TSTP Solution File: GEO012-3 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GEO012-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 10:37:53 EDT 2023
% Result : Timeout 288.92s 256.93s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 56
% Syntax : Number of formulae : 400 ( 223 unt; 17 typ; 0 def)
% Number of atoms : 631 ( 115 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 468 ( 220 ~; 248 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 41 ( 10 >; 31 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-6 aty)
% Number of variables : 410 (; 410 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ equidistant > colinear > between > continuous > inner_pasch > euclid2 > euclid1 > insertion > extension > reflection > #nlpp > lower_dimension_point_3 > lower_dimension_point_2 > lower_dimension_point_1 > d > c > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(lower_dimension_point_1,type,
lower_dimension_point_1: $i ).
tff(euclid2,type,
euclid2: ( $i * $i * $i * $i * $i ) > $i ).
tff(a,type,
a: $i ).
tff(lower_dimension_point_2,type,
lower_dimension_point_2: $i ).
tff(colinear,type,
colinear: ( $i * $i * $i ) > $o ).
tff(equidistant,type,
equidistant: ( $i * $i * $i * $i ) > $o ).
tff(b,type,
b: $i ).
tff(lower_dimension_point_3,type,
lower_dimension_point_3: $i ).
tff(extension,type,
extension: ( $i * $i * $i * $i ) > $i ).
tff(reflection,type,
reflection: ( $i * $i ) > $i ).
tff(d,type,
d: $i ).
tff(euclid1,type,
euclid1: ( $i * $i * $i * $i * $i ) > $i ).
tff(between,type,
between: ( $i * $i * $i ) > $o ).
tff(insertion,type,
insertion: ( $i * $i * $i * $i ) > $i ).
tff(inner_pasch,type,
inner_pasch: ( $i * $i * $i * $i * $i ) > $i ).
tff(continuous,type,
continuous: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(c,type,
c: $i ).
tff(f_778,axiom,
! [W,V,U] :
( ~ between(W,V,U)
| colinear(U,V,W) ),
file(unknown,unknown) ).
tff(f_464,axiom,
! [U,V] : between(U,U,V),
file(unknown,unknown) ).
tff(f_265,axiom,
! [Z,X,Y] :
( ~ between(Z,X,Y)
| colinear(X,Y,Z) ),
file(unknown,unknown) ).
tff(f_849,axiom,
( ~ colinear(a,c,d)
| ~ colinear(b,c,d) ),
file(unknown,unknown) ).
tff(f_449,axiom,
! [U,V] : between(U,V,V),
file(unknown,unknown) ).
tff(f_788,axiom,
! [V,U,W] :
( ~ between(V,U,W)
| colinear(U,V,W) ),
file(unknown,unknown) ).
tff(f_783,axiom,
! [U,W,V] :
( ~ between(U,W,V)
| colinear(U,V,W) ),
file(unknown,unknown) ).
tff(f_844,axiom,
colinear(a,b,d),
file(unknown,unknown) ).
tff(f_274,axiom,
! [X,Y,Z] :
( ~ colinear(X,Y,Z)
| between(X,Y,Z)
| between(Y,Z,X)
| between(Z,X,Y) ),
file(unknown,unknown) ).
tff(f_552,axiom,
! [U,V,W,X] :
( ~ between(U,V,W)
| ~ between(U,W,X)
| between(U,V,X) ),
file(unknown,unknown) ).
tff(f_255,axiom,
! [X,Y,Z] :
( ~ between(X,Y,Z)
| colinear(X,Y,Z) ),
file(unknown,unknown) ).
tff(f_561,axiom,
! [V,U] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) ),
file(unknown,unknown) ).
tff(f_260,axiom,
! [Y,Z,X] :
( ~ between(Y,Z,X)
| colinear(X,Y,Z) ),
file(unknown,unknown) ).
tff(f_679,axiom,
! [U,V,W] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) ),
file(unknown,unknown) ).
tff(f_326,axiom,
! [U1,W1,U,V] : ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) ),
file(unknown,unknown) ).
tff(f_380,axiom,
! [W,U,X,Y,V] :
( ( Y != extension(U,V,W,X) )
| between(U,V,Y) ),
file(unknown,unknown) ).
tff(f_842,axiom,
a != b,
file(unknown,unknown) ).
tff(f_536,axiom,
! [U,V,W,X] :
( ~ between(U,V,W)
| ~ between(V,W,X)
| between(U,V,X)
| ( V = W ) ),
file(unknown,unknown) ).
tff(f_843,axiom,
colinear(a,b,c),
file(unknown,unknown) ).
tff(f_462,axiom,
! [U,V,W] :
( ~ between(U,V,W)
| between(W,V,U) ),
file(unknown,unknown) ).
tff(f_734,axiom,
! [U,W,X,V] :
( ~ between(U,W,X)
| ~ between(V,W,X)
| ( W = X )
| between(U,V,W)
| between(V,U,W) ),
file(unknown,unknown) ).
tff(f_526,axiom,
! [U,V,W,X] :
( ~ between(U,V,W)
| ~ between(V,W,X)
| between(U,W,X)
| ( V = W ) ),
file(unknown,unknown) ).
tff(f_516,axiom,
! [U,V,W,X] :
( ~ between(U,V,W)
| ~ between(U,W,X)
| between(V,W,X) ),
file(unknown,unknown) ).
tff(f_765,axiom,
! [W,U,X,Y,V] :
( ~ between(U,V,Y)
| ~ between(V,W,X)
| ~ between(U,X,Y)
| between(U,W,Y) ),
file(unknown,unknown) ).
tff(f_432,axiom,
! [U,V,W] :
( ~ between(U,V,W)
| ( U = V )
| ( W = extension(U,V,V,W) ) ),
file(unknown,unknown) ).
tff(f_480,axiom,
! [U,V,W] :
( ~ between(U,V,W)
| ~ between(U,W,V)
| ( V = W ) ),
file(unknown,unknown) ).
tff(f_658,axiom,
! [U,V,U1,W1] : equidistant(U,V,U1,insertion(U1,W1,U,V)),
file(unknown,unknown) ).
tff(f_355,axiom,
! [U,V,W,X] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,V,U) ),
file(unknown,unknown) ).
tff(f_75,axiom,
! [X,Y,Z] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(f_447,axiom,
! [U,V] : ( U = reflection(reflection(U,V),V) ),
file(unknown,unknown) ).
tff(f_382,axiom,
! [U,V] : between(U,V,reflection(U,V)),
file(unknown,unknown) ).
tff(f_472,axiom,
! [U,V,W] :
( ~ between(U,V,W)
| ~ between(V,U,W)
| ( U = V ) ),
file(unknown,unknown) ).
tff(f_82,axiom,
! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
file(unknown,unknown) ).
tff(f_425,axiom,
! [U,V,W,X] :
( ~ between(U,V,W)
| ~ between(U,V,X)
| ~ equidistant(V,W,V,X)
| ( U = V )
| ( W = X ) ),
file(unknown,unknown) ).
tff(f_60,axiom,
! [X,Y] : equidistant(X,Y,Y,X),
file(unknown,unknown) ).
tff(f_684,axiom,
! [W,U,Z,X,Y,V] :
( ~ equidistant(W,X,Y,Z)
| ( insertion(U,V,W,X) = insertion(U,V,Y,Z) ) ),
file(unknown,unknown) ).
tff(f_384,axiom,
! [V,U] : equidistant(V,reflection(U,V),U,V),
file(unknown,unknown) ).
tff(f_813,axiom,
! [U,V,W] :
( ~ colinear(U,V,W)
| colinear(V,U,W) ),
file(unknown,unknown) ).
tff(f_544,axiom,
! [U,V,X,W] :
( ~ between(U,V,X)
| ~ between(V,W,X)
| between(U,W,X) ),
file(unknown,unknown) ).
tff(c_176,plain,
! [U_320,V_319,W_318] :
( colinear(U_320,V_319,W_318)
| ~ between(W_318,V_319,U_320) ),
inference(cnfTransformation,[status(thm)],[f_778]) ).
tff(c_104,plain,
! [U_179,V_180] : between(U_179,U_179,V_180),
inference(cnfTransformation,[status(thm)],[f_464]) ).
tff(c_42,plain,
! [X_79,Y_80,Z_78] :
( colinear(X_79,Y_80,Z_78)
| ~ between(Z_78,X_79,Y_80) ),
inference(cnfTransformation,[status(thm)],[f_265]) ).
tff(c_210,plain,
( ~ colinear(b,c,d)
| ~ colinear(a,c,d) ),
inference(cnfTransformation,[status(thm)],[f_849]) ).
