TSTP Solution File: NUM452+6 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM452+6 : 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 : n018.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 10:37:38 EDT 2023
% Result : Theorem 0.20s 0.68s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 68
% Syntax : Number of formulae : 131 ( 17 unt; 54 typ; 0 def)
% Number of atoms : 398 ( 104 equ)
% Maximal formula atoms : 44 ( 5 avg)
% Number of connectives : 501 ( 180 ~; 167 |; 126 &)
% ( 11 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 74 ( 45 >; 29 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 3 prp; 0-3 aty)
% Number of functors : 42 ( 42 usr; 7 con; 0-3 aty)
% Number of variables : 113 ( 0 sgn; 63 !; 13 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
aInteger0: $i > $o ).
tff(decl_23,type,
sz00: $i ).
tff(decl_24,type,
sz10: $i ).
tff(decl_25,type,
smndt0: $i > $i ).
tff(decl_26,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(decl_27,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(decl_28,type,
aDivisorOf0: ( $i * $i ) > $o ).
tff(decl_29,type,
sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).
tff(decl_30,type,
isPrime0: $i > $o ).
tff(decl_31,type,
aSet0: $i > $o ).
tff(decl_32,type,
aElementOf0: ( $i * $i ) > $o ).
tff(decl_33,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(decl_34,type,
isFinite0: $i > $o ).
tff(decl_35,type,
cS1395: $i ).
tff(decl_36,type,
sdtbsmnsldt0: ( $i * $i ) > $i ).
tff(decl_37,type,
sdtslmnbsdt0: ( $i * $i ) > $i ).
tff(decl_38,type,
sbsmnsldt0: $i > $i ).
tff(decl_39,type,
stldt0: $i > $i ).
tff(decl_40,type,
szAzrzSzezqlpdtcmdtrp0: ( $i * $i ) > $i ).
tff(decl_41,type,
isOpen0: $i > $o ).
tff(decl_42,type,
isClosed0: $i > $o ).
tff(decl_43,type,
xS: $i ).
tff(decl_44,type,
cS2043: $i ).
tff(decl_45,type,
cS2076: $i ).
tff(decl_46,type,
xp: $i ).
tff(decl_47,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_48,type,
esk2_1: $i > $i ).
tff(decl_49,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_51,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_52,type,
esk6_1: $i > $i ).
tff(decl_53,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_54,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_56,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_57,type,
esk11_3: ( $i * $i * $i ) > $i ).
tff(decl_58,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_59,type,
esk13_1: $i > $i ).
tff(decl_60,type,
esk14_1: $i > $i ).
tff(decl_61,type,
esk15_1: $i > $i ).
tff(decl_62,type,
esk16_1: $i > $i ).
tff(decl_63,type,
esk17_2: ( $i * $i ) > $i ).
tff(decl_64,type,
esk18_3: ( $i * $i * $i ) > $i ).
tff(decl_65,type,
esk19_1: $i > $i ).
tff(decl_66,type,
esk20_1: $i > $i ).
tff(decl_67,type,
esk21_1: $i > $i ).
tff(decl_68,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_69,type,
esk23_1: $i > $i ).
tff(decl_70,type,
esk24_1: $i > $i ).
tff(decl_71,type,
esk25_2: ( $i * $i ) > $i ).
tff(decl_72,type,
esk26_1: $i > $i ).
tff(decl_73,type,
esk27_1: $i > $i ).
tff(decl_74,type,
epred1_0: $o ).
tff(decl_75,type,
epred2_0: $o ).
fof(m__2171,hypothesis,
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ! [X1] :
( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> ( aInteger0(X1)
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X1,sz10,xp) ) )
& ( ( aInteger0(X1)
& ( ? [X2] :
( aInteger0(X2)
& sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10)) )
| aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(X1,sz10,xp) ) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( aInteger0(X1)
& ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) ) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
& ! [X1] :
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> aElementOf0(X1,stldt0(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2171) ).
fof(mEquModRef,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2)
& X2 != sz00 )
=> sdteqdtlpzmzozddtrp0(X1,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModRef) ).
