TSTP Solution File: NUM516+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM516+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n010.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 10:38:18 EDT 2023
% Result : Theorem 224.64s 224.58s
% Output : CNFRefutation 224.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 52
% Syntax : Number of formulae : 117 ( 22 unt; 36 typ; 0 def)
% Number of atoms : 389 ( 136 equ)
% Maximal formula atoms : 27 ( 4 avg)
% Number of connectives : 488 ( 180 ~; 181 |; 104 &)
% ( 4 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 5 ( 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 : 31 ( 31 usr; 19 con; 0-3 aty)
% Number of variables : 115 ( 0 sgn; 56 !; 10 ?; 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 ).
tff(decl_53,type,
esk16_0: $i ).
tff(decl_54,type,
esk17_0: $i ).
tff(decl_55,type,
esk18_0: $i ).
tff(decl_56,type,
esk19_0: $i ).
tff(decl_57,type,
esk20_0: $i ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mDefDiff,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
=> ! [X3] :
( X3 = sdtmndt0(X2,X1)
<=> ( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(m__,conjecture,
( ~ ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
& ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
=> ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),X1) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mDefQuot,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != sz00
& doDivides0(X1,X2) )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
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/sandbox/benchmark/theBenchmark.p',m__2342) ).
fof(m__2287,hypothesis,
( xn != xp
& ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xn,X1) = xp )
& sdtlseqdt0(xn,xp)
& xm != xp
& ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xm,X1) = xp )
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2287) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(m__2504,hypothesis,
( ~ ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
=> sdtsldt0(xn,xr) = xn )
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtsldt0(xn,xr),X1) = xn )
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2504) ).
fof(m__2487,hypothesis,
( ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xr,X1) )
& doDivides0(xr,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2487) ).
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/sandbox/benchmark/theBenchmark.p',mMonAdd) ).
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/sandbox/benchmark/theBenchmark.p',mAddCanc) ).
fof(c_0_16,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_17,plain,
! [X6,X7] :
( ~ aNaturalNumber0(X6)
| ~ aNaturalNumber0(X7)
| aNaturalNumber0(sdtpldt0(X6,X7)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
fof(c_0_18,plain,
! [X62,X63,X65] :
( ( aNaturalNumber0(esk2_2(X62,X63))
| ~ doDivides0(X62,X63)
| ~ aNaturalNumber0(X62)
| ~ aNaturalNumber0(X63) )
& ( X63 = sdtasdt0(X62,esk2_2(X62,X63))
| ~ doDivides0(X62,X63)
| ~ aNaturalNumber0(X62)
| ~ aNaturalNumber0(X63) )
& ( ~ aNaturalNumber0(X65)
| X63 != sdtasdt0(X62,X65)
| doDivides0(X62,X63)
| ~ aNaturalNumber0(X62)
| ~ aNaturalNumber0(X63) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])]) ).
fof(c_0_19,plain,
! [X8,X9] :
( ~ aNaturalNumber0(X8)
| ~ aNaturalNumber0(X9)
| aNaturalNumber0(sdtasdt0(X8,X9)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(c_0_20,plain,
! [X40,X41,X42] :
( ( aNaturalNumber0(X42)
| X42 != sdtmndt0(X41,X40)
| ~ sdtlseqdt0(X40,X41)
| ~ aNaturalNumber0(X40)
| ~ aNaturalNumber0(X41) )
& ( sdtpldt0(X40,X42) = X41
| X42 != sdtmndt0(X41,X40)
| ~ sdtlseqdt0(X40,X41)
| ~ aNaturalNumber0(X40)
| ~ aNaturalNumber0(X41) )
& ( ~ aNaturalNumber0(X42)
| sdtpldt0(X40,X42) != X41
| X42 = sdtmndt0(X41,X40)
| ~ sdtlseqdt0(X40,X41)
| ~ aNaturalNumber0(X40)
| ~ aNaturalNumber0(X41) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])]) ).
