TSTP Solution File: NUM558+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM558+3 : 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 10:38:41 EDT 2023
% Result : Theorem 0.20s 0.62s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 48
% Syntax : Number of formulae : 66 ( 11 unt; 41 typ; 0 def)
% Number of atoms : 188 ( 32 equ)
% Maximal formula atoms : 67 ( 7 avg)
% Number of connectives : 230 ( 67 ~; 69 |; 75 &)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 39 ( 5 avg)
% Maximal term depth : 3 ( 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 : 33 ( 33 usr; 11 con; 0-3 aty)
% Number of variables : 38 ( 0 sgn; 30 !; 1 ?; 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 ).
fof(m__2227,hypothesis,
( aSet0(slbdtsldtrb0(xS,xk))
& ! [X1] :
( ( aElementOf0(X1,slbdtsldtrb0(xS,xk))
=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xS) )
& aSubsetOf0(X1,xS)
& sbrdtbr0(X1) = xk ) )
& ( ( ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xS) ) )
| aSubsetOf0(X1,xS) )
& sbrdtbr0(X1) = xk )
=> aElementOf0(X1,slbdtsldtrb0(xS,xk)) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X1] :
( ( aElementOf0(X1,slbdtsldtrb0(xT,xk))
=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xT) )
& aSubsetOf0(X1,xT)
& sbrdtbr0(X1) = xk ) )
& ( ( ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xT) ) )
| aSubsetOf0(X1,xT) )
& sbrdtbr0(X1) = xk )
=> aElementOf0(X1,slbdtsldtrb0(xT,xk)) ) )
& ! [X1] :
( aElementOf0(X1,slbdtsldtrb0(xS,xk))
=> aElementOf0(X1,slbdtsldtrb0(xT,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ~ ( ! [X1] :
( ( aElementOf0(X1,slbdtsldtrb0(xS,xk))
=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xS) )
& aSubsetOf0(X1,xS)
& sbrdtbr0(X1) = xk ) )
& ( ( ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xS) ) )
| aSubsetOf0(X1,xS) )
& sbrdtbr0(X1) = xk )
=> aElementOf0(X1,slbdtsldtrb0(xS,xk)) ) )
=> ( ~ ? [X1] : aElementOf0(X1,slbdtsldtrb0(xS,xk))
| slbdtsldtrb0(xS,xk) = slcrc0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2227) ).
fof(m__2378,hypothesis,
( ! [X1] :
( aElementOf0(X1,xP)
=> aElementOf0(X1,xS) )
& aSubsetOf0(xP,xS)
& sbrdtbr0(xP) = xk
& aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2378) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',m__2357) ).
fof(m__2256,hypothesis,
aElementOf0(xx,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2256) ).
fof(m__2202_02,hypothesis,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).
fof(m__,conjecture,
aElementOf0(xx,xT),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(c_0_7,hypothesis,
! [X123,X124,X125,X127,X128,X129,X131,X132,X133,X134] :
( aSet0(slbdtsldtrb0(xS,xk))
& ( aSet0(X123)
| ~ aElementOf0(X123,slbdtsldtrb0(xS,xk)) )
& ( ~ aElementOf0(X124,X123)
| aElementOf0(X124,xS)
| ~ aElementOf0(X123,slbdtsldtrb0(xS,xk)) )
& ( aSubsetOf0(X123,xS)
| ~ aElementOf0(X123,slbdtsldtrb0(xS,xk)) )
& ( sbrdtbr0(X123) = xk
| ~ aElementOf0(X123,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(esk12_1(X125),X125)
| ~ aSet0(X125)
| sbrdtbr0(X125) != xk
| aElementOf0(X125,slbdtsldtrb0(xS,xk)) )
& ( ~ aElementOf0(esk12_1(X125),xS)
| ~ aSet0(X125)
| sbrdtbr0(X125) != xk
| aElementOf0(X125,slbdtsldtrb0(xS,xk)) )
& ( ~ aSubsetOf0(X125,xS)
| sbrdtbr0(X125) != xk
| aElementOf0(X125,slbdtsldtrb0(xS,xk)) )
& aSet0(slbdtsldtrb0(xT,xk))
& ( aSet0(X127)
| ~ aElementOf0(X127,slbdtsldtrb0(xT,xk)) )
& ( ~ aElementOf0(X128,X127)
| aElementOf0(X128,xT)
| ~ aElementOf0(X127,slbdtsldtrb0(xT,xk)) )
& ( aSubsetOf0(X127,xT)
| ~ aElementOf0(X127,slbdtsldtrb0(xT,xk)) )
