TSTP Solution File: NUM539+2 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM539+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 : n003.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 10:38:32 EDT 2023
% Result : Theorem 0.19s 0.60s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 36
% Syntax : Number of formulae : 63 ( 10 unt; 30 typ; 0 def)
% Number of atoms : 145 ( 34 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 170 ( 58 ~; 54 |; 42 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 36 ( 22 >; 14 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 8 con; 0-3 aty)
% Number of variables : 49 ( 1 sgn; 28 !; 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,
xS: $i ).
tff(decl_40,type,
xT: $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_0: $i ).
tff(decl_50,type,
esk10_0: $i ).
tff(decl_51,type,
esk11_0: $i ).
fof(mDefMin,axiom,
! [X1] :
( ( aSubsetOf0(X1,szNzAzT0)
& X1 != slcrc0 )
=> ! [X2] :
( X2 = szmzizndt0(X1)
<=> ( aElementOf0(X2,X1)
& ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X2,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefMin) ).
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( aSet0(X1)
& ~ ? [X2] : aElementOf0(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(m__1779,hypothesis,
( aSet0(xS)
& ! [X1] :
( aElementOf0(X1,xS)
=> aElementOf0(X1,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& aSet0(xT)
& ! [X1] :
( aElementOf0(X1,xT)
=> aElementOf0(X1,szNzAzT0) )
& aSubsetOf0(xT,szNzAzT0)
& ~ ( ~ ? [X1] : aElementOf0(X1,xS)
| xS = slcrc0 )
& ~ ( ~ ? [X1] : aElementOf0(X1,xT)
| xT = slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1779) ).
fof(m__1802,hypothesis,
( aElementOf0(szmzizndt0(xS),xS)
& ! [X1] :
( aElementOf0(X1,xS)
=> sdtlseqdt0(szmzizndt0(xS),X1) )
& aElementOf0(szmzizndt0(xS),xT)
& aElementOf0(szmzizndt0(xT),xT)
& ! [X1] :
( aElementOf0(X1,xT)
=> sdtlseqdt0(szmzizndt0(xT),X1) )
& aElementOf0(szmzizndt0(xT),xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1802) ).
fof(mLessASymm,axiom,
! [X1,X2] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X2,szNzAzT0) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessASymm) ).
fof(m__,conjecture,
( ( aElementOf0(szmzizndt0(xS),xS)
& ! [X1] :
( aElementOf0(X1,xS)
=> sdtlseqdt0(szmzizndt0(xS),X1) ) )
=> ( ! [X1] :
( aElementOf0(X1,xT)
=> sdtlseqdt0(szmzizndt0(xS),X1) )
| szmzizndt0(xS) = szmzizndt0(xT) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(c_0_6,plain,
! [X84,X85,X86,X87] :
( ( aElementOf0(X85,X84)
| X85 != szmzizndt0(X84)
| ~ aSubsetOf0(X84,szNzAzT0)
| X84 = slcrc0 )
& ( ~ aElementOf0(X86,X84)
| sdtlseqdt0(X85,X86)
| X85 != szmzizndt0(X84)
| ~ aSubsetOf0(X84,szNzAzT0)
| X84 = slcrc0 )
& ( aElementOf0(esk7_2(X84,X87),X84)
| ~ aElementOf0(X87,X84)
| X87 = szmzizndt0(X84)
| ~ aSubsetOf0(X84,szNzAzT0)
| X84 = slcrc0 )
& ( ~ sdtlseqdt0(X87,esk7_2(X84,X87))
| ~ aElementOf0(X87,X84)
| X87 = szmzizndt0(X84)
| ~ aSubsetOf0(X84,szNzAzT0)
| X84 = 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)],[mDefMin])])])])])]) ).
fof(c_0_7,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_8,hypothesis,
! [X94,X95] :
( aSet0(xS)
& ( ~ aElementOf0(X94,xS)
| aElementOf0(X94,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& aSet0(xT)
& ( ~ aElementOf0(X95,xT)
| aElementOf0(X95,szNzAzT0) )
& aSubsetOf0(xT,szNzAzT0)
& aElementOf0(esk9_0,xS)
& xS != slcrc0
& aElementOf0(esk10_0,xT)
& xT != slcrc0 ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1779])])])]) ).
