TSTP Solution File: GEO537+1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO537+1 : TPTP v8.1.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n003.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 : Sat Jul 16 02:54:34 EDT 2022
% Result : Timeout 300.05s 300.40s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO537+1 : TPTP v8.1.0. Released v7.0.0.
% 0.11/0.12 % Command : bliksem %s
% 0.13/0.33 % Computer : n003.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Sat Jun 18 06:59:58 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.90/1.26 *** allocated 10000 integers for termspace/termends
% 0.90/1.26 *** allocated 10000 integers for clauses
% 0.90/1.26 *** allocated 10000 integers for justifications
% 0.90/1.26 Bliksem 1.12
% 0.90/1.26
% 0.90/1.26
% 0.90/1.26 Automatic Strategy Selection
% 0.90/1.26
% 0.90/1.26 *** allocated 15000 integers for termspace/termends
% 0.90/1.26 *** allocated 22500 integers for termspace/termends
% 0.90/1.26 *** allocated 33750 integers for termspace/termends
% 0.90/1.26
% 0.90/1.26 Clauses:
% 0.90/1.26
% 0.90/1.26 { s_e( X, Y, Y, X ) }.
% 0.90/1.26 { ! s_e( X, Y, Z, T ), ! s_e( X, Y, U, W ), s_e( Z, T, U, W ) }.
% 0.90/1.26 { ! s_e( X, Y, Z, Z ), X = Y }.
% 0.90/1.26 { s_t( X, Y, ext( X, Y, Z, T ) ) }.
% 0.90/1.26 { s_e( Y, ext( X, Y, Z, T ), Z, T ) }.
% 0.90/1.26 { ! s_e( X, Y, Z, T ), ! s_e( Y, U, T, W ), ! s_e( X, V0, Z, V1 ), ! s_e( Y
% 0.90/1.26 , V0, T, V1 ), ! s_t( X, Y, U ), ! s_t( Z, T, W ), X = Y, s_e( U, V0, W,
% 0.90/1.26 V1 ) }.
% 0.90/1.26 { ! s_t( X, Y, X ), X = Y }.
% 0.90/1.26 { ! s_t( X, Y, Z ), ! s_t( T, U, Z ), s_t( Y, ip( X, Y, Z, T, U ), T ) }.
% 0.90/1.26 { ! s_t( X, Y, Z ), ! s_t( T, U, Z ), s_t( U, ip( X, Y, Z, T, U ), X ) }.
% 0.90/1.26 { ! s_t( alpha, beta, gamma ) }.
% 0.90/1.26 { ! s_t( beta, gamma, alpha ) }.
% 0.90/1.26 { ! s_t( gamma, alpha, beta ) }.
% 0.90/1.26 { s_e( X, Y, X, Y ) }.
% 0.90/1.26 { ! s_e( X, Y, Z, T ), s_e( Z, T, X, Y ) }.
% 0.90/1.26 { ! s_e( X, Y, Z, T ), ! s_e( Z, T, U, W ), s_e( X, Y, U, W ) }.
% 0.90/1.26 { ! s_e( X, Y, Z, T ), s_e( Y, X, Z, T ) }.
% 0.90/1.26 { ! s_e( X, Y, Z, T ), s_e( X, Y, T, Z ) }.
% 0.90/1.26 { s_e( X, X, Y, Y ) }.
% 0.90/1.26 { ! s_t( X, Y, Z ), ! s_t( T, U, W ), ! s_e( X, Y, T, U ), ! s_e( Y, Z, U,
% 0.90/1.26 W ), s_e( X, Z, T, W ) }.
% 0.90/1.26 { X = Y, ! s_t( X, Y, Z ), ! s_e( Y, Z, T, U ), Z = ext( X, Y, T, U ) }.
% 0.90/1.26 { ! s_e( X, Y, Z, Z ), X = Y }.
% 0.90/1.26 { ! s_e( X, Y, Z, T ), s_e( Y, X, T, Z ) }.
% 0.90/1.26 { ! s_t( X, Y, Z ), ! s_t( T, U, W ), ! s_e( X, Y, U, W ), ! s_e( Y, Z, T,
% 0.90/1.26 U ), s_e( X, Z, T, W ) }.
% 0.90/1.26 { s_t( X, Y, Y ) }.
% 0.90/1.26 { ! s_t( X, Y, Z ), s_t( Z, Y, X ) }.
% 0.90/1.26 { s_t( X, X, Y ) }.
% 0.90/1.26 { ! s_t( X, Y, Z ), ! s_t( Y, X, Z ), X = Y }.
% 0.90/1.26 { ! s_t( X, Y, Z ), ! s_t( Y, T, Z ), s_t( X, Y, T ) }.
% 0.90/1.26 { ! s_t( X, Y, Z ), ! s_t( X, Z, T ), s_t( Y, Z, T ) }.
% 0.90/1.26 { ! s_t( X, Y, Z ), ! s_t( Y, Z, T ), Y = Z, s_t( X, Z, T ) }.
% 0.90/1.26 { ! s_t( X, Y, Z ), ! s_t( Y, T, Z ), s_t( X, T, Z ) }.
% 0.90/1.26 { ! s_t( X, Y, Z ), ! s_t( X, Z, T ), s_t( X, Y, T ) }.
% 0.90/1.26 { ! s_t( X, Y, Z ), ! s_t( Y, Z, T ), Y = Z, s_t( X, Y, T ) }.
% 0.90/1.26 { ! alpha = beta }.
% 0.90/1.26 { ! beta = gamma }.
% 0.90/1.26 { ! alpha = gamma }.
% 0.90/1.26 { s_t( X, Y, ext( X, Y, alpha, gamma ) ) }.
% 0.90/1.26 { ! X = ext( Y, X, alpha, gamma ) }.
% 0.90/1.26 { ! s_t( X, Y, Z ), ! s_t( T, U, Z ), ! s_t( X, W, T ), s_t( W, crossbar( X
% 0.90/1.26 , Y, Z, T, U, W ), Z ) }.
% 0.90/1.26 { ! s_t( X, Y, Z ), ! s_t( T, U, Z ), ! s_t( X, W, T ), s_t( Y, crossbar( X
% 0.90/1.26 , Y, Z, T, U, W ), U ) }.
% 0.90/1.26 { ! s_ifs( U, X, W, Y, V0, Z, V1, T ), s_e( X, Y, Z, T ) }.
% 0.90/1.26 { ! s_t( X, Y, Z ), ! s_t( T, U, W ), ! s_e( X, Z, T, W ), ! s_e( Y, Z, U,
% 0.90/1.26 W ), s_e( X, Y, T, U ) }.
% 0.90/1.26 { ! s_t( X, Y, Z ), ! s_e( X, Z, T, U ), s_t( T, insert( X, Y, T, U ), U )
% 0.90/1.26 }.
% 0.90/1.26 { ! s_t( X, Y, Z ), ! s_e( X, Z, T, U ), s_e3( X, Y, Z, T, insert( X, Y, T
% 0.90/1.26 , U ), U ) }.
% 0.90/1.26 { ! s_t( X, Y, Z ), ! s_e3( X, Y, Z, T, U, W ), s_t( T, U, W ) }.
% 0.90/1.26 { ! s_col( X, Y, Z ), s_col( Y, Z, X ) }.
% 0.90/1.26 { ! s_col( X, Y, Z ), s_col( Z, X, Y ) }.
% 0.90/1.26 { ! s_col( X, Y, Z ), s_col( Z, Y, X ) }.
% 0.90/1.26 { ! s_col( X, Y, Z ), s_col( Y, X, Z ) }.
% 0.90/1.26 { ! s_col( X, Y, Z ), s_col( X, Z, Y ) }.
% 0.90/1.26 { s_col( X, X, Y ) }.
% 0.90/1.26 { s_col( X, Y, X ) }.
% 0.90/1.26 { ! s_col( X, Y, Z ), ! s_e3( X, Y, Z, T, U, W ), s_col( T, U, W ) }.
% 0.90/1.26 { ! s_col( X, Y, Z ), ! s_e( X, Y, T, U ), s_e3( X, Y, Z, T, U, insert5( X
% 0.90/1.26 , Y, Z, T, U ) ) }.
% 0.90/1.26 { ! s_fs( X, Y, Z, T, V0, V1, U, W ), X = Y, s_e( Z, T, U, W ) }.
% 0.90/1.26 { X = Y, ! s_col( X, Y, Z ), ! s_e( X, T, X, U ), ! s_e( Y, T, Y, U ), s_e
% 0.90/1.26 ( Z, T, Z, U ) }.
% 0.90/1.26 { X = Y, ! s_col( X, Y, Z ), ! s_e( X, Z, X, T ), ! s_e( Y, Z, Y, T ), Z =
% 0.90/1.26 T }.
% 0.90/1.26 { ! s_t( X, Y, Z ), ! s_e( X, Y, X, T ), ! s_e( Z, Y, Z, T ), Y = T }.
% 0.90/1.26 { X = Y, ! s_t( X, Y, Z ), ! s_t( X, Y, T ), s_t( X, Z, T ), s_t( X, T, Z )
% 0.90/1.26 }.
% 0.90/1.26 { X = Y, ! s_t( X, Y, Z ), ! s_t( X, Y, T ), s_t( Y, Z, T ), s_t( Y, T, Z )
% 0.90/1.26 }.