tff(c_494,plain,
~ colinear(a,c,d),
inference(splitLeft,[status(thm)],[c_210]) ).
tff(c_510,plain,
~ between(d,a,c),
inference(resolution,[status(thm)],[c_42,c_494]) ).
tff(c_98,plain,
! [U_170,V_171] : between(U_170,V_171,V_171),
inference(cnfTransformation,[status(thm)],[f_449]) ).
tff(c_740,plain,
! [U_432,V_433,W_434] :
( colinear(U_432,V_433,W_434)
| ~ between(V_433,U_432,W_434) ),
inference(cnfTransformation,[status(thm)],[f_788]) ).
tff(c_757,plain,
~ between(c,a,d),
inference(resolution,[status(thm)],[c_740,c_494]) ).
tff(c_178,plain,
! [U_321,V_323,W_322] :
( colinear(U_321,V_323,W_322)
| ~ between(U_321,W_322,V_323) ),
inference(cnfTransformation,[status(thm)],[f_783]) ).
tff(c_509,plain,
~ between(a,d,c),
inference(resolution,[status(thm)],[c_178,c_494]) ).
tff(c_208,plain,
colinear(a,b,d),
inference(cnfTransformation,[status(thm)],[f_844]) ).
tff(c_4436,plain,
! [Z_721,X_722,Y_723] :
( between(Z_721,X_722,Y_723)
| between(Y_723,Z_721,X_722)
| between(X_722,Y_723,Z_721)
| ~ colinear(X_722,Y_723,Z_721) ),
inference(cnfTransformation,[status(thm)],[f_274]) ).
tff(c_4521,plain,
( between(d,a,b)
| between(b,d,a)
| between(a,b,d) ),
inference(resolution,[status(thm)],[c_208,c_4436]) ).
tff(c_11708,plain,
between(a,b,d),
inference(splitLeft,[status(thm)],[c_4521]) ).
tff(c_124,plain,
! [U_213,V_214,X_216,W_215] :
( between(U_213,V_214,X_216)
| ~ between(U_213,W_215,X_216)
| ~ between(U_213,V_214,W_215) ),
inference(cnfTransformation,[status(thm)],[f_552]) ).
tff(c_12654,plain,
! [V_1008] :
( between(a,V_1008,d)
| ~ between(a,V_1008,b) ),
inference(resolution,[status(thm)],[c_11708,c_124]) ).
tff(c_595,plain,
! [X_423,Y_424,Z_425] :
( colinear(X_423,Y_424,Z_425)
| ~ between(X_423,Y_424,Z_425) ),
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_609,plain,
~ between(a,c,d),
inference(resolution,[status(thm)],[c_595,c_494]) ).
tff(c_12749,plain,
~ between(a,c,b),
inference(resolution,[status(thm)],[c_12654,c_609]) ).
tff(c_132,plain,
! [U_218,V_217] : ( extension(U_218,V_217,lower_dimension_point_1,lower_dimension_point_2) != V_217 ),
inference(cnfTransformation,[status(thm)],[f_561]) ).
tff(c_40,plain,
! [X_77,Y_75,Z_76] :
( colinear(X_77,Y_75,Z_76)
| ~ between(Y_75,Z_76,X_77) ),
inference(cnfTransformation,[status(thm)],[f_260]) ).
tff(c_507,plain,
~ between(c,d,a),
inference(resolution,[status(thm)],[c_40,c_494]) ).
tff(c_508,plain,
~ between(d,c,a),
inference(resolution,[status(thm)],[c_176,c_494]) ).
tff(c_156,plain,
! [U_275,W_277,V_276] :
( ( insertion(U_275,W_277,U_275,V_276) = V_276 )
| ~ between(U_275,V_276,W_277) ),
inference(cnfTransformation,[status(thm)],[f_679]) ).
tff(c_11781,plain,
insertion(a,d,a,b) = b,
inference(resolution,[status(thm)],[c_11708,c_156]) ).
tff(c_2562,plain,
! [W1_613,U1_614,U_615,V_616] : ( extension(extension(W1_613,U1_614,lower_dimension_point_1,lower_dimension_point_2),U1_614,U_615,V_616) = insertion(U1_614,W1_613,U_615,V_616) ),
inference(cnfTransformation,[status(thm)],[f_326]) ).
tff(c_70,plain,
! [U_130,V_133,W_129,X_131] : between(U_130,V_133,extension(U_130,V_133,W_129,X_131)),
inference(cnfTransformation,[status(thm)],[f_380]) ).
tff(c_2621,plain,
! [W1_613,U1_614,U_615,V_616] : between(extension(W1_613,U1_614,lower_dimension_point_1,lower_dimension_point_2),U1_614,insertion(U1_614,W1_613,U_615,V_616)),
inference(superposition,[status(thm),theory(equality)],[c_2562,c_70]) ).
tff(c_11926,plain,
between(extension(d,a,lower_dimension_point_1,lower_dimension_point_2),a,b),
inference(superposition,[status(thm),theory(equality)],[c_11781,c_2621]) ).
tff(c_204,plain,
b != a,
inference(cnfTransformation,[status(thm)],[f_842]) ).
tff(c_120,plain,
! [W_207,V_206,U_205,X_208] :
( ( W_207 = V_206 )
| between(U_205,V_206,X_208)
| ~ between(V_206,W_207,X_208)
| ~ between(U_205,V_206,W_207) ),
inference(cnfTransformation,[status(thm)],[f_536]) ).
tff(c_11736,plain,
! [U_205] :
( ( b = a )
| between(U_205,a,d)
| ~ between(U_205,a,b) ),
inference(resolution,[status(thm)],[c_11708,c_120]) ).
tff(c_12750,plain,
! [U_1009] :
( between(U_1009,a,d)
| ~ between(U_1009,a,b) ),
inference(negUnitSimplification,[status(thm)],[c_204,c_11736]) ).
tff(c_12868,plain,
~ between(c,a,b),
inference(resolution,[status(thm)],[c_12750,c_757]) ).
tff(c_206,plain,
colinear(a,b,c),
inference(cnfTransformation,[status(thm)],[f_843]) ).
tff(c_4518,plain,
( between(c,a,b)
| between(b,c,a)
| between(a,b,c) ),
inference(resolution,[status(thm)],[c_206,c_4436]) ).
tff(c_16675,plain,
( between(b,c,a)
| between(a,b,c) ),
inference(negUnitSimplification,[status(thm)],[c_12868,c_4518]) ).
tff(c_16676,plain,
between(a,b,c),
inference(splitLeft,[status(thm)],[c_16675]) ).
tff(c_16704,plain,
! [U_205] :
( ( b = a )
| between(U_205,a,c)
| ~ between(U_205,a,b) ),
inference(resolution,[status(thm)],[c_16676,c_120]) ).
tff(c_17189,plain,
! [U_1052] :
( between(U_1052,a,c)
| ~ between(U_1052,a,b) ),
inference(negUnitSimplification,[status(thm)],[c_204,c_16704]) ).
tff(c_102,plain,
! [W_178,V_177,U_176] :
( between(W_178,V_177,U_176)
| ~ between(U_176,V_177,W_178) ),
inference(cnfTransformation,[status(thm)],[f_462]) ).
tff(c_18623,plain,
! [U_1071] :
( between(c,a,U_1071)
| ~ between(U_1071,a,b) ),
inference(resolution,[status(thm)],[c_17189,c_102]) ).
tff(c_18650,plain,
between(c,a,extension(d,a,lower_dimension_point_1,lower_dimension_point_2)),
inference(resolution,[status(thm)],[c_11926,c_18623]) ).
tff(c_5815,plain,
! [V_771,U_772,W_773,X_774] :
( between(V_771,U_772,W_773)
| between(U_772,V_771,W_773)
| ( X_774 = W_773 )
| ~ between(V_771,W_773,X_774)
| ~ between(U_772,W_773,X_774) ),
inference(cnfTransformation,[status(thm)],[f_734]) ).
tff(c_70396,plain,
! [U_1788,W_1791,X_1789,U_1790,V_1792] :
( between(U_1788,U_1790,V_1792)
| between(U_1790,U_1788,V_1792)
| ( extension(U_1788,V_1792,W_1791,X_1789) = V_1792 )
| ~ between(U_1790,V_1792,extension(U_1788,V_1792,W_1791,X_1789)) ),
inference(resolution,[status(thm)],[c_70,c_5815]) ).
tff(c_70467,plain,
( between(d,c,a)
| between(c,d,a)
| ( extension(d,a,lower_dimension_point_1,lower_dimension_point_2) = a ) ),
inference(resolution,[status(thm)],[c_18650,c_70396]) ).
