TSTP Solution File: SWV188+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV188+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n017.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 : 0s
% DateTime : Wed Jul 20 16:22:52 EDT 2022
% Result : Theorem 0.76s 1.30s
% Output : Refutation 0.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SWV188+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.13/0.14 % Command : bliksem %s
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % DateTime : Tue Jun 14 20:54:39 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.74/1.14 *** allocated 10000 integers for termspace/termends
% 0.74/1.14 *** allocated 10000 integers for clauses
% 0.74/1.14 *** allocated 10000 integers for justifications
% 0.74/1.14 Bliksem 1.12
% 0.74/1.14
% 0.74/1.14
% 0.74/1.14 Automatic Strategy Selection
% 0.74/1.14
% 0.74/1.14 *** allocated 15000 integers for termspace/termends
% 0.74/1.14
% 0.74/1.14 Clauses:
% 0.74/1.14
% 0.74/1.14 { gt( X, Y ), gt( Y, X ), X = Y }.
% 0.74/1.14 { ! gt( X, Z ), ! gt( Z, Y ), gt( X, Y ) }.
% 0.74/1.14 { ! gt( X, X ) }.
% 0.74/1.14 { leq( X, X ) }.
% 0.74/1.14 { ! leq( X, Z ), ! leq( Z, Y ), leq( X, Y ) }.
% 0.74/1.14 { ! lt( X, Y ), gt( Y, X ) }.
% 0.74/1.14 { ! gt( Y, X ), lt( X, Y ) }.
% 0.74/1.14 { ! geq( X, Y ), leq( Y, X ) }.
% 0.74/1.14 { ! leq( Y, X ), geq( X, Y ) }.
% 0.74/1.14 { ! gt( Y, X ), leq( X, Y ) }.
% 0.74/1.14 { ! leq( X, Y ), X = Y, gt( Y, X ) }.
% 0.74/1.14 { ! leq( X, pred( Y ) ), gt( Y, X ) }.
% 0.74/1.14 { ! gt( Y, X ), leq( X, pred( Y ) ) }.
% 0.74/1.14 { gt( succ( X ), X ) }.
% 0.74/1.14 { ! leq( X, Y ), leq( X, succ( Y ) ) }.
% 0.74/1.14 { ! leq( X, Y ), gt( succ( Y ), X ) }.
% 0.74/1.14 { ! gt( succ( Y ), X ), leq( X, Y ) }.
% 0.74/1.14 { ! leq( n0, X ), leq( uniform_int_rnd( Y, X ), X ) }.
% 0.74/1.14 { ! leq( n0, X ), leq( n0, uniform_int_rnd( Y, X ) ) }.
% 0.74/1.14 { ! leq( Y, X ), ! leq( X, Z ), a_select2( tptp_const_array1( dim( Y, Z ),
% 0.74/1.14 T ), X ) = T }.
% 0.74/1.14 { ! leq( Y, X ), ! leq( X, Z ), ! leq( U, T ), ! leq( T, W ), a_select3(
% 0.74/1.14 tptp_const_array2( dim( Y, Z ), dim( U, W ), V0 ), X, T ) = V0 }.
% 0.74/1.14 { alpha10( Y, skol1( X, Y ), skol16( X, Y ) ), ! leq( n0, Z ), ! leq( Z, Y
% 0.74/1.14 ), ! leq( n0, T ), ! leq( T, Y ), a_select3( trans( X ), Z, T ) =
% 0.74/1.14 a_select3( trans( X ), T, Z ) }.
% 0.74/1.14 { ! a_select3( X, skol1( X, Y ), skol16( X, Y ) ) = a_select3( X, skol16( X
% 0.74/1.14 , Y ), skol1( X, Y ) ), ! leq( n0, Z ), ! leq( Z, Y ), ! leq( n0, T ), !
% 0.74/1.14 leq( T, Y ), a_select3( trans( X ), Z, T ) = a_select3( trans( X ), T, Z
% 0.74/1.14 ) }.
% 0.74/1.14 { ! alpha10( X, Y, Z ), alpha1( X, Y ) }.
% 0.74/1.14 { ! alpha10( X, Y, Z ), leq( n0, Z ) }.
% 0.74/1.14 { ! alpha10( X, Y, Z ), leq( Z, X ) }.
% 0.74/1.14 { ! alpha1( X, Y ), ! leq( n0, Z ), ! leq( Z, X ), alpha10( X, Y, Z ) }.
% 0.74/1.14 { ! alpha1( X, Y ), leq( n0, Y ) }.
% 0.74/1.14 { ! alpha1( X, Y ), leq( Y, X ) }.
% 0.74/1.14 { ! leq( n0, Y ), ! leq( Y, X ), alpha1( X, Y ) }.
% 0.74/1.14 { alpha11( Y, skol2( X, Y ), skol17( X, Y ) ), ! leq( n0, Z ), ! leq( Z, Y
% 0.74/1.14 ), ! leq( n0, T ), ! leq( T, Y ), a_select3( inv( X ), Z, T ) =
% 0.74/1.14 a_select3( inv( X ), T, Z ) }.
% 0.74/1.14 { ! a_select3( X, skol2( X, Y ), skol17( X, Y ) ) = a_select3( X, skol17( X
% 0.74/1.14 , Y ), skol2( X, Y ) ), ! leq( n0, Z ), ! leq( Z, Y ), ! leq( n0, T ), !
% 0.74/1.14 leq( T, Y ), a_select3( inv( X ), Z, T ) = a_select3( inv( X ), T, Z ) }
% 0.74/1.14 .
% 0.74/1.14 { ! alpha11( X, Y, Z ), alpha2( X, Y ) }.
% 0.74/1.14 { ! alpha11( X, Y, Z ), leq( n0, Z ) }.
% 0.74/1.14 { ! alpha11( X, Y, Z ), leq( Z, X ) }.
% 0.74/1.14 { ! alpha2( X, Y ), ! leq( n0, Z ), ! leq( Z, X ), alpha11( X, Y, Z ) }.
% 0.74/1.14 { ! alpha2( X, Y ), leq( n0, Y ) }.
% 0.74/1.14 { ! alpha2( X, Y ), leq( Y, X ) }.
% 0.74/1.14 { ! leq( n0, Y ), ! leq( Y, X ), alpha2( X, Y ) }.
% 0.74/1.14 { alpha12( Y, skol3( X, Y ), skol18( X, Y ) ), ! leq( n0, Z ), ! leq( Z, Y
% 0.74/1.14 ), ! leq( n0, T ), ! leq( T, Y ), ! leq( n0, U ), ! leq( U, Y ),
% 0.74/1.14 a_select3( tptp_update3( X, U, U, W ), Z, T ) = a_select3( tptp_update3(
% 0.74/1.14 X, U, U, W ), T, Z ) }.
% 0.74/1.14 { ! a_select3( X, skol3( X, Y ), skol18( X, Y ) ) = a_select3( X, skol18( X
% 0.74/1.14 , Y ), skol3( X, Y ) ), ! leq( n0, Z ), ! leq( Z, Y ), ! leq( n0, T ), !
% 0.74/1.14 leq( T, Y ), ! leq( n0, U ), ! leq( U, Y ), a_select3( tptp_update3( X, U
% 0.74/1.14 , U, W ), Z, T ) = a_select3( tptp_update3( X, U, U, W ), T, Z ) }.
% 0.74/1.14 { ! alpha12( X, Y, Z ), alpha3( X, Y ) }.
% 0.74/1.14 { ! alpha12( X, Y, Z ), leq( n0, Z ) }.
% 0.74/1.14 { ! alpha12( X, Y, Z ), leq( Z, X ) }.
% 0.74/1.14 { ! alpha3( X, Y ), ! leq( n0, Z ), ! leq( Z, X ), alpha12( X, Y, Z ) }.
% 0.74/1.14 { ! alpha3( X, Y ), leq( n0, Y ) }.
% 0.74/1.14 { ! alpha3( X, Y ), leq( Y, X ) }.
% 0.74/1.14 { ! leq( n0, Y ), ! leq( Y, X ), alpha3( X, Y ) }.
% 0.74/1.14 { alpha4( X, Z ), alpha22( Z, skol4( Y, Z ), skol19( Y, Z ) ), ! leq( n0, T
% 0.74/1.14 ), ! leq( T, Z ), ! leq( n0, U ), ! leq( U, Z ), a_select3( tptp_madd( X
% 0.74/1.14 , Y ), T, U ) = a_select3( tptp_madd( X, Y ), U, T ) }.
% 0.74/1.14 { alpha4( X, Z ), ! a_select3( Y, skol4( Y, Z ), skol19( Y, Z ) ) =
% 0.74/1.14 a_select3( Y, skol19( Y, Z ), skol4( Y, Z ) ), ! leq( n0, T ), ! leq( T,
% 0.74/1.14 Z ), ! leq( n0, U ), ! leq( U, Z ), a_select3( tptp_madd( X, Y ), T, U )
% 0.74/1.14 = a_select3( tptp_madd( X, Y ), U, T ) }.
% 0.74/1.14 { ! alpha22( X, Y, Z ), alpha13( X, Y ) }.
% 0.74/1.14 { ! alpha22( X, Y, Z ), leq( n0, Z ) }.
% 0.74/1.14 { ! alpha22( X, Y, Z ), leq( Z, X ) }.
% 0.74/1.14 { ! alpha13( X, Y ), ! leq( n0, Z ), ! leq( Z, X ), alpha22( X, Y, Z ) }.
% 0.74/1.14 { ! alpha13( X, Y ), leq( n0, Y ) }.
% 0.74/1.14 { ! alpha13( X, Y ), leq( Y, X ) }.
% 0.74/1.14 { ! leq( n0, Y ), ! leq( Y, X ), alpha13( X, Y ) }.
% 0.74/1.14 { ! alpha4( X, Y ), alpha23( Y, skol5( X, Y ), skol20( X, Y ) ) }.
% 0.74/1.14 { ! alpha4( X, Y ), ! a_select3( X, skol5( X, Y ), skol20( X, Y ) ) =
% 0.74/1.14 a_select3( X, skol20( X, Y ), skol5( X, Y ) ) }.
% 0.74/1.14 { ! alpha23( Y, Z, T ), a_select3( X, Z, T ) = a_select3( X, T, Z ), alpha4
% 0.74/1.14 ( X, Y ) }.
% 0.74/1.14 { ! alpha23( X, Y, Z ), alpha14( X, Y ) }.
% 0.74/1.14 { ! alpha23( X, Y, Z ), leq( n0, Z ) }.
% 0.74/1.14 { ! alpha23( X, Y, Z ), leq( Z, X ) }.
% 0.74/1.14 { ! alpha14( X, Y ), ! leq( n0, Z ), ! leq( Z, X ), alpha23( X, Y, Z ) }.
% 0.74/1.14 { ! alpha14( X, Y ), leq( n0, Y ) }.
% 0.74/1.14 { ! alpha14( X, Y ), leq( Y, X ) }.
% 0.74/1.14 { ! leq( n0, Y ), ! leq( Y, X ), alpha14( X, Y ) }.
% 0.74/1.14 { alpha5( X, Z ), alpha24( Z, skol6( Y, Z ), skol21( Y, Z ) ), ! leq( n0, T
% 0.74/1.14 ), ! leq( T, Z ), ! leq( n0, U ), ! leq( U, Z ), a_select3( tptp_msub( X
% 0.74/1.14 , Y ), T, U ) = a_select3( tptp_msub( X, Y ), U, T ) }.
% 0.74/1.14 { alpha5( X, Z ), ! a_select3( Y, skol6( Y, Z ), skol21( Y, Z ) ) =
% 0.74/1.14 a_select3( Y, skol21( Y, Z ), skol6( Y, Z ) ), ! leq( n0, T ), ! leq( T,
% 0.74/1.14 Z ), ! leq( n0, U ), ! leq( U, Z ), a_select3( tptp_msub( X, Y ), T, U )
% 0.74/1.14 = a_select3( tptp_msub( X, Y ), U, T ) }.
% 0.74/1.14 { ! alpha24( X, Y, Z ), alpha15( X, Y ) }.
% 0.74/1.14 { ! alpha24( X, Y, Z ), leq( n0, Z ) }.
% 0.74/1.14 { ! alpha24( X, Y, Z ), leq( Z, X ) }.