% 0.90/1.26 { ! s_t( X, Y, Z ), ! s_t( X, T, Z ), s_t( X, Y, T ), s_t( X, T, Y ) }.
% 0.90/1.26 { ! le( X, Y, Z, T ), s_t( X, Y, ins( Z, T, X, Y ) ) }.
% 0.90/1.26 { ! le( X, Y, Z, T ), s_e( X, ins( Z, T, X, Y ), Z, T ) }.
% 0.90/1.26 { ! le( X, Y, Z, T ), ins( Z, T, X, Y ) = ext( X, Y, insert( X, Y, Z, T ),
% 0.90/1.26 T ) }.
% 0.90/1.26 { le( X, Y, Z, T ), ! s_t( X, Y, U ), ! s_e( X, U, Z, T ) }.
% 0.90/1.26 { ! le( X, Y, Z, T ), ! s_e( X, Y, U, W ), ! s_e( Z, T, V0, V1 ), le( U, W
% 0.90/1.26 , V0, V1 ) }.
% 0.90/1.26 { le( X, Y, X, Y ) }.
% 0.90/1.26 { ! le( X, Y, Z, T ), ! le( Z, T, U, W ), le( X, Y, U, W ) }.
% 0.90/1.26 { ! le( X, Y, Z, T ), ! le( Z, T, X, Y ), s_e( X, Y, Z, T ) }.
% 0.90/1.26 { le( X, Y, Z, T ), le( Z, T, X, Y ) }.
% 0.90/1.26 { le( X, X, Y, Z ) }.
% 0.90/1.26 { ! s_col( X, Y, Z ), ! s_t( X, Y, Z ), le( X, Y, X, Z ) }.
% 0.90/1.26 { ! s_col( X, Y, Z ), ! s_t( X, Y, Z ), le( Y, Z, X, Z ) }.
% 0.90/1.26 { ! s_t( X, Y, Z ), ! s_e( X, Z, X, Y ), Z = Y }.
% 0.90/1.26 { ! s_col( X, Y, Z ), s_t( X, Y, Z ), ! le( X, Y, X, Z ), ! le( Y, Z, X, Z
% 0.90/1.26 ) }.
% 0.90/1.26 { X = Y, Z = Y, T = Y, ! s_t( X, Y, T ), ! s_t( Z, Y, T ), sameside( X, Y,
% 0.90/1.26 Z ) }.
% 0.90/1.26 { X = Y, Z = Y, T = Y, ! s_t( X, Y, T ), s_t( Z, Y, T ), ! sameside( X, Y,
% 0.90/1.26 Z ) }.
% 0.90/1.26 { ! sameside( X, Y, Z ), ! X = Y }.
% 0.90/1.26 { ! sameside( X, Y, Z ), ! Z = Y }.
% 0.90/1.26 { ! sameside( X, Y, Z ), ! c63( X, Y, Z ) = Y }.
% 0.90/1.26 { ! sameside( X, Y, Z ), s_t( X, Y, c63( X, Y, Z ) ) }.
% 0.90/1.26 { ! sameside( X, Y, Z ), s_t( Z, Y, c63( X, Y, Z ) ) }.
% 0.90/1.26 { sameside( X, Y, Z ), X = Y, Z = Y, T = Y, ! s_t( X, Y, T ), ! s_t( Z, Y,
% 0.90/1.26 T ) }.
% 0.90/1.26 { ! sameside( X, Y, Z ), s_col( X, Y, Z ) }.
% 0.90/1.26 { ! sameside( X, Y, Z ), ! s_t( X, Y, Z ) }.
% 0.90/1.26 { sameside( X, Y, Z ), ! s_col( X, Y, Z ), s_t( X, Y, Z ) }.
% 0.90/1.26 { X = Y, sameside( X, Y, X ) }.
% 0.90/1.26 { ! sameside( X, Y, Z ), sameside( Z, Y, X ) }.
% 0.90/1.26 { ! sameside( X, Y, Z ), ! sameside( Z, Y, T ), sameside( X, Y, T ) }.
% 0.90/1.26 { X = Y, Z = T, sameside( insert( Z, T, Y, X ), Y, X ) }.
% 0.90/1.26 { X = Y, Z = T, s_e( Y, insert( Z, T, Y, X ), Z, T ) }.
% 0.90/1.26 { X = Y, Z = T, ! sameside( U, Y, X ), ! s_e( Y, U, Z, T ), ! sameside( W,
% 0.90/1.26 Y, X ), ! s_e( Y, W, Z, T ), U = W }.
% 0.90/1.26 { ! sameside( X, Y, Z ), ! le( Y, X, Y, Z ), s_t( Y, X, Z ) }.
% 0.90/1.26 { ! sameside( X, Y, Z ), le( Y, X, Y, Z ), ! s_t( Y, X, Z ) }.
% 0.90/1.26 { X = Y, X = Z, ! s_t( Y, X, Z ), ! s_col( T, X, Y ), T = X, sameside( T, X
% 0.90/1.26 , Y ), sameside( T, X, Z ) }.
% 0.90/1.26 { X = Y, X = Z, ! s_t( Y, X, Z ), ! sameside( T, X, Y ), s_col( T, X, Y ) }
% 0.90/1.26 .
% 0.90/1.26 { X = Y, X = Z, ! s_t( Y, X, Z ), ! sameside( T, X, Z ), s_col( T, X, Y ) }
% 0.90/1.26 .
% 0.90/1.26 { X = Y, X = Z, ! s_t( Y, X, Z ), ! T = X, s_col( T, X, Y ) }.
% 0.90/1.26 { X = Y, ! s_t( Z, X, Y ), ! s_t( T, X, Y ), s_t( T, Z, Y ), s_t( Z, T, Y )
% 0.90/1.26 }.
% 0.90/1.26 { X = Y, Z = X, ! s_col( X, Y, Z ), ! s_col( X, Y, T ), s_col( X, Z, T ) }
% 0.90/1.26 .
% 0.90/1.26 { X = Y, s_col( X, Y, X ) }.
% 0.90/1.26 { X = Y, ! s_col( X, Y, Z ), s_col( Y, X, Z ) }.
% 0.90/1.26 { X = Y, Z = T, ! s_col( Z, T, X ), ! s_col( Z, T, Y ), ! s_col( Z, T, U )
% 0.90/1.26 , s_col( X, Y, U ) }.
% 0.90/1.26 { X = Y, Z = T, ! s_col( X, Y, U ), ! s_col( Z, T, U ), ! s_col( X, Y, W )
% 0.90/1.26 , ! s_col( Z, T, W ), U = W, ! s_col( X, Y, V0 ), s_col( Z, T, V0 ) }.
% 0.90/1.26 { X = Y, ! s_col( X, Y, pointOffLine( X, Y ) ) }.
% 0.90/1.26 { ! sameside( X, Y, Z ), ! sameside( T, U, W ), ! s_e( Y, X, U, T ), ! s_e
% 0.90/1.26 ( Y, Z, U, W ), s_e( X, Z, T, W ) }.
% 0.90/1.26 { ! s_m( X, Y, Z ), s_m( Z, Y, X ) }.
% 0.90/1.26 { ! s_m( X, Y, X ), Y = X }.
% 0.90/1.26 { s_m( X, Y, X ), ! Y = X }.
% 0.90/1.26 { s_m( X, Y, s( Y, X ) ) }.
% 0.90/1.26 { ! s_m( X, Y, Z ), ! s_m( X, Y, T ), Z = T }.
% 0.90/1.26 { ! s_m( X, Y, Z ), Z = s( Y, X ) }.
% 0.90/1.26 { s( X, s( X, Y ) ) = Y }.
% 0.90/1.26 { ! s( X, Y ) = Z, ! s( X, T ) = Z, Y = T }.
% 0.90/1.26 { ! s( Z, X ) = s( Z, Y ), X = Y }.
% 0.90/1.26 { ! s( X, Y ) = Y, Y = X }.
% 0.90/1.26 { s( X, Y ) = Y, ! Y = X }.
% 0.90/1.26 { s_e( X, Y, s( Z, X ), s( Z, Y ) ) }.
% 0.90/1.26 { ! s_t( X, Y, Z ), s_t( s( T, X ), s( T, Y ), s( T, Z ) ) }.
% 0.90/1.26 { s_t( X, Y, Z ), ! s_t( s( T, X ), s( T, Y ), s( T, Z ) ) }.
% 0.90/1.26 { ! s_e( X, Y, Z, T ), s_e( s( U, X ), s( U, Y ), s( U, Z ), s( U, T ) ) }
% 0.90/1.26 .
% 0.90/1.26 { s_e( X, Y, Z, T ), ! s_e( s( U, X ), s( U, Y ), s( U, Z ), s( U, T ) ) }
% 0.90/1.26 .
% 0.90/1.26 { ! s_m( X, Y, Z ), ! s_m( X, T, Z ), Y = T }.
% 0.90/1.26 { ! s( X, Z ) = s( Y, Z ), X = Y }.
% 0.90/1.26 { ! s( X, s( Y, Z ) ) = s( Y, s( X, Z ) ), X = Y }.
% 0.90/1.26 { ! s_col( X, Y, Z ), ! s_e( Y, X, Y, Z ), X = Z, s_m( X, Y, Z ) }.