cnf(c_0_21,plain,
( sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_23,negated_conjecture,
~ ( ~ ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
& ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
=> ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),X1) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_24,plain,
! [X66,X67,X68] :
( ( aNaturalNumber0(X68)
| X68 != sdtsldt0(X67,X66)
| X66 = sz00
| ~ doDivides0(X66,X67)
| ~ aNaturalNumber0(X66)
| ~ aNaturalNumber0(X67) )
& ( X67 = sdtasdt0(X66,X68)
| X68 != sdtsldt0(X67,X66)
| X66 = sz00
| ~ doDivides0(X66,X67)
| ~ aNaturalNumber0(X66)
| ~ aNaturalNumber0(X67) )
& ( ~ aNaturalNumber0(X68)
| X67 != sdtasdt0(X66,X68)
| X68 = sdtsldt0(X67,X66)
| X66 = sz00
| ~ doDivides0(X66,X67)
| ~ aNaturalNumber0(X66)
| ~ aNaturalNumber0(X67) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
cnf(c_0_25,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
( X1 = sdtmndt0(X3,X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_21]),c_0_22]) ).
fof(c_0_29,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_30,negated_conjecture,
! [X114] :
( ( aNaturalNumber0(sdtsldt0(xn,xr))
| aNaturalNumber0(sdtsldt0(xn,xr)) )
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| aNaturalNumber0(sdtsldt0(xn,xr)) )
& ( ~ aNaturalNumber0(X114)
| sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),X114) != sdtpldt0(sdtpldt0(xn,xm),xp)
| aNaturalNumber0(sdtsldt0(xn,xr)) )
& ( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| aNaturalNumber0(sdtsldt0(xn,xr)) )
& ( aNaturalNumber0(sdtsldt0(xn,xr))
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
& ( ~ aNaturalNumber0(X114)
| sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),X114) != sdtpldt0(sdtpldt0(xn,xm),xp)
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
& ( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
& ( aNaturalNumber0(sdtsldt0(xn,xr))
| sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
& ( ~ aNaturalNumber0(X114)
| sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),X114) != sdtpldt0(sdtpldt0(xn,xm),xp)
| sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
& ( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = 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_23])])])]) ).
fof(c_0_31,plain,
! [X12,X13,X14] :
( ~ aNaturalNumber0(X12)
| ~ aNaturalNumber0(X13)
| ~ aNaturalNumber0(X14)
| sdtpldt0(sdtpldt0(X12,X13),X14) = sdtpldt0(X12,sdtpldt0(X13,X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
cnf(c_0_32,plain,
( X1 = sdtsldt0(X2,X3)
| X3 = sz00
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_25]),c_0_26]) ).
fof(c_0_34,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])])])])]) ).
cnf(c_0_35,plain,
( sdtmndt0(sdtpldt0(X1,X2),X1) = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_27]),c_0_22]),c_0_28]) ).
cnf(c_0_36,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_37,hypothesis,
( xn != xp
& aNaturalNumber0(esk10_0)
& sdtpldt0(xn,esk10_0) = xp
& sdtlseqdt0(xn,xp)
& xm != xp
& aNaturalNumber0(esk11_0)
& sdtpldt0(xm,esk11_0) = xp
& sdtlseqdt0(xm,xp) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2287])]) ).
cnf(c_0_38,negated_conjecture,
( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_39,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_40,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_41,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_42,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_43,hypothesis,
( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& sdtsldt0(xn,xr) != xn
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(esk19_0)
& sdtpldt0(sdtsldt0(xn,xr),esk19_0) = xn
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2504])])]) ).
cnf(c_0_44,plain,
( sdtsldt0(sdtasdt0(X1,X2),X1) = X2
| X1 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_32]),c_0_26]),c_0_33]) ).
cnf(c_0_45,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_46,hypothesis,
xr != sz00,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_47,hypothesis,
( aNaturalNumber0(esk18_0)
& xn = sdtasdt0(xr,esk18_0)
& doDivides0(xr,xn) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2487])]) ).
cnf(c_0_48,plain,
( sdtpldt0(X1,X2) = X3
| X2 != sdtmndt0(X3,X1)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_49,plain,
( sdtmndt0(sdtpldt0(X1,X2),X2) = X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_50,hypothesis,
sdtpldt0(xm,esk11_0) = xp,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_51,hypothesis,
aNaturalNumber0(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_52,plain,
( sdtlseqdt0(X1,sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_36]) ).
cnf(c_0_53,negated_conjecture,
( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(xn,sdtpldt0(xm,xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(xn,sdtpldt0(xm,xp))) ),
inference(cn,[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_40]),c_0_41]),c_0_42])]) ).