% 0.74/1.14 { ! alpha15( X, Y ), ! leq( n0, Z ), ! leq( Z, X ), alpha24( X, Y, Z ) }.
% 0.74/1.14 { ! alpha15( X, Y ), leq( n0, Y ) }.
% 0.74/1.14 { ! alpha15( X, Y ), leq( Y, X ) }.
% 0.74/1.14 { ! leq( n0, Y ), ! leq( Y, X ), alpha15( X, Y ) }.
% 0.74/1.14 { ! alpha5( X, Y ), alpha25( Y, skol7( X, Y ), skol22( X, Y ) ) }.
% 0.74/1.14 { ! alpha5( X, Y ), ! a_select3( X, skol7( X, Y ), skol22( X, Y ) ) =
% 0.74/1.14 a_select3( X, skol22( X, Y ), skol7( X, Y ) ) }.
% 0.74/1.14 { ! alpha25( Y, Z, T ), a_select3( X, Z, T ) = a_select3( X, T, Z ), alpha5
% 0.74/1.14 ( X, Y ) }.
% 0.74/1.14 { ! alpha25( X, Y, Z ), alpha16( X, Y ) }.
% 0.74/1.14 { ! alpha25( X, Y, Z ), leq( n0, Z ) }.
% 0.74/1.14 { ! alpha25( X, Y, Z ), leq( Z, X ) }.
% 0.74/1.14 { ! alpha16( X, Y ), ! leq( n0, Z ), ! leq( Z, X ), alpha25( X, Y, Z ) }.
% 0.74/1.14 { ! alpha16( X, Y ), leq( n0, Y ) }.
% 0.74/1.14 { ! alpha16( X, Y ), leq( Y, X ) }.
% 0.74/1.14 { ! leq( n0, Y ), ! leq( Y, X ), alpha16( X, Y ) }.
% 0.74/1.14 { alpha17( Y, skol8( X, Y ), skol23( X, Y ) ), ! leq( n0, Z ), ! leq( Z, Y
% 0.74/1.14 ), ! leq( n0, T ), ! leq( T, Y ), a_select3( tptp_mmul( U, tptp_mmul( X
% 0.74/1.14 , trans( U ) ) ), Z, T ) = a_select3( tptp_mmul( U, tptp_mmul( X, trans(
% 0.74/1.14 U ) ) ), T, Z ) }.
% 0.74/1.14 { ! a_select3( X, skol8( X, Y ), skol23( X, Y ) ) = a_select3( X, skol23( X
% 0.74/1.14 , Y ), skol8( X, Y ) ), ! leq( n0, Z ), ! leq( Z, Y ), ! leq( n0, T ), !
% 0.74/1.14 leq( T, Y ), a_select3( tptp_mmul( U, tptp_mmul( X, trans( U ) ) ), Z, T
% 0.74/1.14 ) = a_select3( tptp_mmul( U, tptp_mmul( X, trans( U ) ) ), T, Z ) }.
% 0.74/1.14 { ! alpha17( X, Y, Z ), alpha6( X, Y ) }.
% 0.74/1.14 { ! alpha17( X, Y, Z ), leq( n0, Z ) }.
% 0.74/1.14 { ! alpha17( X, Y, Z ), leq( Z, X ) }.
% 0.74/1.14 { ! alpha6( X, Y ), ! leq( n0, Z ), ! leq( Z, X ), alpha17( X, Y, Z ) }.
% 0.74/1.14 { ! alpha6( X, Y ), leq( n0, Y ) }.
% 0.74/1.14 { ! alpha6( X, Y ), leq( Y, X ) }.
% 0.74/1.14 { ! leq( n0, Y ), ! leq( Y, X ), alpha6( X, Y ) }.
% 0.74/1.14 { alpha18( Y, skol9( X, Y ), skol24( X, Y ) ), ! leq( n0, Z ), ! leq( Z, U
% 0.74/1.14 ), ! leq( n0, T ), ! leq( T, U ), a_select3( tptp_mmul( W, tptp_mmul( X
% 0.74/1.14 , trans( W ) ) ), Z, T ) = a_select3( tptp_mmul( W, tptp_mmul( X, trans(
% 0.74/1.14 W ) ) ), T, Z ) }.
% 0.74/1.14 { ! a_select3( X, skol9( X, Y ), skol24( X, Y ) ) = a_select3( X, skol24( X
% 0.74/1.14 , Y ), skol9( X, Y ) ), ! leq( n0, Z ), ! leq( Z, U ), ! leq( n0, T ), !
% 0.74/1.14 leq( T, U ), a_select3( tptp_mmul( W, tptp_mmul( X, trans( W ) ) ), Z, T
% 0.74/1.14 ) = a_select3( tptp_mmul( W, tptp_mmul( X, trans( W ) ) ), T, Z ) }.
% 0.74/1.14 { ! alpha18( X, Y, Z ), alpha7( X, Y ) }.
% 0.74/1.14 { ! alpha18( X, Y, Z ), leq( n0, Z ) }.
% 0.74/1.14 { ! alpha18( X, Y, Z ), leq( Z, X ) }.
% 0.74/1.14 { ! alpha7( X, Y ), ! leq( n0, Z ), ! leq( Z, X ), alpha18( X, Y, Z ) }.
% 0.74/1.14 { ! alpha7( X, Y ), leq( n0, Y ) }.
% 0.74/1.14 { ! alpha7( X, Y ), leq( Y, X ) }.
% 0.74/1.14 { ! leq( n0, Y ), ! leq( Y, X ), alpha7( X, Y ) }.
% 0.74/1.14 { alpha8( Y ), alpha19( X, T ), alpha29( T, skol10( Z, T ), skol25( Z, T )
% 0.74/1.14 ), ! leq( n0, U ), ! leq( U, T ), ! leq( n0, W ), ! leq( W, T ),
% 0.74/1.14 a_select3( tptp_madd( X, tptp_mmul( V0, tptp_mmul( tptp_madd( tptp_mmul(
% 0.74/1.14 V1, tptp_mmul( Y, trans( V1 ) ) ), tptp_mmul( V2, tptp_mmul( Z, trans( V2
% 0.74/1.14 ) ) ) ), trans( V0 ) ) ) ), U, W ) = a_select3( tptp_madd( X, tptp_mmul
% 0.74/1.14 ( V0, tptp_mmul( tptp_madd( tptp_mmul( V1, tptp_mmul( Y, trans( V1 ) ) )
% 0.74/1.14 , tptp_mmul( V2, tptp_mmul( Z, trans( V2 ) ) ) ), trans( V0 ) ) ) ), W, U
% 0.74/1.14 ) }.
% 0.74/1.14 { alpha8( Y ), alpha19( X, T ), ! a_select3( Z, skol10( Z, T ), skol25( Z,
% 0.74/1.14 T ) ) = a_select3( Z, skol25( Z, T ), skol10( Z, T ) ), ! leq( n0, U ), !
% 0.74/1.14 leq( U, T ), ! leq( n0, W ), ! leq( W, T ), a_select3( tptp_madd( X,
% 0.74/1.14 tptp_mmul( V0, tptp_mmul( tptp_madd( tptp_mmul( V1, tptp_mmul( Y, trans(
% 0.74/1.14 V1 ) ) ), tptp_mmul( V2, tptp_mmul( Z, trans( V2 ) ) ) ), trans( V0 ) ) )
% 0.74/1.14 ), U, W ) = a_select3( tptp_madd( X, tptp_mmul( V0, tptp_mmul( tptp_madd
% 0.74/1.14 ( tptp_mmul( V1, tptp_mmul( Y, trans( V1 ) ) ), tptp_mmul( V2, tptp_mmul
% 0.74/1.14 ( Z, trans( V2 ) ) ) ), trans( V0 ) ) ) ), W, U ) }.
% 0.74/1.14 { ! alpha29( X, Y, Z ), alpha26( X, Y ) }.
% 0.74/1.14 { ! alpha29( X, Y, Z ), leq( n0, Z ) }.
% 0.74/1.14 { ! alpha29( X, Y, Z ), leq( Z, X ) }.
% 0.74/1.14 { ! alpha26( X, Y ), ! leq( n0, Z ), ! leq( Z, X ), alpha29( X, Y, Z ) }.
% 0.74/1.14 { ! alpha26( X, Y ), leq( n0, Y ) }.
% 0.74/1.14 { ! alpha26( X, Y ), leq( Y, X ) }.
% 0.74/1.14 { ! leq( n0, Y ), ! leq( Y, X ), alpha26( X, Y ) }.
% 0.74/1.14 { ! alpha19( X, Y ), alpha30( Y, skol11( X, Y ), skol26( X, Y ) ) }.
% 0.74/1.14 { ! alpha19( X, Y ), ! a_select3( X, skol11( X, Y ), skol26( X, Y ) ) =
% 0.74/1.14 a_select3( X, skol26( X, Y ), skol11( X, Y ) ) }.
% 0.74/1.14 { ! alpha30( Y, Z, T ), a_select3( X, Z, T ) = a_select3( X, T, Z ),
% 0.74/1.14 alpha19( X, Y ) }.
% 0.74/1.14 { ! alpha30( X, Y, Z ), alpha27( X, Y ) }.
% 0.74/1.14 { ! alpha30( X, Y, Z ), leq( n0, Z ) }.
% 0.74/1.14 { ! alpha30( X, Y, Z ), leq( Z, X ) }.
% 0.74/1.14 { ! alpha27( X, Y ), ! leq( n0, Z ), ! leq( Z, X ), alpha30( X, Y, Z ) }.
% 0.74/1.14 { ! alpha27( X, Y ), leq( n0, Y ) }.
% 0.74/1.14 { ! alpha27( X, Y ), leq( Y, X ) }.
% 0.74/1.14 { ! leq( n0, Y ), ! leq( Y, X ), alpha27( X, Y ) }.
% 0.74/1.14 { ! alpha8( X ), alpha28( Y, skol12( X, Y ), skol27( X, Y ) ) }.
% 0.74/1.14 { ! alpha8( X ), ! a_select3( X, skol12( X, Y ), skol27( X, Y ) ) =
% 0.74/1.14 a_select3( X, skol27( X, Y ), skol12( X, Y ) ) }.
% 0.74/1.14 { ! alpha28( skol29( X ), Y, Z ), a_select3( X, Y, Z ) = a_select3( X, Z, Y
% 0.74/1.14 ), alpha8( X ) }.
% 0.74/1.14 { ! alpha28( X, Y, Z ), alpha20( X, Y ) }.
% 0.74/1.14 { ! alpha28( X, Y, Z ), leq( n0, Z ) }.
% 0.74/1.14 { ! alpha28( X, Y, Z ), leq( Z, X ) }.
% 0.74/1.14 { ! alpha20( X, Y ), ! leq( n0, Z ), ! leq( Z, X ), alpha28( X, Y, Z ) }.
% 0.74/1.14 { ! alpha20( X, Y ), leq( n0, Y ) }.
% 0.74/1.14 { ! alpha20( X, Y ), leq( Y, X ) }.
% 0.74/1.14 { ! leq( n0, Y ), ! leq( Y, X ), alpha20( X, Y ) }.
% 0.74/1.14 { sum( n0, tptp_minus_1, X ) = n0 }.
% 0.74/1.14 { tptp_float_0_0 = sum( n0, tptp_minus_1, X ) }.
% 0.74/1.14 { succ( tptp_minus_1 ) = n0 }.
% 0.74/1.14 { plus( X, n1 ) = succ( X ) }.
% 0.74/1.14 { plus( n1, X ) = succ( X ) }.
% 0.74/1.14 { plus( X, n2 ) = succ( succ( X ) ) }.
% 0.74/1.14 { plus( n2, X ) = succ( succ( X ) ) }.
% 0.74/1.14 { plus( X, n3 ) = succ( succ( succ( X ) ) ) }.
% 0.74/1.14 { plus( n3, X ) = succ( succ( succ( X ) ) ) }.
% 0.74/1.14 { plus( X, n4 ) = succ( succ( succ( succ( X ) ) ) ) }.
% 0.74/1.14 { plus( n4, X ) = succ( succ( succ( succ( X ) ) ) ) }.
% 0.74/1.14 { plus( X, n5 ) = succ( succ( succ( succ( succ( X ) ) ) ) ) }.
