TSTP Solution File: NUM507+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM507+3 : 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 : n032.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 10:38:12 EDT 2023
% Result : Theorem 29.73s 29.84s
% Output : CNFRefutation 29.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 49
% Syntax : Number of formulae : 113 ( 23 unt; 31 typ; 0 def)
% Number of atoms : 380 ( 135 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 467 ( 169 ~; 182 |; 95 &)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 17 >; 17 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 14 con; 0-3 aty)
% Number of variables : 93 ( 0 sgn; 52 !; 11 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
aNaturalNumber0: $i > $o ).
tff(decl_23,type,
sz00: $i ).
tff(decl_24,type,
sz10: $i ).
tff(decl_25,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(decl_26,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(decl_27,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(decl_28,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(decl_29,type,
iLess0: ( $i * $i ) > $o ).
tff(decl_30,type,
doDivides0: ( $i * $i ) > $o ).
tff(decl_31,type,
sdtsldt0: ( $i * $i ) > $i ).
tff(decl_32,type,
isPrime0: $i > $o ).
tff(decl_33,type,
xn: $i ).
tff(decl_34,type,
xm: $i ).
tff(decl_35,type,
xp: $i ).
tff(decl_36,type,
xk: $i ).
tff(decl_37,type,
xr: $i ).
tff(decl_38,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_39,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_40,type,
esk3_1: $i > $i ).
tff(decl_41,type,
esk4_1: $i > $i ).
tff(decl_42,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_43,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_44,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_45,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
esk9_0: $i ).
tff(decl_47,type,
esk10_0: $i ).
tff(decl_48,type,
esk11_0: $i ).
tff(decl_49,type,
esk12_0: $i ).
tff(decl_50,type,
esk13_0: $i ).
tff(decl_51,type,
esk14_0: $i ).
tff(decl_52,type,
esk15_0: $i ).
fof(m__,conjecture,
( sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp)
& ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),X1) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(m__2342,hypothesis,
( aNaturalNumber0(xr)
& ? [X1] :
( aNaturalNumber0(X1)
& xk = sdtasdt0(xr,X1) )
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& xr = sdtasdt0(X1,X2) )
| doDivides0(X1,xr) ) )
=> ( X1 = sz10
| X1 = xr ) )
& isPrime0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(mLETran,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X3) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETran) ).
fof(m__2377,hypothesis,
( xk != xp
& ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xk,X1) = xp )
& sdtlseqdt0(xk,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2377) ).
fof(m__2362,hypothesis,
( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xr,X1) = xk )
& ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xn,xm) = sdtasdt0(xr,X1) )
& doDivides0(xr,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2362) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(mMonAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != X2
& sdtlseqdt0(X1,X2) )
=> ! [X3] :
( aNaturalNumber0(X3)
=> ( sdtpldt0(X3,X1) != sdtpldt0(X3,X2)
& sdtlseqdt0(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
& sdtpldt0(X1,X3) != sdtpldt0(X2,X3)
& sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X3)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonAdd) ).
fof(m__2306,hypothesis,
( aNaturalNumber0(xk)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(m__1860,hypothesis,
( xp != sz00
& xp != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& xp = sdtasdt0(X1,X2) )
| doDivides0(X1,xp) ) )
=> ( X1 = sz10
| X1 = xp ) )
& isPrime0(xp)
& ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X1) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(mPrimDiv,axiom,
! [X1] :
( ( aNaturalNumber0(X1)
& X1 != sz00
& X1 != sz10 )
=> ? [X2] :
( aNaturalNumber0(X2)
& doDivides0(X2,X1)
& isPrime0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPrimDiv) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(mAddCanc,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtpldt0(X1,X2) = sdtpldt0(X1,X3)
| sdtpldt0(X2,X1) = sdtpldt0(X3,X1) )
=> X2 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddCanc) ).
fof(mDefPrime,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( isPrime0(X1)
<=> ( X1 != sz00
& X1 != sz10
& ! [X2] :
( ( aNaturalNumber0(X2)
& doDivides0(X2,X1) )
=> ( X2 = sz10
| X2 = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(mDivLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( doDivides0(X1,X2)
& X2 != sz00 )
=> sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivLE) ).