% 0.90/1.26 { s_col( X, Y, Z ), Y = T, ! s_e( X, Y, Z, T ), ! s_e( Y, Z, T, X ), !
% 0.90/1.26 s_col( X, U, Z ), ! s_col( Y, U, T ), s_m( X, U, Z ) }.
% 0.90/1.26 { ! s_kf( X, Y, W, Z, V0, T, U ), s_t( Y, Z, T ), ! le( Z, X, Z, U ) }.
% 0.90/1.26 { ! s_kf( T, X, U, Y, W, Z, V0 ), s_t( X, Y, Z ) }.
% 0.90/1.26 { ! s_t( X, Y, Z ), ! s_t( T, Y, U ), ! s_e( Y, X, Y, T ), ! s_e( Y, Z, Y,
% 0.90/1.26 U ), ! s_m( X, W, T ), ! s_m( Z, V0, U ), s_t( W, Y, V0 ) }.
% 0.90/1.26 { ! s_e( X, Y, X, Z ), s_m( Y, isomidpoint( Y, Z, X ), Z ) }.
% 0.90/1.26 { ! s_r( X, Y, Z ), s_r( Z, Y, X ) }.
% 0.90/1.26 { ! s_r( X, Y, Z ), X = Y, ! s_col( Y, X, T ), s_r( T, Y, Z ) }.
% 0.90/1.26 { ! s_r( X, Y, Z ), s_r( X, Y, s( Y, Z ) ) }.
% 0.90/1.26 { s_r( X, Y, Y ) }.
% 0.90/1.26 { ! s_r( X, Y, Z ), ! s_r( T, Y, Z ), ! s_t( X, Z, T ), Y = Z }.
% 0.90/1.26 { ! s_r( X, Y, Z ), ! s_r( X, Z, Y ), Y = Z }.
% 0.90/1.26 { ! s_r( X, Y, X ), X = Y }.
% 0.90/1.26 { ! s_r( X, Y, Z ), ! s_col( X, Y, Z ), X = Y, Z = Y }.
% 0.90/1.26 { ! s_r( X, Y, Z ), ! s_e3( X, Y, Z, T, U, W ), s_r( T, U, W ) }.
% 0.90/1.26 { ! perpAt( X, Y, Z, T, U ), perpAt( T, U, Z, X, Y ) }.
% 0.90/1.26 { ! perp( X, Y, Z, T ), perp( Z, T, X, Y ) }.
% 0.90/1.26 { ! perpAt( X, Y, Z, T, U ), ! X = Y }.
% 0.90/1.26 { ! perpAt( X, Y, Z, T, U ), ! T = U }.
% 0.90/1.26 { ! perpAt( X, Y, Z, T, U ), s_col( T, U, Z ) }.
% 0.90/1.26 { ! perpAt( X, Y, Z, T, U ), s_col( X, Y, Z ) }.
% 0.90/1.26 { ! perpAt( X, Y, Z, T, U ), s_col( X, Y, f813( X, Y, T, U, Z ) ) }.
% 0.90/1.26 { ! perpAt( X, Y, Z, T, U ), s_col( T, U, g813( X, Y, T, U, Z ) ) }.
% 0.90/1.26 { ! perpAt( X, Y, Z, T, U ), ! Z = f813( X, Y, T, U, Z ) }.
% 0.90/1.26 { ! perpAt( X, Y, Z, T, U ), ! Z = g813( X, Y, T, U, Z ) }.
% 0.90/1.26 { ! perpAt( X, Y, Z, T, U ), s_r( f813( X, Y, T, U, Z ), Z, g813( X, Y, T,
% 0.90/1.26 U, Z ) ) }.
% 0.90/1.26 { X = Y, Z = T, ! s_col( Z, T, U ), ! s_col( X, Y, U ), ! s_col( X, Y, W )
% 0.90/1.26 , ! s_col( Z, T, V0 ), U = W, U = V0, ! s_r( W, U, V0 ), perpAt( X, Y, U
% 0.90/1.26 , Z, T ) }.
% 0.90/1.26 { ! perp( X, Y, Z, T ), ! s_col( X, Y, Z ), ! s_col( X, Y, T ) }.
% 0.90/1.26 { ! perp( X, Y, Z, T ), ! s_col( X, Y, U ), ! s_col( Z, T, U ), perpAt( X,
% 0.90/1.26 Y, U, Z, T ) }.
% 0.90/1.26 { ! perpAt( X, Y, Z, T, U ), Z = il( X, Y, T, U ) }.
% 0.90/1.26 { X = Y, ! s_col( X, Y, Z ), ! perp( X, Y, T, Z ), perpAt( X, Y, Z, T, Z )
% 0.90/1.26 }.
% 0.90/1.26 { X = Y, ! s_col( X, Y, Z ), ! s_col( X, Y, T ), T = Z, ! s_col( X, Y, U )
% 0.90/1.26 , ! perp( X, Y, U, Z ) }.
% 0.90/1.26 { X = Y, ! s_col( X, Y, Z ), ! s_col( X, Y, T ), T = Z, s_r( U, Z, T ), !
% 0.90/1.26 perp( X, Y, U, Z ) }.
% 0.90/1.26 { X = Y, ! s_col( X, Y, Z ), ! s_col( X, Y, T ), T = Z, perp( X, Y, U, Z )
% 0.90/1.26 , s_col( X, Y, U ), ! s_r( U, Z, T ) }.
% 0.90/1.26 { s_col( X, Y, Z ), ! s_col( X, Y, T ), ! s_col( X, Y, U ), ! perp( X, Y, Z
% 0.90/1.26 , T ), ! perp( X, Y, Z, U ), T = U }.
% 0.90/1.26 { s_col( X, Y, Z ), s_col( X, Y, foot( X, Y, Z ) ) }.
% 0.90/1.26 { s_col( X, Y, Z ), perp( X, Y, Z, foot( X, Y, Z ) ) }.
% 0.90/1.26 { ! s_r( X, Y, Z ), ! s_m( s( X, Z ), T, s( Y, Z ) ), s_r( Y, X, T ) }.
% 0.90/1.26 { ! s_r( X, Y, Z ), ! s_m( s( X, Z ), T, s( Y, Z ) ), Y = Z, ! X = T }.
% 0.90/1.26 { ! perp( X, Y, Z, T ), perp( Y, X, Z, T ) }.
% 0.90/1.26 { X = Y, Z = T, ! s_col( X, Y, Z ), ! s_col( X, Y, T ), ! s_col( Z, T, U )
% 0.90/1.26 , s_col( X, Y, U ) }.
% 0.90/1.26 { X = Y, perp( X, Y, erect21a( X, Y, Z ), X ), s_col( X, Y, Z ) }.
% 0.90/1.26 { X = Y, s_col( X, Y, erectAux21a( X, Y, Z ) ), s_col( X, Y, Z ) }.
% 0.90/1.26 { X = Y, s_t( Z, erectAux21a( X, Y, Z ), erect21a( X, Y, Z ) ), s_col( X, Y
% 0.90/1.26 , Z ) }.
% 0.90/1.26 { X = Y, perp( X, Y, erect( X, Y, Z ), X ) }.
% 0.90/1.26 { X = Y, s_col( X, Y, erectAux( X, Y, Z ) ) }.
% 0.90/1.26 { X = Y, s_t( Z, erectAux( X, Y, Z ), erect( X, Y, Z ) ) }.
% 0.90/1.26 { ! le( X, Y, Z, T ), ! perp( X, Z, X, Y ), ! perp( X, Z, Z, T ), ! s_t( Y
% 0.90/1.26 , U, T ), ! s_col( X, Z, U ), s_m( X, midpointAux( X, Z, Y, T, U ), Z ) }
% 0.90/1.26 .
% 0.90/1.26 { s_m( X, midpoint( X, Y ), Y ) }.
% 0.90/1.26 { ! perp( X, Y, Y, Z ), ! perp( T, Z, Y, Z ), ! s_col( Y, Z, U ), ! s_t( X
% 0.90/1.26 , U, T ), ! s_t( Z, W, T ), ! s_e( Y, X, Z, W ), ! V0 = ip( X, U, T, Z, W
% 0.90/1.26 ), s_m( Y, V0, Z ) }.
% 0.90/1.26 { ! perp( X, Y, Y, Z ), ! perp( T, Z, Y, Z ), ! s_col( Y, Z, U ), ! s_t( X
% 0.90/1.26 , U, T ), ! s_t( Z, W, T ), ! s_e( Y, X, Z, W ), ! V0 = ip( X, U, T, Z, W
% 0.90/1.26 ), s_m( X, V0, W ) }.
% 0.90/1.26 { ! perp( X, Y, Y, Z ), ! perp( T, Z, Y, Z ), ! s_col( Y, Z, U ), ! s_t( X
% 0.90/1.26 , U, T ), ! s_t( Z, W, T ), ! s_e( Y, X, Z, W ), s_m( X, midpoint( Y, Z )
% 0.90/1.26 , W ) }.
% 0.90/1.26 { ! s_col( X, Y, Z ), ! s_col( X, Y, T ), X = Y, s_col( X, Z, T ) }.
% 0.90/1.26 { ! s_col( X, Y, Z ), ! s_col( X, Y, T ), Z = T, X = Y, ! perpAt( Z, T, U,
% 0.90/1.26 W, V0 ), perpAt( X, Y, U, W, V0 ) }.
