm)],[c_0_32,c_0_16]) ).
cnf(c_0_36,hypothesis,
aElementOf0(szmzazxdt0(xS),xS),
inference(er,[status(thm)],[c_0_33]) ).
cnf(c_0_37,hypothesis,
( X1 != szmzazxdt0(xS)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_19]) ).
cnf(c_0_38,hypothesis,
aElementOf0(szmzazxdt0(xS),szNzAzT0),
inference(spm,[status(thm)],[c_0_32,c_0_36]) ).
cnf(c_0_39,hypothesis,
$false,
inference(spm,[status(thm)],[c_0_37,c_0_38]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM543+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 15:16:03 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 1.39/1.50 % Version : CSE_E---1.5
% 1.39/1.50 % Problem : theBenchmark.p
% 1.39/1.50 % Proof found
% 1.39/1.50 % SZS status Theorem for theBenchmark.p
% 1.39/1.50 % SZS output start Proof
% See solution above
% 1.39/1.51 % Total time : 0.928000 s
% 1.39/1.51 % SZS output end Proof
% 1.39/1.51 % Total time : 0.932000 s
%------------------------------------------------------------------------------