TSTP Solution File: NUM495+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM495+1 : 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 : n012.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 10:38:03 EDT 2023
% Result : Theorem 0.20s 0.58s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 30
% Syntax : Number of formulae : 59 ( 19 unt; 19 typ; 0 def)
% Number of atoms : 115 ( 15 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 132 ( 57 ~; 51 |; 15 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 13 >; 9 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn; 20 !; 0 ?; 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,
xr: $i ).
tff(decl_37,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_39,type,
esk3_1: $i > $i ).
tff(decl_40,type,
esk4_1: $i > $i ).
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/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(m__,conjecture,
( doDivides0(xp,xr)
| doDivides0(xp,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__1799,hypothesis,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( isPrime0(X3)
& doDivides0(X3,sdtasdt0(X1,X2)) )
=> ( iLess0(sdtpldt0(sdtpldt0(X1,X2),X3),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(X3,X1)
| doDivides0(X3,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1799) ).
fof(m__1870,hypothesis,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
fof(m__1883,hypothesis,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1883) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(mIH_03,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != X2
& sdtlseqdt0(X1,X2) )
=> iLess0(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH_03) ).
fof(m__1913,hypothesis,
doDivides0(xp,sdtasdt0(xr,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1913) ).
fof(m__1860,hypothesis,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(m__2062,hypothesis,
( sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp)
& sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2062) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(c_0_11,plain,
! [X38,X39,X40] :
( ( aNaturalNumber0(X40)
| X40 != sdtmndt0(X39,X38)
| ~ sdtlseqdt0(X38,X39)
| ~ aNaturalNumber0(X38)
| ~ aNaturalNumber0(X39) )
& ( sdtpldt0(X38,X40) = X39
| X40 != sdtmndt0(X39,X38)
| ~ sdtlseqdt0(X38,X39)
| ~ aNaturalNumber0(X38)
| ~ aNaturalNumber0(X39) )
& ( ~ aNaturalNumber0(X40)
| sdtpldt0(X38,X40) != X39
| X40 = sdtmndt0(X39,X38)
| ~ sdtlseqdt0(X38,X39)
| ~ aNaturalNumber0(X38)
| ~ aNaturalNumber0(X39) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])]) ).
cnf(c_0_12,plain,
( aNaturalNumber0(X1)
| X1 != sdtmndt0(X2,X3)
| ~ sdtlseqdt0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_13,negated_conjecture,
~ ( doDivides0(xp,xr)
| doDivides0(xp,xm) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_14,hypothesis,
! [X86,X87,X88] :
( ~ aNaturalNumber0(X86)
| ~ aNaturalNumber0(X87)
| ~ aNaturalNumber0(X88)
| ~ isPrime0(X88)
| ~ doDivides0(X88,sdtasdt0(X86,X87))
| ~ iLess0(sdtpldt0(sdtpldt0(X86,X87),X88),sdtpldt0(sdtpldt0(xn,xm),xp))
| doDivides0(X88,X86)
| doDivides0(X88,X87) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1799])]) ).
cnf(c_0_15,plain,
( aNaturalNumber0(sdtmndt0(X1,X2))
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_16,hypothesis,
sdtlseqdt0(xp,xn),
inference(split_conjunct,[status(thm)],[m__1870]) ).
cnf(c_0_17,hypothesis,
xr = sdtmndt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__1883]) ).
cnf(c_0_18,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_19,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_20,negated_conjecture,
( ~ doDivides0(xp,xr)
& ~ doDivides0(xp,xm) ),
inference(fof_nnf,[status(thm)],[c_0_13]) ).
fof(c_0_21,plain,
! [X58,X59] :
( ~ aNaturalNumber0(X58)
| ~ aNaturalNumber0(X59)
| X58 = X59
| ~ sdtlseqdt0(X58,X59)
| iLess0(X58,X59) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIH_03])]) ).
cnf(c_0_22,hypothesis,
( doDivides0(X3,X1)
| doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ isPrime0(X3)
| ~ doDivides0(X3,sdtasdt0(X1,X2))
| ~ iLess0(sdtpldt0(sdtpldt0(X1,X2),X3),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,hypothesis,
doDivides0(xp,sdtasdt0(xr,xm)),
inference(split_conjunct,[status(thm)],[m__1913]) ).
cnf(c_0_24,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_25,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_26,hypothesis,
aNaturalNumber0(xr),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18]),c_0_19])]) ).
cnf(c_0_27,negated_conjecture,
~ doDivides0(xp,xm),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,negated_conjecture,
~ doDivides0(xp,xr),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,plain,
( X1 = X2
| iLess0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,hypothesis,
sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(split_conjunct,[status(thm)],[m__2062]) ).
cnf(c_0_31,hypothesis,
sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[m__2062]) ).
cnf(c_0_32,hypothesis,
~ iLess0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[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_22,c_0_23]),c_0_24]),c_0_18]),c_0_25]),c_0_26])]),c_0_27]),c_0_28]) ).
fof(c_0_33,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| aNaturalNumber0(sdtpldt0(X4,X5)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
cnf(c_0_34,hypothesis,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32]) ).
cnf(c_0_35,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_36,hypothesis,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_18])]) ).
cnf(c_0_37,hypothesis,
~ aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_35]),c_0_25]),c_0_19])]) ).
cnf(c_0_38,hypothesis,
~ aNaturalNumber0(sdtpldt0(xr,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_35]),c_0_18])]) ).
cnf(c_0_39,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_35]),c_0_25]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.16 % Problem : NUM495+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.17 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Aug 25 08:19:41 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.20/0.54 start to proof: theBenchmark
% 0.20/0.58 % Version : CSE_E---1.5
% 0.20/0.58 % Problem : theBenchmark.p
% 0.20/0.58 % Proof found
% 0.20/0.58 % SZS status Theorem for theBenchmark.p
% 0.20/0.58 % SZS output start Proof
% See solution above
% 0.20/0.58 % Total time : 0.028000 s
% 0.20/0.58 % SZS output end Proof
% 0.20/0.58 % Total time : 0.030000 s
%------------------------------------------------------------------------------