%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GEO053-3 : TPTP v9.0.0. 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 : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Apr 9 06:13:37 PM UTC 2025
% Result : Unsatisfiable 11.49s 3.75s
% Output : CNFRefutation 11.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 64 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 112 ( 41 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 95 ( 47 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-6 aty)
% Number of variables : 84 ( 84 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ equidistant > between > continuous > inner_pasch > euclid2 > euclid1 > insertion > extension > reflection > #nlpp > w > v > u > lower_dimension_point_3 > lower_dimension_point_2 > lower_dimension_point_1
%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(lower_dimension_point_2,type,
lower_dimension_point_2: $i ).
tff(w,type,
w: $i ).
tff(equidistant,type,
equidistant: ( $i * $i * $i * $i ) > $o ).
tff(u,type,
u: $i ).
tff(lower_dimension_point_3,type,
lower_dimension_point_3: $i ).
tff(v,type,
v: $i ).
tff(extension,type,
extension: ( $i * $i * $i * $i ) > $i ).
tff(reflection,type,
reflection: ( $i * $i ) > $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(f_410,axiom,
! [U,V] : between(U,U,V),
file(unknown,unknown) ).
tff(f_395,axiom,
! [U,V] : between(U,V,V),
file(unknown,unknown) ).
tff(f_712,axiom,
between(u,v,w),
file(unknown,unknown) ).
tff(f_378,axiom,
! [U,V,W] :
( ~ between(U,V,W)
| ( U = V )
| ( W = extension(U,V,V,W) ) ),
file(unknown,unknown) ).
tff(f_408,axiom,
! [U,V,W] :
( ~ between(U,V,W)
| between(W,V,U) ),
file(unknown,unknown) ).
tff(f_426,axiom,
! [U,V,W] :
( ~ between(U,V,W)
| ~ between(U,W,V)
| ( V = W ) ),
file(unknown,unknown) ).
tff(f_393,axiom,
! [U,V] : ( U = reflection(reflection(U,V),V) ),
file(unknown,unknown) ).
tff(f_328,axiom,
! [U,V] : between(U,V,reflection(U,V)),
file(unknown,unknown) ).
tff(f_482,axiom,
! [U,V,W,X] :
( ~ between(U,V,W)
| ~ between(V,W,X)
| between(U,V,X)
| ( V = W ) ),
file(unknown,unknown) ).
tff(f_715,axiom,
v != w,
file(unknown,unknown) ).
tff(f_713,axiom,
equidistant(u,v,u,w),
file(unknown,unknown) ).
tff(f_371,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_342,axiom,
! [V,U] :
( ( V != reflection(U,V) )
| ( U = V ) ),
file(unknown,unknown) ).
tff(f_418,axiom,
! [U,V,W] :
( ~ between(U,V,W)
| ~ between(V,U,W)
| ( U = V ) ),
file(unknown,unknown) ).
tff(f_306,axiom,
! [U,V,W,X] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,U,V) ),
file(unknown,unknown) ).
tff(f_72,axiom,
! [X,Y,Z] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(c_96,plain,
! [U_167,V_168] : between(U_167,U_167,V_168),
inference(cnfTransformation,[status(thm)],[f_410]) ).
tff(c_90,plain,
! [U_158,V_159] : between(U_158,V_159,V_159),
inference(cnfTransformation,[status(thm)],[f_395]) ).
tff(c_166,plain,
between(u,v,w),
inference(cnfTransformation,[status(thm)],[f_712]) ).
tff(c_1173,plain,
! [U_413,V_414,W_415] :
( ( extension(U_413,V_414,V_414,W_415) = W_415 )
| ( V_414 = U_413 )
| ~ between(U_413,V_414,W_415) ),
inference(cnfTransformation,[status(thm)],[f_378]) ).
tff(c_1197,plain,
( ( extension(u,v,v,w) = w )
| ( v = u ) ),
inference(resolution,[status(thm)],[c_166,c_1173]) ).
tff(c_1470,plain,
v = u,
inference(splitLeft,[status(thm)],[c_1197]) ).
tff(c_347,plain,
! [W_345,V_346,U_347] :
( between(W_345,V_346,U_347)
| ~ between(U_347,V_346,W_345) ),
inference(cnfTransformation,[status(thm)],[f_408]) ).
tff(c_365,plain,
between(w,v,u),
inference(resolution,[status(thm)],[c_166,c_347]) ).
tff(c_403,plain,
! [W_360,V_361,U_362] :
( ( W_360 = V_361 )
| ~ between(U_362,W_360,V_361)
| ~ between(U_362,V_361,W_360) ),
inference(cnfTransformation,[status(thm)],[f_426]) ).
tff(c_421,plain,
( ( v = u )
| ~ between(w,u,v) ),
inference(resolution,[status(thm)],[c_365,c_403]) ).
tff(c_620,plain,
~ between(w,u,v),
inference(splitLeft,[status(thm)],[c_421]) ).
tff(c_1478,plain,
~ between(w,u,u),
inference(demodulation,[status(thm),theory(equality)],[c_1470,c_620]) ).
tff(c_1494,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_90,c_1478]) ).
tff(c_1496,plain,
v != u,
inference(splitRight,[status(thm)],[c_1197]) ).
tff(c_88,plain,
! [U_156,V_157] : ( reflection(reflection(U_156,V_157),V_157) = U_156 ),
inference(cnfTransformation,[status(thm)],[f_393]) ).
tff(c_225,plain,
! [U_318,V_319] : between(U_318,V_319,reflection(U_318,V_319)),
inference(cnfTransformation,[status(thm)],[f_328]) ).