fof(mIntOne,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntOne) ).
fof(mZeroDiv,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroDiv) ).
fof(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).
fof(m__2079,hypothesis,
( aSet0(sbsmnsldt0(xS))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( aInteger0(X1)
& ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) ) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( X1 = sz10
| X1 = smndt0(sz10) ) )
& stldt0(sbsmnsldt0(xS)) = cS2076 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2079) ).
fof(m__,conjecture,
( ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) )
| aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
| aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)) )
| aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
| aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3) )
=> sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(mDivisor,axiom,
! [X1] :
( aInteger0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( aInteger0(X2)
& X2 != sz00
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivisor) ).
fof(mMulOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulOne) ).
fof(mMulMinOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
& smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulMinOne) ).
fof(c_0_14,hypothesis,
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ! [X1] :
( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> ( aInteger0(X1)
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X1,sz10,xp) ) )
& ( ( aInteger0(X1)
& ( ? [X2] :
( aInteger0(X2)
& sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10)) )
| aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(X1,sz10,xp) ) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( aInteger0(X1)
& ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) ) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
& ! [X1] :
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> aElementOf0(X1,stldt0(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
inference(fof_simplification,[status(thm)],[m__2171]) ).
fof(c_0_15,hypothesis,
! [X155,X157,X158,X159,X161,X162,X163,X164] :
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ( aInteger0(X155)
| ~ aElementOf0(X155,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aInteger0(esk26_1(X155))
| ~ aElementOf0(X155,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( sdtasdt0(xp,esk26_1(X155)) = sdtpldt0(X155,smndt0(sz10))
| ~ aElementOf0(X155,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aDivisorOf0(xp,sdtpldt0(X155,smndt0(sz10)))
| ~ aElementOf0(X155,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( sdteqdtlpzmzozddtrp0(X155,sz10,xp)
| ~ aElementOf0(X155,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ aInteger0(X158)
| sdtasdt0(xp,X158) != sdtpldt0(X157,smndt0(sz10))
| ~ aInteger0(X157)
| aElementOf0(X157,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ aDivisorOf0(xp,sdtpldt0(X157,smndt0(sz10)))
| ~ aInteger0(X157)
| aElementOf0(X157,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ sdteqdtlpzmzozddtrp0(X157,sz10,xp)
| ~ aInteger0(X157)
| aElementOf0(X157,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& aSet0(sbsmnsldt0(xS))
& ( aInteger0(X159)
| ~ aElementOf0(X159,sbsmnsldt0(xS)) )
& ( aElementOf0(esk27_1(X159),xS)
| ~ aElementOf0(X159,sbsmnsldt0(xS)) )
& ( aElementOf0(X159,esk27_1(X159))
| ~ aElementOf0(X159,sbsmnsldt0(xS)) )
& ( ~ aInteger0(X161)
| ~ aElementOf0(X162,xS)
| ~ aElementOf0(X161,X162)
| aElementOf0(X161,sbsmnsldt0(xS)) )
& ( aInteger0(X163)
| ~ aElementOf0(X163,stldt0(sbsmnsldt0(xS))) )
& ( ~ aElementOf0(X163,sbsmnsldt0(xS))
| ~ aElementOf0(X163,stldt0(sbsmnsldt0(xS))) )
& ( ~ aInteger0(X163)
| aElementOf0(X163,sbsmnsldt0(xS))
| aElementOf0(X163,stldt0(sbsmnsldt0(xS))) )
& ( ~ aElementOf0(X164,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(X164,stldt0(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
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_14])])])])])]) ).
fof(c_0_16,plain,
! [X38,X39] :
( ~ aInteger0(X38)
| ~ aInteger0(X39)
| X39 = sz00
| sdteqdtlpzmzozddtrp0(X38,X38,X39) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquModRef])]) ).
cnf(c_0_17,hypothesis,
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ sdteqdtlpzmzozddtrp0(X1,sz10,xp)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,plain,
( X2 = sz00
| sdteqdtlpzmzozddtrp0(X1,X1,X2)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]) ).