fof(c_0_9,hypothesis,
! [X98,X99] :
( aElementOf0(szmzizndt0(xS),xS)
& ( ~ aElementOf0(X98,xS)
| sdtlseqdt0(szmzizndt0(xS),X98) )
& aElementOf0(szmzizndt0(xS),xT)
& aElementOf0(szmzizndt0(xT),xT)
& ( ~ aElementOf0(X99,xT)
| sdtlseqdt0(szmzizndt0(xT),X99) )
& aElementOf0(szmzizndt0(xT),xS) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1802])])]) ).
cnf(c_0_10,plain,
( sdtlseqdt0(X3,X1)
| X2 = slcrc0
| ~ aElementOf0(X1,X2)
| X3 != szmzizndt0(X2)
| ~ aSubsetOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( ~ aElementOf0(X1,X2)
| X2 != slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,plain,
! [X64,X65] :
( ~ aElementOf0(X64,szNzAzT0)
| ~ aElementOf0(X65,szNzAzT0)
| ~ sdtlseqdt0(X64,X65)
| ~ sdtlseqdt0(X65,X64)
| X64 = X65 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLessASymm])]) ).
cnf(c_0_13,hypothesis,
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,hypothesis,
aElementOf0(szmzizndt0(xS),xS),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( sdtlseqdt0(X1,X2)
| X1 != szmzizndt0(X3)
| ~ aSubsetOf0(X3,szNzAzT0)
| ~ aElementOf0(X2,X3) ),
inference(csr,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,hypothesis,
aSubsetOf0(xS,szNzAzT0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_17,negated_conjecture,
~ ( ( aElementOf0(szmzizndt0(xS),xS)
& ! [X1] :
( aElementOf0(X1,xS)
=> sdtlseqdt0(szmzizndt0(xS),X1) ) )
=> ( ! [X1] :
( aElementOf0(X1,xT)
=> sdtlseqdt0(szmzizndt0(xS),X1) )
| szmzizndt0(xS) = szmzizndt0(xT) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_18,plain,
( X1 = X2
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,hypothesis,
aElementOf0(szmzizndt0(xS),szNzAzT0),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,hypothesis,
( sdtlseqdt0(X1,X2)
| X1 != szmzizndt0(xS)
| ~ aElementOf0(X2,xS) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,hypothesis,
aElementOf0(szmzizndt0(xT),xS),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_22,negated_conjecture,
! [X100] :
( aElementOf0(szmzizndt0(xS),xS)
& ( ~ aElementOf0(X100,xS)
| sdtlseqdt0(szmzizndt0(xS),X100) )
& aElementOf0(esk11_0,xT)
& ~ sdtlseqdt0(szmzizndt0(xS),esk11_0)
& szmzizndt0(xS) != szmzizndt0(xT) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])]) ).
cnf(c_0_23,hypothesis,
aSubsetOf0(xT,szNzAzT0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_24,hypothesis,
( X1 = szmzizndt0(xS)
| ~ sdtlseqdt0(szmzizndt0(xS),X1)
| ~ sdtlseqdt0(X1,szmzizndt0(xS))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,hypothesis,
( sdtlseqdt0(X1,szmzizndt0(xT))
| X1 != szmzizndt0(xS) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,hypothesis,
aElementOf0(szmzizndt0(xT),szNzAzT0),
inference(spm,[status(thm)],[c_0_13,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
szmzizndt0(xS) != szmzizndt0(xT),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,hypothesis,
( sdtlseqdt0(X1,X2)
| X1 != szmzizndt0(xT)
| ~ aElementOf0(X2,xT) ),
inference(spm,[status(thm)],[c_0_15,c_0_23]) ).
cnf(c_0_29,hypothesis,
aElementOf0(szmzizndt0(xS),xT),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_30,hypothesis,
~ sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]),c_0_27]) ).
cnf(c_0_31,hypothesis,
( sdtlseqdt0(X1,szmzizndt0(xS))
| X1 != szmzizndt0(xT) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,hypothesis,
$false,
inference(spm,[status(thm)],[c_0_30,c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM539+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
% 0.13/0.34 % Computer : n003.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 12:59:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.60 % Version : CSE_E---1.5
% 0.19/0.60 % Problem : theBenchmark.p
% 0.19/0.60 % Proof found
% 0.19/0.60 % SZS status Theorem for theBenchmark.p
% 0.19/0.60 % SZS output start Proof
% See solution above
% 0.19/0.61 % Total time : 0.028000 s
% 0.19/0.61 % SZS output end Proof
% 0.19/0.61 % Total time : 0.032000 s
%------------------------------------------------------------------------------