% 0.90/1.26 { ! s_col( X, Y, Z ), ! s_col( X, Y, T ), Z = T, X = Y, ! perp( Z, T, U, W
% 0.90/1.26 ), perp( X, Y, U, W ) }.
% 0.90/1.26 { X = Y, X = Z, Y = Z, T = Z, X = T, ! perp( Y, X, X, Z ), ! s_col( X, Z, T
% 0.90/1.26 ), perp( Y, X, X, T ) }.
% 0.90/1.26 { ! perp( X, Y, Z, T ), perp( X, Y, T, Z ) }.
% 0.90/1.26 { ! s_col( X, Y, Z ), ! s_col( X, Y, T ), Z = T, X = Y, perp( Z, T, U, W )
% 0.90/1.26 , ! perp( X, Y, U, W ) }.
% 0.90/1.26 { ! s_col( xa, xb, xp ), ! s_col( xa, xb, xq ), xp = xq, xa = xb, perp( xc
% 0.90/1.26 , xd, xp, xq ), ! perp( xc, xd, xa, xb ) }.
% 0.90/1.26 { ! s_col( X, Y, Z ), X = Y, X = Z, ! samesideline( T, U, X, Y ),
% 0.90/1.26 samesideline( T, U, X, Z ) }.
% 0.90/1.26 { X = Y, ! samesideline( Z, T, X, Y ), samesideline( Z, T, Y, X ) }.
% 0.90/1.26 { ! opposite( X, Y, Z, T ), opposite( T, Y, Z, X ) }.
% 0.90/1.26 { ! opposite( X, Y, Z, T ), ! s_col( Y, Z, U ), ! s_m( X, U, T ), ! s_col(
% 0.90/1.26 Y, Z, W ), ! sameside( X, W, V0 ), opposite( V0, Y, Z, T ), ! s_t( W, V0
% 0.90/1.26 , X ) }.
% 0.90/1.26 { ! opposite( X, Y, Z, T ), ! s_col( Y, Z, U ), ! s_m( X, U, T ), ! s_col(
% 0.90/1.26 Y, Z, W ), ! sameside( X, W, V0 ), opposite( V0, Y, Z, T ) }.
% 0.90/1.26 { ! sameside( X, Y, Z ), sameside( s( T, X ), s( T, Y ), s( T, Z ) ) }.
% 0.90/1.26 { ! opposite( X, Y, Z, T ), Y = Z, ! s_col( Y, Z, U ), ! s_col( Y, Z, W ),
% 0.90/1.26 ! perp( Y, Z, X, W ), ! perp( Y, Z, T, U ), ! s_m( W, V0, U ), ! sameside
% 0.90/1.26 ( V1, W, X ), ! le( U, T, W, X ), W = U, sameside( s( V0, V1 ), U, T ) }
% 0.90/1.26 .
% 0.90/1.26 { ! opposite( X, Y, Z, T ), Y = Z, ! s_col( Y, Z, U ), ! s_col( Y, Z, W ),
% 0.90/1.26 ! perp( Y, Z, X, W ), ! perp( Y, Z, T, U ), ! s_m( W, V0, U ), sameside(
% 0.90/1.26 V1, W, X ), ! le( U, T, W, X ), W = U, ! sameside( s( V0, V1 ), U, T ) }
% 0.90/1.26 .
% 0.90/1.26 { ! opposite( X, Y, Z, T ), Y = Z, ! s_col( Y, Z, U ), ! s_col( Y, Z, W ),
% 0.90/1.26 ! perp( Y, Z, X, W ), ! perp( Y, Z, T, U ), ! s_m( W, V0, U ), ! sameside
% 0.90/1.26 ( V1, W, X ), ! W = U, sameside( s( V0, V1 ), U, T ) }.
% 0.90/1.26 { ! opposite( X, Y, Z, T ), Y = Z, ! s_col( Y, Z, U ), ! s_col( Y, Z, W ),
% 0.90/1.26 ! perp( Y, Z, X, W ), ! perp( Y, Z, T, U ), ! s_m( W, V0, U ), ! sameside
% 0.90/1.26 ( V1, W, X ), sameside( s( V0, V1 ), U, T ) }.
% 0.90/1.26 { ! opposite( X, Y, Z, T ), Y = Z, ! s_col( Y, Z, U ), ! s_col( Y, Z, W ),
% 0.90/1.26 ! perp( Y, Z, X, W ), ! perp( Y, Z, T, U ), ! s_m( W, V0, U ), ! sameside
% 0.90/1.26 ( V1, W, X ), ! sameside( V2, U, T ), opposite( V1, Y, Z, V2 ) }.
% 0.90/1.26 { ! opposite( X, Y, Z, T ), ! s_col( Y, Z, U ), ! sameside( X, U, W ),
% 0.90/1.26 opposite( W, Y, Z, T ) }.
% 0.90/1.26 { ! s_t( X, Y, Z ), ! s_t( T, U, Y ), s_t( X, op( U, T, Z, Y, X ), T ) }.
% 0.90/1.26 { ! s_t( X, Y, Z ), ! s_t( T, U, Y ), s_t( Z, U, op( U, T, Z, Y, X ) ) }.
% 0.90/1.26 { ! opposite( X, Y, Z, T ), opposite( U, Y, Z, T ), ! samesideline( X, U, Y
% 0.90/1.26 , Z ) }.
% 0.90/1.26 { ! opposite( X, Y, Z, T ), ! samesideline( X, T, Y, Z ) }.
% 0.90/1.26 { X = Y, ! samesideline( Z, T, X, Y ), ! samesideline( T, U, X, Y ),
% 0.90/1.26 samesideline( Z, U, X, Y ) }.
% 0.90/1.26 { ! samesideline( X, Y, Z, T ), samesideline( X, Y, T, Z ) }.
% 0.90/1.26 { X = Y, ! s_m( Z, T, U ), ! s_col( X, Y, Z ), ! s_col( X, Y, U ), s_col( X
% 0.90/1.26 , Y, T ) }.
% 0.90/1.26 { X = Y, ! s_t( Y, X, Z ), ! samesideline( T, U, Z, Y ), samesideline( T, U
% 0.90/1.26 , X, Y ) }.
% 0.90/1.26 { X = Y, ! samesideline( Z, T, X, Y ), samesideline( T, Z, X, Y ) }.
% 0.90/1.26 { ! opposite( X, Y, Z, T ), ! samesideline( T, U, Y, Z ), opposite( X, Y, Z
% 0.90/1.26 , U ) }.
% 0.90/1.26 { X = Y, ! perpAt( X, Y, Z, T, Z ), ! perpAt( X, Y, Z, U, Z ), T = Z, s_col
% 0.90/1.26 ( Z, T, U ) }.
% 0.90/1.26 { X = Y, s_col( X, Y, Z ), s_col( X, Y, T ), samesideline( Z, T, X, Y ),
% 0.90/1.26 opposite( Z, X, Y, T ), ! X = foot( X, Y, Z ) }.
% 0.90/1.26 { X = Y, s_col( X, Y, Z ), s_col( X, Y, T ), samesideline( Z, T, X, Y ),
% 0.90/1.26 opposite( Z, X, Y, T ), X = foot( X, Y, Z ) }.
% 0.90/1.26 { X = Y, s_col( X, Y, Z ), s_col( X, Y, T ), samesideline( Z, T, X, Y ),
% 0.90/1.26 opposite( Z, X, Y, T ) }.
% 0.90/1.26 { ! samesideline( X, Y, Z, T ), ! sameside( X, T, U ), samesideline( U, Y,
% 0.90/1.26 Z, T ) }.
% 0.90/1.26 { X = Y, ! s_col( X, Y, Z ), ! s_col( T, U, Z ), ! sameside( T, Z, U ),
% 0.90/1.26 s_col( X, Y, T ), samesideline( T, U, X, Y ) }.
% 0.90/1.26 { X = Y, s_col( X, Y, midpoint( Z, reflect( X, Y, Z ) ) ) }.
% 0.90/1.26 { X = Y, Z = reflect( X, Y, Z ), perp( X, Y, Z, reflect( X, Y, Z ) ) }.
% 0.90/1.26 { X = Y, ! s_col( X, Y, midpoint( Z, T ) ), ! perp( X, Y, Z, T ), T =
% 0.90/1.26 reflect( X, Y, Z ) }.
% 0.90/1.26 { X = Y, ! s_col( X, Y, midpoint( Z, T ) ), ! Z = T, T = reflect( X, Y, Z )
% 0.90/1.26 }.
% 0.90/1.26 { X = Y, ! reflect( X, Y, Z ) = T, reflect( X, Y, T ) = Z }.
% 0.90/1.26 { X = Y, reflect( X, Y, reflect( X, Y, Z ) ) = Z }.
% 0.90/1.26 { X = Y, ! reflect( X, Y, Z ) = T, Z = reflect( X, Y, T ) }.
% 0.90/1.26 { X = Y, ! reflect( X, Y, Z ) = reflect( X, Y, T ), Z = T }.
% 0.90/1.26 { X = Y, ! reflect( X, Y, Z ) = Z, s_col( X, Y, Z ) }.
% 0.90/1.26 { X = Y, ! s_col( X, Y, Z ), reflect( X, Y, Z ) = Z }.