tff(c_70608,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_132,c_507,c_508,c_70467]) ).
tff(c_70609,plain,
between(b,c,a),
inference(splitRight,[status(thm)],[c_16675]) ).
tff(c_70654,plain,
between(a,c,b),
inference(resolution,[status(thm)],[c_70609,c_102]) ).
tff(c_70679,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12749,c_70654]) ).
tff(c_70680,plain,
( between(b,d,a)
| between(d,a,b) ),
inference(splitRight,[status(thm)],[c_4521]) ).
tff(c_70682,plain,
between(d,a,b),
inference(splitLeft,[status(thm)],[c_70680]) ).
tff(c_70753,plain,
between(b,a,d),
inference(resolution,[status(thm)],[c_70682,c_102]) ).
tff(c_74972,plain,
between(a,b,c),
inference(splitLeft,[status(thm)],[c_4518]) ).
tff(c_75050,plain,
between(c,b,a),
inference(resolution,[status(thm)],[c_74972,c_102]) ).
tff(c_118,plain,
! [W_203,V_202,U_201,X_204] :
( ( W_203 = V_202 )
| between(U_201,W_203,X_204)
| ~ between(V_202,W_203,X_204)
| ~ between(U_201,V_202,W_203) ),
inference(cnfTransformation,[status(thm)],[f_526]) ).
tff(c_70779,plain,
! [U_201] :
( ( b = a )
| between(U_201,a,d)
| ~ between(U_201,b,a) ),
inference(resolution,[status(thm)],[c_70753,c_118]) ).
tff(c_70816,plain,
! [U_201] :
( between(U_201,a,d)
| ~ between(U_201,b,a) ),
inference(negUnitSimplification,[status(thm)],[c_204,c_70779]) ).
tff(c_75055,plain,
between(c,a,d),
inference(resolution,[status(thm)],[c_75050,c_70816]) ).
tff(c_75104,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_757,c_75055]) ).
tff(c_75105,plain,
( between(b,c,a)
| between(c,a,b) ),
inference(splitRight,[status(thm)],[c_4518]) ).
tff(c_75190,plain,
between(c,a,b),
inference(splitLeft,[status(thm)],[c_75105]) ).
tff(c_75260,plain,
between(b,a,c),
inference(resolution,[status(thm)],[c_75190,c_102]) ).
tff(c_75333,plain,
insertion(b,c,b,a) = a,
inference(resolution,[status(thm)],[c_75260,c_156]) ).
tff(c_75750,plain,
between(extension(c,b,lower_dimension_point_1,lower_dimension_point_2),b,a),
inference(superposition,[status(thm),theory(equality)],[c_75333,c_2621]) ).
tff(c_70781,plain,
! [U_205] :
( ( b = a )
| between(U_205,b,d)
| ~ between(U_205,b,a) ),
inference(resolution,[status(thm)],[c_70753,c_120]) ).
tff(c_73895,plain,
! [U_1825] :
( between(U_1825,b,d)
| ~ between(U_1825,b,a) ),
inference(negUnitSimplification,[status(thm)],[c_204,c_70781]) ).
tff(c_74020,plain,
! [U_1825] :
( between(d,b,U_1825)
| ~ between(U_1825,b,a) ),
inference(resolution,[status(thm)],[c_73895,c_102]) ).
tff(c_79773,plain,
between(d,b,extension(c,b,lower_dimension_point_1,lower_dimension_point_2)),
inference(resolution,[status(thm)],[c_75750,c_74020]) ).
tff(c_130617,plain,
! [U_2580,X_2581,W_2583,U_2582,V_2584] :
( between(U_2580,U_2582,V_2584)
| between(U_2582,U_2580,V_2584)
| ( extension(U_2580,V_2584,W_2583,X_2581) = V_2584 )
| ~ between(U_2582,V_2584,extension(U_2580,V_2584,W_2583,X_2581)) ),
inference(resolution,[status(thm)],[c_70,c_5815]) ).
tff(c_130673,plain,
( between(c,d,b)
| between(d,c,b)
| ( extension(c,b,lower_dimension_point_1,lower_dimension_point_2) = b ) ),
inference(resolution,[status(thm)],[c_79773,c_130617]) ).
tff(c_130805,plain,
( between(c,d,b)
| between(d,c,b) ),
inference(negUnitSimplification,[status(thm)],[c_132,c_130673]) ).
tff(c_130867,plain,
between(d,c,b),
inference(splitLeft,[status(thm)],[c_130805]) ).
tff(c_130969,plain,
between(b,c,d),
inference(resolution,[status(thm)],[c_130867,c_102]) ).
tff(c_116,plain,
! [V_198,W_199,X_200,U_197] :
( between(V_198,W_199,X_200)
| ~ between(U_197,W_199,X_200)
| ~ between(U_197,V_198,W_199) ),
inference(cnfTransformation,[status(thm)],[f_516]) ).
tff(c_134219,plain,
! [V_2604] :
( between(V_2604,c,d)
| ~ between(b,V_2604,c) ),
inference(resolution,[status(thm)],[c_130969,c_116]) ).
tff(c_134259,plain,
between(a,c,d),
inference(resolution,[status(thm)],[c_75260,c_134219]) ).
tff(c_134302,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_609,c_134259]) ).
tff(c_134304,plain,
~ between(d,c,b),
inference(splitRight,[status(thm)],[c_130805]) ).
tff(c_70826,plain,
insertion(b,d,b,a) = a,
inference(resolution,[status(thm)],[c_70753,c_156]) ).
tff(c_71054,plain,
between(extension(d,b,lower_dimension_point_1,lower_dimension_point_2),b,a),
inference(superposition,[status(thm),theory(equality)],[c_70826,c_2621]) ).
tff(c_75288,plain,
! [U_205] :
( ( b = a )
| between(U_205,b,c)
| ~ between(U_205,b,a) ),
inference(resolution,[status(thm)],[c_75260,c_120]) ).
tff(c_78074,plain,
! [U_1878] :
( between(U_1878,b,c)
| ~ between(U_1878,b,a) ),
inference(negUnitSimplification,[status(thm)],[c_204,c_75288]) ).
tff(c_79000,plain,
! [U_1889] :
( between(c,b,U_1889)
| ~ between(U_1889,b,a) ),
inference(resolution,[status(thm)],[c_78074,c_102]) ).
tff(c_79027,plain,
between(c,b,extension(d,b,lower_dimension_point_1,lower_dimension_point_2)),
inference(resolution,[status(thm)],[c_71054,c_79000]) ).
tff(c_130686,plain,
( between(d,c,b)
| between(c,d,b)
| ( extension(d,b,lower_dimension_point_1,lower_dimension_point_2) = b ) ),
inference(resolution,[status(thm)],[c_79027,c_130617]) ).
tff(c_130818,plain,
( between(d,c,b)
| between(c,d,b) ),
inference(negUnitSimplification,[status(thm)],[c_132,c_130686]) ).
tff(c_134317,plain,
between(c,d,b),
inference(negUnitSimplification,[status(thm)],[c_134304,c_130818]) ).
tff(c_134419,plain,
between(b,d,c),
inference(resolution,[status(thm)],[c_134317,c_102]) ).
tff(c_137064,plain,
! [V_2621] :
( between(V_2621,d,c)
| ~ between(b,V_2621,d) ),
inference(resolution,[status(thm)],[c_134419,c_116]) ).
tff(c_137113,plain,
between(a,d,c),
inference(resolution,[status(thm)],[c_70753,c_137064]) ).
tff(c_137154,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_509,c_137113]) ).
tff(c_137155,plain,
between(b,c,a),
inference(splitRight,[status(thm)],[c_75105]) ).
tff(c_70822,plain,
! [V_198] :
( between(V_198,a,d)
| ~ between(b,V_198,a) ),
inference(resolution,[status(thm)],[c_70753,c_116]) ).
tff(c_137158,plain,
between(c,a,d),
inference(resolution,[status(thm)],[c_137155,c_70822]) ).
tff(c_137206,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_757,c_137158]) ).
tff(c_137207,plain,
between(b,d,a),
inference(splitRight,[status(thm)],[c_70680]) ).
tff(c_137274,plain,
between(a,d,b),
inference(resolution,[status(thm)],[c_137207,c_102]) ).
tff(c_3984,plain,
! [V_694,Y_696,U_693,X_695,W_697] :
( between(U_693,W_697,Y_696)
| ~ between(U_693,X_695,Y_696)
| ~ between(V_694,W_697,X_695)
| ~ between(U_693,V_694,Y_696) ),
inference(cnfTransformation,[status(thm)],[f_765]) ).