cnf(c_0_20,hypothesis,
aInteger0(xp),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_22,plain,
! [X28,X29] :
( ~ aInteger0(X28)
| ~ aInteger0(X29)
| sdtasdt0(X28,X29) != sz00
| X28 = sz00
| X29 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroDiv])]) ).
cnf(c_0_23,hypothesis,
( sdtasdt0(xp,esk26_1(X1)) = sdtpldt0(X1,smndt0(sz10))
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,hypothesis,
aElementOf0(sz10,szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]),c_0_21]) ).
cnf(c_0_25,hypothesis,
( aInteger0(esk26_1(X1))
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_26,plain,
( X1 = sz00
| X2 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,hypothesis,
sdtasdt0(xp,esk26_1(sz10)) = sdtpldt0(sz10,smndt0(sz10)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,hypothesis,
aInteger0(esk26_1(sz10)),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
fof(c_0_29,plain,
! [X16] :
( ( sdtpldt0(X16,smndt0(X16)) = sz00
| ~ aInteger0(X16) )
& ( sz00 = sdtpldt0(smndt0(X16),X16)
| ~ aInteger0(X16) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])]) ).
fof(c_0_30,hypothesis,
( aSet0(sbsmnsldt0(xS))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( aInteger0(X1)
& ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) ) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( X1 = sz10
| X1 = smndt0(sz10) ) )
& stldt0(sbsmnsldt0(xS)) = cS2076 ),
inference(fof_simplification,[status(thm)],[m__2079]) ).
cnf(c_0_31,hypothesis,
( esk26_1(sz10) = sz00
| sdtpldt0(sz10,smndt0(sz10)) != sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_20])]),c_0_21]) ).
cnf(c_0_32,plain,
( sdtpldt0(X1,smndt0(X1)) = sz00
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_33,hypothesis,
! [X125,X127,X128,X129,X130] :
( aSet0(sbsmnsldt0(xS))
& ( aInteger0(X125)
| ~ aElementOf0(X125,sbsmnsldt0(xS)) )
& ( aElementOf0(esk19_1(X125),xS)
| ~ aElementOf0(X125,sbsmnsldt0(xS)) )
& ( aElementOf0(X125,esk19_1(X125))
| ~ aElementOf0(X125,sbsmnsldt0(xS)) )
& ( ~ aInteger0(X127)
| ~ aElementOf0(X128,xS)
| ~ aElementOf0(X127,X128)
| aElementOf0(X127,sbsmnsldt0(xS)) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ( aInteger0(X129)
| ~ aElementOf0(X129,stldt0(sbsmnsldt0(xS))) )
& ( ~ aElementOf0(X129,sbsmnsldt0(xS))
| ~ aElementOf0(X129,stldt0(sbsmnsldt0(xS))) )
& ( ~ aInteger0(X129)
| aElementOf0(X129,sbsmnsldt0(xS))
| aElementOf0(X129,stldt0(sbsmnsldt0(xS))) )
& ( ~ aElementOf0(X130,stldt0(sbsmnsldt0(xS)))
| X130 = sz10
| X130 = smndt0(sz10) )
& ( X130 != sz10
| aElementOf0(X130,stldt0(sbsmnsldt0(xS))) )
& ( X130 != smndt0(sz10)
| aElementOf0(X130,stldt0(sbsmnsldt0(xS))) )
& stldt0(sbsmnsldt0(xS)) = cS2076 ),
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_30])])])])])]) ).
cnf(c_0_34,hypothesis,
esk26_1(sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_19])]) ).
cnf(c_0_35,hypothesis,
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
| X1 != smndt0(sz10) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_36,hypothesis,
stldt0(sbsmnsldt0(xS)) = cS2076,
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_37,negated_conjecture,
~ ( ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) )
| aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
| aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)) )
| aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
| aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_38,hypothesis,
sdtpldt0(sz10,smndt0(sz10)) = sdtasdt0(xp,sz00),
inference(rw,[status(thm)],[c_0_27,c_0_34]) ).