cnf(c_0_54,hypothesis,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_55,hypothesis,
( sdtsldt0(sdtasdt0(xr,X1),xr) = X1
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
cnf(c_0_56,hypothesis,
xn = sdtasdt0(xr,esk18_0),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_57,hypothesis,
aNaturalNumber0(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_58,plain,
( sdtpldt0(X1,sdtmndt0(X2,X1)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[c_0_48]) ).
cnf(c_0_59,hypothesis,
sdtmndt0(xp,esk11_0) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_41])]) ).
cnf(c_0_60,hypothesis,
sdtlseqdt0(esk11_0,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_50]),c_0_51]),c_0_41])]) ).
cnf(c_0_61,negated_conjecture,
( sdtpldt0(sdtsldt0(xn,xr),sdtpldt0(xm,xp)) = sdtpldt0(xn,sdtpldt0(xm,xp))
| ~ sdtlseqdt0(sdtpldt0(sdtsldt0(xn,xr),sdtpldt0(xm,xp)),sdtpldt0(xn,sdtpldt0(xm,xp))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_39]),c_0_40]),c_0_41]),c_0_54])]) ).
fof(c_0_62,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_63,hypothesis,
sdtlseqdt0(sdtsldt0(xn,xr),xn),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_64,hypothesis,
sdtsldt0(xn,xr) = esk18_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57])]) ).
cnf(c_0_65,hypothesis,
sdtsldt0(xn,xr) != xn,
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_66,hypothesis,
( sdtpldt0(xm,sdtpldt0(esk11_0,X1)) = sdtpldt0(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_50]),c_0_51]),c_0_41])]) ).
cnf(c_0_67,hypothesis,
sdtpldt0(esk11_0,xm) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]),c_0_40]),c_0_51])]) ).
fof(c_0_68,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_69,negated_conjecture,
( sdtpldt0(sdtsldt0(xn,xr),sdtpldt0(xp,xm)) = sdtpldt0(xn,sdtpldt0(xp,xm))
| ~ sdtlseqdt0(sdtpldt0(sdtsldt0(xn,xr),sdtpldt0(xp,xm)),sdtpldt0(xn,sdtpldt0(xp,xm))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_36]),c_0_40]),c_0_41])]) ).
cnf(c_0_70,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_62]) ).
cnf(c_0_71,hypothesis,
sdtlseqdt0(esk18_0,xn),
inference(rw,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_72,hypothesis,
esk18_0 != xn,
inference(rw,[status(thm)],[c_0_65,c_0_64]) ).
cnf(c_0_73,hypothesis,
sdtpldt0(xm,xp) = sdtpldt0(xp,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_41])]) ).
cnf(c_0_74,plain,
( X1 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X3,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_75,negated_conjecture,
( sdtpldt0(esk18_0,sdtpldt0(xp,xm)) = sdtpldt0(xn,sdtpldt0(xp,xm))
| ~ sdtlseqdt0(sdtpldt0(esk18_0,sdtpldt0(xp,xm)),sdtpldt0(xn,sdtpldt0(xp,xm))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_64]),c_0_64]) ).
cnf(c_0_76,hypothesis,
( sdtlseqdt0(sdtpldt0(esk18_0,X1),sdtpldt0(xn,X1))
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_42]),c_0_57])]),c_0_72]) ).
cnf(c_0_77,hypothesis,
aNaturalNumber0(sdtpldt0(xp,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_73]),c_0_40]),c_0_41])]) ).
cnf(c_0_78,hypothesis,
( X1 = xn
| sdtpldt0(X1,X2) != sdtpldt0(xn,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_74,c_0_42]) ).
cnf(c_0_79,negated_conjecture,
sdtpldt0(esk18_0,sdtpldt0(xp,xm)) = sdtpldt0(xn,sdtpldt0(xp,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77])]) ).
cnf(c_0_80,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_77]),c_0_57])]),c_0_72]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM516+3 : 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 : n010.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 09:18:05 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 224.64/224.58 % Version : CSE_E---1.5
% 224.64/224.58 % Problem : theBenchmark.p
% 224.64/224.58 % Proof found
% 224.64/224.58 % SZS status Theorem for theBenchmark.p
% 224.64/224.58 % SZS output start Proof
% See solution above
% 224.69/224.59 % Total time : 224.006000 s
% 224.69/224.59 % SZS output end Proof
% 224.69/224.59 % Total time : 224.019000 s
%------------------------------------------------------------------------------