tff(c_4019,plain,
! [U_179,W_697,V_180,V_694] :
( between(U_179,W_697,V_180)
| ~ between(V_694,W_697,U_179)
| ~ between(U_179,V_694,V_180) ),
inference(resolution,[status(thm)],[c_104,c_3984]) ).
tff(c_137319,plain,
! [V_180] :
( between(b,d,V_180)
| ~ between(b,a,V_180) ),
inference(resolution,[status(thm)],[c_137274,c_4019]) ).
tff(c_88,plain,
! [U_155,V_156,W_157] :
( ( extension(U_155,V_156,V_156,W_157) = W_157 )
| ( V_156 = U_155 )
| ~ between(U_155,V_156,W_157) ),
inference(cnfTransformation,[status(thm)],[f_432]) ).
tff(c_137336,plain,
( ( extension(a,d,d,b) = b )
| ( d = a ) ),
inference(resolution,[status(thm)],[c_137274,c_88]) ).
tff(c_139071,plain,
d = a,
inference(splitLeft,[status(thm)],[c_137336]) ).
tff(c_108,plain,
! [W_186,V_185,U_184] :
( ( W_186 = V_185 )
| ~ between(U_184,W_186,V_185)
| ~ between(U_184,V_185,W_186) ),
inference(cnfTransformation,[status(thm)],[f_480]) ).
tff(c_137273,plain,
( ( d = a )
| ~ between(b,a,d) ),
inference(resolution,[status(thm)],[c_137207,c_108]) ).
tff(c_137342,plain,
~ between(b,a,d),
inference(splitLeft,[status(thm)],[c_137273]) ).
tff(c_139084,plain,
~ between(b,a,a),
inference(demodulation,[status(thm),theory(equality)],[c_139071,c_137342]) ).
tff(c_139111,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_98,c_139084]) ).
tff(c_139113,plain,
d != a,
inference(splitRight,[status(thm)],[c_137336]) ).
tff(c_150,plain,
! [U_261,V_262,U1_263,W1_264] : equidistant(U_261,V_262,U1_263,insertion(U1_263,W1_264,U_261,V_262)),
inference(cnfTransformation,[status(thm)],[f_658]) ).
tff(c_1068,plain,
! [W_476,X_477,V_478,U_479] :
( equidistant(W_476,X_477,V_478,U_479)
| ~ equidistant(U_479,V_478,W_476,X_477) ),
inference(cnfTransformation,[status(thm)],[f_355]) ).
tff(c_1261,plain,
! [U1_498,W1_499,U_500,V_501] : equidistant(U1_498,insertion(U1_498,W1_499,U_500,V_501),V_501,U_500),
inference(resolution,[status(thm)],[c_150,c_1068]) ).
tff(c_6,plain,
! [Y_10,X_9,Z_11] :
( ( Y_10 = X_9 )
| ~ equidistant(X_9,Y_10,Z_11,Z_11) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_1279,plain,
! [U1_498,W1_499,U_500] : ( insertion(U1_498,W1_499,U_500,U_500) = U1_498 ),
inference(resolution,[status(thm)],[c_1261,c_6]) ).
tff(c_269,plain,
! [U_385,V_386] : ( reflection(reflection(U_385,V_386),V_386) = U_385 ),
inference(cnfTransformation,[status(thm)],[f_447]) ).
tff(c_72,plain,
! [U_134,V_135] : between(U_134,V_135,reflection(U_134,V_135)),
inference(cnfTransformation,[status(thm)],[f_382]) ).
tff(c_278,plain,
! [U_385,V_386] : between(reflection(U_385,V_386),V_386,U_385),
inference(superposition,[status(thm),theory(equality)],[c_269,c_72]) ).
tff(c_139112,plain,
extension(a,d,d,b) = b,
inference(splitRight,[status(thm)],[c_137336]) ).
tff(c_2716,plain,
! [W_623,V_624,U_625,X_626] :
( ( W_623 = V_624 )
| between(U_625,V_624,X_626)
| ~ between(V_624,W_623,X_626)
| ~ between(U_625,V_624,W_623) ),
inference(cnfTransformation,[status(thm)],[f_536]) ).
tff(c_149859,plain,
! [V_2786,U_2782,X_2784,W_2785,U_2783] :
( ( V_2786 = U_2783 )
| between(U_2782,U_2783,extension(U_2783,V_2786,W_2785,X_2784))
| ~ between(U_2782,U_2783,V_2786) ),
inference(resolution,[status(thm)],[c_70,c_2716]) ).
tff(c_149997,plain,
! [U_2782] :
( ( d = a )
| between(U_2782,a,b)
| ~ between(U_2782,a,d) ),
inference(superposition,[status(thm),theory(equality)],[c_139112,c_149859]) ).
tff(c_151104,plain,
! [U_2801] :
( between(U_2801,a,b)
| ~ between(U_2801,a,d) ),
inference(negUnitSimplification,[status(thm)],[c_139113,c_149997]) ).
tff(c_151148,plain,
between(reflection(d,a),a,b),
inference(resolution,[status(thm)],[c_278,c_151104]) ).
tff(c_151225,plain,
between(b,a,reflection(d,a)),
inference(resolution,[status(thm)],[c_151148,c_102]) ).
tff(c_151379,plain,
! [V_214] :
( between(b,V_214,reflection(d,a))
| ~ between(b,V_214,a) ),
inference(resolution,[status(thm)],[c_151225,c_124]) ).
tff(c_717,plain,
! [W_429,V_430,U_431] :
( between(W_429,V_430,U_431)
| ~ between(U_431,V_430,W_429) ),
inference(cnfTransformation,[status(thm)],[f_462]) ).
tff(c_728,plain,
! [U_130,V_133,W_129,X_131] : between(extension(U_130,V_133,W_129,X_131),V_133,U_130),
inference(resolution,[status(thm)],[c_70,c_717]) ).
tff(c_137929,plain,
! [V_2632] :
( between(a,d,V_2632)
| ~ between(a,b,V_2632) ),
inference(resolution,[status(thm)],[c_137207,c_4019]) ).
tff(c_138035,plain,
~ between(a,b,c),
inference(resolution,[status(thm)],[c_137929,c_509]) ).
tff(c_141705,plain,
( between(c,a,b)
| between(b,c,a) ),
inference(negUnitSimplification,[status(thm)],[c_138035,c_4518]) ).
tff(c_141706,plain,
between(b,c,a),
inference(splitLeft,[status(thm)],[c_141705]) ).
tff(c_141772,plain,
between(a,c,b),
inference(resolution,[status(thm)],[c_141706,c_102]) ).
tff(c_141834,plain,
( ( extension(a,c,c,b) = b )
| ( c = a ) ),
inference(resolution,[status(thm)],[c_141772,c_88]) ).
tff(c_143259,plain,
c = a,
inference(splitLeft,[status(thm)],[c_141834]) ).
tff(c_106,plain,
! [V_182,U_181,W_183] :
( ( V_182 = U_181 )
| ~ between(V_182,U_181,W_183)
| ~ between(U_181,V_182,W_183) ),
inference(cnfTransformation,[status(thm)],[f_472]) ).
tff(c_141836,plain,
( ( c = a )
| ~ between(c,a,b) ),
inference(resolution,[status(thm)],[c_141772,c_106]) ).
tff(c_141888,plain,
~ between(c,a,b),
inference(splitLeft,[status(thm)],[c_141836]) ).
tff(c_143276,plain,
~ between(a,a,b),
inference(demodulation,[status(thm),theory(equality)],[c_143259,c_141888]) ).
tff(c_143309,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_104,c_143276]) ).
tff(c_143311,plain,
c != a,
inference(splitRight,[status(thm)],[c_141834]) ).
tff(c_143310,plain,
extension(a,c,c,b) = b,
inference(splitRight,[status(thm)],[c_141834]) ).
tff(c_149973,plain,
! [U_2782] :
( ( c = a )
| between(U_2782,a,b)
| ~ between(U_2782,a,c) ),
inference(superposition,[status(thm),theory(equality)],[c_143310,c_149859]) ).
tff(c_150167,plain,
! [U_2789] :
( between(U_2789,a,b)
| ~ between(U_2789,a,c) ),
inference(negUnitSimplification,[status(thm)],[c_143311,c_149973]) ).
tff(c_153762,plain,
! [W_2838,X_2839] : between(extension(c,a,W_2838,X_2839),a,b),
inference(resolution,[status(thm)],[c_728,c_150167]) ).
