TSTP Solution File: NUM454+6 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM454+6 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/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 10:37:39 EDT 2023
% Result : Theorem 0.71s 0.78s
% Output : CNFRefutation 0.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 70
% Syntax : Number of formulae : 147 ( 42 unt; 54 typ; 0 def)
% Number of atoms : 302 ( 100 equ)
% Maximal formula atoms : 44 ( 3 avg)
% Number of connectives : 305 ( 96 ~; 94 |; 93 &)
% ( 4 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 4 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 : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 44 ( 44 usr; 9 con; 0-3 aty)
% Number of variables : 97 ( 0 sgn; 58 !; 8 ?; 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,
esk28_0: $i ).
tff(decl_75,type,
esk29_0: $i ).
fof(m__,conjecture,
( sdtpldt0(sz10,xp) != smndt0(sz10)
| sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
fof(m__2232,hypothesis,
( ? [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/sandbox2/benchmark/theBenchmark.p',m__2232) ).
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/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(mIntOne,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntOne) ).
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/sandbox2/benchmark/theBenchmark.p',m__2171) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(mIntMult,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).
fof(mIntZero,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(mMulMinOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
& smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMinOne) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3) )
=> sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(mDistrib,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistrib) ).
fof(mZeroDiv,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroDiv) ).
fof(c_0_16,negated_conjecture,
~ ( sdtpldt0(sz10,xp) != smndt0(sz10)
| sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_17,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_18,negated_conjecture,
( sdtpldt0(sz10,xp) = smndt0(sz10)
& sdtpldt0(sz10,smndt0(xp)) = smndt0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_16]) ).
fof(c_0_19,plain,
! [X5] :
( ~ aInteger0(X5)
| aInteger0(smndt0(X5)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).
fof(c_0_20,hypothesis,
( aInteger0(esk28_0)
& sdtasdt0(xp,esk28_0) = 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))
& aInteger0(esk29_0)
& sdtasdt0(xp,esk29_0) = 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(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2232])]) ).
fof(c_0_21,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_22,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
sdtpldt0(sz10,xp) = smndt0(sz10),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]) ).
cnf(c_0_25,plain,
( aInteger0(smndt0(X1))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
sdtpldt0(sz10,smndt0(xp)) = smndt0(sz10),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,hypothesis,
sdtasdt0(xp,esk28_0) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_28,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]) ).
cnf(c_0_29,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,negated_conjecture,
sdtpldt0(sdtpldt0(sz10,xp),sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_31,negated_conjecture,
aInteger0(sdtpldt0(sz10,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_23]),c_0_24])]) ).
cnf(c_0_32,hypothesis,
sdtasdt0(xp,esk29_0) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_33,negated_conjecture,
sdtpldt0(sz10,smndt0(xp)) = sdtpldt0(sz10,xp),
inference(rw,[status(thm)],[c_0_26,c_0_23]) ).
cnf(c_0_34,hypothesis,
sdtpldt0(sdtpldt0(sz10,xp),sdtpldt0(sz10,xp)) = sdtasdt0(xp,esk28_0),
inference(rw,[status(thm)],[c_0_27,c_0_23]) ).
fof(c_0_35,plain,
! [X20,X21] :
( ~ aInteger0(X20)
| ~ aInteger0(X21)
| sdtasdt0(X20,X21) = sdtasdt0(X21,X20) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
fof(c_0_36,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_28])])])])])]) ).
fof(c_0_37,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])])]) ).
cnf(c_0_38,negated_conjecture,
( sdtpldt0(sdtpldt0(sz10,xp),sdtpldt0(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_29,c_0_30]),c_0_24]),c_0_31])]) ).
cnf(c_0_39,plain,
( sdtpldt0(X1,smndt0(X1)) = sz00
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_40,hypothesis,
sdtasdt0(xp,esk29_0) = sdtasdt0(xp,esk28_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_23]),c_0_34]) ).
