TSTP Solution File: NUM544+1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM544+1 : 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 : n001.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 3.15s 3.21s
% Output : CNFRefutation 3.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 37
% Syntax : Number of formulae : 79 ( 11 unt; 28 typ; 0 def)
% Number of atoms : 219 ( 41 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 291 ( 123 ~; 125 |; 28 &)
% ( 6 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 39 ( 24 >; 15 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 4 con; 0-3 aty)
% Number of variables : 77 ( 1 sgn; 32 !; 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,
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 ).
fof(m__,conjecture,
( xS != slcrc0
=> aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(mDefSeg,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ! [X2] :
( X2 = slbdtrb0(X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSeg) ).
fof(mSuccNum,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(X1),szNzAzT0)
& szszuzczcdt0(X1) != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNum) ).
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/sandbox/benchmark/theBenchmark.p',mDefMax) ).
fof(m__1986,hypothesis,
( aSubsetOf0(xS,szNzAzT0)
& isFinite0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1986) ).
fof(mNATSet,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
fof(mSuccLess,axiom,
! [X1,X2] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X2,szNzAzT0) )
=> ( sdtlseqdt0(X1,X2)
<=> sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccLess) ).
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( aSet0(X1)
& ~ ? [X2] : aElementOf0(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(c_0_9,negated_conjecture,
~ ( xS != slcrc0
=> aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_10,plain,
! [X13,X14,X15,X16] :
( ( aSet0(X14)
| ~ aSubsetOf0(X14,X13)
| ~ aSet0(X13) )
& ( ~ aElementOf0(X15,X14)
| aElementOf0(X15,X13)
| ~ aSubsetOf0(X14,X13)
| ~ aSet0(X13) )
& ( aElementOf0(esk2_2(X13,X16),X16)
| ~ aSet0(X16)
| aSubsetOf0(X16,X13)
| ~ aSet0(X13) )
& ( ~ aElementOf0(esk2_2(X13,X16),X13)
| ~ aSet0(X16)
| aSubsetOf0(X16,X13)
| ~ aSet0(X13) ) ),
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)],[mDefSub])])])])])]) ).
fof(c_0_11,plain,
! [X96,X97,X98,X99,X100] :
( ( aSet0(X97)
| X97 != slbdtrb0(X96)
| ~ aElementOf0(X96,szNzAzT0) )
& ( aElementOf0(X98,szNzAzT0)
| ~ aElementOf0(X98,X97)
| X97 != slbdtrb0(X96)
| ~ aElementOf0(X96,szNzAzT0) )
& ( sdtlseqdt0(szszuzczcdt0(X98),X96)
| ~ aElementOf0(X98,X97)
| X97 != slbdtrb0(X96)
| ~ aElementOf0(X96,szNzAzT0) )
& ( ~ aElementOf0(X99,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X99),X96)
| aElementOf0(X99,X97)
| X97 != slbdtrb0(X96)
| ~ aElementOf0(X96,szNzAzT0) )
& ( ~ aElementOf0(esk9_2(X96,X100),X100)
| ~ aElementOf0(esk9_2(X96,X100),szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(esk9_2(X96,X100)),X96)
| ~ aSet0(X100)
| X100 = slbdtrb0(X96)
| ~ aElementOf0(X96,szNzAzT0) )
& ( aElementOf0(esk9_2(X96,X100),szNzAzT0)
| aElementOf0(esk9_2(X96,X100),X100)
| ~ aSet0(X100)
| X100 = slbdtrb0(X96)
| ~ aElementOf0(X96,szNzAzT0) )
& ( sdtlseqdt0(szszuzczcdt0(esk9_2(X96,X100)),X96)
| aElementOf0(esk9_2(X96,X100),X100)
| ~ aSet0(X100)
| X100 = slbdtrb0(X96)
| ~ aElementOf0(X96,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)],[mDefSeg])])])])])]) ).