fof(c_0_18,negated_conjecture,
~ ( sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp)
& ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),X1) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_19,negated_conjecture,
! [X109] :
( ( ~ aNaturalNumber0(X109)
| sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),X109) != sdtpldt0(sdtpldt0(xn,xm),xp)
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp) )
& ( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])]) ).
fof(c_0_20,plain,
! [X10,X11] :
( ~ aNaturalNumber0(X10)
| ~ aNaturalNumber0(X11)
| sdtpldt0(X10,X11) = sdtpldt0(X11,X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
fof(c_0_21,hypothesis,
! [X104,X105] :
( aNaturalNumber0(xr)
& aNaturalNumber0(esk12_0)
& xk = sdtasdt0(xr,esk12_0)
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ( ~ aNaturalNumber0(X105)
| xr != sdtasdt0(X104,X105)
| ~ aNaturalNumber0(X104)
| X104 = sz10
| X104 = xr )
& ( ~ doDivides0(X104,xr)
| ~ aNaturalNumber0(X104)
| X104 = sz10
| X104 = xr )
& isPrime0(xr) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2342])])])])]) ).
fof(c_0_22,plain,
! [X36,X37,X39] :
( ( aNaturalNumber0(esk1_2(X36,X37))
| ~ sdtlseqdt0(X36,X37)
| ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X37) )
& ( sdtpldt0(X36,esk1_2(X36,X37)) = X37
| ~ sdtlseqdt0(X36,X37)
| ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X37) )
& ( ~ aNaturalNumber0(X39)
| sdtpldt0(X36,X39) != X37
| sdtlseqdt0(X36,X37)
| ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X37) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefLE])])])])]) ).
fof(c_0_23,plain,
! [X6,X7] :
( ~ aNaturalNumber0(X6)
| ~ aNaturalNumber0(X7)
| aNaturalNumber0(sdtpldt0(X6,X7)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
cnf(c_0_24,negated_conjecture,
( sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_27,plain,
! [X46,X47,X48] :
( ~ aNaturalNumber0(X46)
| ~ aNaturalNumber0(X47)
| ~ aNaturalNumber0(X48)
| ~ sdtlseqdt0(X46,X47)
| ~ sdtlseqdt0(X47,X48)
| sdtlseqdt0(X46,X48) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])]) ).
fof(c_0_28,hypothesis,
( xk != xp
& aNaturalNumber0(esk15_0)
& sdtpldt0(xk,esk15_0) = xp
& sdtlseqdt0(xk,xp) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2377])]) ).
cnf(c_0_29,plain,
( sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_31,hypothesis,
( aNaturalNumber0(esk13_0)
& sdtpldt0(xr,esk13_0) = xk
& aNaturalNumber0(esk14_0)
& sdtasdt0(xn,xm) = sdtasdt0(xr,esk14_0)
& doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2362])]) ).
cnf(c_0_32,negated_conjecture,
( sdtpldt0(xr,sdtpldt0(xn,xm)) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ sdtlseqdt0(sdtpldt0(xr,sdtpldt0(xn,xm)),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_33,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_34,plain,
! [X51,X52,X53] :
( ( sdtpldt0(X53,X51) != sdtpldt0(X53,X52)
| ~ aNaturalNumber0(X53)
| X51 = X52
| ~ sdtlseqdt0(X51,X52)
| ~ aNaturalNumber0(X51)
| ~ aNaturalNumber0(X52) )
& ( sdtlseqdt0(sdtpldt0(X53,X51),sdtpldt0(X53,X52))
| ~ aNaturalNumber0(X53)
| X51 = X52
| ~ sdtlseqdt0(X51,X52)
| ~ aNaturalNumber0(X51)
| ~ aNaturalNumber0(X52) )
& ( sdtpldt0(X51,X53) != sdtpldt0(X52,X53)
| ~ aNaturalNumber0(X53)
| X51 = X52
| ~ sdtlseqdt0(X51,X52)
| ~ aNaturalNumber0(X51)
| ~ aNaturalNumber0(X52) )
& ( sdtlseqdt0(sdtpldt0(X51,X53),sdtpldt0(X52,X53))
| ~ aNaturalNumber0(X53)
| X51 = X52
| ~ sdtlseqdt0(X51,X52)
| ~ aNaturalNumber0(X51)
| ~ aNaturalNumber0(X52) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonAdd])])])]) ).