tff(c_153866,plain,
! [W_2838,X_2839] : between(b,a,extension(c,a,W_2838,X_2839)),
inference(resolution,[status(thm)],[c_153762,c_102]) ).
tff(c_10,plain,
! [Y_16,X_17,W_18,V_19] : equidistant(Y_16,extension(X_17,Y_16,W_18,V_19),W_18,V_19),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_4649,plain,
! [X_730,W_731,V_732,U_733] :
( ( X_730 = W_731 )
| ( V_732 = U_733 )
| ~ equidistant(V_732,W_731,V_732,X_730)
| ~ between(U_733,V_732,X_730)
| ~ between(U_733,V_732,W_731) ),
inference(cnfTransformation,[status(thm)],[f_425]) ).
tff(c_183062,plain,
! [X_3267,W_3268,V_3269,U_3270] :
( ( extension(X_3267,W_3268,W_3268,V_3269) = V_3269 )
| ( W_3268 = U_3270 )
| ~ between(U_3270,W_3268,V_3269)
| ~ between(U_3270,W_3268,extension(X_3267,W_3268,W_3268,V_3269)) ),
inference(resolution,[status(thm)],[c_10,c_4649]) ).
tff(c_183093,plain,
! [X_2839] :
( ( extension(c,a,a,X_2839) = X_2839 )
| ( b = a )
| ~ between(b,a,X_2839) ),
inference(resolution,[status(thm)],[c_153866,c_183062]) ).
tff(c_281028,plain,
! [X_4229] :
( ( extension(c,a,a,X_4229) = X_4229 )
| ~ between(b,a,X_4229) ),
inference(negUnitSimplification,[status(thm)],[c_204,c_183093]) ).
tff(c_281080,plain,
( ( extension(c,a,a,reflection(d,a)) = reflection(d,a) )
| ~ between(b,a,a) ),
inference(resolution,[status(thm)],[c_151379,c_281028]) ).
tff(c_281303,plain,
extension(c,a,a,reflection(d,a)) = reflection(d,a),
inference(demodulation,[status(thm),theory(equality)],[c_98,c_281080]) ).
tff(c_411801,plain,
between(c,a,reflection(d,a)),
inference(superposition,[status(thm),theory(equality)],[c_281303,c_70]) ).
tff(c_5873,plain,
! [U_134,U_772,V_135] :
( between(U_134,U_772,V_135)
| between(U_772,U_134,V_135)
| ( reflection(U_134,V_135) = V_135 )
| ~ between(U_772,V_135,reflection(U_134,V_135)) ),
inference(resolution,[status(thm)],[c_72,c_5815]) ).
tff(c_411935,plain,
( between(d,c,a)
| between(c,d,a)
| ( reflection(d,a) = a ) ),
inference(resolution,[status(thm)],[c_411801,c_5873]) ).
tff(c_412031,plain,
reflection(d,a) = a,
inference(negUnitSimplification,[status(thm)],[c_507,c_508,c_411935]) ).
tff(c_151388,plain,
( ( reflection(d,a) = a )
| ~ between(b,reflection(d,a),a) ),
inference(resolution,[status(thm)],[c_151225,c_108]) ).
tff(c_265204,plain,
~ between(b,reflection(d,a),a),
inference(splitLeft,[status(thm)],[c_151388]) ).
tff(c_412147,plain,
~ between(b,a,a),
inference(demodulation,[status(thm),theory(equality)],[c_412031,c_265204]) ).
tff(c_412258,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_98,c_412147]) ).
tff(c_412259,plain,
reflection(d,a) = a,
inference(splitRight,[status(thm)],[c_151388]) ).
tff(c_151222,plain,
( ( reflection(d,a) = a )
| ~ between(a,reflection(d,a),b) ),
inference(resolution,[status(thm)],[c_151148,c_106]) ).
tff(c_227832,plain,
~ between(a,reflection(d,a),b),
inference(splitLeft,[status(thm)],[c_151222]) ).
tff(c_412277,plain,
~ between(a,a,b),
inference(demodulation,[status(thm),theory(equality)],[c_412259,c_227832]) ).
tff(c_412342,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_104,c_412277]) ).
tff(c_412343,plain,
reflection(d,a) = a,
inference(splitRight,[status(thm)],[c_151222]) ).
tff(c_96,plain,
! [U_168,V_169] : ( reflection(reflection(U_168,V_169),V_169) = U_168 ),
inference(cnfTransformation,[status(thm)],[f_447]) ).
tff(c_2,plain,
! [X_1,Y_2] : equidistant(X_1,Y_2,Y_2,X_1),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_3328,plain,
! [U_667,W_668,X_664,Z_666,V_663,Y_665] :
( ( insertion(U_667,V_663,Y_665,Z_666) = insertion(U_667,V_663,W_668,X_664) )
| ~ equidistant(W_668,X_664,Y_665,Z_666) ),
inference(cnfTransformation,[status(thm)],[f_684]) ).
tff(c_3410,plain,
! [U_667,V_663,Y_2,X_1] : ( insertion(U_667,V_663,Y_2,X_1) = insertion(U_667,V_663,X_1,Y_2) ),
inference(resolution,[status(thm)],[c_2,c_3328]) ).
tff(c_74,plain,
! [V_136,U_137] : equidistant(V_136,reflection(U_137,V_136),U_137,V_136),
inference(cnfTransformation,[status(thm)],[f_384]) ).
tff(c_137346,plain,
! [U_2622,V_2623,V_2624,U_2625] : ( insertion(U_2622,V_2623,V_2624,reflection(U_2625,V_2624)) = insertion(U_2622,V_2623,U_2625,V_2624) ),
inference(resolution,[status(thm)],[c_74,c_3328]) ).
tff(c_1766,plain,
! [U_554,W_555,V_556] :
( ( insertion(U_554,W_555,U_554,V_556) = V_556 )
| ~ between(U_554,V_556,W_555) ),
inference(cnfTransformation,[status(thm)],[f_679]) ).
tff(c_1782,plain,
! [U_134,V_135] : ( insertion(U_134,reflection(U_134,V_135),U_134,V_135) = V_135 ),
inference(resolution,[status(thm)],[c_72,c_1766]) ).
tff(c_3454,plain,
! [U_671,V_672,Y_673,X_674] : ( insertion(U_671,V_672,Y_673,X_674) = insertion(U_671,V_672,X_674,Y_673) ),
inference(resolution,[status(thm)],[c_2,c_3328]) ).
tff(c_3573,plain,
! [U_134,V_135] : ( insertion(U_134,reflection(U_134,V_135),V_135,U_134) = V_135 ),
inference(superposition,[status(thm),theory(equality)],[c_1782,c_3454]) ).
tff(c_137375,plain,
! [U_2625,V_2624] : ( insertion(reflection(U_2625,V_2624),reflection(reflection(U_2625,V_2624),V_2624),U_2625,V_2624) = V_2624 ),
inference(superposition,[status(thm),theory(equality)],[c_137346,c_3573]) ).
tff(c_138151,plain,
! [U_2634,V_2635] : ( insertion(reflection(U_2634,V_2635),U_2634,U_2634,V_2635) = V_2635 ),
inference(demodulation,[status(thm),theory(equality)],[c_96,c_137375]) ).
tff(c_140911,plain,
! [Y_2662,X_2663] : ( insertion(reflection(Y_2662,X_2663),Y_2662,X_2663,Y_2662) = X_2663 ),
inference(superposition,[status(thm),theory(equality)],[c_3410,c_138151]) ).
tff(c_141064,plain,
! [U_168,V_169] : ( insertion(U_168,reflection(U_168,V_169),V_169,reflection(U_168,V_169)) = V_169 ),
inference(superposition,[status(thm),theory(equality)],[c_96,c_140911]) ).
tff(c_412584,plain,
insertion(d,reflection(d,a),a,a) = a,
inference(superposition,[status(thm),theory(equality)],[c_412343,c_141064]) ).
tff(c_412944,plain,
d = a,
inference(demodulation,[status(thm),theory(equality)],[c_1279,c_412343,c_412584]) ).
tff(c_412946,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_139113,c_412944]) ).
tff(c_412947,plain,
c = a,
inference(splitRight,[status(thm)],[c_141836]) ).
tff(c_141771,plain,
( ( c = a )
| ~ between(b,a,c) ),
inference(resolution,[status(thm)],[c_141706,c_108]) ).
tff(c_141887,plain,
~ between(b,a,c),
inference(splitLeft,[status(thm)],[c_141771]) ).
tff(c_412949,plain,
~ between(b,a,a),
inference(demodulation,[status(thm),theory(equality)],[c_412947,c_141887]) ).