% 0.90/1.26 { X = Y, ! s_col( X, Y, Z ), s_e( Z, T, reflect( X, Y, Z ), reflect( X, Y,
% 0.90/1.26 T ) ) }.
% 0.90/1.26 { X = Y, s_e( Z, T, reflect( X, Y, Z ), reflect( X, Y, T ) ) }.
% 0.90/1.26 { ! s_r( X, Y, Z ), ! s_r( T, Y, Z ), ! s_e( X, Y, T, Y ), s_e( X, Z, T, Z
% 0.90/1.26 ) }.
% 0.90/1.26 { ! s_r( X, Y, Z ), ! s_r( T, Y, U ), ! s_e( X, Y, T, Y ), ! s_e( Y, Z, Y,
% 0.90/1.26 U ), s_e( X, Z, T, U ), ! Y = midpoint( Z, U ), Z = U }.
% 0.90/1.26 { ! s_r( X, Y, Z ), ! s_r( T, Y, U ), ! s_e( X, Y, T, Y ), ! s_e( Y, Z, Y,
% 0.90/1.26 U ), s_e( X, Z, T, U ) }.
% 0.90/1.26 { ! s_r( X, Y, Z ), ! s_r( T, U, W ), ! s_e( X, Y, T, U ), ! s_e( Y, Z, U,
% 0.90/1.26 W ), s_e( X, Z, T, W ) }.
% 0.90/1.26 { X = Y, ! reflect( X, Y, Z ) = T, s_col( X, Y, Z ), opposite( Z, X, Y, T )
% 0.90/1.26 }.
% 0.90/1.26 { X = Y, ! s_col( X, Y, Z ), s_col( X, Y, T ), perp( X, Y, erectsameside( X
% 0.90/1.26 , Y, Z, T ), Z ) }.
% 0.90/1.26 { X = Y, ! s_col( X, Y, Z ), s_col( X, Y, T ), samesideline( erectsameside
% 0.90/1.26 ( X, Y, Z, T ), T, X, Y ) }.
% 0.90/1.26 { X = Y, s_col( X, Y, Z ), s_col( T, U, W ), ! s_e( X, Y, T, U ), s_e3( X,
% 0.90/1.26 Y, Z, T, U, triangle( X, Y, Z, T, U, W ) ) }.
% 0.90/1.26 { X = Y, s_col( X, Y, Z ), s_col( T, U, W ), ! s_e( X, Y, T, U ),
% 0.90/1.26 samesideline( triangle( X, Y, Z, T, U, W ), W, T, U ) }.
% 0.90/1.26 { X = Y, s_col( X, Y, Z ), s_col( T, U, W ), ! s_e( X, Y, T, U ), ! s_e3( X
% 0.90/1.26 , Y, Z, T, U, V0 ), ! samesideline( V0, W, T, U ), ! s_e3( X, Y, Z, T, U
% 0.90/1.26 , V1 ), ! samesideline( V1, W, T, U ), V0 = V1 }.
% 0.90/1.26 { ! congruent( X, Y, Z, T, U, W ), sameside( ext( Y, X, U, T ), Y, X ) }.
% 0.90/1.26 { ! congruent( X, Y, Z, T, U, W ), sameside( ext( Y, Z, U, W ), Y, Z ) }.
% 0.90/1.26 { ! congruent( X, Y, Z, T, U, W ), sameside( ext( U, T, Y, X ), U, T ) }.
% 0.90/1.26 { ! congruent( X, Y, Z, T, U, W ), sameside( ext( U, W, Y, Z ), U, W ) }.
% 0.90/1.26 { ! congruent( X, Y, Z, T, U, W ), s_e3( ext( Y, X, U, T ), Y, ext( Y, Z, U
% 0.90/1.26 , W ), ext( U, T, Y, X ), U, ext( U, W, Y, Z ) ) }.
% 0.90/1.26 { ! sameside( X, Y, Z ), ! sameside( T, Y, U ), ! sameside( W, V0, V1 ), !
% 0.90/1.26 sameside( V2, V0, V3 ), ! s_e3( X, Y, T, W, V0, V2 ), congruent( Z, Y, U
% 0.90/1.26 , V1, V0, V3 ) }.
% 0.90/1.26 { X = Y, Z = Y, T = U, W = U, sameside( f113a( X, Y, Z, T, U, W ), Y, X ),
% 0.90/1.26 congruent( X, Y, Z, T, U, W ) }.
% 0.90/1.26 { X = Y, Z = Y, T = U, W = U, sameside( f113c( X, Y, Z, T, U, W ), Y, Z ),
% 0.90/1.26 congruent( X, Y, Z, T, U, W ) }.
% 0.90/1.26 { X = Y, Z = Y, T = U, W = U, sameside( f113d( X, Y, Z, T, U, W ), U, T ),
% 0.90/1.26 congruent( X, Y, Z, T, U, W ) }.
% 0.90/1.26 { X = Y, Z = Y, T = U, W = U, sameside( f113f( X, Y, Z, T, U, W ), U, W ),
% 0.90/1.26 congruent( X, Y, Z, T, U, W ) }.
% 0.90/1.26 { X = Y, Z = Y, T = U, W = U, s_e( Y, f113a( X, Y, Z, T, U, W ), U, f113d(
% 0.90/1.26 X, Y, Z, T, U, W ) ), congruent( X, Y, Z, T, U, W ) }.
% 0.90/1.26 { X = Y, Z = Y, T = U, W = U, s_e( Y, f113c( X, Y, Z, T, U, W ), U, f113f(
% 0.90/1.26 X, Y, Z, T, U, W ) ), congruent( X, Y, Z, T, U, W ) }.
% 0.90/1.26 { X = Y, Z = Y, T = U, W = U, ! s_e( f113a( X, Y, Z, T, U, W ), f113c( X, Y
% 0.90/1.26 , Z, T, U, W ), f113d( X, Y, Z, T, U, W ), f113f( X, Y, Z, T, U, W ) ),
% 0.90/1.26 congruent( X, Y, Z, T, U, W ) }.
% 0.90/1.26 { ! congruent( X, Y, Z, T, U, W ), ! sameside( V0, Y, X ), ! sameside( V1,
% 0.90/1.26 Y, Z ), ! sameside( V2, U, T ), ! sameside( V3, U, W ), ! s_e( Y, V0, U,
% 0.90/1.26 V2 ), ! s_e( Y, V1, U, V3 ), s_e( V0, V1, V2, V3 ) }.
% 0.90/1.26 { ! sameside( X, Y, Z ), ! sameside( T, Y, U ), ! sameside( W, V0, V1 ), !
% 0.90/1.26 sameside( V2, V0, V3 ), ! s_e3( X, Y, T, W, V0, V2 ), V4 = Y, V5 = Y, V6
% 0.90/1.26 = V0, V7 = V0, ! sameside( Z, Y, V4 ), ! sameside( U, Y, V5 ), ! sameside
% 0.90/1.26 ( V1, V0, V6 ), ! sameside( V3, V0, V7 ), ! s_e( Y, Z, V0, V1 ), ! s_e( Y
% 0.90/1.26 , U, V0, V3 ), s_e( Z, U, V1, V3 ) }.
% 0.90/1.26 { X = Y, Z = Y, congruent( X, Y, Z, X, Y, Z ) }.
% 0.90/1.26 { ! congruent( X, Y, Z, T, U, W ), congruent( T, U, W, X, Y, Z ) }.
% 0.90/1.26 { ! congruent( X, Y, Z, T, U, W ), ! congruent( T, U, W, V0, V1, V2 ),
% 0.90/1.26 congruent( X, Y, Z, V0, V1, V2 ) }.
% 0.90/1.26 { X = Y, Z = Y, congruent( X, Y, Z, Z, Y, X ) }.
% 0.90/1.26 { s_col( X, Y, Z ), s_col( T, U, W ), congruent( X, Y, Z, T, U,
% 0.90/1.26 constructAngle( X, Y, Z, T, U, W ) ) }.
% 0.90/1.26 { s_col( X, Y, Z ), s_col( T, U, W ), samesideline( constructAngle( X, Y, Z
% 0.90/1.26 , T, U, W ), W, T, U ) }.
% 0.90/1.26 { s_col( X, Y, Z ), s_col( T, U, W ), ! congruent( X, Y, Z, T, U, V0 ), !
% 0.90/1.26 samesideline( V0, W, U, T ), ! congruent( X, Y, Z, T, U, V1 ), !
% 0.90/1.26 samesideline( V1, W, U, T ), sameside( V0, U, V1 ) }.
% 0.90/1.26 { ! congruent( X, Y, Z, T, U, W ), ! s_e( Y, X, U, T ), ! s_e( Y, Z, U, W )
% 0.90/1.26 , s_e( X, Z, T, W ) }.
% 0.90/1.26 { ! congruent( X, Y, Z, T, U, W ), ! s_e( Y, X, U, T ), ! s_e( Y, Z, U, W )
% 0.90/1.26 , X = Z, congruent( Y, X, Z, U, T, W ) }.
% 0.90/1.26 { ! parallel( X, Y, Z, T ), parallel( X, Y, T, Z ) }.
% 0.90/1.26 { parallel( skol1, skol2, skol3, skol4 ) }.
% 0.90/1.26 { s_col( skol3, skol4, skol5 ) }.
% 0.90/1.26 { s_col( skol3, skol4, skol6 ) }.