% 0.74/1.14 { plus( n5, X ) = succ( succ( succ( succ( succ( X ) ) ) ) ) }.
% 0.74/1.14 { minus( X, n1 ) = pred( X ) }.
% 0.74/1.14 { pred( succ( X ) ) = X }.
% 0.74/1.14 { succ( pred( X ) ) = X }.
% 0.74/1.14 { ! leq( succ( X ), succ( Y ) ), leq( X, Y ) }.
% 0.74/1.14 { ! leq( X, Y ), leq( succ( X ), succ( Y ) ) }.
% 0.74/1.14 { ! leq( succ( X ), Y ), gt( Y, X ) }.
% 0.74/1.14 { ! leq( minus( Y, X ), Y ), leq( n0, X ) }.
% 0.74/1.14 { a_select3( tptp_update3( X, Y, Z, T ), Y, Z ) = T }.
% 0.74/1.14 { X = Z, ! Y = T, ! a_select3( U, Z, T ) = W, a_select3( tptp_update3( U, X
% 0.74/1.14 , Y, V0 ), Z, T ) = W }.
% 0.74/1.14 { leq( skol28( V0, T, V1, V2 ), T ), ! leq( n0, X ), ! leq( X, Z ), ! leq(
% 0.74/1.14 n0, Y ), ! leq( Y, T ), a_select3( tptp_update3( U, Z, T, W ), X, Y ) = W
% 0.74/1.14 }.
% 0.74/1.14 { alpha21( Z, skol13( Z, T, U, W ), skol28( Z, T, U, W ) ), ! leq( n0, X )
% 0.74/1.14 , ! leq( X, Z ), ! leq( n0, Y ), ! leq( Y, T ), a_select3( tptp_update3(
% 0.74/1.14 U, Z, T, W ), X, Y ) = W }.
% 0.74/1.14 { ! a_select3( U, skol13( Z, T, U, W ), skol28( Z, T, U, W ) ) = W, ! leq(
% 0.74/1.14 n0, X ), ! leq( X, Z ), ! leq( n0, Y ), ! leq( Y, T ), a_select3(
% 0.74/1.14 tptp_update3( U, Z, T, W ), X, Y ) = W }.
% 0.74/1.14 { ! alpha21( X, Y, Z ), alpha9( Y, Z ) }.
% 0.74/1.14 { ! alpha21( X, Y, Z ), leq( Y, X ) }.
% 0.74/1.14 { ! alpha9( Y, Z ), ! leq( Y, X ), alpha21( X, Y, Z ) }.
% 0.74/1.14 { ! alpha9( X, Y ), leq( n0, X ) }.
% 0.74/1.14 { ! alpha9( X, Y ), leq( n0, Y ) }.
% 0.74/1.14 { ! leq( n0, X ), ! leq( n0, Y ), alpha9( X, Y ) }.
% 0.74/1.14 { a_select2( tptp_update2( X, Y, Z ), Y ) = Z }.
% 0.74/1.14 { X = Y, ! a_select2( Z, Y ) = T, a_select2( tptp_update2( Z, X, U ), Y ) =
% 0.74/1.14 T }.
% 0.74/1.14 { leq( n0, skol14( U, W, V0 ) ), ! leq( n0, X ), ! leq( X, Y ), a_select2(
% 0.74/1.14 tptp_update2( Z, Y, T ), X ) = T }.
% 0.74/1.14 { leq( skol14( Y, U, W ), Y ), ! leq( n0, X ), ! leq( X, Y ), a_select2(
% 0.74/1.14 tptp_update2( Z, Y, T ), X ) = T }.
% 0.74/1.14 { ! a_select2( Z, skol14( Y, Z, T ) ) = T, ! leq( n0, X ), ! leq( X, Y ),
% 0.74/1.14 a_select2( tptp_update2( Z, Y, T ), X ) = T }.
% 0.74/1.14 { true }.
% 0.74/1.14 { ! def = use }.
% 0.74/1.14 { ! leq( n0, X ), ! leq( X, n135299 ), ! leq( n0, Y ), ! leq( Y, n4 ),
% 0.74/1.14 a_select3( q_init, X, Y ) = init }.
% 0.74/1.14 { ! leq( n0, X ), ! leq( X, n4 ), a_select2( rho_init, X ) = init }.
% 0.74/1.14 { ! leq( n0, X ), ! leq( X, n4 ), a_select3( center_init, X, n0 ) = init }
% 0.74/1.14 .
% 0.74/1.14 { ! gt( loopcounter, n1 ), ! leq( n0, X ), ! leq( X, n4 ), a_select2(
% 0.74/1.14 muold_init, X ) = init }.
% 0.74/1.14 { ! gt( loopcounter, n1 ), ! leq( n0, X ), ! leq( X, n4 ), a_select2(
% 0.74/1.14 rhoold_init, X ) = init }.
% 0.74/1.14 { ! gt( loopcounter, n1 ), ! leq( n0, X ), ! leq( X, n4 ), a_select2(
% 0.74/1.14 sigmaold_init, X ) = init }.
% 0.74/1.14 { leq( n0, skol15 ) }.
% 0.74/1.14 { leq( skol15, tptp_minus_1 ) }.
% 0.74/1.14 { ! a_select2( mu_init, skol15 ) = init }.
% 0.74/1.14 { gt( n5, n4 ) }.
% 0.74/1.14 { gt( n135299, n4 ) }.
% 0.74/1.14 { gt( n135299, n5 ) }.
% 0.74/1.14 { gt( n4, tptp_minus_1 ) }.
% 0.74/1.14 { gt( n5, tptp_minus_1 ) }.
% 0.74/1.14 { gt( n135299, tptp_minus_1 ) }.
% 0.74/1.14 { gt( n0, tptp_minus_1 ) }.
% 0.74/1.14 { gt( n1, tptp_minus_1 ) }.
% 0.74/1.14 { gt( n2, tptp_minus_1 ) }.
% 0.74/1.14 { gt( n3, tptp_minus_1 ) }.
% 0.74/1.14 { gt( n4, n0 ) }.
% 0.74/1.14 { gt( n5, n0 ) }.
% 0.74/1.14 { gt( n135299, n0 ) }.
% 0.74/1.14 { gt( n1, n0 ) }.
% 0.74/1.14 { gt( n2, n0 ) }.
% 0.74/1.14 { gt( n3, n0 ) }.
% 0.74/1.14 { gt( n4, n1 ) }.
% 0.74/1.14 { gt( n5, n1 ) }.
% 0.74/1.14 { gt( n135299, n1 ) }.
% 0.74/1.14 { gt( n2, n1 ) }.
% 0.74/1.14 { gt( n3, n1 ) }.
% 0.74/1.14 { gt( n4, n2 ) }.
% 0.74/1.14 { gt( n5, n2 ) }.
% 0.74/1.14 { gt( n135299, n2 ) }.
% 0.74/1.14 { gt( n3, n2 ) }.
% 0.74/1.14 { gt( n4, n3 ) }.
% 0.74/1.14 { gt( n5, n3 ) }.
% 0.74/1.14 { gt( n135299, n3 ) }.
% 0.74/1.14 { ! leq( n0, X ), ! leq( X, n4 ), X = n0, X = n1, X = n2, X = n3, X = n4 }
% 0.74/1.14 .
% 0.74/1.14 { ! leq( n0, X ), ! leq( X, n5 ), X = n0, X = n1, X = n2, X = n3, X = n4, X
% 0.74/1.14 = n5 }.
% 0.74/1.14 { ! leq( n0, X ), ! leq( X, n0 ), X = n0 }.
% 0.74/1.14 { ! leq( n0, X ), ! leq( X, n1 ), X = n0, X = n1 }.
% 0.74/1.14 { ! leq( n0, X ), ! leq( X, n2 ), X = n0, X = n1, X = n2 }.
% 0.74/1.14 { ! leq( n0, X ), ! leq( X, n3 ), X = n0, X = n1, X = n2, X = n3 }.
% 0.74/1.14 { succ( succ( succ( succ( n0 ) ) ) ) = n4 }.
% 0.74/1.14 { succ( succ( succ( succ( succ( n0 ) ) ) ) ) = n5 }.
% 0.74/1.14 { succ( n0 ) = n1 }.
% 0.74/1.14 { succ( succ( n0 ) ) = n2 }.
% 0.74/1.14 { succ( succ( succ( n0 ) ) ) = n3 }.
% 0.74/1.14
% 0.74/1.14 percentage equality = 0.184588, percentage horn = 0.872146
% 0.74/1.14 This is a problem with some equality
% 0.74/1.14
% 0.74/1.14
% 0.74/1.14
% 0.74/1.14 Options Used:
% 0.74/1.14
% 0.74/1.14 useres = 1
% 0.74/1.14 useparamod = 1
% 0.74/1.14 useeqrefl = 1
% 0.74/1.14 useeqfact = 1
% 0.74/1.14 usefactor = 1
% 0.74/1.14 usesimpsplitting = 0
% 0.74/1.14 usesimpdemod = 5
% 0.74/1.14 usesimpres = 3
% 0.74/1.14
% 0.74/1.14 resimpinuse = 1000
% 0.74/1.14 resimpclauses = 20000
% 0.74/1.14 substype = eqrewr
% 0.74/1.14 backwardsubs = 1
% 0.74/1.14 selectoldest = 5
% 0.74/1.14
% 0.74/1.14 litorderings [0] = split
% 0.74/1.14 litorderings [1] = extend the termordering, first sorting on arguments
% 0.74/1.14
% 0.74/1.14 termordering = kbo
% 0.74/1.14
% 0.74/1.14 litapriori = 0
% 0.74/1.14 termapriori = 1
% 0.74/1.14 litaposteriori = 0
% 0.74/1.14 termaposteriori = 0
% 0.74/1.14 demodaposteriori = 0
% 0.74/1.14 ordereqreflfact = 0
% 0.74/1.14
% 0.74/1.14 litselect = negord
% 0.74/1.14
% 0.74/1.14 maxweight = 15
% 0.74/1.14 maxdepth = 30000
% 0.74/1.14 maxlength = 115
% 0.74/1.14 maxnrvars = 195
% 0.74/1.14 excuselevel = 1
% 0.74/1.14 increasemaxweight = 1
% 0.74/1.14
% 0.74/1.14 maxselected = 10000000
% 0.74/1.14 maxnrclauses = 10000000
% 0.74/1.14
% 0.74/1.14 showgenerated = 0
% 0.74/1.14 showkept = 0
% 0.74/1.14 showselected = 0
% 0.74/1.14 showdeleted = 0
% 0.74/1.14 showresimp = 1
% 0.74/1.14 showstatus = 2000
% 0.74/1.14
% 0.74/1.14 prologoutput = 0
% 0.74/1.14 nrgoals = 5000000
% 0.74/1.14 totalproof = 1
% 0.74/1.14
% 0.74/1.14 Symbols occurring in the translation:
% 0.74/1.14
% 0.74/1.14 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.74/1.14 . [1, 2] (w:1, o:68, a:1, s:1, b:0),
% 0.74/1.14 ! [4, 1] (w:0, o:57, a:1, s:1, b:0),
% 0.74/1.14 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.74/1.14 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.74/1.14 gt [37, 2] (w:1, o:92, a:1, s:1, b:0),
% 0.74/1.14 leq [39, 2] (w:1, o:93, a:1, s:1, b:0),
% 0.74/1.14 lt [40, 2] (w:1, o:94, a:1, s:1, b:0),
% 0.74/1.14 geq [41, 2] (w:1, o:95, a:1, s:1, b:0),
% 0.74/1.14 pred [42, 1] (w:1, o:62, a:1, s:1, b:0),
% 0.76/1.30 succ [43, 1] (w:1, o:63, a:1, s:1, b:0),
% 0.76/1.30 n0 [45, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.76/1.30 uniform_int_rnd [46, 2] (w:1, o:124, a:1, s:1, b:0),
% 0.76/1.30 dim [51, 2] (w:1, o:125, a:1, s:1, b:0),
% 0.76/1.30 tptp_const_array1 [52, 2] (w:1, o:120, a:1, s:1, b:0),