tff(c_412970,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_98,c_412949]) ).
tff(c_412971,plain,
c = a,
inference(splitRight,[status(thm)],[c_141771]) ).
tff(c_412978,plain,
~ between(a,a,d),
inference(demodulation,[status(thm),theory(equality)],[c_412971,c_757]) ).
tff(c_412996,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_104,c_412978]) ).
tff(c_412997,plain,
between(c,a,b),
inference(splitRight,[status(thm)],[c_141705]) ).
tff(c_413067,plain,
between(b,a,c),
inference(resolution,[status(thm)],[c_412997,c_102]) ).
tff(c_416244,plain,
! [V_5089] :
( between(V_5089,a,c)
| ~ between(b,V_5089,a) ),
inference(resolution,[status(thm)],[c_413067,c_116]) ).
tff(c_416253,plain,
( between(d,a,c)
| ~ between(b,a,a) ),
inference(resolution,[status(thm)],[c_137319,c_416244]) ).
tff(c_416281,plain,
between(d,a,c),
inference(demodulation,[status(thm),theory(equality)],[c_98,c_416253]) ).
tff(c_416283,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_510,c_416281]) ).
tff(c_416284,plain,
d = a,
inference(splitRight,[status(thm)],[c_137273]) ).
tff(c_137208,plain,
~ between(d,a,b),
inference(splitRight,[status(thm)],[c_70680]) ).
tff(c_416286,plain,
~ between(a,a,b),
inference(demodulation,[status(thm),theory(equality)],[c_416284,c_137208]) ).
tff(c_416305,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_104,c_416286]) ).
tff(c_416306,plain,
~ colinear(b,c,d),
inference(splitRight,[status(thm)],[c_210]) ).
tff(c_416321,plain,
~ between(d,c,b),
inference(resolution,[status(thm)],[c_176,c_416306]) ).
tff(c_416323,plain,
~ between(d,b,c),
inference(resolution,[status(thm)],[c_42,c_416306]) ).
tff(c_416322,plain,
~ between(b,d,c),
inference(resolution,[status(thm)],[c_178,c_416306]) ).
tff(c_373,plain,
! [V_412,U_413,W_414] :
( colinear(V_412,U_413,W_414)
| ~ colinear(U_413,V_412,W_414) ),
inference(cnfTransformation,[status(thm)],[f_813]) ).
tff(c_401,plain,
colinear(b,a,d),
inference(resolution,[status(thm)],[c_208,c_373]) ).
tff(c_416320,plain,
~ between(c,d,b),
inference(resolution,[status(thm)],[c_40,c_416306]) ).
tff(c_416307,plain,
colinear(a,c,d),
inference(splitRight,[status(thm)],[c_210]) ).
tff(c_420267,plain,
! [Z_5385,X_5386,Y_5387] :
( between(Z_5385,X_5386,Y_5387)
| between(Y_5387,Z_5385,X_5386)
| between(X_5386,Y_5387,Z_5385)
| ~ colinear(X_5386,Y_5387,Z_5385) ),
inference(cnfTransformation,[status(thm)],[f_274]) ).
tff(c_420361,plain,
( between(d,a,c)
| between(c,d,a)
| between(a,c,d) ),
inference(resolution,[status(thm)],[c_416307,c_420267]) ).
tff(c_429794,plain,
between(a,c,d),
inference(splitLeft,[status(thm)],[c_420361]) ).
tff(c_122,plain,
! [U_209,W_212,X_211,V_210] :
( between(U_209,W_212,X_211)
| ~ between(V_210,W_212,X_211)
| ~ between(U_209,V_210,X_211) ),
inference(cnfTransformation,[status(thm)],[f_544]) ).
tff(c_429852,plain,
! [U_209] :
( between(U_209,c,d)
| ~ between(U_209,a,d) ),
inference(resolution,[status(thm)],[c_429794,c_122]) ).
tff(c_416630,plain,
! [U_5102,V_5103,W_5104] :
( colinear(U_5102,V_5103,W_5104)
| ~ between(V_5103,U_5102,W_5104) ),
inference(cnfTransformation,[status(thm)],[f_788]) ).
tff(c_416647,plain,
~ between(c,b,d),
inference(resolution,[status(thm)],[c_416630,c_416306]) ).
tff(c_416405,plain,
! [X_5093,Y_5094,Z_5095] :
( colinear(X_5093,Y_5094,Z_5095)
| ~ between(X_5093,Y_5094,Z_5095) ),
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_416419,plain,
~ between(b,c,d),
inference(resolution,[status(thm)],[c_416405,c_416306]) ).
tff(c_420373,plain,
( between(c,a,b)
| between(b,c,a)
| between(a,b,c) ),
inference(resolution,[status(thm)],[c_206,c_420267]) ).
tff(c_430226,plain,
between(a,b,c),
inference(splitLeft,[status(thm)],[c_420373]) ).
tff(c_430252,plain,
! [U_201] :
( ( b = a )
| between(U_201,b,c)
| ~ between(U_201,a,b) ),
inference(resolution,[status(thm)],[c_430226,c_118]) ).
tff(c_430289,plain,
! [U_201] :
( between(U_201,b,c)
| ~ between(U_201,a,b) ),
inference(negUnitSimplification,[status(thm)],[c_204,c_430252]) ).
tff(c_432243,plain,
! [V_5757] :
( between(V_5757,c,d)
| ~ between(a,V_5757,c) ),
inference(resolution,[status(thm)],[c_429794,c_116]) ).
tff(c_432248,plain,
( between(b,c,d)
| ~ between(a,a,b) ),
inference(resolution,[status(thm)],[c_430289,c_432243]) ).
tff(c_432284,plain,
between(b,c,d),
inference(demodulation,[status(thm),theory(equality)],[c_104,c_432248]) ).
tff(c_432286,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_416419,c_432284]) ).
tff(c_432287,plain,
( between(b,c,a)
| between(c,a,b) ),
inference(splitRight,[status(thm)],[c_420373]) ).
tff(c_432404,plain,
between(c,a,b),
inference(splitLeft,[status(thm)],[c_432287]) ).
tff(c_420376,plain,
( between(d,a,b)
| between(b,d,a)
| between(a,b,d) ),
inference(resolution,[status(thm)],[c_208,c_420267]) ).
tff(c_429968,plain,
between(a,b,d),
inference(splitLeft,[status(thm)],[c_420376]) ).
tff(c_429992,plain,
! [U_205] :
( ( b = a )
| between(U_205,a,d)
| ~ between(U_205,a,b) ),
inference(resolution,[status(thm)],[c_429968,c_120]) ).
tff(c_434441,plain,
! [U_5778] :
( between(U_5778,a,d)
| ~ between(U_5778,a,b) ),
inference(negUnitSimplification,[status(thm)],[c_204,c_429992]) ).
tff(c_429856,plain,
( ( c = a )
| ~ between(c,a,d) ),
inference(resolution,[status(thm)],[c_429794,c_106]) ).
tff(c_429966,plain,
~ between(c,a,d),
inference(splitLeft,[status(thm)],[c_429856]) ).
tff(c_434455,plain,
~ between(c,a,b),
inference(resolution,[status(thm)],[c_434441,c_429966]) ).
tff(c_434539,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_432404,c_434455]) ).
tff(c_434540,plain,
between(b,c,a),
inference(splitRight,[status(thm)],[c_432287]) ).
tff(c_434659,plain,
between(a,c,b),
inference(resolution,[status(thm)],[c_434540,c_102]) ).
tff(c_436799,plain,
! [V_5801] :
( between(V_5801,b,d)
| ~ between(a,V_5801,b) ),
inference(resolution,[status(thm)],[c_429968,c_116]) ).
tff(c_436801,plain,
between(c,b,d),
inference(resolution,[status(thm)],[c_434659,c_436799]) ).
tff(c_436823,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_416647,c_436801]) ).
tff(c_436824,plain,
( between(b,d,a)
| between(d,a,b) ),
inference(splitRight,[status(thm)],[c_420376]) ).
tff(c_436826,plain,
between(d,a,b),
inference(splitLeft,[status(thm)],[c_436824]) ).
tff(c_436893,plain,
between(b,a,d),
inference(resolution,[status(thm)],[c_436826,c_102]) ).
tff(c_438410,plain,
! [U_5816] :
( between(U_5816,c,d)
| ~ between(U_5816,a,d) ),
inference(resolution,[status(thm)],[c_429794,c_122]) ).
tff(c_438486,plain,
~ between(b,a,d),
inference(resolution,[status(thm)],[c_438410,c_416419]) ).
