TSTP Solution File: NUM545+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM545+2 : 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 : n025.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 10:38:35 EDT 2023
% Result : Theorem 0.20s 0.60s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 36
% Syntax : Number of formulae : 60 ( 11 unt; 29 typ; 0 def)
% Number of atoms : 140 ( 16 equ)
% Maximal formula atoms : 44 ( 4 avg)
% Number of connectives : 162 ( 53 ~; 54 |; 42 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 4 ( 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 : 30 ( 2 sgn; 20 !; 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/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__2035,hypothesis,
( ~ ( ~ ? [X1] : aElementOf0(X1,xS)
& xS = slcrc0 )
=> ( aElementOf0(szmzazxdt0(xS),xS)
& ! [X1] :
( aElementOf0(X1,xS)
=> sdtlseqdt0(X1,szmzazxdt0(xS)) )
& aSet0(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& ! [X1] :
( aElementOf0(X1,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
<=> ( aElementOf0(X1,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(szmzazxdt0(xS))) ) )
& ! [X1] :
( aElementOf0(X1,xS)
=> aElementOf0(X1,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) )
& aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2035) ).
fof(m__1986,hypothesis,
( aSet0(xS)
& ! [X1] :
( aElementOf0(X1,xS)
=> aElementOf0(X1,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& isFinite0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1986) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).
fof(mSuccNum,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(X1),szNzAzT0)
& szszuzczcdt0(X1) != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNum) ).
fof(mSegZero,axiom,
slbdtrb0(sz00) = slcrc0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSegZero) ).
fof(mSubRefl,axiom,
! [X1] :
( aSet0(X1)
=> aSubsetOf0(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubRefl) ).
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,hypothesis,
! [X108,X109,X110,X111] :
( ( aElementOf0(szmzazxdt0(xS),xS)
| ~ aElementOf0(X108,xS) )
& ( ~ aElementOf0(X109,xS)
| sdtlseqdt0(X109,szmzazxdt0(xS))
| ~ aElementOf0(X108,xS) )
& ( aSet0(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| ~ aElementOf0(X108,xS) )
& ( aElementOf0(X110,szNzAzT0)
| ~ aElementOf0(X110,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| ~ aElementOf0(X108,xS) )
& ( sdtlseqdt0(szszuzczcdt0(X110),szszuzczcdt0(szmzazxdt0(xS)))
| ~ aElementOf0(X110,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| ~ aElementOf0(X108,xS) )
& ( ~ aElementOf0(X110,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X110),szszuzczcdt0(szmzazxdt0(xS)))
| aElementOf0(X110,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| ~ aElementOf0(X108,xS) )
& ( ~ aElementOf0(X111,xS)
| aElementOf0(X111,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| ~ aElementOf0(X108,xS) )
& ( aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| ~ aElementOf0(X108,xS) )
& ( aElementOf0(szmzazxdt0(xS),xS)
| xS = slcrc0 )
& ( ~ aElementOf0(X109,xS)
| sdtlseqdt0(X109,szmzazxdt0(xS))
| xS = slcrc0 )
& ( aSet0(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| xS = slcrc0 )
& ( aElementOf0(X110,szNzAzT0)
| ~ aElementOf0(X110,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| xS = slcrc0 )
& ( sdtlseqdt0(szszuzczcdt0(X110),szszuzczcdt0(szmzazxdt0(xS)))
| ~ aElementOf0(X110,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| xS = slcrc0 )
& ( ~ aElementOf0(X110,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X110),szszuzczcdt0(szmzazxdt0(xS)))
| aElementOf0(X110,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| xS = slcrc0 )
& ( ~ aElementOf0(X111,xS)
| aElementOf0(X111,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| xS = slcrc0 )
& ( aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| xS = slcrc0 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2035])])])]) ).
fof(c_0_9,negated_conjecture,
! [X112,X113,X114] :
( ( aSet0(slbdtrb0(X112))
| ~ aElementOf0(X112,szNzAzT0) )
& ( aElementOf0(X113,szNzAzT0)
| ~ aElementOf0(X113,slbdtrb0(X112))
| ~ aElementOf0(X112,szNzAzT0) )
& ( sdtlseqdt0(szszuzczcdt0(X113),X112)
| ~ aElementOf0(X113,slbdtrb0(X112))
| ~ aElementOf0(X112,szNzAzT0) )
& ( ~ aElementOf0(X114,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X114),X112)
| aElementOf0(X114,slbdtrb0(X112))
| ~ aElementOf0(X112,szNzAzT0) )
& ( aElementOf0(esk10_1(X112),xS)
| ~ aElementOf0(X112,szNzAzT0) )
& ( ~ aElementOf0(esk10_1(X112),slbdtrb0(X112))
| ~ aElementOf0(X112,szNzAzT0) )
& ( ~ aSubsetOf0(xS,slbdtrb0(X112))
| ~ aElementOf0(X112,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])])])])])]) ).
cnf(c_0_10,hypothesis,
( aElementOf0(szmzazxdt0(xS),xS)
| ~ aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,negated_conjecture,
( aElementOf0(esk10_1(X1),xS)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,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_13,negated_conjecture,
( aElementOf0(szmzazxdt0(xS),xS)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
aElementOf0(sz00,szNzAzT0),
inference(split_conjunct,[status(thm)],[mZeroNum]) ).
cnf(c_0_15,negated_conjecture,
( ~ aSubsetOf0(xS,slbdtrb0(X1))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,hypothesis,
( aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| xS = slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_17,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_18,hypothesis,
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
aElementOf0(szmzazxdt0(xS),xS),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
slbdtrb0(sz00) = slcrc0,
inference(split_conjunct,[status(thm)],[mSegZero]) ).
cnf(c_0_21,negated_conjecture,
( slcrc0 = xS
| ~ aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
( aElementOf0(szszuzczcdt0(X1),szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,hypothesis,
aElementOf0(szmzazxdt0(xS),szNzAzT0),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
~ aSubsetOf0(xS,slcrc0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_20]),c_0_14])]) ).
cnf(c_0_25,negated_conjecture,
slcrc0 = xS,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
fof(c_0_26,plain,
! [X20] :
( ~ aSet0(X20)
| aSubsetOf0(X20,X20) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubRefl])]) ).
cnf(c_0_27,negated_conjecture,
~ aSubsetOf0(xS,xS),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,plain,
( aSubsetOf0(X1,X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_29,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM545+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n025.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 17:59:07 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.60 % Version : CSE_E---1.5
% 0.20/0.60 % Problem : theBenchmark.p
% 0.20/0.60 % Proof found
% 0.20/0.60 % SZS status Theorem for theBenchmark.p
% 0.20/0.60 % SZS output start Proof
% See solution above
% 0.20/0.60 % Total time : 0.024000 s
% 0.20/0.60 % SZS output end Proof
% 0.20/0.60 % Total time : 0.028000 s
%------------------------------------------------------------------------------