% 0.76/1.30 a_select2 [53, 2] (w:1, o:126, a:1, s:1, b:0),
% 0.76/1.30 tptp_const_array2 [59, 3] (w:1, o:147, a:1, s:1, b:0),
% 0.76/1.30 a_select3 [60, 3] (w:1, o:148, a:1, s:1, b:0),
% 0.76/1.30 trans [63, 1] (w:1, o:65, a:1, s:1, b:0),
% 0.76/1.30 inv [64, 1] (w:1, o:66, a:1, s:1, b:0),
% 0.76/1.30 tptp_update3 [67, 4] (w:1, o:165, a:1, s:1, b:0),
% 0.76/1.30 tptp_madd [69, 2] (w:1, o:121, a:1, s:1, b:0),
% 0.76/1.30 tptp_msub [70, 2] (w:1, o:122, a:1, s:1, b:0),
% 0.76/1.30 tptp_mmul [71, 2] (w:1, o:123, a:1, s:1, b:0),
% 0.76/1.30 tptp_minus_1 [77, 0] (w:1, o:37, a:1, s:1, b:0),
% 0.76/1.30 sum [78, 3] (w:1, o:145, a:1, s:1, b:0),
% 0.76/1.30 tptp_float_0_0 [79, 0] (w:1, o:38, a:1, s:1, b:0),
% 0.76/1.30 n1 [80, 0] (w:1, o:39, a:1, s:1, b:0),
% 0.76/1.30 plus [81, 2] (w:1, o:127, a:1, s:1, b:0),
% 0.76/1.30 n2 [82, 0] (w:1, o:41, a:1, s:1, b:0),
% 0.76/1.30 n3 [83, 0] (w:1, o:42, a:1, s:1, b:0),
% 0.76/1.30 n4 [84, 0] (w:1, o:43, a:1, s:1, b:0),
% 0.76/1.30 n5 [85, 0] (w:1, o:44, a:1, s:1, b:0),
% 0.76/1.30 minus [86, 2] (w:1, o:128, a:1, s:1, b:0),
% 0.76/1.30 tptp_update2 [91, 3] (w:1, o:149, a:1, s:1, b:0),
% 0.76/1.30 true [92, 0] (w:1, o:47, a:1, s:1, b:0),
% 0.76/1.30 def [93, 0] (w:1, o:49, a:1, s:1, b:0),
% 0.76/1.30 use [94, 0] (w:1, o:50, a:1, s:1, b:0),
% 0.76/1.30 n135299 [95, 0] (w:1, o:40, a:1, s:1, b:0),
% 0.76/1.30 q_init [96, 0] (w:1, o:51, a:1, s:1, b:0),
% 0.76/1.30 init [97, 0] (w:1, o:52, a:1, s:1, b:0),
% 0.76/1.30 rho_init [98, 0] (w:1, o:53, a:1, s:1, b:0),
% 0.76/1.30 center_init [99, 0] (w:1, o:48, a:1, s:1, b:0),
% 0.76/1.30 loopcounter [100, 0] (w:1, o:54, a:1, s:1, b:0),
% 0.76/1.30 muold_init [101, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.76/1.30 rhoold_init [102, 0] (w:1, o:55, a:1, s:1, b:0),
% 0.76/1.30 sigmaold_init [104, 0] (w:1, o:35, a:1, s:1, b:0),
% 0.76/1.30 mu_init [106, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.76/1.30 alpha1 [107, 2] (w:1, o:129, a:1, s:1, b:1),
% 0.76/1.30 alpha2 [108, 2] (w:1, o:135, a:1, s:1, b:1),
% 0.76/1.30 alpha3 [109, 2] (w:1, o:139, a:1, s:1, b:1),
% 0.76/1.30 alpha4 [110, 2] (w:1, o:140, a:1, s:1, b:1),
% 0.76/1.30 alpha5 [111, 2] (w:1, o:141, a:1, s:1, b:1),
% 0.76/1.30 alpha6 [112, 2] (w:1, o:142, a:1, s:1, b:1),
% 0.76/1.30 alpha7 [113, 2] (w:1, o:143, a:1, s:1, b:1),
% 0.76/1.30 alpha8 [114, 1] (w:1, o:67, a:1, s:1, b:1),
% 0.76/1.30 alpha9 [115, 2] (w:1, o:144, a:1, s:1, b:1),
% 0.76/1.30 alpha10 [116, 3] (w:1, o:150, a:1, s:1, b:1),
% 0.76/1.30 alpha11 [117, 3] (w:1, o:151, a:1, s:1, b:1),
% 0.76/1.30 alpha12 [118, 3] (w:1, o:152, a:1, s:1, b:1),
% 0.76/1.30 alpha13 [119, 2] (w:1, o:130, a:1, s:1, b:1),
% 0.76/1.30 alpha14 [120, 2] (w:1, o:131, a:1, s:1, b:1),
% 0.76/1.30 alpha15 [121, 2] (w:1, o:132, a:1, s:1, b:1),
% 0.76/1.30 alpha16 [122, 2] (w:1, o:133, a:1, s:1, b:1),
% 0.76/1.30 alpha17 [123, 3] (w:1, o:153, a:1, s:1, b:1),
% 0.76/1.30 alpha18 [124, 3] (w:1, o:154, a:1, s:1, b:1),
% 0.76/1.30 alpha19 [125, 2] (w:1, o:134, a:1, s:1, b:1),
% 0.76/1.30 alpha20 [126, 2] (w:1, o:136, a:1, s:1, b:1),
% 0.76/1.30 alpha21 [127, 3] (w:1, o:155, a:1, s:1, b:1),
% 0.76/1.30 alpha22 [128, 3] (w:1, o:156, a:1, s:1, b:1),
% 0.76/1.30 alpha23 [129, 3] (w:1, o:157, a:1, s:1, b:1),
% 0.76/1.30 alpha24 [130, 3] (w:1, o:158, a:1, s:1, b:1),
% 0.76/1.30 alpha25 [131, 3] (w:1, o:159, a:1, s:1, b:1),
% 0.76/1.30 alpha26 [132, 2] (w:1, o:137, a:1, s:1, b:1),
% 0.76/1.30 alpha27 [133, 2] (w:1, o:138, a:1, s:1, b:1),
% 0.76/1.30 alpha28 [134, 3] (w:1, o:160, a:1, s:1, b:1),
% 0.76/1.30 alpha29 [135, 3] (w:1, o:161, a:1, s:1, b:1),
% 0.76/1.30 alpha30 [136, 3] (w:1, o:162, a:1, s:1, b:1),
% 0.76/1.30 skol1 [137, 2] (w:1, o:96, a:1, s:1, b:1),
% 0.76/1.30 skol2 [138, 2] (w:1, o:104, a:1, s:1, b:1),
% 0.76/1.30 skol3 [139, 2] (w:1, o:113, a:1, s:1, b:1),
% 0.76/1.30 skol4 [140, 2] (w:1, o:114, a:1, s:1, b:1),
% 0.76/1.30 skol5 [141, 2] (w:1, o:115, a:1, s:1, b:1),
% 0.76/1.30 skol6 [142, 2] (w:1, o:116, a:1, s:1, b:1),
% 0.76/1.30 skol7 [143, 2] (w:1, o:117, a:1, s:1, b:1),
% 0.76/1.30 skol8 [144, 2] (w:1, o:118, a:1, s:1, b:1),
% 0.76/1.30 skol9 [145, 2] (w:1, o:119, a:1, s:1, b:1),
% 0.76/1.30 skol10 [146, 2] (w:1, o:97, a:1, s:1, b:1),
% 0.76/1.30 skol11 [147, 2] (w:1, o:98, a:1, s:1, b:1),
% 0.76/1.30 skol12 [148, 2] (w:1, o:99, a:1, s:1, b:1),
% 0.76/1.30 skol13 [149, 4] (w:1, o:163, a:1, s:1, b:1),
% 0.76/1.30 skol14 [150, 3] (w:1, o:146, a:1, s:1, b:1),
% 0.76/1.30 skol15 [151, 0] (w:1, o:36, a:1, s:1, b:1),
% 0.76/1.30 skol16 [152, 2] (w:1, o:100, a:1, s:1, b:1),
% 0.76/1.30 skol17 [153, 2] (w:1, o:101, a:1, s:1, b:1),
% 0.76/1.30 skol18 [154, 2] (w:1, o:102, a:1, s:1, b:1),
% 0.76/1.30 skol19 [155, 2] (w:1, o:103, a:1, s:1, b:1),
% 0.76/1.30 skol20 [156, 2] (w:1, o:105, a:1, s:1, b:1),
% 0.76/1.30 skol21 [157, 2] (w:1, o:106, a:1, s:1, b:1),
% 0.76/1.30 skol22 [158, 2] (w:1, o:107, a:1, s:1, b:1),
% 0.76/1.30 skol23 [159, 2] (w:1, o:108, a:1, s:1, b:1),
% 0.76/1.30 skol24 [160, 2] (w:1, o:109, a:1, s:1, b:1),
% 0.76/1.30 skol25 [161, 2] (w:1, o:110, a:1, s:1, b:1),
% 0.76/1.30 skol26 [162, 2] (w:1, o:111, a:1, s:1, b:1),
% 0.76/1.30 skol27 [163, 2] (w:1, o:112, a:1, s:1, b:1),
% 0.76/1.30 skol28 [164, 4] (w:1, o:164, a:1, s:1, b:1),
% 0.76/1.30 skol29 [165, 1] (w:1, o:64, a:1, s:1, b:1).
% 0.76/1.30
% 0.76/1.30
% 0.76/1.30 Starting Search:
% 0.76/1.30
% 0.76/1.30 *** allocated 15000 integers for clauses
% 0.76/1.30 *** allocated 22500 integers for clauses
% 0.76/1.30 *** allocated 33750 integers for clauses
% 0.76/1.30 *** allocated 22500 integers for termspace/termends
% 0.76/1.30 *** allocated 50625 integers for clauses
% 0.76/1.30 *** allocated 75937 integers for clauses
% 0.76/1.30 Resimplifying inuse:
% 0.76/1.30 Done
% 0.76/1.30
% 0.76/1.30 *** allocated 33750 integers for termspace/termends
% 0.76/1.30 *** allocated 113905 integers for clauses
% 0.76/1.30 *** allocated 50625 integers for termspace/termends
% 0.76/1.30
% 0.76/1.30 Intermediate Status:
% 0.76/1.30 Generated: 7960
% 0.76/1.30 Kept: 2040
% 0.76/1.30 Inuse: 171
% 0.76/1.30 Deleted: 0
% 0.76/1.30 Deletedinuse: 0
% 0.76/1.30
% 0.76/1.30 Resimplifying inuse:
% 0.76/1.30 Done
% 0.76/1.30
% 0.76/1.30 *** allocated 170857 integers for clauses
% 0.76/1.30 *** allocated 75937 integers for termspace/termends
% 0.76/1.30
% 0.76/1.30 Bliksems!, er is een bewijs:
% 0.76/1.30 % SZS status Theorem
% 0.76/1.30 % SZS output start Refutation
% 0.76/1.30
% 0.76/1.30 (0) {G0,W9,D2,L3,V2,M3} I { gt( X, Y ), gt( Y, X ), X = Y }.
% 0.76/1.30 (1) {G0,W9,D2,L3,V3,M3} I { ! gt( X, Z ), ! gt( Z, Y ), gt( X, Y ) }.
% 0.76/1.30 (2) {G0,W3,D2,L1,V1,M1} I { ! gt( X, X ) }.
% 0.76/1.30 (10) {G0,W9,D2,L3,V2,M3} I { ! leq( X, Y ), X = Y, gt( Y, X ) }.
% 0.76/1.30 (15) {G0,W7,D3,L2,V2,M2} I { ! leq( X, Y ), gt( succ( Y ), X ) }.
% 0.76/1.30 (135) {G0,W4,D3,L1,V0,M1} I { succ( tptp_minus_1 ) ==> n0 }.
% 0.76/1.30 (177) {G0,W3,D2,L1,V0,M1} I { leq( n0, skol15 ) }.
% 0.76/1.30 (178) {G0,W3,D2,L1,V0,M1} I { leq( skol15, tptp_minus_1 ) }.
% 0.76/1.30 (2059) {G1,W3,D2,L1,V0,M1} R(178,15);d(135) { gt( n0, skol15 ) }.
% 0.76/1.30 (2073) {G2,W6,D2,L2,V1,M2} R(2059,1) { ! gt( X, n0 ), gt( X, skol15 ) }.