tff(c_438524,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_436893,c_438486]) ).
tff(c_438525,plain,
between(b,d,a),
inference(splitRight,[status(thm)],[c_436824]) ).
tff(c_438589,plain,
between(a,d,b),
inference(resolution,[status(thm)],[c_438525,c_102]) ).
tff(c_453404,plain,
! [V_5975] :
( between(V_5975,d,b)
| ~ between(a,V_5975,d) ),
inference(resolution,[status(thm)],[c_438589,c_116]) ).
tff(c_453418,plain,
( between(c,d,b)
| ~ between(a,a,d) ),
inference(resolution,[status(thm)],[c_429852,c_453404]) ).
tff(c_453450,plain,
between(c,d,b),
inference(demodulation,[status(thm),theory(equality)],[c_104,c_453418]) ).
tff(c_453452,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_416320,c_453450]) ).
tff(c_453453,plain,
c = a,
inference(splitRight,[status(thm)],[c_429856]) ).
tff(c_453474,plain,
~ colinear(b,a,d),
inference(demodulation,[status(thm),theory(equality)],[c_453453,c_416306]) ).
tff(c_453492,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_401,c_453474]) ).
tff(c_453493,plain,
( between(c,d,a)
| between(d,a,c) ),
inference(splitRight,[status(thm)],[c_420361]) ).
tff(c_453495,plain,
between(d,a,c),
inference(splitLeft,[status(thm)],[c_453493]) ).
tff(c_453558,plain,
between(c,a,d),
inference(resolution,[status(thm)],[c_453495,c_102]) ).
tff(c_455852,plain,
! [V_6003] :
( between(c,V_6003,d)
| ~ between(c,V_6003,a) ),
inference(resolution,[status(thm)],[c_453558,c_124]) ).
tff(c_455954,plain,
~ between(c,b,a),
inference(resolution,[status(thm)],[c_455852,c_416647]) ).
tff(c_458703,plain,
between(a,b,c),
inference(splitLeft,[status(thm)],[c_420373]) ).
tff(c_458747,plain,
between(c,b,a),
inference(resolution,[status(thm)],[c_458703,c_102]) ).
tff(c_458784,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_455954,c_458747]) ).
tff(c_458785,plain,
( between(b,c,a)
| between(c,a,b) ),
inference(splitRight,[status(thm)],[c_420373]) ).
tff(c_458787,plain,
between(c,a,b),
inference(splitLeft,[status(thm)],[c_458785]) ).
tff(c_458961,plain,
insertion(c,b,c,a) = a,
inference(resolution,[status(thm)],[c_458787,c_156]) ).
tff(c_418648,plain,
! [W1_5294,U1_5295,U_5296,V_5297] : ( extension(extension(W1_5294,U1_5295,lower_dimension_point_1,lower_dimension_point_2),U1_5295,U_5296,V_5297) = insertion(U1_5295,W1_5294,U_5296,V_5297) ),
inference(cnfTransformation,[status(thm)],[f_326]) ).
tff(c_418707,plain,
! [W1_5294,U1_5295,U_5296,V_5297] : between(extension(W1_5294,U1_5295,lower_dimension_point_1,lower_dimension_point_2),U1_5295,insertion(U1_5295,W1_5294,U_5296,V_5297)),
inference(superposition,[status(thm),theory(equality)],[c_418648,c_70]) ).
tff(c_459054,plain,
between(extension(b,c,lower_dimension_point_1,lower_dimension_point_2),c,a),
inference(superposition,[status(thm),theory(equality)],[c_458961,c_418707]) ).
tff(c_453615,plain,
( ( extension(c,a,a,d) = d )
| ( c = a ) ),
inference(resolution,[status(thm)],[c_453558,c_88]) ).
tff(c_455458,plain,
c = a,
inference(splitLeft,[status(thm)],[c_453615]) ).
tff(c_453555,plain,
( ( c = a )
| ~ between(d,c,a) ),
inference(resolution,[status(thm)],[c_453495,c_108]) ).
tff(c_453623,plain,
~ between(d,c,a),
inference(splitLeft,[status(thm)],[c_453555]) ).
tff(c_455477,plain,
~ between(d,a,a),
inference(demodulation,[status(thm),theory(equality)],[c_455458,c_453623]) ).
tff(c_455515,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_98,c_455477]) ).
tff(c_455517,plain,
c != a,
inference(splitRight,[status(thm)],[c_453615]) ).
tff(c_455516,plain,
extension(c,a,a,d) = d,
inference(splitRight,[status(thm)],[c_453615]) ).
tff(c_418884,plain,
! [W_5308,V_5309,U_5310,X_5311] :
( ( W_5308 = V_5309 )
| between(U_5310,V_5309,X_5311)
| ~ between(V_5309,W_5308,X_5311)
| ~ between(U_5310,V_5309,W_5308) ),
inference(cnfTransformation,[status(thm)],[f_536]) ).
tff(c_467135,plain,
! [W_6135,U_6133,U_6132,V_6136,X_6134] :
( ( V_6136 = U_6132 )
| between(U_6133,U_6132,extension(U_6132,V_6136,W_6135,X_6134))
| ~ between(U_6133,U_6132,V_6136) ),
inference(resolution,[status(thm)],[c_70,c_418884]) ).
tff(c_467271,plain,
! [U_6133] :
( ( c = a )
| between(U_6133,c,d)
| ~ between(U_6133,c,a) ),
inference(superposition,[status(thm),theory(equality)],[c_455516,c_467135]) ).
tff(c_470075,plain,
! [U_6175] :
( between(U_6175,c,d)
| ~ between(U_6175,c,a) ),
inference(negUnitSimplification,[status(thm)],[c_455517,c_467271]) ).
tff(c_476106,plain,
! [U_6243] :
( between(d,c,U_6243)
| ~ between(U_6243,c,a) ),
inference(resolution,[status(thm)],[c_470075,c_102]) ).
tff(c_476135,plain,
between(d,c,extension(b,c,lower_dimension_point_1,lower_dimension_point_2)),
inference(resolution,[status(thm)],[c_459054,c_476106]) ).
tff(c_421835,plain,
! [V_5445,U_5446,W_5447,X_5448] :
( between(V_5445,U_5446,W_5447)
| between(U_5446,V_5445,W_5447)
| ( X_5448 = W_5447 )
| ~ between(V_5445,W_5447,X_5448)
| ~ between(U_5446,W_5447,X_5448) ),
inference(cnfTransformation,[status(thm)],[f_734]) ).
tff(c_519439,plain,
! [U_6781,U_6782,W_6784,X_6783,V_6785] :
( between(U_6781,U_6782,V_6785)
| between(U_6782,U_6781,V_6785)
| ( extension(U_6781,V_6785,W_6784,X_6783) = V_6785 )
| ~ between(U_6782,V_6785,extension(U_6781,V_6785,W_6784,X_6783)) ),
inference(resolution,[status(thm)],[c_70,c_421835]) ).
tff(c_519481,plain,
( between(b,d,c)
| between(d,b,c)
| ( extension(b,c,lower_dimension_point_1,lower_dimension_point_2) = c ) ),
inference(resolution,[status(thm)],[c_476135,c_519439]) ).
tff(c_519646,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_132,c_416323,c_416322,c_519481]) ).
tff(c_519647,plain,
between(b,c,a),
inference(splitRight,[status(thm)],[c_458785]) ).
tff(c_453875,plain,
! [V_5980] :
( between(d,V_5980,c)
| ~ between(d,V_5980,a) ),
inference(resolution,[status(thm)],[c_453495,c_124]) ).
tff(c_453965,plain,
~ between(d,b,a),
inference(resolution,[status(thm)],[c_453875,c_416323]) ).
tff(c_520053,plain,
between(a,b,d),
inference(splitLeft,[status(thm)],[c_420376]) ).
tff(c_520097,plain,
between(d,b,a),
inference(resolution,[status(thm)],[c_520053,c_102]) ).
tff(c_520134,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_453965,c_520097]) ).
tff(c_520135,plain,
( between(b,d,a)
| between(d,a,b) ),
inference(splitRight,[status(thm)],[c_420376]) ).
tff(c_520364,plain,
between(d,a,b),
inference(splitLeft,[status(thm)],[c_520135]) ).
tff(c_520445,plain,
between(b,a,d),
inference(resolution,[status(thm)],[c_520364,c_102]) ).
tff(c_523216,plain,
! [V_6820] :
( between(b,V_6820,d)
| ~ between(b,V_6820,a) ),
inference(resolution,[status(thm)],[c_520445,c_124]) ).