cnf(c_0_41,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_42,hypothesis,
aInteger0(xp),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_43,hypothesis,
aInteger0(esk29_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_44,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_45,negated_conjecture,
sdtpldt0(sdtpldt0(sz10,xp),sz00) = sdtpldt0(sz00,sdtpldt0(sz10,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_23]),c_0_23]),c_0_31]),c_0_24])]) ).
fof(c_0_46,plain,
! [X8,X9] :
( ~ aInteger0(X8)
| ~ aInteger0(X9)
| aInteger0(sdtasdt0(X8,X9)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntMult])]) ).
cnf(c_0_47,hypothesis,
sdtasdt0(xp,esk28_0) = sdtasdt0(esk29_0,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_43])]) ).
cnf(c_0_48,hypothesis,
aInteger0(esk28_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_49,negated_conjecture,
sdtpldt0(sz00,sdtpldt0(sz10,xp)) = sdtpldt0(sz10,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_31])]) ).
cnf(c_0_50,plain,
( aInteger0(sdtasdt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_51,hypothesis,
sdtasdt0(esk29_0,xp) = sdtasdt0(esk28_0,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_47]),c_0_48]),c_0_42])]) ).
cnf(c_0_52,negated_conjecture,
sdtpldt0(sdtpldt0(sz10,xp),sz00) = sdtpldt0(sz10,xp),
inference(rw,[status(thm)],[c_0_45,c_0_49]) ).
cnf(c_0_53,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]) ).
fof(c_0_54,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_55,hypothesis,
aInteger0(sdtasdt0(xp,esk28_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_40]),c_0_43]),c_0_42])]) ).
cnf(c_0_56,hypothesis,
sdtpldt0(sdtpldt0(sz10,xp),sdtpldt0(sz10,xp)) = sdtasdt0(esk28_0,xp),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_47]),c_0_51]) ).
cnf(c_0_57,negated_conjecture,
sdtpldt0(sz10,sdtpldt0(xp,sz00)) = sdtpldt0(sz10,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_52]),c_0_53]),c_0_42]),c_0_24])]) ).
cnf(c_0_58,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_59,hypothesis,
aInteger0(sdtasdt0(esk28_0,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_41]),c_0_48]),c_0_42])]) ).
cnf(c_0_60,hypothesis,
sdtasdt0(esk28_0,xp) = sdtpldt0(sz00,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_38]),c_0_42])]) ).
cnf(c_0_61,negated_conjecture,
sdtpldt0(sz10,sdtpldt0(sz00,xp)) = sdtpldt0(sz10,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_53]),c_0_42])]) ).
cnf(c_0_62,hypothesis,
aInteger0(sdtpldt0(sz00,xp)),
inference(rw,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_63,negated_conjecture,
sdtpldt0(sz00,sdtpldt0(sz00,xp)) = sdtpldt0(sz00,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_61]),c_0_34]),c_0_47]),c_0_51]),c_0_60]),c_0_62])]) ).
cnf(c_0_64,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_65,negated_conjecture,
sdtpldt0(sz00,xp) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_42])]) ).
fof(c_0_66,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_67,hypothesis,
sdtasdt0(xp,esk29_0) = sdtasdt0(esk29_0,xp),
inference(rw,[status(thm)],[c_0_40,c_0_47]) ).
cnf(c_0_68,negated_conjecture,
( sdtpldt0(sz00,smndt0(xp)) = xp
| ~ aInteger0(smndt0(xp)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_33]),c_0_34]),c_0_47]),c_0_51]),c_0_60]),c_0_65]) ).
fof(c_0_69,plain,
! [X17,X18,X19] :
( ~ aInteger0(X17)
| ~ aInteger0(X18)
| ~ aInteger0(X19)
| sdtasdt0(X17,sdtasdt0(X18,X19)) = sdtasdt0(sdtasdt0(X17,X18),X19) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
cnf(c_0_70,plain,
( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_71,hypothesis,
sdtasdt0(xp,esk29_0) = sdtasdt0(esk28_0,xp),
inference(rw,[status(thm)],[c_0_67,c_0_51]) ).