% 0.76/1.30 (2074) {G3,W6,D2,L2,V1,M2} P(10,2059);r(2073) { gt( X, skol15 ), ! leq( n0
% 0.76/1.30 , X ) }.
% 0.76/1.30 (2831) {G4,W6,D2,L2,V1,M2} P(0,177);r(2074) { gt( skol15, X ), gt( X,
% 0.76/1.30 skol15 ) }.
% 0.76/1.30 (2832) {G5,W0,D0,L0,V0,M0} F(2831);r(2) { }.
% 0.76/1.30
% 0.76/1.30
% 0.76/1.30 % SZS output end Refutation
% 0.76/1.30 found a proof!
% 0.76/1.30
% 0.76/1.30
% 0.76/1.30 Unprocessed initial clauses:
% 0.76/1.30
% 0.76/1.30 (2834) {G0,W9,D2,L3,V2,M3} { gt( X, Y ), gt( Y, X ), X = Y }.
% 0.76/1.30 (2835) {G0,W9,D2,L3,V3,M3} { ! gt( X, Z ), ! gt( Z, Y ), gt( X, Y ) }.
% 0.76/1.30 (2836) {G0,W3,D2,L1,V1,M1} { ! gt( X, X ) }.
% 0.76/1.30 (2837) {G0,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 0.76/1.30 (2838) {G0,W9,D2,L3,V3,M3} { ! leq( X, Z ), ! leq( Z, Y ), leq( X, Y ) }.
% 0.76/1.30 (2839) {G0,W6,D2,L2,V2,M2} { ! lt( X, Y ), gt( Y, X ) }.
% 0.76/1.30 (2840) {G0,W6,D2,L2,V2,M2} { ! gt( Y, X ), lt( X, Y ) }.
% 0.76/1.30 (2841) {G0,W6,D2,L2,V2,M2} { ! geq( X, Y ), leq( Y, X ) }.
% 0.76/1.30 (2842) {G0,W6,D2,L2,V2,M2} { ! leq( Y, X ), geq( X, Y ) }.
% 0.76/1.30 (2843) {G0,W6,D2,L2,V2,M2} { ! gt( Y, X ), leq( X, Y ) }.
% 0.76/1.30 (2844) {G0,W9,D2,L3,V2,M3} { ! leq( X, Y ), X = Y, gt( Y, X ) }.
% 0.76/1.30 (2845) {G0,W7,D3,L2,V2,M2} { ! leq( X, pred( Y ) ), gt( Y, X ) }.
% 0.76/1.30 (2846) {G0,W7,D3,L2,V2,M2} { ! gt( Y, X ), leq( X, pred( Y ) ) }.
% 0.76/1.30 (2847) {G0,W4,D3,L1,V1,M1} { gt( succ( X ), X ) }.
% 0.76/1.30 (2848) {G0,W7,D3,L2,V2,M2} { ! leq( X, Y ), leq( X, succ( Y ) ) }.
% 0.76/1.30 (2849) {G0,W7,D3,L2,V2,M2} { ! leq( X, Y ), gt( succ( Y ), X ) }.
% 0.76/1.30 (2850) {G0,W7,D3,L2,V2,M2} { ! gt( succ( Y ), X ), leq( X, Y ) }.
% 0.76/1.30 (2851) {G0,W8,D3,L2,V2,M2} { ! leq( n0, X ), leq( uniform_int_rnd( Y, X )
% 0.76/1.30 , X ) }.
% 0.76/1.30 (2852) {G0,W8,D3,L2,V2,M2} { ! leq( n0, X ), leq( n0, uniform_int_rnd( Y,
% 0.76/1.30 X ) ) }.
% 0.76/1.30 (2853) {G0,W15,D5,L3,V4,M3} { ! leq( Y, X ), ! leq( X, Z ), a_select2(
% 0.76/1.30 tptp_const_array1( dim( Y, Z ), T ), X ) = T }.
% 0.76/1.30 (2854) {G0,W25,D5,L5,V7,M5} { ! leq( Y, X ), ! leq( X, Z ), ! leq( U, T )
% 0.76/1.30 , ! leq( T, W ), a_select3( tptp_const_array2( dim( Y, Z ), dim( U, W ),
% 0.76/1.30 V0 ), X, T ) = V0 }.
% 0.76/1.30 (2855) {G0,W31,D4,L6,V4,M6} { alpha10( Y, skol1( X, Y ), skol16( X, Y ) )
% 0.76/1.30 , ! leq( n0, Z ), ! leq( Z, Y ), ! leq( n0, T ), ! leq( T, Y ), a_select3
% 0.76/1.30 ( trans( X ), Z, T ) = a_select3( trans( X ), T, Z ) }.
% 0.76/1.30 (2856) {G0,W40,D4,L6,V4,M6} { ! a_select3( X, skol1( X, Y ), skol16( X, Y
% 0.76/1.30 ) ) = a_select3( X, skol16( X, Y ), skol1( X, Y ) ), ! leq( n0, Z ), !
% 0.76/1.30 leq( Z, Y ), ! leq( n0, T ), ! leq( T, Y ), a_select3( trans( X ), Z, T )
% 0.76/1.30 = a_select3( trans( X ), T, Z ) }.
% 0.76/1.30 (2857) {G0,W7,D2,L2,V3,M2} { ! alpha10( X, Y, Z ), alpha1( X, Y ) }.
% 0.76/1.30 (2858) {G0,W7,D2,L2,V3,M2} { ! alpha10( X, Y, Z ), leq( n0, Z ) }.
% 0.76/1.30 (2859) {G0,W7,D2,L2,V3,M2} { ! alpha10( X, Y, Z ), leq( Z, X ) }.
% 0.76/1.30 (2860) {G0,W13,D2,L4,V3,M4} { ! alpha1( X, Y ), ! leq( n0, Z ), ! leq( Z,
% 0.76/1.30 X ), alpha10( X, Y, Z ) }.
% 0.76/1.30 (2861) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), leq( n0, Y ) }.
% 0.76/1.30 (2862) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), leq( Y, X ) }.
% 0.76/1.30 (2863) {G0,W9,D2,L3,V2,M3} { ! leq( n0, Y ), ! leq( Y, X ), alpha1( X, Y )
% 0.76/1.30 }.
% 0.76/1.30 (2864) {G0,W31,D4,L6,V4,M6} { alpha11( Y, skol2( X, Y ), skol17( X, Y ) )
% 0.76/1.30 , ! leq( n0, Z ), ! leq( Z, Y ), ! leq( n0, T ), ! leq( T, Y ), a_select3
% 0.76/1.30 ( inv( X ), Z, T ) = a_select3( inv( X ), T, Z ) }.
% 0.76/1.30 (2865) {G0,W40,D4,L6,V4,M6} { ! a_select3( X, skol2( X, Y ), skol17( X, Y
% 0.76/1.30 ) ) = a_select3( X, skol17( X, Y ), skol2( X, Y ) ), ! leq( n0, Z ), !
% 0.76/1.30 leq( Z, Y ), ! leq( n0, T ), ! leq( T, Y ), a_select3( inv( X ), Z, T ) =
% 0.76/1.30 a_select3( inv( X ), T, Z ) }.
% 0.76/1.30 (2866) {G0,W7,D2,L2,V3,M2} { ! alpha11( X, Y, Z ), alpha2( X, Y ) }.
% 0.76/1.30 (2867) {G0,W7,D2,L2,V3,M2} { ! alpha11( X, Y, Z ), leq( n0, Z ) }.
% 0.76/1.30 (2868) {G0,W7,D2,L2,V3,M2} { ! alpha11( X, Y, Z ), leq( Z, X ) }.
% 0.76/1.30 (2869) {G0,W13,D2,L4,V3,M4} { ! alpha2( X, Y ), ! leq( n0, Z ), ! leq( Z,
% 0.76/1.30 X ), alpha11( X, Y, Z ) }.
% 0.76/1.30 (2870) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), leq( n0, Y ) }.
% 0.76/1.30 (2871) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), leq( Y, X ) }.
% 0.76/1.30 (2872) {G0,W9,D2,L3,V2,M3} { ! leq( n0, Y ), ! leq( Y, X ), alpha2( X, Y )
% 0.76/1.30 }.
% 0.76/1.30 (2873) {G0,W43,D4,L8,V6,M8} { alpha12( Y, skol3( X, Y ), skol18( X, Y ) )
% 0.76/1.30 , ! leq( n0, Z ), ! leq( Z, Y ), ! leq( n0, T ), ! leq( T, Y ), ! leq( n0
% 0.76/1.30 , U ), ! leq( U, Y ), a_select3( tptp_update3( X, U, U, W ), Z, T ) =
% 0.76/1.30 a_select3( tptp_update3( X, U, U, W ), T, Z ) }.
% 0.76/1.30 (2874) {G0,W52,D4,L8,V6,M8} { ! a_select3( X, skol3( X, Y ), skol18( X, Y
% 0.76/1.30 ) ) = a_select3( X, skol18( X, Y ), skol3( X, Y ) ), ! leq( n0, Z ), !
% 0.76/1.30 leq( Z, Y ), ! leq( n0, T ), ! leq( T, Y ), ! leq( n0, U ), ! leq( U, Y )
% 0.76/1.30 , a_select3( tptp_update3( X, U, U, W ), Z, T ) = a_select3( tptp_update3
% 0.76/1.30 ( X, U, U, W ), T, Z ) }.
% 0.76/1.30 (2875) {G0,W7,D2,L2,V3,M2} { ! alpha12( X, Y, Z ), alpha3( X, Y ) }.
% 0.76/1.30 (2876) {G0,W7,D2,L2,V3,M2} { ! alpha12( X, Y, Z ), leq( n0, Z ) }.
% 0.76/1.30 (2877) {G0,W7,D2,L2,V3,M2} { ! alpha12( X, Y, Z ), leq( Z, X ) }.
% 0.76/1.30 (2878) {G0,W13,D2,L4,V3,M4} { ! alpha3( X, Y ), ! leq( n0, Z ), ! leq( Z,
% 0.76/1.30 X ), alpha12( X, Y, Z ) }.
% 0.76/1.30 (2879) {G0,W6,D2,L2,V2,M2} { ! alpha3( X, Y ), leq( n0, Y ) }.
% 0.76/1.30 (2880) {G0,W6,D2,L2,V2,M2} { ! alpha3( X, Y ), leq( Y, X ) }.
% 0.76/1.30 (2881) {G0,W9,D2,L3,V2,M3} { ! leq( n0, Y ), ! leq( Y, X ), alpha3( X, Y )
% 0.76/1.30 }.
% 0.76/1.30 (2882) {G0,W36,D4,L7,V5,M7} { alpha4( X, Z ), alpha22( Z, skol4( Y, Z ),
% 0.76/1.30 skol19( Y, Z ) ), ! leq( n0, T ), ! leq( T, Z ), ! leq( n0, U ), ! leq( U
% 0.76/1.30 , Z ), a_select3( tptp_madd( X, Y ), T, U ) = a_select3( tptp_madd( X, Y
% 0.76/1.30 ), U, T ) }.
% 0.76/1.30 (2883) {G0,W45,D4,L7,V5,M7} { alpha4( X, Z ), ! a_select3( Y, skol4( Y, Z
% 0.76/1.30 ), skol19( Y, Z ) ) = a_select3( Y, skol19( Y, Z ), skol4( Y, Z ) ), !
% 0.76/1.30 leq( n0, T ), ! leq( T, Z ), ! leq( n0, U ), ! leq( U, Z ), a_select3(
% 0.76/1.30 tptp_madd( X, Y ), T, U ) = a_select3( tptp_madd( X, Y ), U, T ) }.
% 0.76/1.30 (2884) {G0,W7,D2,L2,V3,M2} { ! alpha22( X, Y, Z ), alpha13( X, Y ) }.
% 0.76/1.30 (2885) {G0,W7,D2,L2,V3,M2} { ! alpha22( X, Y, Z ), leq( n0, Z ) }.
% 0.76/1.30 (2886) {G0,W7,D2,L2,V3,M2} { ! alpha22( X, Y, Z ), leq( Z, X ) }.
% 0.76/1.30 (2887) {G0,W13,D2,L4,V3,M4} { ! alpha13( X, Y ), ! leq( n0, Z ), ! leq( Z
% 0.76/1.30 , X ), alpha22( X, Y, Z ) }.