tff(c_228,plain,
! [U_156,V_157] : between(reflection(U_156,V_157),V_157,U_156),
inference(superposition,[status(thm),theory(equality)],[c_88,c_225]) ).
tff(c_1610,plain,
! [W_448,V_449,U_450,X_451] :
( ( W_448 = V_449 )
| between(U_450,V_449,X_451)
| ~ between(V_449,W_448,X_451)
| ~ between(U_450,V_449,W_448) ),
inference(cnfTransformation,[status(thm)],[f_482]) ).
tff(c_1626,plain,
! [U_450] :
( ( v = u )
| between(U_450,u,w)
| ~ between(U_450,u,v) ),
inference(resolution,[status(thm)],[c_166,c_1610]) ).
tff(c_1648,plain,
! [U_452] :
( between(U_452,u,w)
| ~ between(U_452,u,v) ),
inference(negUnitSimplification,[status(thm)],[c_1496,c_1626]) ).
tff(c_94,plain,
! [W_166,V_165,U_164] :
( between(W_166,V_165,U_164)
| ~ between(U_164,V_165,W_166) ),
inference(cnfTransformation,[status(thm)],[f_408]) ).
tff(c_2695,plain,
! [U_503] :
( between(w,u,U_503)
| ~ between(U_503,u,v) ),
inference(resolution,[status(thm)],[c_1648,c_94]) ).
tff(c_2706,plain,
between(w,u,reflection(v,u)),
inference(resolution,[status(thm)],[c_228,c_2695]) ).
tff(c_2809,plain,
between(reflection(v,u),u,w),
inference(resolution,[status(thm)],[c_2706,c_94]) ).
tff(c_170,plain,
w != v,
inference(cnfTransformation,[status(thm)],[f_715]) ).
tff(c_168,plain,
equidistant(u,v,u,w),
inference(cnfTransformation,[status(thm)],[f_713]) ).
tff(c_3711,plain,
! [X_547,W_548,V_549,U_550] :
( ( X_547 = W_548 )
| ( V_549 = U_550 )
| ~ equidistant(V_549,W_548,V_549,X_547)
| ~ between(U_550,V_549,X_547)
| ~ between(U_550,V_549,W_548) ),
inference(cnfTransformation,[status(thm)],[f_371]) ).
tff(c_3742,plain,
! [U_550] :
( ( w = v )
| ( u = U_550 )
| ~ between(U_550,u,w)
| ~ between(U_550,u,v) ),
inference(resolution,[status(thm)],[c_168,c_3711]) ).
tff(c_7352,plain,
! [U_739] :
( ( u = U_739 )
| ~ between(U_739,u,w)
| ~ between(U_739,u,v) ),
inference(negUnitSimplification,[status(thm)],[c_170,c_3742]) ).
tff(c_7358,plain,
( ( reflection(v,u) = u )
| ~ between(reflection(v,u),u,v) ),
inference(resolution,[status(thm)],[c_2809,c_7352]) ).
tff(c_7383,plain,
reflection(v,u) = u,
inference(demodulation,[status(thm),theory(equality)],[c_228,c_7358]) ).
tff(c_72,plain,
! [V_129,U_130] :
( ( V_129 = U_130 )
| ( reflection(U_130,V_129) != V_129 ) ),
inference(cnfTransformation,[status(thm)],[f_342]) ).
tff(c_7450,plain,
v = u,
inference(superposition,[status(thm),theory(equality)],[c_7383,c_72]) ).
tff(c_7466,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1496,c_7450]) ).
tff(c_7467,plain,
v = u,
inference(splitRight,[status(thm)],[c_421]) ).
tff(c_479,plain,
! [V_368,U_369,W_370] :
( ( V_368 = U_369 )
| ~ between(V_368,U_369,W_370)
| ~ between(U_369,V_368,W_370) ),
inference(cnfTransformation,[status(thm)],[f_418]) ).
tff(c_503,plain,
( ( v = u )
| ~ between(v,u,w) ),
inference(resolution,[status(thm)],[c_166,c_479]) ).
tff(c_532,plain,
~ between(v,u,w),
inference(splitLeft,[status(thm)],[c_503]) ).
tff(c_7473,plain,
~ between(u,u,w),
inference(demodulation,[status(thm),theory(equality)],[c_7467,c_532]) ).
tff(c_7484,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_96,c_7473]) ).
tff(c_7485,plain,
v = u,
inference(splitRight,[status(thm)],[c_503]) ).
tff(c_7493,plain,
w != u,
inference(demodulation,[status(thm),theory(equality)],[c_7485,c_170]) ).
tff(c_7491,plain,
equidistant(u,u,u,w),
inference(demodulation,[status(thm),theory(equality)],[c_7485,c_168]) ).
tff(c_54,plain,
! [X_103,W_102,U_100,V_101] :
( equidistant(X_103,W_102,U_100,V_101)
| ~ equidistant(U_100,V_101,W_102,X_103) ),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_7529,plain,
equidistant(w,u,u,u),
inference(resolution,[status(thm)],[c_7491,c_54]) ).
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_72]) ).
tff(c_7583,plain,
w = u,
inference(resolution,[status(thm)],[c_7529,c_6]) ).
tff(c_7588,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_7493,c_7583]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO053-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.07/0.13 % 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
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 7 19:22:40 EDT 2025
% 0.13/0.34 % CPUTime :
% 11.49/3.75 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.49/3.76
% 11.49/3.76 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------