% 0.90/1.26 { ! samesideline( skol5, skol6, skol1, skol2 ) }.
% 0.90/1.26 { insert( X, Y, Z, T ) = ext( ext( T, Z, alpha, gamma ), Z, X, Y ) }.
% 0.90/1.26 { ! s_afs( X, Y, Z, T, U, W, V0, V1 ), s_t( X, Y, Z ) }.
% 0.90/1.26 { ! s_afs( X, Y, Z, T, U, W, V0, V1 ), s_t( U, W, V0 ) }.
% 0.90/1.26 { ! s_afs( X, Y, Z, T, U, W, V0, V1 ), s_e( X, Y, U, W ) }.
% 0.90/1.26 { ! s_afs( X, Y, Z, T, U, W, V0, V1 ), s_e( Y, Z, W, V0 ) }.
% 0.90/1.26 { ! s_afs( X, Y, Z, T, U, W, V0, V1 ), s_e( X, T, U, V1 ) }.
% 0.90/1.26 { ! s_afs( X, Y, Z, T, U, W, V0, V1 ), s_e( Y, T, W, V1 ) }.
% 0.90/1.26 { ! s_t( X, Y, Z ), ! s_t( U, W, V0 ), ! s_e( X, Y, U, W ), ! s_e( Y, Z, W
% 0.90/1.26 , V0 ), ! s_e( X, T, U, V1 ), ! s_e( Y, T, W, V1 ), s_afs( X, Y, Z, T, U
% 0.90/1.26 , W, V0, V1 ) }.
% 0.90/1.26 { ! s_ifs( X, Y, Z, T, U, W, V0, V1 ), s_t( X, Y, Z ) }.
% 0.90/1.26 { ! s_ifs( X, Y, Z, T, U, W, V0, V1 ), s_t( U, W, V0 ) }.
% 0.90/1.26 { ! s_ifs( X, Y, Z, T, U, W, V0, V1 ), s_e( X, Z, U, V0 ) }.
% 0.90/1.26 { ! s_ifs( X, Y, Z, T, U, W, V0, V1 ), s_e( Y, Z, W, V0 ) }.
% 0.90/1.26 { ! s_ifs( X, Y, Z, T, U, W, V0, V1 ), s_e( X, T, U, V1 ) }.
% 0.90/1.26 { ! s_ifs( X, Y, Z, T, U, W, V0, V1 ), s_e( Z, T, V0, V1 ) }.
% 0.90/1.26 { ! s_t( X, Y, Z ), ! s_t( U, W, V0 ), ! s_e( X, Z, U, V0 ), ! s_e( Y, Z, W
% 0.90/1.26 , V0 ), ! s_e( X, T, U, V1 ), ! s_e( Z, T, V0, V1 ), s_ifs( X, Y, Z, T, U
% 0.90/1.26 , W, V0, V1 ) }.
% 0.90/1.26 { ! s_e3( X, Y, Z, T, U, W ), s_e( X, Y, T, U ) }.
% 0.90/1.26 { ! s_e3( X, Y, Z, T, U, W ), s_e( X, Z, T, W ) }.
% 0.90/1.26 { ! s_e3( X, Y, Z, T, U, W ), s_e( Y, Z, U, W ) }.
% 0.90/1.26 { ! s_e( X, Y, T, U ), ! s_e( X, Z, T, W ), ! s_e( Y, Z, U, W ), s_e3( X, Y
% 0.90/1.26 , Z, T, U, W ) }.
% 0.90/1.26 { ! s_col( X, Y, Z ), s_t( X, Y, Z ), s_t( Y, Z, X ), s_t( Z, X, Y ) }.
% 0.90/1.26 { s_col( X, Y, Z ), ! s_t( X, Y, Z ) }.
% 0.90/1.26 { s_col( X, Y, Z ), ! s_t( Y, Z, X ) }.
% 0.90/1.26 { s_col( X, Y, Z ), ! s_t( Z, X, Y ) }.
% 0.90/1.26 { ! s_fs( X, Y, Z, T, U, W, V0, V1 ), s_col( X, Y, Z ) }.
% 0.90/1.26 { ! s_fs( X, Y, Z, T, U, W, V0, V1 ), s_e3( X, Y, Z, U, W, V0 ) }.
% 0.90/1.26 { ! s_fs( X, Y, Z, T, U, W, V0, V1 ), s_e( X, T, U, V1 ) }.
% 0.90/1.26 { ! s_fs( X, Y, Z, T, U, W, V0, V1 ), s_e( Y, T, W, V1 ) }.
% 0.90/1.26 { ! s_col( X, Y, Z ), ! s_e3( X, Y, Z, U, W, V0 ), ! s_e( X, T, U, V1 ), !
% 0.90/1.26 s_e( Y, T, W, V1 ), s_fs( X, Y, Z, T, U, W, V0, V1 ) }.
% 0.90/1.26 { ! le( X, Y, Z, T ), s_t( Z, insert( X, Y, Z, T ), T ) }.
% 0.90/1.26 { ! le( X, Y, Z, T ), s_e( X, Y, Z, insert( X, Y, Z, T ) ) }.
% 0.90/1.26 { ! s_t( Z, U, T ), ! s_e( X, Y, Z, U ), le( X, Y, Z, T ) }.
% 0.90/1.26 { ! sameside( X, Y, Z ), ! X = Y }.
% 0.90/1.26 { ! sameside( X, Y, Z ), ! Z = Y }.
% 0.90/1.26 { ! sameside( X, Y, Z ), s_t( Y, X, Z ), s_t( Y, Z, X ) }.
% 0.90/1.26 { ! s_t( Y, X, Z ), X = Y, xb = Y, sameside( X, Y, Z ) }.
% 0.90/1.26 { ! s_t( Y, Z, X ), X = Y, Z = Y, sameside( X, Y, Z ) }.
% 0.90/1.26 { ! s_m( X, Y, Z ), s_t( X, Y, Z ) }.
% 0.90/1.26 { ! s_m( X, Y, Z ), s_e( Y, X, Y, Z ) }.
% 0.90/1.26 { ! s_t( X, Y, Z ), ! s_e( Y, X, Y, Z ), s_m( X, Y, Z ) }.
% 0.90/1.26 { ! s_kf( X, Y, Z, T, U, W, V0 ), s_t( X, T, V0 ) }.
% 0.90/1.26 { ! s_kf( X, Y, Z, T, U, W, V0 ), s_t( Z, T, U ) }.
% 0.90/1.26 { ! s_kf( X, Y, Z, T, U, W, V0 ), s_e( T, X, T, Z ) }.
% 0.90/1.26 { ! s_kf( X, Y, Z, T, U, W, V0 ), s_e( T, V0, T, U ) }.
% 0.90/1.26 { ! s_kf( X, Y, Z, T, U, W, V0 ), s_m( X, Y, Z ) }.
% 0.90/1.26 { ! s_kf( X, Y, Z, T, U, W, V0 ), s_m( V0, W, U ) }.
% 0.90/1.26 { ! s_t( X, T, V0 ), ! s_t( Z, T, U ), ! s_e( T, X, T, Z ), ! s_e( T, V0, T
% 0.90/1.26 , U ), ! s_m( X, Y, Z ), ! s_m( V0, W, U ), s_kf( X, Y, Z, T, U, W, V0 )
% 0.90/1.26 }.
% 0.90/1.26 { ! s_r( X, Y, Z ), s_e( X, Z, X, s( Y, Z ) ) }.
% 0.90/1.26 { s_r( X, Y, Z ), ! s_e( X, Z, X, s( Y, Z ) ) }.
% 0.90/1.26 { ! perpAt( X, Y, Z, T, U ), s_col( X, Y, Z ) }.
% 0.90/1.26 { ! perpAt( X, Y, Z, T, U ), s_col( T, U, Z ) }.
% 0.90/1.26 { ! perpAt( X, Y, Z, T, U ), ! X = Y }.
% 0.90/1.26 { ! perpAt( X, Y, Z, T, U ), ! T = U }.
% 0.90/1.26 { ! perpAt( X, Y, Z, T, U ), ! s_col( X, Y, W ), ! s_col( T, U, V0 ), s_r(
% 0.90/1.26 W, Z, V0 ) }.
% 0.90/1.26 { perpAt( X, Y, Z, T, U ), X = Y, T = U, ! s_col( X, Y, Z ), ! s_col( T, U
% 0.90/1.26 , Z ), s_col( X, Y, f811( X, Y, T, U, Z ) ) }.
% 0.90/1.26 { perpAt( X, Y, Z, T, U ), X = Y, T = U, ! s_col( X, Y, Z ), ! s_col( T, U
% 0.90/1.26 , Z ), s_col( T, U, g811( X, Y, T, U, Z ) ) }.
% 0.90/1.26 { perpAt( X, Y, Z, T, U ), X = Y, T = U, ! s_col( X, Y, Z ), ! s_col( T, U
% 0.90/1.26 , Z ), ! s_r( f811( X, Y, T, U, Z ), Z, g811( X, Y, T, U, Z ) ) }.
% 0.90/1.26 { ! perp( X, Y, Z, T ), perpAt( X, Y, il( X, Y, Z, T ), Z, T ) }.
% 0.90/1.26 { perp( X, Y, Z, T ), ! perpAt( X, Y, U, Z, T ) }.