% 0.76/1.30 (2888) {G0,W6,D2,L2,V2,M2} { ! alpha13( X, Y ), leq( n0, Y ) }.
% 0.76/1.30 (2889) {G0,W6,D2,L2,V2,M2} { ! alpha13( X, Y ), leq( Y, X ) }.
% 0.76/1.30 (2890) {G0,W9,D2,L3,V2,M3} { ! leq( n0, Y ), ! leq( Y, X ), alpha13( X, Y
% 0.76/1.30 ) }.
% 0.76/1.30 (2891) {G0,W11,D3,L2,V2,M2} { ! alpha4( X, Y ), alpha23( Y, skol5( X, Y )
% 0.76/1.30 , skol20( X, Y ) ) }.
% 0.76/1.30 (2892) {G0,W20,D4,L2,V2,M2} { ! alpha4( X, Y ), ! a_select3( X, skol5( X,
% 0.76/1.30 Y ), skol20( X, Y ) ) = a_select3( X, skol20( X, Y ), skol5( X, Y ) ) }.
% 0.76/1.30 (2893) {G0,W16,D3,L3,V4,M3} { ! alpha23( Y, Z, T ), a_select3( X, Z, T ) =
% 0.76/1.30 a_select3( X, T, Z ), alpha4( X, Y ) }.
% 0.76/1.30 (2894) {G0,W7,D2,L2,V3,M2} { ! alpha23( X, Y, Z ), alpha14( X, Y ) }.
% 0.76/1.30 (2895) {G0,W7,D2,L2,V3,M2} { ! alpha23( X, Y, Z ), leq( n0, Z ) }.
% 0.76/1.30 (2896) {G0,W7,D2,L2,V3,M2} { ! alpha23( X, Y, Z ), leq( Z, X ) }.
% 0.76/1.30 (2897) {G0,W13,D2,L4,V3,M4} { ! alpha14( X, Y ), ! leq( n0, Z ), ! leq( Z
% 0.76/1.30 , X ), alpha23( X, Y, Z ) }.
% 0.76/1.30 (2898) {G0,W6,D2,L2,V2,M2} { ! alpha14( X, Y ), leq( n0, Y ) }.
% 0.76/1.30 (2899) {G0,W6,D2,L2,V2,M2} { ! alpha14( X, Y ), leq( Y, X ) }.
% 0.76/1.30 (2900) {G0,W9,D2,L3,V2,M3} { ! leq( n0, Y ), ! leq( Y, X ), alpha14( X, Y
% 0.76/1.30 ) }.
% 0.76/1.30 (2901) {G0,W36,D4,L7,V5,M7} { alpha5( X, Z ), alpha24( Z, skol6( Y, Z ),
% 0.76/1.30 skol21( Y, Z ) ), ! leq( n0, T ), ! leq( T, Z ), ! leq( n0, U ), ! leq( U
% 0.76/1.30 , Z ), a_select3( tptp_msub( X, Y ), T, U ) = a_select3( tptp_msub( X, Y
% 0.76/1.30 ), U, T ) }.
% 0.76/1.30 (2902) {G0,W45,D4,L7,V5,M7} { alpha5( X, Z ), ! a_select3( Y, skol6( Y, Z
% 0.76/1.30 ), skol21( Y, Z ) ) = a_select3( Y, skol21( Y, Z ), skol6( Y, Z ) ), !
% 0.76/1.30 leq( n0, T ), ! leq( T, Z ), ! leq( n0, U ), ! leq( U, Z ), a_select3(
% 0.76/1.30 tptp_msub( X, Y ), T, U ) = a_select3( tptp_msub( X, Y ), U, T ) }.
% 0.76/1.30 (2903) {G0,W7,D2,L2,V3,M2} { ! alpha24( X, Y, Z ), alpha15( X, Y ) }.
% 0.76/1.30 (2904) {G0,W7,D2,L2,V3,M2} { ! alpha24( X, Y, Z ), leq( n0, Z ) }.
% 0.76/1.30 (2905) {G0,W7,D2,L2,V3,M2} { ! alpha24( X, Y, Z ), leq( Z, X ) }.
% 0.76/1.30 (2906) {G0,W13,D2,L4,V3,M4} { ! alpha15( X, Y ), ! leq( n0, Z ), ! leq( Z
% 0.76/1.30 , X ), alpha24( X, Y, Z ) }.
% 0.76/1.30 (2907) {G0,W6,D2,L2,V2,M2} { ! alpha15( X, Y ), leq( n0, Y ) }.
% 0.76/1.30 (2908) {G0,W6,D2,L2,V2,M2} { ! alpha15( X, Y ), leq( Y, X ) }.
% 0.76/1.30 (2909) {G0,W9,D2,L3,V2,M3} { ! leq( n0, Y ), ! leq( Y, X ), alpha15( X, Y
% 0.76/1.30 ) }.
% 0.76/1.30 (2910) {G0,W11,D3,L2,V2,M2} { ! alpha5( X, Y ), alpha25( Y, skol7( X, Y )
% 0.76/1.30 , skol22( X, Y ) ) }.
% 0.76/1.30 (2911) {G0,W20,D4,L2,V2,M2} { ! alpha5( X, Y ), ! a_select3( X, skol7( X,
% 0.76/1.30 Y ), skol22( X, Y ) ) = a_select3( X, skol22( X, Y ), skol7( X, Y ) ) }.
% 0.76/1.30 (2912) {G0,W16,D3,L3,V4,M3} { ! alpha25( Y, Z, T ), a_select3( X, Z, T ) =
% 0.76/1.30 a_select3( X, T, Z ), alpha5( X, Y ) }.
% 0.76/1.30 (2913) {G0,W7,D2,L2,V3,M2} { ! alpha25( X, Y, Z ), alpha16( X, Y ) }.
% 0.76/1.30 (2914) {G0,W7,D2,L2,V3,M2} { ! alpha25( X, Y, Z ), leq( n0, Z ) }.
% 0.76/1.30 (2915) {G0,W7,D2,L2,V3,M2} { ! alpha25( X, Y, Z ), leq( Z, X ) }.
% 0.76/1.30 (2916) {G0,W13,D2,L4,V3,M4} { ! alpha16( X, Y ), ! leq( n0, Z ), ! leq( Z
% 0.76/1.30 , X ), alpha25( X, Y, Z ) }.
% 0.76/1.30 (2917) {G0,W6,D2,L2,V2,M2} { ! alpha16( X, Y ), leq( n0, Y ) }.
% 0.76/1.30 (2918) {G0,W6,D2,L2,V2,M2} { ! alpha16( X, Y ), leq( Y, X ) }.
% 0.76/1.30 (2919) {G0,W9,D2,L3,V2,M3} { ! leq( n0, Y ), ! leq( Y, X ), alpha16( X, Y
% 0.76/1.30 ) }.
% 0.76/1.30 (2920) {G0,W39,D6,L6,V5,M6} { alpha17( Y, skol8( X, Y ), skol23( X, Y ) )
% 0.76/1.30 , ! leq( n0, Z ), ! leq( Z, Y ), ! leq( n0, T ), ! leq( T, Y ), a_select3
% 0.76/1.30 ( tptp_mmul( U, tptp_mmul( X, trans( U ) ) ), Z, T ) = a_select3(
% 0.76/1.30 tptp_mmul( U, tptp_mmul( X, trans( U ) ) ), T, Z ) }.
% 0.76/1.30 (2921) {G0,W48,D6,L6,V5,M6} { ! a_select3( X, skol8( X, Y ), skol23( X, Y
% 0.76/1.30 ) ) = a_select3( X, skol23( X, Y ), skol8( X, Y ) ), ! leq( n0, Z ), !
% 0.76/1.30 leq( Z, Y ), ! leq( n0, T ), ! leq( T, Y ), a_select3( tptp_mmul( U,
% 0.76/1.30 tptp_mmul( X, trans( U ) ) ), Z, T ) = a_select3( tptp_mmul( U, tptp_mmul
% 0.76/1.30 ( X, trans( U ) ) ), T, Z ) }.
% 0.76/1.30 (2922) {G0,W7,D2,L2,V3,M2} { ! alpha17( X, Y, Z ), alpha6( X, Y ) }.
% 0.76/1.30 (2923) {G0,W7,D2,L2,V3,M2} { ! alpha17( X, Y, Z ), leq( n0, Z ) }.
% 0.76/1.30 (2924) {G0,W7,D2,L2,V3,M2} { ! alpha17( X, Y, Z ), leq( Z, X ) }.
% 0.76/1.30 (2925) {G0,W13,D2,L4,V3,M4} { ! alpha6( X, Y ), ! leq( n0, Z ), ! leq( Z,
% 0.76/1.30 X ), alpha17( X, Y, Z ) }.
% 0.76/1.30 (2926) {G0,W6,D2,L2,V2,M2} { ! alpha6( X, Y ), leq( n0, Y ) }.
% 0.76/1.30 (2927) {G0,W6,D2,L2,V2,M2} { ! alpha6( X, Y ), leq( Y, X ) }.
% 0.76/1.30 (2928) {G0,W9,D2,L3,V2,M3} { ! leq( n0, Y ), ! leq( Y, X ), alpha6( X, Y )
% 0.76/1.30 }.
% 0.76/1.30 (2929) {G0,W39,D6,L6,V6,M6} { alpha18( Y, skol9( X, Y ), skol24( X, Y ) )
% 0.76/1.30 , ! leq( n0, Z ), ! leq( Z, U ), ! leq( n0, T ), ! leq( T, U ), a_select3
% 0.76/1.30 ( tptp_mmul( W, tptp_mmul( X, trans( W ) ) ), Z, T ) = a_select3(
% 0.76/1.30 tptp_mmul( W, tptp_mmul( X, trans( W ) ) ), T, Z ) }.
% 0.76/1.30 (2930) {G0,W48,D6,L6,V6,M6} { ! a_select3( X, skol9( X, Y ), skol24( X, Y
% 0.76/1.30 ) ) = a_select3( X, skol24( X, Y ), skol9( X, Y ) ), ! leq( n0, Z ), !
% 0.76/1.30 leq( Z, U ), ! leq( n0, T ), ! leq( T, U ), a_select3( tptp_mmul( W,
% 0.76/1.30 tptp_mmul( X, trans( W ) ) ), Z, T ) = a_select3( tptp_mmul( W, tptp_mmul
% 0.76/1.30 ( X, trans( W ) ) ), T, Z ) }.
% 0.76/1.30 (2931) {G0,W7,D2,L2,V3,M2} { ! alpha18( X, Y, Z ), alpha7( X, Y ) }.
% 0.76/1.30 (2932) {G0,W7,D2,L2,V3,M2} { ! alpha18( X, Y, Z ), leq( n0, Z ) }.
% 0.76/1.30 (2933) {G0,W7,D2,L2,V3,M2} { ! alpha18( X, Y, Z ), leq( Z, X ) }.
% 0.76/1.30 (2934) {G0,W13,D2,L4,V3,M4} { ! alpha7( X, Y ), ! leq( n0, Z ), ! leq( Z,
% 0.76/1.30 X ), alpha18( X, Y, Z ) }.
% 0.76/1.30 (2935) {G0,W6,D2,L2,V2,M2} { ! alpha7( X, Y ), leq( n0, Y ) }.
% 0.76/1.30 (2936) {G0,W6,D2,L2,V2,M2} { ! alpha7( X, Y ), leq( Y, X ) }.
% 0.76/1.30 (2937) {G0,W9,D2,L3,V2,M3} { ! leq( n0, Y ), ! leq( Y, X ), alpha7( X, Y )
% 0.76/1.30 }.
% 0.76/1.30 (2938) {G0,W72,D10,L8,V9,M8} { alpha8( Y ), alpha19( X, T ), alpha29( T,
% 0.76/1.30 skol10( Z, T ), skol25( Z, T ) ), ! leq( n0, U ), ! leq( U, T ), ! leq(
% 0.76/1.30 n0, W ), ! leq( W, T ), a_select3( tptp_madd( X, tptp_mmul( V0, tptp_mmul
% 0.76/1.30 ( tptp_madd( tptp_mmul( V1, tptp_mmul( Y, trans( V1 ) ) ), tptp_mmul( V2
% 0.76/1.30 , tptp_mmul( Z, trans( V2 ) ) ) ), trans( V0 ) ) ) ), U, W ) = a_select3
% 0.76/1.30 ( tptp_madd( X, tptp_mmul( V0, tptp_mmul( tptp_madd( tptp_mmul( V1,
% 0.76/1.30 tptp_mmul( Y, trans( V1 ) ) ), tptp_mmul( V2, tptp_mmul( Z, trans( V2 ) )
% 0.76/1.30 ) ), trans( V0 ) ) ) ), W, U ) }.
