TSTP Solution File: NUM583+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM583+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 : 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 10:38:58 EDT 2023
% Result : Theorem 4.34s 4.46s
% Output : CNFRefutation 4.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 71
% Syntax : Number of formulae : 89 ( 8 unt; 67 typ; 0 def)
% Number of atoms : 124 ( 16 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 134 ( 32 ~; 36 |; 50 &)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 112 ( 55 >; 57 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 58 ( 58 usr; 12 con; 0-4 aty)
% Number of variables : 24 ( 0 sgn; 20 !; 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,
aFunction0: $i > $o ).
tff(decl_42,type,
szDzozmdt0: $i > $i ).
tff(decl_43,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(decl_44,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(decl_45,type,
sdtlcdtrc0: ( $i * $i ) > $i ).
tff(decl_46,type,
sdtexdt0: ( $i * $i ) > $i ).
tff(decl_47,type,
szDzizrdt0: $i > $i ).
tff(decl_48,type,
xT: $i ).
tff(decl_49,type,
xK: $i ).
tff(decl_50,type,
xS: $i ).
tff(decl_51,type,
xc: $i ).
tff(decl_52,type,
xk: $i ).
tff(decl_53,type,
xN: $i ).
tff(decl_54,type,
xi: $i ).
tff(decl_55,type,
xQ: $i ).
tff(decl_56,type,
esk1_1: $i > $i ).
tff(decl_57,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_58,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_59,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_60,type,
esk5_1: $i > $i ).
tff(decl_61,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_62,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_63,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_64,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_65,type,
esk10_1: $i > $i ).
tff(decl_66,type,
esk11_3: ( $i * $i * $i ) > $i ).
tff(decl_67,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_68,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_69,type,
esk14_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_70,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_71,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_72,type,
esk17_3: ( $i * $i * $i ) > $i ).
tff(decl_73,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_74,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_75,type,
esk20_1: $i > $i ).
tff(decl_76,type,
esk21_1: $i > $i ).
tff(decl_77,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_78,type,
esk23_3: ( $i * $i * $i ) > $i ).
tff(decl_79,type,
esk24_3: ( $i * $i * $i ) > $i ).
tff(decl_80,type,
esk25_3: ( $i * $i * $i ) > $i ).
tff(decl_81,type,
esk26_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_82,type,
esk27_3: ( $i * $i * $i ) > $i ).
tff(decl_83,type,
esk28_3: ( $i * $i * $i ) > $i ).
tff(decl_84,type,
esk29_3: ( $i * $i * $i ) > $i ).
tff(decl_85,type,
esk30_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_86,type,
esk31_1: $i > $i ).
tff(decl_87,type,
esk32_2: ( $i * $i ) > $i ).
tff(decl_88,type,
esk33_0: $i ).
fof(m__,conjecture,
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) ) )
=> ( ( aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X1)
& ( aElementOf0(X1,xQ)
| X1 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )
=> ( ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
=> aElementOf0(X1,xS) )
| aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__4037,hypothesis,
( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> aElementOf0(X1,xS) )
& aSubsetOf0(sdtlpdtrp0(xN,xi),xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4037) ).
fof(m__3989_02,hypothesis,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& X1 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
& aSet0(xQ)
& ! [X1] :
( aElementOf0(X1,xQ)
=> aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3989_02) ).
fof(m__4007,hypothesis,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X1)
& ( aElementOf0(X1,xQ)
| X1 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
& sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4007) ).
fof(c_0_4,negated_conjecture,
~ ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) ) )
=> ( ( aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X1)
& ( aElementOf0(X1,xQ)
| X1 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )
=> ( ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
=> aElementOf0(X1,xS) )
| aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_5,hypothesis,
! [X217] :
( ( ~ aElementOf0(X217,sdtlpdtrp0(xN,xi))
| aElementOf0(X217,xS) )
& aSubsetOf0(sdtlpdtrp0(xN,xi),xS) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4037])])]) ).
fof(c_0_6,hypothesis,
! [X212,X213,X214] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ( ~ aElementOf0(X212,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X212) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( aElement0(X213)
| ~ aElementOf0(X213,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( aElementOf0(X213,sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X213,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( X213 != szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X213,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( ~ aElement0(X213)
| ~ aElementOf0(X213,sdtlpdtrp0(xN,xi))
| X213 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X213,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSet0(xQ)
& ( ~ aElementOf0(X214,xQ)
| aElementOf0(X214,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3989_02])])])]) ).
fof(c_0_7,hypothesis,
! [X215,X216] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ( ~ aElementOf0(X215,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X215) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( aElement0(X216)
| ~ aElementOf0(X216,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( aElementOf0(X216,xQ)
| X216 = szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X216,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( ~ aElementOf0(X216,xQ)
| ~ aElement0(X216)
| aElementOf0(X216,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( X216 != szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElement0(X216)
| aElementOf0(X216,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4007])])])]) ).
fof(c_0_8,negated_conjecture,
! [X218,X219] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ( ~ aElementOf0(X218,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X218) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( aElement0(X219)
| ~ aElementOf0(X219,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( aElementOf0(X219,xQ)
| X219 = szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X219,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( ~ aElementOf0(X219,xQ)
| ~ aElement0(X219)
| aElementOf0(X219,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( X219 != szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElement0(X219)
| aElementOf0(X219,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aElementOf0(esk33_0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ~ aElementOf0(esk33_0,xS)
& ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])]) ).
cnf(c_0_9,hypothesis,
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xi)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,hypothesis,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,hypothesis,
( aElementOf0(X1,xQ)
| X1 = szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
aElementOf0(esk33_0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,hypothesis,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xS),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
( szmzizndt0(sdtlpdtrp0(xN,xi)) = esk33_0
| aElementOf0(esk33_0,xQ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,negated_conjecture,
~ aElementOf0(esk33_0,xS),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,hypothesis,
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(X1,xQ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,hypothesis,
aElementOf0(esk33_0,xQ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_18,hypothesis,
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,hypothesis,
aElementOf0(esk33_0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,hypothesis,
aElementOf0(esk33_0,sdtlpdtrp0(xN,xi)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_20]),c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM583+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 08:50:18 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.22/0.58 start to proof: theBenchmark
% 4.34/4.46 % Version : CSE_E---1.5
% 4.34/4.46 % Problem : theBenchmark.p
% 4.34/4.46 % Proof found
% 4.34/4.46 % SZS status Theorem for theBenchmark.p
% 4.34/4.46 % SZS output start Proof
% See solution above
% 4.34/4.46 % Total time : 3.864000 s
% 4.34/4.46 % SZS output end Proof
% 4.34/4.46 % Total time : 3.872000 s
%------------------------------------------------------------------------------