% 0.90/1.26 { X = Y, s_col( X, Y, Z ), s_col( X, Y, T ), ! s_t( Z, U, T ), ! s_col( X,
% 0.90/1.26 Y, U ), opposite( Z, X, Y, T ) }.
% 0.90/1.26 { ! opposite( Z, X, Y, T ), ! s_col( X, Y, Z ) }.
% 8.57/8.97 { ! opposite( Z, X, Y, T ), ! s_col( X, Y, T ) }.
% 8.57/8.97 { ! opposite( Z, X, Y, T ), s_t( Z, il( Z, T, X, Y ), T ) }.
% 8.57/8.97 { ! opposite( Z, X, Y, T ), s_col( X, Y, il( Z, T, X, Y ) ) }.
% 8.57/8.97 { ! samesideline( X, Y, Z, T ), s_col( Z, T, ss1( X, Y, Z, T ) ) }.
% 8.57/8.97 { ! samesideline( X, Y, Z, T ), s_col( Z, T, ss2( X, Y, Z, T ) ) }.
% 8.57/8.97 { ! samesideline( X, Y, Z, T ), s_t( X, ss1( X, Y, Z, T ), ss3( X, Y, Z, T
% 8.57/8.97 ) ) }.
% 8.57/8.97 { ! samesideline( X, Y, Z, T ), s_t( Y, ss2( X, Y, Z, T ), ss3( X, Y, Z, T
% 8.57/8.97 ) ) }.
% 8.57/8.97 { ! samesideline( X, Y, Z, T ), ! X = ss1( X, Y, Z, T ) }.
% 8.57/8.97 { ! samesideline( X, Y, Z, T ), ! Y = ss2( X, Y, Z, T ) }.
% 8.57/8.97 { ! samesideline( X, Y, Z, T ), ! ss3( X, Y, Z, T ) = ss1( X, Y, Z, T ) }.
% 8.57/8.97 { ! samesideline( X, Y, Z, T ), ! ss3( X, Y, Z, T ) = ss2( X, Y, Z, T ) }.
% 8.57/8.97 { ! samesideline( X, Y, Z, T ), ! Z = T }.
% 8.57/8.97 { ! samesideline( X, Y, Z, T ), ! s_col( Z, T, X ) }.
% 8.57/8.97 { ! samesideline( X, Y, Z, T ), ! s_col( Z, T, Y ) }.
% 8.57/8.97 { ! s_t( X, U, W ), ! s_t( Y, V0, W ), ! s_col( Z, T, U ), ! s_col( Z, T,
% 8.57/8.97 V0 ), Z = T, W = U, W = V0, X = U, Y = V0, s_col( Z, T, X ), s_col( Z, T
% 8.57/8.97 , Y ), samesideline( X, Y, Z, T ) }.
% 8.57/8.97
% 8.57/8.97 *** allocated 15000 integers for clauses
% 8.57/8.97 percentage equality = 0.218778, percentage horn = 0.670769
% 8.57/8.97 This is a problem with some equality
% 8.57/8.97
% 8.57/8.97
% 8.57/8.97
% 8.57/8.97 Options Used:
% 8.57/8.97
% 8.57/8.97 useres = 1
% 8.57/8.97 useparamod = 1
% 8.57/8.97 useeqrefl = 1
% 8.57/8.97 useeqfact = 1
% 8.57/8.97 usefactor = 1
% 8.57/8.97 usesimpsplitting = 0
% 8.57/8.97 usesimpdemod = 5
% 8.57/8.97 usesimpres = 3
% 8.57/8.97
% 8.57/8.97 resimpinuse = 1000
% 8.57/8.97 resimpclauses = 20000
% 8.57/8.97 substype = eqrewr
% 8.57/8.97 backwardsubs = 1
% 8.57/8.97 selectoldest = 5
% 8.57/8.97
% 8.57/8.97 litorderings [0] = split
% 8.57/8.97 litorderings [1] = extend the termordering, first sorting on arguments
% 8.57/8.97
% 8.57/8.97 termordering = kbo
% 8.57/8.97
% 8.57/8.97 litapriori = 0
% 8.57/8.97 termapriori = 1
% 8.57/8.97 litaposteriori = 0
% 8.57/8.97 termaposteriori = 0
% 8.57/8.97 demodaposteriori = 0
% 8.57/8.97 ordereqreflfact = 0
% 8.57/8.97
% 8.57/8.97 litselect = negord
% 8.57/8.97
% 8.57/8.97 maxweight = 15
% 8.57/8.97 maxdepth = 30000
% 8.57/8.97 maxlength = 115
% 8.57/8.97 maxnrvars = 195
% 8.57/8.97 excuselevel = 1
% 8.57/8.97 increasemaxweight = 1
% 8.57/8.97
% 8.57/8.97 maxselected = 10000000
% 8.57/8.97 maxnrclauses = 10000000
% 8.57/8.97
% 8.57/8.97 showgenerated = 0
% 8.57/8.97 showkept = 0
% 8.57/8.97 showselected = 0
% 8.57/8.97 showdeleted = 0
% 8.57/8.97 showresimp = 1
% 8.57/8.97 showstatus = 2000
% 8.57/8.97
% 8.57/8.97 prologoutput = 0
% 8.57/8.97 nrgoals = 5000000
% 8.57/8.97 totalproof = 1
% 8.57/8.97
% 8.57/8.97 Symbols occurring in the translation:
% 8.57/8.97
% 8.57/8.97 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 8.57/8.97 . [1, 2] (w:1, o:78, a:1, s:1, b:0),
% 8.57/8.97 ! [4, 1] (w:0, o:73, a:1, s:1, b:0),
% 8.57/8.97 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 8.57/8.97 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 8.57/8.97 s_e [37, 4] (w:1, o:118, a:1, s:1, b:0),
% 8.57/8.97 ext [43, 4] (w:1, o:119, a:1, s:1, b:0),
% 8.57/8.97 s_t [44, 3] (w:1, o:106, a:1, s:1, b:0),
% 8.57/8.97 ip [54, 5] (w:1, o:132, a:1, s:1, b:0),
% 8.57/8.97 alpha [55, 0] (w:1, o:54, a:1, s:1, b:0),
% 8.57/8.97 beta [56, 0] (w:1, o:55, a:1, s:1, b:0),
% 8.57/8.97 gamma [57, 0] (w:1, o:56, a:1, s:1, b:0),
% 8.57/8.97 crossbar [67, 6] (w:1, o:141, a:1, s:1, b:0),
% 8.57/8.97 s_ifs [69, 8] (w:1, o:151, a:1, s:1, b:0),
% 8.57/8.97 insert [70, 4] (w:1, o:120, a:1, s:1, b:0),
% 8.57/8.97 s_e3 [71, 6] (w:1, o:142, a:1, s:1, b:0),
% 8.57/8.97 s_col [72, 3] (w:1, o:107, a:1, s:1, b:0),
% 8.57/8.97 insert5 [73, 5] (w:1, o:133, a:1, s:1, b:0),
% 8.57/8.97 s_fs [74, 8] (w:1, o:152, a:1, s:1, b:0),
% 8.57/8.97 le [75, 4] (w:1, o:121, a:1, s:1, b:0),
% 8.57/8.97 ins [76, 4] (w:1, o:122, a:1, s:1, b:0),
% 8.57/8.97 sameside [77, 3] (w:1, o:108, a:1, s:1, b:0),
% 8.57/8.97 c63 [78, 3] (w:1, o:109, a:1, s:1, b:0),
% 8.57/8.97 pointOffLine [81, 2] (w:1, o:102, a:1, s:1, b:0),
% 8.57/8.97 s_m [83, 3] (w:1, o:110, a:1, s:1, b:0),
% 8.57/8.97 s [84, 2] (w:1, o:103, a:1, s:1, b:0),
% 8.57/8.97 s_kf [89, 7] (w:1, o:150, a:1, s:1, b:0),
% 8.57/8.97 isomidpoint [90, 3] (w:1, o:111, a:1, s:1, b:0),
% 8.57/8.97 s_r [91, 3] (w:1, o:112, a:1, s:1, b:0),
% 8.57/8.97 perpAt [92, 5] (w:1, o:135, a:1, s:1, b:0),
% 8.57/8.97 perp [93, 4] (w:1, o:124, a:1, s:1, b:0),
% 8.57/8.97 f813 [94, 5] (w:1, o:136, a:1, s:1, b:0),
% 8.57/8.97 g813 [95, 5] (w:1, o:138, a:1, s:1, b:0),
% 8.57/8.97 il [98, 4] (w:1, o:125, a:1, s:1, b:0),
% 8.57/8.97 foot [99, 3] (w:1, o:117, a:1, s:1, b:0),
% 8.57/8.97 erect21a [100, 3] (w:1, o:113, a:1, s:1, b:0),
% 8.57/8.97 erectAux21a [101, 3] (w:1, o:114, a:1, s:1, b:0),
% 8.57/8.97 erect [102, 3] (w:1, o:115, a:1, s:1, b:0),
% 82.52/82.87 erectAux [103, 3] (w:1, o:116, a:1, s:1, b:0),
% 82.52/82.87 midpointAux [105, 5] (w:1, o:139, a:1, s:1, b:0),
% 82.52/82.87 midpoint [106, 2] (w:1, o:104, a:1, s:1, b:0),
% 82.52/82.87 xa [107, 0] (w:1, o:57, a:1, s:1, b:0),
% 82.52/82.87 xb [108, 0] (w:1, o:58, a:1, s:1, b:0),
% 82.52/82.87 xp [109, 0] (w:1, o:59, a:1, s:1, b:0),
% 82.52/82.87 xq [110, 0] (w:1, o:60, a:1, s:1, b:0),
% 82.52/82.87 xc [111, 0] (w:1, o:61, a:1, s:1, b:0),