% 0.76/1.30 (2939) {G0,W81,D10,L8,V9,M8} { alpha8( Y ), alpha19( X, T ), ! a_select3(
% 0.76/1.30 Z, skol10( Z, T ), skol25( Z, T ) ) = a_select3( Z, skol25( Z, T ),
% 0.76/1.30 skol10( Z, T ) ), ! leq( n0, U ), ! leq( U, T ), ! leq( n0, W ), ! leq( W
% 0.76/1.30 , T ), a_select3( tptp_madd( X, tptp_mmul( V0, tptp_mmul( tptp_madd(
% 0.76/1.30 tptp_mmul( V1, tptp_mmul( Y, trans( V1 ) ) ), tptp_mmul( V2, tptp_mmul( Z
% 0.76/1.30 , trans( V2 ) ) ) ), trans( V0 ) ) ) ), U, W ) = a_select3( tptp_madd( X
% 0.76/1.30 , tptp_mmul( V0, tptp_mmul( tptp_madd( tptp_mmul( V1, tptp_mmul( Y, trans
% 0.76/1.30 ( V1 ) ) ), tptp_mmul( V2, tptp_mmul( Z, trans( V2 ) ) ) ), trans( V0 ) )
% 0.76/1.30 ) ), W, U ) }.
% 0.76/1.30 (2940) {G0,W7,D2,L2,V3,M2} { ! alpha29( X, Y, Z ), alpha26( X, Y ) }.
% 0.76/1.30 (2941) {G0,W7,D2,L2,V3,M2} { ! alpha29( X, Y, Z ), leq( n0, Z ) }.
% 0.76/1.30 (2942) {G0,W7,D2,L2,V3,M2} { ! alpha29( X, Y, Z ), leq( Z, X ) }.
% 0.76/1.30 (2943) {G0,W13,D2,L4,V3,M4} { ! alpha26( X, Y ), ! leq( n0, Z ), ! leq( Z
% 0.76/1.30 , X ), alpha29( X, Y, Z ) }.
% 0.76/1.30 (2944) {G0,W6,D2,L2,V2,M2} { ! alpha26( X, Y ), leq( n0, Y ) }.
% 0.76/1.30 (2945) {G0,W6,D2,L2,V2,M2} { ! alpha26( X, Y ), leq( Y, X ) }.
% 0.76/1.30 (2946) {G0,W9,D2,L3,V2,M3} { ! leq( n0, Y ), ! leq( Y, X ), alpha26( X, Y
% 0.76/1.30 ) }.
% 0.76/1.30 (2947) {G0,W11,D3,L2,V2,M2} { ! alpha19( X, Y ), alpha30( Y, skol11( X, Y
% 0.76/1.30 ), skol26( X, Y ) ) }.
% 0.76/1.30 (2948) {G0,W20,D4,L2,V2,M2} { ! alpha19( X, Y ), ! a_select3( X, skol11( X
% 0.76/1.30 , Y ), skol26( X, Y ) ) = a_select3( X, skol26( X, Y ), skol11( X, Y ) )
% 0.76/1.30 }.
% 0.76/1.30 (2949) {G0,W16,D3,L3,V4,M3} { ! alpha30( Y, Z, T ), a_select3( X, Z, T ) =
% 0.76/1.30 a_select3( X, T, Z ), alpha19( X, Y ) }.
% 0.76/1.30 (2950) {G0,W7,D2,L2,V3,M2} { ! alpha30( X, Y, Z ), alpha27( X, Y ) }.
% 0.76/1.30 (2951) {G0,W7,D2,L2,V3,M2} { ! alpha30( X, Y, Z ), leq( n0, Z ) }.
% 0.76/1.30 (2952) {G0,W7,D2,L2,V3,M2} { ! alpha30( X, Y, Z ), leq( Z, X ) }.
% 0.76/1.30 (2953) {G0,W13,D2,L4,V3,M4} { ! alpha27( X, Y ), ! leq( n0, Z ), ! leq( Z
% 0.76/1.30 , X ), alpha30( X, Y, Z ) }.
% 0.76/1.30 (2954) {G0,W6,D2,L2,V2,M2} { ! alpha27( X, Y ), leq( n0, Y ) }.
% 0.76/1.30 (2955) {G0,W6,D2,L2,V2,M2} { ! alpha27( X, Y ), leq( Y, X ) }.
% 0.76/1.30 (2956) {G0,W9,D2,L3,V2,M3} { ! leq( n0, Y ), ! leq( Y, X ), alpha27( X, Y
% 0.76/1.30 ) }.
% 0.76/1.30 (2957) {G0,W10,D3,L2,V2,M2} { ! alpha8( X ), alpha28( Y, skol12( X, Y ),
% 0.76/1.30 skol27( X, Y ) ) }.
% 0.76/1.30 (2958) {G0,W19,D4,L2,V2,M2} { ! alpha8( X ), ! a_select3( X, skol12( X, Y
% 0.76/1.30 ), skol27( X, Y ) ) = a_select3( X, skol27( X, Y ), skol12( X, Y ) ) }.
% 0.76/1.30 (2959) {G0,W16,D3,L3,V3,M3} { ! alpha28( skol29( X ), Y, Z ), a_select3( X
% 0.76/1.30 , Y, Z ) = a_select3( X, Z, Y ), alpha8( X ) }.
% 0.76/1.30 (2960) {G0,W7,D2,L2,V3,M2} { ! alpha28( X, Y, Z ), alpha20( X, Y ) }.
% 0.76/1.30 (2961) {G0,W7,D2,L2,V3,M2} { ! alpha28( X, Y, Z ), leq( n0, Z ) }.
% 0.76/1.30 (2962) {G0,W7,D2,L2,V3,M2} { ! alpha28( X, Y, Z ), leq( Z, X ) }.
% 0.76/1.30 (2963) {G0,W13,D2,L4,V3,M4} { ! alpha20( X, Y ), ! leq( n0, Z ), ! leq( Z
% 0.76/1.30 , X ), alpha28( X, Y, Z ) }.
% 0.76/1.30 (2964) {G0,W6,D2,L2,V2,M2} { ! alpha20( X, Y ), leq( n0, Y ) }.
% 0.76/1.30 (2965) {G0,W6,D2,L2,V2,M2} { ! alpha20( X, Y ), leq( Y, X ) }.
% 0.76/1.30 (2966) {G0,W9,D2,L3,V2,M3} { ! leq( n0, Y ), ! leq( Y, X ), alpha20( X, Y
% 0.76/1.30 ) }.
% 0.76/1.30 (2967) {G0,W6,D3,L1,V1,M1} { sum( n0, tptp_minus_1, X ) = n0 }.
% 0.76/1.30 (2968) {G0,W6,D3,L1,V1,M1} { tptp_float_0_0 = sum( n0, tptp_minus_1, X )
% 0.76/1.30 }.
% 0.76/1.30 (2969) {G0,W4,D3,L1,V0,M1} { succ( tptp_minus_1 ) = n0 }.
% 0.76/1.30 (2970) {G0,W6,D3,L1,V1,M1} { plus( X, n1 ) = succ( X ) }.
% 0.76/1.30 (2971) {G0,W6,D3,L1,V1,M1} { plus( n1, X ) = succ( X ) }.
% 0.76/1.30 (2972) {G0,W7,D4,L1,V1,M1} { plus( X, n2 ) = succ( succ( X ) ) }.
% 0.76/1.30 (2973) {G0,W7,D4,L1,V1,M1} { plus( n2, X ) = succ( succ( X ) ) }.
% 0.76/1.30 (2974) {G0,W8,D5,L1,V1,M1} { plus( X, n3 ) = succ( succ( succ( X ) ) ) }.
% 0.76/1.30 (2975) {G0,W8,D5,L1,V1,M1} { plus( n3, X ) = succ( succ( succ( X ) ) ) }.
% 0.76/1.30 (2976) {G0,W9,D6,L1,V1,M1} { plus( X, n4 ) = succ( succ( succ( succ( X ) )
% 0.76/1.30 ) ) }.
% 0.76/1.30 (2977) {G0,W9,D6,L1,V1,M1} { plus( n4, X ) = succ( succ( succ( succ( X ) )
% 0.76/1.30 ) ) }.
% 0.76/1.30 (2978) {G0,W10,D7,L1,V1,M1} { plus( X, n5 ) = succ( succ( succ( succ( succ
% 0.76/1.30 ( X ) ) ) ) ) }.
% 0.76/1.30 (2979) {G0,W10,D7,L1,V1,M1} { plus( n5, X ) = succ( succ( succ( succ( succ
% 0.76/1.30 ( X ) ) ) ) ) }.
% 0.76/1.30 (2980) {G0,W6,D3,L1,V1,M1} { minus( X, n1 ) = pred( X ) }.
% 0.76/1.30 (2981) {G0,W5,D4,L1,V1,M1} { pred( succ( X ) ) = X }.
% 0.76/1.30 (2982) {G0,W5,D4,L1,V1,M1} { succ( pred( X ) ) = X }.
% 0.76/1.30 (2983) {G0,W8,D3,L2,V2,M2} { ! leq( succ( X ), succ( Y ) ), leq( X, Y )
% 0.76/1.30 }.
% 0.76/1.30 (2984) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), leq( succ( X ), succ( Y ) )
% 0.76/1.30 }.
% 0.76/1.30 (2985) {G0,W7,D3,L2,V2,M2} { ! leq( succ( X ), Y ), gt( Y, X ) }.
% 0.76/1.30 (2986) {G0,W8,D3,L2,V2,M2} { ! leq( minus( Y, X ), Y ), leq( n0, X ) }.
% 0.76/1.30 (2987) {G0,W10,D4,L1,V4,M1} { a_select3( tptp_update3( X, Y, Z, T ), Y, Z
% 0.76/1.30 ) = T }.
% 0.76/1.30 (2988) {G0,W22,D4,L4,V7,M4} { X = Z, ! Y = T, ! a_select3( U, Z, T ) = W,
% 0.76/1.30 a_select3( tptp_update3( U, X, Y, V0 ), Z, T ) = W }.
% 0.76/1.30 (2989) {G0,W29,D4,L6,V9,M6} { leq( skol28( V0, T, V1, V2 ), T ), ! leq( n0
% 0.76/1.30 , X ), ! leq( X, Z ), ! leq( n0, Y ), ! leq( Y, T ), a_select3(
% 0.76/1.30 tptp_update3( U, Z, T, W ), X, Y ) = W }.
% 0.76/1.30 (2990) {G0,W34,D4,L6,V6,M6} { alpha21( Z, skol13( Z, T, U, W ), skol28( Z
% 0.76/1.30 , T, U, W ) ), ! leq( n0, X ), ! leq( X, Z ), ! leq( n0, Y ), ! leq( Y, T
% 0.76/1.30 ), a_select3( tptp_update3( U, Z, T, W ), X, Y ) = W }.
% 0.76/1.30 (2991) {G0,W36,D4,L6,V6,M6} { ! a_select3( U, skol13( Z, T, U, W ), skol28
% 0.76/1.30 ( Z, T, U, W ) ) = W, ! leq( n0, X ), ! leq( X, Z ), ! leq( n0, Y ), !
% 0.76/1.30 leq( Y, T ), a_select3( tptp_update3( U, Z, T, W ), X, Y ) = W }.
% 0.76/1.30 (2992) {G0,W7,D2,L2,V3,M2} { ! alpha21( X, Y, Z ), alpha9( Y, Z ) }.
% 0.76/1.30 (2993) {G0,W7,D2,L2,V3,M2} { ! alpha21( X, Y, Z ), leq( Y, X ) }.
% 0.76/1.30 (2994) {G0,W10,D2,L3,V3,M3} { ! alpha9( Y, Z ), ! leq( Y, X ), alpha21( X
% 0.76/1.30 , Y, Z ) }.