& ( sbrdtbr0(X127) = xk
| ~ aElementOf0(X127,slbdtsldtrb0(xT,xk)) )
& ( aElementOf0(esk13_1(X129),X129)
| ~ aSet0(X129)
| sbrdtbr0(X129) != xk
| aElementOf0(X129,slbdtsldtrb0(xT,xk)) )
& ( ~ aElementOf0(esk13_1(X129),xT)
| ~ aSet0(X129)
| sbrdtbr0(X129) != xk
| aElementOf0(X129,slbdtsldtrb0(xT,xk)) )
& ( ~ aSubsetOf0(X129,xT)
| sbrdtbr0(X129) != xk
| aElementOf0(X129,slbdtsldtrb0(xT,xk)) )
& ( ~ aElementOf0(X131,slbdtsldtrb0(xS,xk))
| aElementOf0(X131,slbdtsldtrb0(xT,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ( aSet0(X132)
| ~ aElementOf0(X132,slbdtsldtrb0(xS,xk)) )
& ( ~ aElementOf0(X133,X132)
| aElementOf0(X133,xS)
| ~ aElementOf0(X132,slbdtsldtrb0(xS,xk)) )
& ( aSubsetOf0(X132,xS)
| ~ aElementOf0(X132,slbdtsldtrb0(xS,xk)) )
& ( sbrdtbr0(X132) = xk
| ~ aElementOf0(X132,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(esk14_1(X134),X134)
| ~ aSet0(X134)
| sbrdtbr0(X134) != xk
| aElementOf0(X134,slbdtsldtrb0(xS,xk)) )
& ( ~ aElementOf0(esk14_1(X134),xS)
| ~ aSet0(X134)
| sbrdtbr0(X134) != xk
| aElementOf0(X134,slbdtsldtrb0(xS,xk)) )
& ( ~ aSubsetOf0(X134,xS)
| sbrdtbr0(X134) != xk
| aElementOf0(X134,slbdtsldtrb0(xS,xk)) )
& aElementOf0(esk15_0,slbdtsldtrb0(xS,xk))
& slbdtsldtrb0(xS,xk) != 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)],[m__2227])])])])])]) ).
fof(c_0_8,hypothesis,
! [X140] :
( ( ~ aElementOf0(X140,xP)
| aElementOf0(X140,xS) )
& aSubsetOf0(xP,xS)
& sbrdtbr0(xP) = xk
& aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2378])])]) ).
fof(c_0_9,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])])]) ).
cnf(c_0_10,hypothesis,
( aElementOf0(X1,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X1,slbdtsldtrb0(xS,xk)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,hypothesis,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,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_13,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,hypothesis,
aElementOf0(xx,xS),
inference(split_conjunct,[status(thm)],[m__2256]) ).
cnf(c_0_15,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[m__2202_02]) ).
cnf(c_0_16,hypothesis,
( aElementOf0(X1,xT)
| ~ aElementOf0(X1,X2)
| ~ aElementOf0(X2,slbdtsldtrb0(xT,xk)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,hypothesis,
aElementOf0(xP,slbdtsldtrb0(xT,xk)),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_18,hypothesis,
( aElementOf0(X1,xP)
| X1 != xx
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,hypothesis,
aElement0(xx),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
fof(c_0_20,negated_conjecture,
~ aElementOf0(xx,xT),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_21,hypothesis,
( aElementOf0(X1,xT)
| ~ aElementOf0(X1,xP) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,hypothesis,
aElementOf0(xx,xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_18]),c_0_19])]) ).
cnf(c_0_23,negated_conjecture,
~ aElementOf0(xx,xT),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM558+3 : 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 : 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 17:55:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.62 % Version : CSE_E---1.5
% 0.20/0.62 % Problem : theBenchmark.p
% 0.20/0.62 % Proof found
% 0.20/0.62 % SZS status Theorem for theBenchmark.p
% 0.20/0.62 % SZS output start Proof
% See solution above
% 0.20/0.62 % Total time : 0.047000 s
% 0.20/0.62 % SZS output end Proof
% 0.20/0.62 % Total time : 0.051000 s
%------------------------------------------------------------------------------