TSTP Solution File: NUM505+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM505+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 : n019.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 10:38:10 EDT 2023
% Result : Theorem 0.18s 0.60s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 36
% Syntax : Number of formulae : 50 ( 7 unt; 30 typ; 0 def)
% Number of atoms : 65 ( 22 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 72 ( 27 ~; 23 |; 18 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 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 : 25 ( 25 usr; 13 con; 0-3 aty)
% Number of variables : 16 ( 0 sgn; 8 !; 4 ?; 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 ).
fof(m__,conjecture,
( ~ ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xp,X1) = xk )
| sdtlseqdt0(xp,xk) )
=> ( xk != xp
& ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xk,X1) = xp )
| sdtlseqdt0(xk,xp) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
| ( X2 != X1
& sdtlseqdt0(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(m__2306,hypothesis,
( aNaturalNumber0(xk)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(c_0_6,negated_conjecture,
~ ( ~ ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xp,X1) = xk )
| sdtlseqdt0(xp,xk) )
=> ( xk != xp
& ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xk,X1) = xp )
| sdtlseqdt0(xk,xp) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_7,negated_conjecture,
! [X108,X109] :
( ( ~ aNaturalNumber0(X108)
| sdtpldt0(xp,X108) != xk )
& ~ sdtlseqdt0(xp,xk)
& ( ~ aNaturalNumber0(X109)
| sdtpldt0(xk,X109) != xp
| xk = xp )
& ( ~ sdtlseqdt0(xk,xp)
| xk = xp ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_8,plain,
! [X15] :
( ( sdtpldt0(X15,sz00) = X15
| ~ aNaturalNumber0(X15) )
& ( X15 = sdtpldt0(sz00,X15)
| ~ aNaturalNumber0(X15) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
fof(c_0_9,plain,
! [X49,X50] :
( ( X50 != X49
| sdtlseqdt0(X49,X50)
| ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X50) )
& ( sdtlseqdt0(X50,X49)
| sdtlseqdt0(X49,X50)
| ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X50) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).
cnf(c_0_10,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(xp,X1) != xk ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_13,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_14,negated_conjecture,
( xk = xp
| ~ sdtlseqdt0(xk,xp) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,hypothesis,
aNaturalNumber0(xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_17,negated_conjecture,
xk != xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13])]) ).
cnf(c_0_18,negated_conjecture,
~ sdtlseqdt0(xp,xk),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_13]),c_0_16])]),c_0_17]),c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM505+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
% 0.12/0.33 % Computer : n019.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Aug 25 16:13:13 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.53 start to proof: theBenchmark
% 0.18/0.60 % Version : CSE_E---1.5
% 0.18/0.60 % Problem : theBenchmark.p
% 0.18/0.60 % Proof found
% 0.18/0.60 % SZS status Theorem for theBenchmark.p
% 0.18/0.60 % SZS output start Proof
% See solution above
% 0.18/0.60 % Total time : 0.061000 s
% 0.18/0.60 % SZS output end Proof
% 0.18/0.60 % Total time : 0.064000 s
%------------------------------------------------------------------------------