% 0.76/1.30 (2995) {G0,W6,D2,L2,V2,M2} { ! alpha9( X, Y ), leq( n0, X ) }.
% 0.76/1.30 (2996) {G0,W6,D2,L2,V2,M2} { ! alpha9( X, Y ), leq( n0, Y ) }.
% 0.76/1.30 (2997) {G0,W9,D2,L3,V2,M3} { ! leq( n0, X ), ! leq( n0, Y ), alpha9( X, Y
% 0.76/1.30 ) }.
% 0.76/1.30 (2998) {G0,W8,D4,L1,V3,M1} { a_select2( tptp_update2( X, Y, Z ), Y ) = Z
% 0.76/1.30 }.
% 0.76/1.30 (2999) {G0,W16,D4,L3,V5,M3} { X = Y, ! a_select2( Z, Y ) = T, a_select2(
% 0.76/1.30 tptp_update2( Z, X, U ), Y ) = T }.
% 0.76/1.30 (3000) {G0,W20,D4,L4,V7,M4} { leq( n0, skol14( U, W, V0 ) ), ! leq( n0, X
% 0.76/1.30 ), ! leq( X, Y ), a_select2( tptp_update2( Z, Y, T ), X ) = T }.
% 0.76/1.30 (3001) {G0,W20,D4,L4,V6,M4} { leq( skol14( Y, U, W ), Y ), ! leq( n0, X )
% 0.76/1.30 , ! leq( X, Y ), a_select2( tptp_update2( Z, Y, T ), X ) = T }.
% 0.76/1.30 (3002) {G0,W22,D4,L4,V4,M4} { ! a_select2( Z, skol14( Y, Z, T ) ) = T, !
% 0.76/1.30 leq( n0, X ), ! leq( X, Y ), a_select2( tptp_update2( Z, Y, T ), X ) = T
% 0.76/1.30 }.
% 0.76/1.30 (3003) {G0,W1,D1,L1,V0,M1} { true }.
% 0.76/1.30 (3004) {G0,W3,D2,L1,V0,M1} { ! def = use }.
% 0.76/1.30 (3005) {G0,W18,D3,L5,V2,M5} { ! leq( n0, X ), ! leq( X, n135299 ), ! leq(
% 0.76/1.30 n0, Y ), ! leq( Y, n4 ), a_select3( q_init, X, Y ) = init }.
% 0.76/1.30 (3006) {G0,W11,D3,L3,V1,M3} { ! leq( n0, X ), ! leq( X, n4 ), a_select2(
% 0.76/1.30 rho_init, X ) = init }.
% 0.76/1.30 (3007) {G0,W12,D3,L3,V1,M3} { ! leq( n0, X ), ! leq( X, n4 ), a_select3(
% 0.76/1.30 center_init, X, n0 ) = init }.
% 0.76/1.30 (3008) {G0,W14,D3,L4,V1,M4} { ! gt( loopcounter, n1 ), ! leq( n0, X ), !
% 0.76/1.30 leq( X, n4 ), a_select2( muold_init, X ) = init }.
% 0.76/1.30 (3009) {G0,W14,D3,L4,V1,M4} { ! gt( loopcounter, n1 ), ! leq( n0, X ), !
% 0.76/1.30 leq( X, n4 ), a_select2( rhoold_init, X ) = init }.
% 0.76/1.30 (3010) {G0,W14,D3,L4,V1,M4} { ! gt( loopcounter, n1 ), ! leq( n0, X ), !
% 0.76/1.30 leq( X, n4 ), a_select2( sigmaold_init, X ) = init }.
% 0.76/1.30 (3011) {G0,W3,D2,L1,V0,M1} { leq( n0, skol15 ) }.
% 0.76/1.30 (3012) {G0,W3,D2,L1,V0,M1} { leq( skol15, tptp_minus_1 ) }.
% 0.76/1.30 (3013) {G0,W5,D3,L1,V0,M1} { ! a_select2( mu_init, skol15 ) = init }.
% 0.76/1.30 (3014) {G0,W3,D2,L1,V0,M1} { gt( n5, n4 ) }.
% 0.76/1.30 (3015) {G0,W3,D2,L1,V0,M1} { gt( n135299, n4 ) }.
% 0.76/1.30 (3016) {G0,W3,D2,L1,V0,M1} { gt( n135299, n5 ) }.
% 0.76/1.30 (3017) {G0,W3,D2,L1,V0,M1} { gt( n4, tptp_minus_1 ) }.
% 0.76/1.30 (3018) {G0,W3,D2,L1,V0,M1} { gt( n5, tptp_minus_1 ) }.
% 0.76/1.30 (3019) {G0,W3,D2,L1,V0,M1} { gt( n135299, tptp_minus_1 ) }.
% 0.76/1.30 (3020) {G0,W3,D2,L1,V0,M1} { gt( n0, tptp_minus_1 ) }.
% 0.76/1.30 (3021) {G0,W3,D2,L1,V0,M1} { gt( n1, tptp_minus_1 ) }.
% 0.76/1.30 (3022) {G0,W3,D2,L1,V0,M1} { gt( n2, tptp_minus_1 ) }.
% 0.76/1.30 (3023) {G0,W3,D2,L1,V0,M1} { gt( n3, tptp_minus_1 ) }.
% 0.76/1.30 (3024) {G0,W3,D2,L1,V0,M1} { gt( n4, n0 ) }.
% 0.76/1.30 (3025) {G0,W3,D2,L1,V0,M1} { gt( n5, n0 ) }.
% 0.76/1.30 (3026) {G0,W3,D2,L1,V0,M1} { gt( n135299, n0 ) }.
% 0.76/1.30 (3027) {G0,W3,D2,L1,V0,M1} { gt( n1, n0 ) }.
% 0.76/1.30 (3028) {G0,W3,D2,L1,V0,M1} { gt( n2, n0 ) }.
% 0.76/1.30 (3029) {G0,W3,D2,L1,V0,M1} { gt( n3, n0 ) }.
% 0.76/1.30 (3030) {G0,W3,D2,L1,V0,M1} { gt( n4, n1 ) }.
% 0.76/1.30 (3031) {G0,W3,D2,L1,V0,M1} { gt( n5, n1 ) }.
% 0.76/1.30 (3032) {G0,W3,D2,L1,V0,M1} { gt( n135299, n1 ) }.
% 0.76/1.30 (3033) {G0,W3,D2,L1,V0,M1} { gt( n2, n1 ) }.
% 0.76/1.30 (3034) {G0,W3,D2,L1,V0,M1} { gt( n3, n1 ) }.
% 0.76/1.30 (3035) {G0,W3,D2,L1,V0,M1} { gt( n4, n2 ) }.
% 0.76/1.30 (3036) {G0,W3,D2,L1,V0,M1} { gt( n5, n2 ) }.
% 0.76/1.30 (3037) {G0,W3,D2,L1,V0,M1} { gt( n135299, n2 ) }.
% 0.76/1.30 (3038) {G0,W3,D2,L1,V0,M1} { gt( n3, n2 ) }.
% 0.76/1.30 (3039) {G0,W3,D2,L1,V0,M1} { gt( n4, n3 ) }.
% 0.76/1.30 (3040) {G0,W3,D2,L1,V0,M1} { gt( n5, n3 ) }.
% 0.76/1.30 (3041) {G0,W3,D2,L1,V0,M1} { gt( n135299, n3 ) }.
% 0.76/1.30 (3042) {G0,W21,D2,L7,V1,M7} { ! leq( n0, X ), ! leq( X, n4 ), X = n0, X =
% 0.76/1.30 n1, X = n2, X = n3, X = n4 }.
% 0.76/1.30 (3043) {G0,W24,D2,L8,V1,M8} { ! leq( n0, X ), ! leq( X, n5 ), X = n0, X =
% 0.76/1.30 n1, X = n2, X = n3, X = n4, X = n5 }.
% 0.76/1.30 (3044) {G0,W9,D2,L3,V1,M3} { ! leq( n0, X ), ! leq( X, n0 ), X = n0 }.
% 0.76/1.30 (3045) {G0,W12,D2,L4,V1,M4} { ! leq( n0, X ), ! leq( X, n1 ), X = n0, X =
% 0.76/1.30 n1 }.
% 0.76/1.30 (3046) {G0,W15,D2,L5,V1,M5} { ! leq( n0, X ), ! leq( X, n2 ), X = n0, X =
% 0.76/1.30 n1, X = n2 }.
% 0.76/1.30 (3047) {G0,W18,D2,L6,V1,M6} { ! leq( n0, X ), ! leq( X, n3 ), X = n0, X =
% 0.76/1.30 n1, X = n2, X = n3 }.
% 0.76/1.30 (3048) {G0,W7,D6,L1,V0,M1} { succ( succ( succ( succ( n0 ) ) ) ) = n4 }.
% 0.76/1.30 (3049) {G0,W8,D7,L1,V0,M1} { succ( succ( succ( succ( succ( n0 ) ) ) ) ) =
% 0.76/1.30 n5 }.
% 0.76/1.30 (3050) {G0,W4,D3,L1,V0,M1} { succ( n0 ) = n1 }.
% 0.76/1.30 (3051) {G0,W5,D4,L1,V0,M1} { succ( succ( n0 ) ) = n2 }.
% 0.76/1.30 (3052) {G0,W6,D5,L1,V0,M1} { succ( succ( succ( n0 ) ) ) = n3 }.
% 0.76/1.30
% 0.76/1.30
% 0.76/1.30 Total Proof:
% 0.76/1.30
% 0.76/1.30 subsumption: (0) {G0,W9,D2,L3,V2,M3} I { gt( X, Y ), gt( Y, X ), X = Y }.
% 0.76/1.30 parent0: (2834) {G0,W9,D2,L3,V2,M3} { gt( X, Y ), gt( Y, X ), X = Y }.
% 0.76/1.30 substitution0:
% 0.76/1.30 X := X
% 0.76/1.30 Y := Y
% 0.76/1.30 end
% 0.76/1.30 permutation0:
% 0.76/1.30 0 ==> 0
% 0.76/1.30 1 ==> 1
% 0.76/1.30 2 ==> 2
% 0.76/1.30 end
% 0.76/1.30
% 0.76/1.30 subsumption: (1) {G0,W9,D2,L3,V3,M3} I { ! gt( X, Z ), ! gt( Z, Y ), gt( X
% 0.76/1.30 , Y ) }.
% 0.76/1.30 parent0: (2835) {G0,W9,D2,L3,V3,M3} { ! gt( X, Z ), ! gt( Z, Y ), gt( X, Y
% 0.76/1.30 ) }.
% 0.76/1.30 substitution0:
% 0.76/1.30 X := X
% 0.76/1.30 Y := Y
% 0.76/1.30 Z := Z
% 0.76/1.30 end
% 0.76/1.30 permutation0:
% 0.76/1.30 0 ==> 0
% 0.76/1.30 1 ==> 1
% 0.76/1.30 2 ==> 2
% 0.76/1.30 end
% 0.76/1.30
% 0.76/1.30 subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! gt( X, X ) }.
% 0.76/1.30 parent0: (2836) {G0,W3,D2,L1,V1,M1} { ! gt( X, X ) }.
% 0.76/1.30 substitution0:
% 0.76/1.30 X := X
% 0.76/1.30 end
% 0.76/1.30 permutation0:
% 0.76/1.30 0 ==> 0
% 0.76/1.30 end
% 0.76/1.30
% 0.76/1.30 subsumption: (10) {G0,W9,D2,L3,V2,M3} I { ! leq( X, Y ), X = Y, gt( Y, X )
% 0.76/1.30 }.
% 0.76/1.30 parent0: (2844) {G0,W9,D2,L3,V2,M3} { ! leq( X, Y ), X = Y, gt( Y, X ) }.
% 0.76/1.30 substitution0:
% 0.76/1.30 X := X
% 0.76/1.30 Y := Y
% 0.76/1.30 end
% 0.76/1.30 permutation0:
% 0.76/1.30 0 ==> 0
% 0.76/1.30 1 ==> 1
% 0.76/1.30 2 ==> 2
% 0.76/1.30 end
% 0.76/1.30
% 0.76/1.30 subsumption: (15) {G0,W7,D3,L2,V2,M2} I { ! leq( X, Y ), gt( succ( Y ), X )
% 0.76/1.30 }.
% 0.76/1.30 parent0Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------