% 82.52/82.87 xd [112, 0] (w:1, o:62, a:1, s:1, b:0),
% 82.52/82.87 samesideline [113, 4] (w:1, o:126, a:1, s:1, b:0),
% 82.52/82.87 opposite [114, 4] (w:1, o:123, a:1, s:1, b:0),
% 82.52/82.87 op [115, 5] (w:1, o:134, a:1, s:1, b:0),
% 82.52/82.87 reflect [116, 3] (w:1, o:105, a:1, s:1, b:0),
% 82.52/82.87 erectsameside [118, 4] (w:1, o:127, a:1, s:1, b:0),
% 82.52/82.87 triangle [119, 6] (w:1, o:143, a:1, s:1, b:0),
% 82.52/82.87 congruent [121, 6] (w:1, o:144, a:1, s:1, b:0),
% 82.52/82.87 f113a [123, 6] (w:1, o:145, a:1, s:1, b:0),
% 82.52/82.87 f113c [124, 6] (w:1, o:146, a:1, s:1, b:0),
% 82.52/82.87 f113d [125, 6] (w:1, o:147, a:1, s:1, b:0),
% 82.52/82.87 f113f [126, 6] (w:1, o:148, a:1, s:1, b:0),
% 82.52/82.87 constructAngle [132, 6] (w:1, o:149, a:1, s:1, b:0),
% 82.52/82.87 parallel [133, 4] (w:1, o:128, a:1, s:1, b:0),
% 82.52/82.87 s_afs [139, 8] (w:1, o:153, a:1, s:1, b:0),
% 82.52/82.87 f811 [140, 5] (w:1, o:137, a:1, s:1, b:0),
% 82.52/82.87 g811 [141, 5] (w:1, o:140, a:1, s:1, b:0),
% 82.52/82.87 ss1 [145, 4] (w:1, o:129, a:1, s:1, b:0),
% 82.52/82.87 ss2 [146, 4] (w:1, o:130, a:1, s:1, b:0),
% 82.52/82.87 ss3 [147, 4] (w:1, o:131, a:1, s:1, b:0),
% 82.52/82.87 skol1 [148, 0] (w:1, o:67, a:1, s:1, b:1),
% 82.52/82.87 skol2 [149, 0] (w:1, o:68, a:1, s:1, b:1),
% 82.52/82.87 skol3 [150, 0] (w:1, o:69, a:1, s:1, b:1),
% 82.52/82.87 skol4 [151, 0] (w:1, o:70, a:1, s:1, b:1),
% 82.52/82.87 skol5 [152, 0] (w:1, o:71, a:1, s:1, b:1),
% 82.52/82.87 skol6 [153, 0] (w:1, o:72, a:1, s:1, b:1).
% 82.52/82.87
% 82.52/82.87
% 82.52/82.87 Starting Search:
% 82.52/82.87
% 82.52/82.87 *** allocated 22500 integers for clauses
% 82.52/82.87 *** allocated 33750 integers for clauses
% 82.52/82.87 *** allocated 50625 integers for clauses
% 82.52/82.87 *** allocated 50625 integers for termspace/termends
% 82.52/82.87 *** allocated 75937 integers for clauses
% 82.52/82.87 *** allocated 75937 integers for termspace/termends
% 82.52/82.87 Resimplifying inuse:
% 82.52/82.87 Done
% 82.52/82.87
% 82.52/82.87 *** allocated 113905 integers for clauses
% 82.52/82.87
% 82.52/82.87 Intermediate Status:
% 82.52/82.87 Generated: 23069
% 82.52/82.87 Kept: 2186
% 82.52/82.87 Inuse: 77
% 82.52/82.87 Deleted: 0
% 82.52/82.87 Deletedinuse: 0
% 82.52/82.87
% 82.52/82.87 Resimplifying inuse:
% 82.52/82.87 Done
% 82.52/82.87
% 82.52/82.87 *** allocated 170857 integers for clauses
% 82.52/82.87 *** allocated 113905 integers for termspace/termends
% 82.52/82.87 Resimplifying inuse:
% 82.52/82.87 Done
% 82.52/82.87
% 82.52/82.87 *** allocated 256285 integers for clauses
% 82.52/82.87
% 82.52/82.87 Intermediate Status:
% 82.52/82.87 Generated: 31460
% 82.52/82.87 Kept: 4202
% 82.52/82.87 Inuse: 136
% 82.52/82.87 Deleted: 5
% 82.52/82.87 Deletedinuse: 0
% 82.52/82.87
% 82.52/82.87 Resimplifying inuse:
% 82.52/82.87 Done
% 82.52/82.87
% 82.52/82.87 *** allocated 170857 integers for termspace/termends
% 82.52/82.87 Resimplifying inuse:
% 82.52/82.87 Done
% 82.52/82.87
% 82.52/82.87 *** allocated 384427 integers for clauses
% 82.52/82.87
% 82.52/82.87 Intermediate Status:
% 82.52/82.87 Generated: 39035
% 82.52/82.87 Kept: 6236
% 82.52/82.87 Inuse: 201
% 82.52/82.87 Deleted: 9
% 82.52/82.87 Deletedinuse: 0
% 82.52/82.87
% 82.52/82.87 Resimplifying inuse:
% 82.52/82.87 Done
% 82.52/82.87
% 82.52/82.87 Resimplifying inuse:
% 82.52/82.87 Done
% 82.52/82.87
% 82.52/82.87 *** allocated 256285 integers for termspace/termends
% 82.52/82.87
% 82.52/82.87 Intermediate Status:
% 82.52/82.87 Generated: 53113
% 82.52/82.87 Kept: 8285
% 82.52/82.87 Inuse: 237
% 82.52/82.87 Deleted: 9
% 82.52/82.87 Deletedinuse: 0
% 82.52/82.87
% 82.52/82.87 Resimplifying inuse:
% 82.52/82.87 Done
% 82.52/82.87
% 82.52/82.87 *** allocated 576640 integers for clauses
% 82.52/82.87 Resimplifying inuse:
% 82.52/82.87 Done
% 82.52/82.87
% 82.52/82.87
% 82.52/82.87 Intermediate Status:
% 82.52/82.87 Generated: 60110
% 82.52/82.87 Kept: 10603
% 82.52/82.87 Inuse: 279
% 82.52/82.87 Deleted: 11
% 82.52/82.87 Deletedinuse: 0
% 82.52/82.87
% 82.52/82.87 Resimplifying inuse:
% 82.52/82.87 Done
% 82.52/82.87
% 82.52/82.87 Resimplifying inuse:
% 82.52/82.87 Done
% 82.52/82.87
% 82.52/82.87 *** allocated 384427 integers for termspace/termends
% 82.52/82.87
% 82.52/82.87 Intermediate Status:
% 82.52/82.87 Generated: 79497
% 82.52/82.87 Kept: 12638
% 82.52/82.87 Inuse: 301
% 82.52/82.87 Deleted: 11
% 82.52/82.87 Deletedinuse: 0
% 82.52/82.87
% 82.52/82.87 Resimplifying inuse:
% 82.52/82.87 Done
% 82.52/82.87
% 82.52/82.87 *** allocated 864960 integers for clauses
% 82.52/82.87 Resimplifying inuse:
% 82.52/82.87 Done
% 82.52/82.87
% 82.52/82.87
% 82.52/82.87 Intermediate Status:
% 82.52/82.87 Generated: 87576
% 82.52/82.87 Kept: 14664
% 82.52/82.87 Inuse: 336
% 82.52/82.87 Deleted: 11
% 82.52/82.87 Deletedinuse: 0
% 82.52/82.87
% 82.52/82.87 Resimplifying inuse:
% 82.52/82.87 Done
% 82.52/82.87
% 82.52/82.87
% 82.52/82.87 Intermediate Status:
% 82.52/82.87 Generated: 108122
% 82.52/82.87 Kept: 16678
% 82.52/82.87 Inuse: 350
% 82.52/82.87 Deleted: 11
% 82.52/82.87 Deletedinuse: 0
% 82.52/82.87
% 82.52/82.87 Resimplifying inuse:
% 82.52/82.87 Done
% 82.52/82.87
% 82.52/82.87 Resimplifying inuse:
% 82.52/82.87 Done
% 82.52/82.87
% 82.52/82.87
% 82.52/82.87 Intermediate Status:
% 82.52/82.87 Generated: 130808
% 82.52/82.87 Kept: 18709
% 82.52/82.87 Inuse: 373
% 82.52/82.87 Deleted: 12
% 82.52/82.87 Deletedinuse: 0
% 82.52/82.87
% 82.52/82.87 Resimplifying inuse:
% 82.52/82.87 Done
% 82.52/82.87
% 82.52/82.87 *** allocated 576640 integers for termspace/termends
% 82.52/82.87 *** allocated 1297440 integCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------