cnf(c_0_35,plain,
( sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_36,hypothesis,
sdtlseqdt0(xk,xp),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_37,hypothesis,
aNaturalNumber0(xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_38,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_29]),c_0_30]) ).
cnf(c_0_39,hypothesis,
sdtpldt0(xr,esk13_0) = xk,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_40,hypothesis,
aNaturalNumber0(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_41,negated_conjecture,
( sdtpldt0(xr,sdtpldt0(xn,xm)) = sdtpldt0(xp,sdtpldt0(xn,xm))
| ~ sdtlseqdt0(sdtpldt0(xr,sdtpldt0(xn,xm)),sdtpldt0(xp,sdtpldt0(xn,xm)))
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_25]),c_0_33])]) ).
cnf(c_0_42,plain,
( sdtlseqdt0(sdtpldt0(X1,X2),sdtpldt0(X3,X2))
| X1 = X3
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_43,hypothesis,
( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,xk)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_33]),c_0_37])]) ).
cnf(c_0_44,hypothesis,
sdtlseqdt0(xr,xk),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_26]),c_0_40])]) ).
fof(c_0_45,hypothesis,
! [X96,X97] :
( xp != sz00
& xp != sz10
& ( ~ aNaturalNumber0(X97)
| xp != sdtasdt0(X96,X97)
| ~ aNaturalNumber0(X96)
| X96 = sz10
| X96 = xp )
& ( ~ doDivides0(X96,xp)
| ~ aNaturalNumber0(X96)
| X96 = sz10
| X96 = xp )
& isPrime0(xp)
& aNaturalNumber0(esk9_0)
& sdtasdt0(xn,xm) = sdtasdt0(xp,esk9_0)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1860])])])])]) ).
fof(c_0_46,plain,
! [X86] :
( ( aNaturalNumber0(esk4_1(X86))
| ~ aNaturalNumber0(X86)
| X86 = sz00
| X86 = sz10 )
& ( doDivides0(esk4_1(X86),X86)
| ~ aNaturalNumber0(X86)
| X86 = sz00
| X86 = sz10 )
& ( isPrime0(esk4_1(X86))
| ~ aNaturalNumber0(X86)
| X86 = sz00
| X86 = sz10 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPrimDiv])])])]) ).
fof(c_0_47,plain,
! [X44,X45] :
( ~ aNaturalNumber0(X44)
| ~ aNaturalNumber0(X45)
| ~ sdtlseqdt0(X44,X45)
| ~ sdtlseqdt0(X45,X44)
| X44 = X45 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])]) ).
fof(c_0_48,plain,
! [X26,X27,X28] :
( ( sdtpldt0(X26,X27) != sdtpldt0(X26,X28)
| X27 = X28
| ~ aNaturalNumber0(X26)
| ~ aNaturalNumber0(X27)
| ~ aNaturalNumber0(X28) )
& ( sdtpldt0(X27,X26) != sdtpldt0(X28,X26)
| X27 = X28
| ~ aNaturalNumber0(X26)
| ~ aNaturalNumber0(X27)
| ~ aNaturalNumber0(X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])]) ).
cnf(c_0_49,negated_conjecture,
( sdtpldt0(xr,sdtpldt0(xn,xm)) = sdtpldt0(xp,sdtpldt0(xn,xm))
| xr = xp
| ~ sdtlseqdt0(xr,xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_33]),c_0_26])]) ).
cnf(c_0_50,hypothesis,
sdtlseqdt0(xr,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_26])]) ).
cnf(c_0_51,hypothesis,
( X1 = sz10
| X1 = xp
| ~ doDivides0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_52,plain,
( doDivides0(esk4_1(X1),X1)
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_53,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_54,hypothesis,
xp != sz10,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_55,plain,
! [X83,X84] :
( ( X83 != sz00
| ~ isPrime0(X83)
| ~ aNaturalNumber0(X83) )
& ( X83 != sz10
| ~ isPrime0(X83)
| ~ aNaturalNumber0(X83) )
& ( ~ aNaturalNumber0(X84)
| ~ doDivides0(X84,X83)
| X84 = sz10
| X84 = X83
| ~ isPrime0(X83)
| ~ aNaturalNumber0(X83) )
& ( aNaturalNumber0(esk3_1(X83))
| X83 = sz00
| X83 = sz10
| isPrime0(X83)
| ~ aNaturalNumber0(X83) )
& ( doDivides0(esk3_1(X83),X83)
| X83 = sz00
| X83 = sz10
| isPrime0(X83)
| ~ aNaturalNumber0(X83) )
& ( esk3_1(X83) != sz10
| X83 = sz00
| X83 = sz10
| isPrime0(X83)
| ~ aNaturalNumber0(X83) )
& ( esk3_1(X83) != X83
| X83 = sz00
| X83 = sz10
| isPrime0(X83)
| ~ aNaturalNumber0(X83) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefPrime])])])])]) ).