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])])]) ).
fof(c_0_13,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_14,negated_conjecture,
( xS != slcrc0
& ~ aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ),
inference(fof_nnf,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( aSet0(X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,hypothesis,
aSubsetOf0(xS,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__1986]) ).
cnf(c_0_17,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
cnf(c_0_18,plain,
( aSet0(X1)
| X1 != slbdtrb0(X2)
| ~ 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,
( aElementOf0(X1,X2)
| X2 = slcrc0
| X1 != szmzazxdt0(X2)
| ~ aSubsetOf0(X2,szNzAzT0)
| ~ isFinite0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,hypothesis,
isFinite0(xS),
inference(split_conjunct,[status(thm)],[m__1986]) ).
cnf(c_0_22,negated_conjecture,
xS != slcrc0,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_23,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_24,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])])])])])]) ).
cnf(c_0_25,plain,
( aElementOf0(esk2_2(X1,X2),X2)
| aSubsetOf0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_26,hypothesis,
aSet0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
cnf(c_0_27,plain,
( aSet0(X1)
| X1 != slbdtrb0(szszuzczcdt0(X2))
| ~ aElementOf0(X2,szNzAzT0) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_28,plain,
( aElementOf0(X1,X3)
| ~ aElementOf0(X1,X2)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_29,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_20,c_0_16]),c_0_21])]),c_0_22]) ).
cnf(c_0_30,plain,
( aElementOf0(X1,X3)
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X1),X2)
| X3 != slbdtrb0(X2)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_31,plain,
( sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,plain,
( sdtlseqdt0(X1,X3)
| X2 = slcrc0
| ~ aElementOf0(X1,X2)
| X3 != szmzazxdt0(X2)
| ~ aSubsetOf0(X2,szNzAzT0)
| ~ isFinite0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_33,plain,
( ~ aElementOf0(X1,X2)
| X2 != slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,hypothesis,
( aSubsetOf0(xS,X1)
| aElementOf0(esk2_2(X1,xS),xS)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_35,plain,
( aSet0(slbdtrb0(szszuzczcdt0(X1)))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_36,hypothesis,
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_16]),c_0_17])]) ).
cnf(c_0_37,hypothesis,
aElementOf0(szmzazxdt0(xS),xS),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_38,plain,
( aElementOf0(X1,X2)
| X2 != slbdtrb0(szszuzczcdt0(X3))
| ~ sdtlseqdt0(X1,X3)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X3,szNzAzT0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_19]) ).
cnf(c_0_39,plain,
( sdtlseqdt0(X1,X2)
| X2 != szmzazxdt0(X3)
| ~ aSubsetOf0(X3,szNzAzT0)
| ~ isFinite0(X3)
| ~ aElementOf0(X1,X3) ),
inference(csr,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_40,hypothesis,
( aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(X1)))
| aElementOf0(esk2_2(slbdtrb0(szszuzczcdt0(X1)),xS),xS)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,hypothesis,
aElementOf0(szmzazxdt0(xS),szNzAzT0),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,negated_conjecture,
~ aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_43,plain,
( aSubsetOf0(X2,X1)
| ~ aElementOf0(esk2_2(X1,X2),X1)
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_44,plain,
( aElementOf0(X1,slbdtrb0(szszuzczcdt0(X2)))
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(er,[status(thm)],[c_0_38]) ).
cnf(c_0_45,hypothesis,
( sdtlseqdt0(X1,X2)
| X2 != szmzazxdt0(xS)
| ~ aElementOf0(X1,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_16]),c_0_21])]) ).
cnf(c_0_46,hypothesis,
aElementOf0(esk2_2(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))),xS),xS),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_47,plain,
( aSubsetOf0(X1,slbdtrb0(szszuzczcdt0(X2)))
| ~ sdtlseqdt0(esk2_2(slbdtrb0(szszuzczcdt0(X2)),X1),X2)
| ~ aElementOf0(esk2_2(slbdtrb0(szszuzczcdt0(X2)),X1),szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aSet0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_35]) ).
cnf(c_0_48,hypothesis,
( sdtlseqdt0(esk2_2(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))),xS),X1)
| X1 != szmzazxdt0(xS) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_49,hypothesis,
~ aElementOf0(esk2_2(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))),xS),szNzAzT0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_41]),c_0_26])]),c_0_42]) ).
cnf(c_0_50,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_46]),c_0_49]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM544+1 : 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 : n001.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 10:35:58 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 3.15/3.21 % Version : CSE_E---1.5
% 3.15/3.21 % Problem : theBenchmark.p
% 3.15/3.21 % Proof found
% 3.15/3.21 % SZS status Theorem for theBenchmark.p
% 3.15/3.21 % SZS output start Proof
% See solution above
% 3.15/3.21 % Total time : 2.636000 s
% 3.15/3.21 % SZS output end Proof
% 3.15/3.21 % Total time : 2.640000 s
%------------------------------------------------------------------------------