cnf(c_0_72,negated_conjecture,
sdtpldt0(sz00,smndt0(xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_25]),c_0_42])]) ).
cnf(c_0_73,plain,
( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_74,plain,
( sdtasdt0(sdtpldt0(sz10,xp),X1) = smndt0(X1)
| ~ aInteger0(X1) ),
inference(rw,[status(thm)],[c_0_70,c_0_23]) ).
cnf(c_0_75,hypothesis,
sdtasdt0(xp,esk29_0) = sdtpldt0(sz00,xp),
inference(rw,[status(thm)],[c_0_71,c_0_60]) ).
cnf(c_0_76,negated_conjecture,
( smndt0(xp) = xp
| ~ aInteger0(smndt0(xp)) ),
inference(spm,[status(thm)],[c_0_64,c_0_72]) ).
fof(c_0_77,plain,
! [X23,X24,X25] :
( ( sdtasdt0(X23,sdtpldt0(X24,X25)) = sdtpldt0(sdtasdt0(X23,X24),sdtasdt0(X23,X25))
| ~ aInteger0(X23)
| ~ aInteger0(X24)
| ~ aInteger0(X25) )
& ( sdtasdt0(sdtpldt0(X23,X24),X25) = sdtpldt0(sdtasdt0(X23,X25),sdtasdt0(X24,X25))
| ~ aInteger0(X23)
| ~ aInteger0(X24)
| ~ aInteger0(X25) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistrib])])]) ).
cnf(c_0_78,plain,
( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_79,plain,
( sdtasdt0(sdtpldt0(sz10,xp),sdtasdt0(X1,X2)) = sdtasdt0(smndt0(X1),X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_31])]) ).
cnf(c_0_80,hypothesis,
sdtasdt0(xp,esk29_0) = xp,
inference(rw,[status(thm)],[c_0_75,c_0_65]) ).
cnf(c_0_81,negated_conjecture,
smndt0(xp) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_25]),c_0_42])]) ).
cnf(c_0_82,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_83,plain,
( sdtasdt0(X1,sdtpldt0(sz10,xp)) = smndt0(X1)
| ~ aInteger0(X1) ),
inference(rw,[status(thm)],[c_0_78,c_0_23]) ).
cnf(c_0_84,hypothesis,
sdtasdt0(sdtpldt0(sz10,xp),xp) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]),c_0_80]),c_0_43]),c_0_42])]) ).
fof(c_0_85,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_86,plain,
( sdtpldt0(sdtasdt0(X1,X2),smndt0(X1)) = sdtasdt0(X1,sdtpldt0(X2,sdtpldt0(sz10,xp)))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_31])]) ).
cnf(c_0_87,hypothesis,
sdtasdt0(xp,sdtpldt0(sz10,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_84]),c_0_42]),c_0_31])]) ).
cnf(c_0_88,negated_conjecture,
sdtpldt0(xp,xp) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_81]),c_0_42])]) ).
cnf(c_0_89,plain,
( X1 = sz00
| X2 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_90,hypothesis,
sdtasdt0(xp,xp) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_81]),c_0_88]),c_0_34]),c_0_47]),c_0_51]),c_0_60]),c_0_65]),c_0_31]),c_0_42])]) ).
cnf(c_0_91,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_92,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_42])]),c_0_91]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM454+6 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 08:47:08 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.58 start to proof: theBenchmark
% 0.71/0.78 % Version : CSE_E---1.5
% 0.71/0.78 % Problem : theBenchmark.p
% 0.71/0.78 % Proof found
% 0.71/0.78 % SZS status Theorem for theBenchmark.p
% 0.71/0.78 % SZS output start Proof
% See solution above
% 0.71/0.79 % Total time : 0.187000 s
% 0.71/0.79 % SZS output end Proof
% 0.71/0.79 % Total time : 0.192000 s
%------------------------------------------------------------------------------