cnf(c_0_56,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_57,hypothesis,
xk != xp,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_58,plain,
( X1 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X3,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_59,negated_conjecture,
( sdtpldt0(xr,sdtpldt0(xn,xm)) = sdtpldt0(xp,sdtpldt0(xn,xm))
| xr = xp
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]) ).
cnf(c_0_60,hypothesis,
( esk4_1(xp) = xp
| esk4_1(xp) = sz10
| ~ aNaturalNumber0(esk4_1(xp)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_33])]),c_0_53]),c_0_54]) ).
cnf(c_0_61,plain,
( aNaturalNumber0(esk4_1(X1))
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_62,plain,
( X1 != sz10
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_63,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_64,hypothesis,
~ sdtlseqdt0(xp,xk),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_36]),c_0_37]),c_0_33])]),c_0_57]) ).
cnf(c_0_65,hypothesis,
( sdtlseqdt0(X1,xk)
| ~ sdtlseqdt0(X1,xr)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_44]),c_0_37]),c_0_26])]) ).
fof(c_0_66,plain,
! [X78,X79] :
( ~ aNaturalNumber0(X78)
| ~ aNaturalNumber0(X79)
| ~ doDivides0(X78,X79)
| X79 = sz00
| sdtlseqdt0(X78,X79) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivLE])]) ).
cnf(c_0_67,negated_conjecture,
( xr = xp
| X1 = xr
| sdtpldt0(X1,sdtpldt0(xn,xm)) != sdtpldt0(xp,sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_26])]) ).
cnf(c_0_68,plain,
( isPrime0(esk4_1(X1))
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_69,hypothesis,
( esk4_1(xp) = sz10
| esk4_1(xp) = xp ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_33])]),c_0_53]),c_0_54]) ).
cnf(c_0_70,plain,
~ isPrime0(sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_62]),c_0_63])]) ).
cnf(c_0_71,hypothesis,
~ sdtlseqdt0(xp,xr),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_33])]) ).
cnf(c_0_72,plain,
( X2 = sz00
| sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_73,hypothesis,
xr != sz00,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_74,negated_conjecture,
( xr = xp
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_67]),c_0_33])]) ).
cnf(c_0_75,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_76,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_77,hypothesis,
esk4_1(xp) = xp,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_33])]),c_0_53]),c_0_54]),c_0_70]) ).
cnf(c_0_78,hypothesis,
~ doDivides0(xp,xr),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_26]),c_0_33])]),c_0_73]) ).
cnf(c_0_79,negated_conjecture,
xr = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_30]),c_0_75]),c_0_76])]) ).
cnf(c_0_80,hypothesis,
doDivides0(xp,xp),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_77]),c_0_33])]),c_0_53]),c_0_54]) ).
cnf(c_0_81,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_79]),c_0_80])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : NUM507+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.10 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.08/0.30 % Computer : n032.cluster.edu
% 0.08/0.30 % Model : x86_64 x86_64
% 0.08/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.30 % Memory : 8042.1875MB
% 0.08/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.30 % CPULimit : 300
% 0.08/0.30 % WCLimit : 300
% 0.08/0.30 % DateTime : Fri Aug 25 13:39:13 EDT 2023
% 0.08/0.30 % CPUTime :
% 0.14/0.45 start to proof: theBenchmark
% 29.73/29.84 % Version : CSE_E---1.5
% 29.73/29.84 % Problem : theBenchmark.p
% 29.73/29.84 % Proof found
% 29.73/29.84 % SZS status Theorem for theBenchmark.p
% 29.73/29.84 % SZS output start Proof
% See solution above
% 29.73/29.85 % Total time : 29.379000 s
% 29.73/29.85 % SZS output end Proof
% 29.73/29.85 % Total time : 29.383000 s
%------------------------------------------------------------------------------