cnf(c_0_39,hypothesis,
( aInteger0(X1)
| ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,hypothesis,
( aElementOf0(X1,cS2076)
| X1 != smndt0(sz10) ),
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_41,negated_conjecture,
! [X165,X166] :
( ( ~ aInteger0(X166)
| sdtasdt0(xp,X166) != sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
| ~ aInteger0(X165)
| sdtasdt0(xp,X165) != sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) )
& ( ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
| ~ aInteger0(X165)
| sdtasdt0(xp,X165) != sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) )
& ( ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
| ~ aInteger0(X165)
| sdtasdt0(xp,X165) != sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) )
& ( ~ aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X165)
| sdtasdt0(xp,X165) != sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) )
& ( ~ aInteger0(X166)
| sdtasdt0(xp,X166) != sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
| ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))) )
& ( ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
| ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))) )
& ( ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
| ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))) )
& ( ~ aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))) )
& ( ~ aInteger0(X166)
| sdtasdt0(xp,X166) != sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
| ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp) )
& ( ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
| ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp) )
& ( ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
| ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp) )
& ( ~ aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp) )
& ( ~ aInteger0(X166)
| sdtasdt0(xp,X166) != sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
| ~ aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
| ~ aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
| ~ aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])])]) ).
fof(c_0_42,plain,
! [X10,X11,X12] :
( ~ aInteger0(X10)
| ~ aInteger0(X11)
| ~ aInteger0(X12)
| sdtpldt0(X10,sdtpldt0(X11,X12)) = sdtpldt0(sdtpldt0(X10,X11),X12) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
cnf(c_0_43,hypothesis,
sdtasdt0(xp,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_38]),c_0_19])]) ).
cnf(c_0_44,hypothesis,
( aInteger0(X1)
| ~ aElementOf0(X1,cS2076) ),
inference(rw,[status(thm)],[c_0_39,c_0_36]) ).
cnf(c_0_45,hypothesis,
aElementOf0(smndt0(sz10),cS2076),
inference(er,[status(thm)],[c_0_40]) ).
cnf(c_0_46,negated_conjecture,
( ~ aInteger0(X1)
| sdtasdt0(xp,X1) != sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
| ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_47,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_48,plain,
! [X5] :
( ~ aInteger0(X5)
| aInteger0(smndt0(X5)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).
cnf(c_0_49,hypothesis,
sdtpldt0(sz10,smndt0(sz10)) = sz00,
inference(rw,[status(thm)],[c_0_38,c_0_43]) ).
cnf(c_0_50,hypothesis,
aInteger0(smndt0(sz10)),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
fof(c_0_51,plain,
! [X13,X14] :
( ~ aInteger0(X13)
| ~ aInteger0(X14)
| sdtpldt0(X13,X14) = sdtpldt0(X14,X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_52,negated_conjecture,
( sdtasdt0(xp,X1) != sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
| ~ aDivisorOf0(xp,sdtpldt0(sz10,sdtpldt0(xp,smndt0(sz10))))
| ~ aInteger0(smndt0(sz10))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_20]),c_0_19])]) ).
cnf(c_0_53,plain,
( aInteger0(smndt0(X1))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_54,hypothesis,
( sdtpldt0(sz10,sdtpldt0(smndt0(sz10),X1)) = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_49]),c_0_50]),c_0_19])]) ).
cnf(c_0_55,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_56,negated_conjecture,
( sdtasdt0(xp,X1) != sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
| ~ aDivisorOf0(xp,sdtpldt0(sz10,sdtpldt0(xp,smndt0(sz10))))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_19])]) ).
cnf(c_0_57,hypothesis,
( sdtpldt0(sz10,sdtpldt0(X1,smndt0(sz10))) = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_50])]) ).