tff(c_523287,plain,
~ between(b,c,a),
inference(resolution,[status(thm)],[c_523216,c_416419]) ).
tff(c_523322,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_519647,c_523287]) ).
tff(c_523324,plain,
~ between(d,a,b),
inference(splitRight,[status(thm)],[c_520135]) ).
tff(c_455955,plain,
! [V_6003] :
( between(d,V_6003,c)
| ~ between(c,V_6003,a) ),
inference(resolution,[status(thm)],[c_455852,c_102]) ).
tff(c_519718,plain,
between(a,c,b),
inference(resolution,[status(thm)],[c_519647,c_102]) ).
tff(c_519744,plain,
! [U_205] :
( ( c = a )
| between(U_205,a,b)
| ~ between(U_205,a,c) ),
inference(resolution,[status(thm)],[c_519718,c_120]) ).
tff(c_525897,plain,
! [U_6849] :
( between(U_6849,a,b)
| ~ between(U_6849,a,c) ),
inference(negUnitSimplification,[status(thm)],[c_455517,c_519744]) ).
tff(c_525904,plain,
( between(d,a,b)
| ~ between(c,a,a) ),
inference(resolution,[status(thm)],[c_455955,c_525897]) ).
tff(c_525953,plain,
between(d,a,b),
inference(demodulation,[status(thm),theory(equality)],[c_98,c_525904]) ).
tff(c_525955,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_523324,c_525953]) ).
tff(c_525956,plain,
c = a,
inference(splitRight,[status(thm)],[c_453555]) ).
tff(c_453494,plain,
~ between(a,c,d),
inference(splitRight,[status(thm)],[c_420361]) ).
tff(c_525960,plain,
~ between(a,a,d),
inference(demodulation,[status(thm),theory(equality)],[c_525956,c_453494]) ).
tff(c_525984,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_104,c_525960]) ).
tff(c_525985,plain,
between(c,d,a),
inference(splitRight,[status(thm)],[c_453493]) ).
tff(c_526049,plain,
between(a,d,c),
inference(resolution,[status(thm)],[c_525985,c_102]) ).
tff(c_526107,plain,
! [U_209] :
( between(U_209,d,c)
| ~ between(U_209,a,c) ),
inference(resolution,[status(thm)],[c_526049,c_122]) ).
tff(c_531674,plain,
between(a,b,d),
inference(splitLeft,[status(thm)],[c_420376]) ).
tff(c_526105,plain,
! [V_198] :
( between(V_198,d,c)
| ~ between(a,V_198,d) ),
inference(resolution,[status(thm)],[c_526049,c_116]) ).
tff(c_531679,plain,
between(b,d,c),
inference(resolution,[status(thm)],[c_531674,c_526105]) ).
tff(c_531729,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_416322,c_531679]) ).
tff(c_531730,plain,
( between(b,d,a)
| between(d,a,b) ),
inference(splitRight,[status(thm)],[c_420376]) ).
tff(c_531844,plain,
between(d,a,b),
inference(splitLeft,[status(thm)],[c_531730]) ).
tff(c_419972,plain,
! [W_5371,Y_5370,U_5367,X_5369,V_5368] :
( between(U_5367,W_5371,Y_5370)
| ~ between(U_5367,X_5369,Y_5370)
| ~ between(V_5368,W_5371,X_5369)
| ~ between(U_5367,V_5368,Y_5370) ),
inference(cnfTransformation,[status(thm)],[f_765]) ).
tff(c_526159,plain,
! [U_6850,W_6851,V_6852,V_6853] :
( between(U_6850,W_6851,V_6852)
| ~ between(V_6853,W_6851,U_6850)
| ~ between(U_6850,V_6853,V_6852) ),
inference(resolution,[status(thm)],[c_104,c_419972]) ).
tff(c_527527,plain,
! [V_6866] :
( between(c,d,V_6866)
| ~ between(c,a,V_6866) ),
inference(resolution,[status(thm)],[c_526049,c_526159]) ).
tff(c_527666,plain,
~ between(c,a,b),
inference(resolution,[status(thm)],[c_527527,c_416320]) ).
tff(c_531341,plain,
( between(b,c,a)
| between(a,b,c) ),
inference(negUnitSimplification,[status(thm)],[c_527666,c_420373]) ).
tff(c_531342,plain,
between(a,b,c),
inference(splitLeft,[status(thm)],[c_531341]) ).
tff(c_531370,plain,
! [U_201] :
( ( b = a )
| between(U_201,b,c)
| ~ between(U_201,a,b) ),
inference(resolution,[status(thm)],[c_531342,c_118]) ).
tff(c_533136,plain,
! [U_6926] :
( between(U_6926,b,c)
| ~ between(U_6926,a,b) ),
inference(negUnitSimplification,[status(thm)],[c_204,c_531370]) ).
tff(c_533215,plain,
~ between(d,a,b),
inference(resolution,[status(thm)],[c_533136,c_416323]) ).
tff(c_533255,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_531844,c_533215]) ).
tff(c_533256,plain,
between(b,d,a),
inference(splitRight,[status(thm)],[c_531730]) ).
tff(c_533327,plain,
between(a,d,b),
inference(resolution,[status(thm)],[c_533256,c_102]) ).
tff(c_534015,plain,
! [V_6933] :
( between(V_6933,b,c)
| ~ between(a,V_6933,b) ),
inference(resolution,[status(thm)],[c_531342,c_116]) ).
tff(c_534017,plain,
between(d,b,c),
inference(resolution,[status(thm)],[c_533327,c_534015]) ).
tff(c_534048,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_416323,c_534017]) ).
tff(c_534049,plain,
between(b,c,a),
inference(splitRight,[status(thm)],[c_531341]) ).
tff(c_534119,plain,
between(a,c,b),
inference(resolution,[status(thm)],[c_534049,c_102]) ).
tff(c_536659,plain,
! [V_6953] :
( between(V_6953,c,b)
| ~ between(a,V_6953,c) ),
inference(resolution,[status(thm)],[c_534119,c_116]) ).
tff(c_536671,plain,
( between(d,c,b)
| ~ between(a,a,c) ),
inference(resolution,[status(thm)],[c_526107,c_536659]) ).
tff(c_536701,plain,
between(d,c,b),
inference(demodulation,[status(thm),theory(equality)],[c_104,c_536671]) ).
tff(c_536703,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_416321,c_536701]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : GEO012-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.15/0.15 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.36 % Computer : n025.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Aug 4 00:57:50 EDT 2023
% 0.15/0.36 % CPUTime :
% 288.92/256.93 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 289.01/256.98
% 289.01/256.98 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 289.01/257.04
% 289.01/257.04 Inference rules
% 289.01/257.04 ----------------------
% 289.01/257.04 #Ref : 0
% 289.01/257.04 #Sup : 140396
% 289.01/257.04 #Fact : 64
% 289.01/257.04 #Define : 0
% 289.01/257.04 #Split : 247
% 289.01/257.04 #Chain : 0
% 289.01/257.04 #Close : 0
% 289.01/257.04
% 289.01/257.04 Ordering : KBO
% 289.01/257.04
% 289.01/257.04 Simplification rules
% 289.01/257.04 ----------------------
% 289.01/257.04 #Subsume : 15007
% 289.01/257.04 #Demod : 43372
% 289.01/257.04 #Tautology : 27177
% 289.01/257.04 #SimpNegUnit : 10746
% 289.01/257.04 #BackRed : 2457
% 289.01/257.04
% 289.01/257.04 #Partial instantiations: 0
% 289.01/257.05 #Strategies tried : 1
% 289.01/257.05
% 289.01/257.05 Timing (in seconds)
% 289.01/257.05 ----------------------
% 289.43/257.05 Preprocessing : 0.72
% 289.43/257.05 Parsing : 0.30
% 289.43/257.05 CNF conversion : 0.05
% 289.43/257.05 Main loop : 255.15
% 289.43/257.05 Inferencing : 15.98
% 289.43/257.05 Reduction : 126.99
% 289.43/257.05 Demodulation : 107.40
% 289.43/257.05 BG Simplification : 0.99
% 289.43/257.05 Subsumption : 94.03
% 289.43/257.05 Abstraction : 1.28
% 289.43/257.05 MUC search : 0.00
% 289.43/257.05 Cooper : 0.00
% 289.43/257.05 Total : 256.01
% 289.43/257.05 Index Insertion : 0.00
% 289.43/257.05 Index Deletion : 0.00
% 289.43/257.05 Index Matching : 0.00
% 289.43/257.05 BG Taut test : 0.00
%------------------------------------------------------------------------------