fof(c_0_58,plain,
! [X15] :
( ( sdtpldt0(X15,sz00) = X15
| ~ aInteger0(X15) )
& ( X15 = sdtpldt0(sz00,X15)
| ~ aInteger0(X15) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
fof(c_0_59,plain,
! [X30,X31,X33,X34] :
( ( aInteger0(X31)
| ~ aDivisorOf0(X31,X30)
| ~ aInteger0(X30) )
& ( X31 != sz00
| ~ aDivisorOf0(X31,X30)
| ~ aInteger0(X30) )
& ( aInteger0(esk1_2(X30,X31))
| ~ aDivisorOf0(X31,X30)
| ~ aInteger0(X30) )
& ( sdtasdt0(X31,esk1_2(X30,X31)) = X30
| ~ aDivisorOf0(X31,X30)
| ~ aInteger0(X30) )
& ( ~ aInteger0(X33)
| X33 = sz00
| ~ aInteger0(X34)
| sdtasdt0(X33,X34) != X30
| aDivisorOf0(X33,X30)
| ~ aInteger0(X30) ) ),
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)],[mDivisor])])])])])]) ).
fof(c_0_60,plain,
! [X22] :
( ( sdtasdt0(X22,sz10) = X22
| ~ aInteger0(X22) )
& ( X22 = sdtasdt0(sz10,X22)
| ~ aInteger0(X22) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulOne])])]) ).
cnf(c_0_61,negated_conjecture,
( sdtasdt0(xp,X1) != sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
| ~ aDivisorOf0(xp,sdtpldt0(sz00,xp))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_20])]) ).
cnf(c_0_62,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_63,plain,
( X1 = sz00
| aDivisorOf0(X1,X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X3
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_64,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_65,negated_conjecture,
( sdtasdt0(xp,X1) != sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
| ~ aDivisorOf0(xp,xp)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_20])]) ).
cnf(c_0_66,plain,
( X1 = sz00
| aDivisorOf0(X1,X1)
| ~ aInteger0(X1) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_19])])]) ).
cnf(c_0_67,negated_conjecture,
( sdtasdt0(xp,X1) != sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
| ~ aInteger0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_20])]),c_0_21]) ).
cnf(c_0_68,negated_conjecture,
( sdtasdt0(xp,X1) != sdtpldt0(sz10,sdtpldt0(smndt0(xp),smndt0(sz10)))
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_47]),c_0_50]),c_0_19])]) ).
cnf(c_0_69,negated_conjecture,
( sdtasdt0(xp,X1) != sdtpldt0(sz10,sdtpldt0(smndt0(xp),smndt0(sz10)))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_53]),c_0_20])]) ).
cnf(c_0_70,hypothesis,
( sdtasdt0(xp,X1) != sdtpldt0(sz00,smndt0(xp))
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(X1) ),
inference(spm,[status(thm)],[c_0_69,c_0_57]) ).
fof(c_0_71,plain,
! [X27] :
( ( sdtasdt0(smndt0(sz10),X27) = smndt0(X27)
| ~ aInteger0(X27) )
& ( smndt0(X27) = sdtasdt0(X27,smndt0(sz10))
| ~ aInteger0(X27) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMinOne])])]) ).
cnf(c_0_72,hypothesis,
( sdtasdt0(xp,X1) != sdtpldt0(sz00,smndt0(xp))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_53]),c_0_20])]) ).
cnf(c_0_73,plain,
( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_74,hypothesis,
sdtpldt0(sz00,smndt0(xp)) != smndt0(xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_50]),c_0_20])]) ).
cnf(c_0_75,hypothesis,
~ aInteger0(smndt0(xp)),
inference(spm,[status(thm)],[c_0_74,c_0_62]) ).
cnf(c_0_76,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_53]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM452+6 : 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
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 11:26:44 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.20/0.68 % Version : CSE_E---1.5
% 0.20/0.68 % Problem : theBenchmark.p
% 0.20/0.68 % Proof found
% 0.20/0.68 % SZS status Theorem for theBenchmark.p
% 0.20/0.68 % SZS output start Proof
% See solution above
% 0.20/0.69 % Total time : 0.094000 s
% 0.20/0.69 % SZS output end Proof
% 0.20/0.69 % Total time : 0.099000 s
%------------------------------------------------------------------------------