%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GEO026-2 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n032.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 06:13:30 PM UTC 2025
% Result : Unsatisfiable 9.08s 3.15s
% Output : CNFRefutation 9.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 28 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 68 ( 14 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 79 ( 39 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 1 ( 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 : 12 ( 12 usr; 7 con; 0-6 aty)
% Number of variables : 56 ( 56 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ equidistant > between > continuous > inner_pasch > euclid2 > euclid1 > extension > #nlpp > x > 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(x,type,
x: $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(euclid1,type,
euclid1: ( $i * $i * $i * $i * $i ) > $i ).
tff(between,type,
between: ( $i * $i * $i ) > $o ).
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_228,axiom,
w != x,
file(unknown,unknown) ).
tff(f_56,axiom,
! [X,Y] : equidistant(X,Y,Y,X),
file(unknown,unknown) ).
tff(f_65,axiom,
! [W,Z,X,Y,V,V2] :
( ~ equidistant(X,Y,Z,V)
| ~ equidistant(X,Y,V2,W)
| equidistant(Z,V,V2,W) ),
file(unknown,unknown) ).
tff(f_226,axiom,
u != v,
file(unknown,unknown) ).
tff(f_224,axiom,
equidistant(v,w,v,x),
file(unknown,unknown) ).
tff(f_222,axiom,
between(u,v,w),
file(unknown,unknown) ).
tff(f_223,axiom,
between(u,v,x),
file(unknown,unknown) ).
tff(f_101,axiom,
! [Y1,Z,X1,V1,X,Y,V,Z1] :
( ~ equidistant(X,Y,X1,Y1)
| ~ equidistant(Y,Z,Y1,Z1)
| ~ equidistant(X,V,X1,V1)
| ~ equidistant(Y,V,Y1,V1)
| ~ between(X,Y,Z)
| ~ between(X1,Y1,Z1)
| ( X = Y )
| equidistant(Z,V,Z1,V1) ),
file(unknown,unknown) ).
tff(f_71,axiom,
! [X,Y,Z] :
( ~ equidistant(X,Y,Z,Z)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(c_46,plain,
x != w,
inference(cnfTransformation,[status(thm)],[f_228]) ).
tff(c_2,plain,
! [X_1,Y_2] : equidistant(X_1,Y_2,Y_2,X_1),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_85,plain,
! [X_97,W_96,V2_93,Y_95,Z_94,V_92] :
( equidistant(Z_94,V_92,V2_93,W_96)
| ~ equidistant(X_97,Y_95,V2_93,W_96)
| ~ equidistant(X_97,Y_95,Z_94,V_92) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_124,plain,
! [Z_107,V_108,Y_109,X_110] :
( equidistant(Z_107,V_108,Y_109,X_110)
| ~ equidistant(X_110,Y_109,Z_107,V_108) ),
inference(resolution,[status(thm)],[c_2,c_85]) ).
tff(c_144,plain,
! [Y_2,X_1] : equidistant(Y_2,X_1,Y_2,X_1),
inference(resolution,[status(thm)],[c_2,c_124]) ).
tff(c_44,plain,
v != u,
inference(cnfTransformation,[status(thm)],[f_226]) ).
tff(c_42,plain,
equidistant(v,w,v,x),
inference(cnfTransformation,[status(thm)],[f_224]) ).
tff(c_38,plain,
between(u,v,w),
inference(cnfTransformation,[status(thm)],[f_222]) ).
tff(c_40,plain,
between(u,v,x),
inference(cnfTransformation,[status(thm)],[f_223]) ).
tff(c_586,plain,
! [Y_209,Y1_205,X1_206,Z1_202,V1_208,Z_203,X_207,V_204] :
( equidistant(Z_203,V_204,Z1_202,V1_208)
| ( Y_209 = X_207 )
| ~ between(X1_206,Y1_205,Z1_202)
| ~ between(X_207,Y_209,Z_203)
| ~ equidistant(Y_209,V_204,Y1_205,V1_208)
| ~ equidistant(X_207,V_204,X1_206,V1_208)
| ~ equidistant(Y_209,Z_203,Y1_205,Z1_202)
| ~ equidistant(X_207,Y_209,X1_206,Y1_205) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_2011,plain,
! [X_329,V1_327,Y_331,V_328,Z_330] :
( equidistant(Z_330,V_328,x,V1_327)
| ( Y_331 = X_329 )
| ~ between(X_329,Y_331,Z_330)
| ~ equidistant(Y_331,V_328,v,V1_327)
| ~ equidistant(X_329,V_328,u,V1_327)
| ~ equidistant(Y_331,Z_330,v,x)
| ~ equidistant(X_329,Y_331,u,v) ),
inference(resolution,[status(thm)],[c_40,c_586]) ).
tff(c_2037,plain,
! [V_328,V1_327] :
( equidistant(w,V_328,x,V1_327)
| ( v = u )
| ~ equidistant(v,V_328,v,V1_327)
| ~ equidistant(u,V_328,u,V1_327)
| ~ equidistant(v,w,v,x)
| ~ equidistant(u,v,u,v) ),
inference(resolution,[status(thm)],[c_38,c_2011]) ).
tff(c_2055,plain,
! [V_328,V1_327] :
( equidistant(w,V_328,x,V1_327)
| ( v = u )
| ~ equidistant(v,V_328,v,V1_327)
| ~ equidistant(u,V_328,u,V1_327) ),
inference(demodulation,[status(thm),theory(equality)],[c_144,c_42,c_2037]) ).
tff(c_6085,plain,
! [V_730,V1_731] :
( equidistant(w,V_730,x,V1_731)
| ~ equidistant(v,V_730,v,V1_731)
| ~ equidistant(u,V_730,u,V1_731) ),
inference(negUnitSimplification,[status(thm)],[c_44,c_2055]) ).
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_71]) ).
tff(c_6132,plain,
! [V_732] :
( ( w = V_732 )
| ~ equidistant(v,V_732,v,x)
| ~ equidistant(u,V_732,u,x) ),
inference(resolution,[status(thm)],[c_6085,c_6]) ).
tff(c_6180,plain,
( ( x = w )
| ~ equidistant(u,x,u,x) ),
inference(resolution,[status(thm)],[c_144,c_6132]) ).
tff(c_6201,plain,
x = w,
inference(demodulation,[status(thm),theory(equality)],[c_144,c_6180]) ).
tff(c_6203,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_6201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08 % Problem : GEO026-2 : TPTP v9.0.0. Released v1.0.0.
% 0.02/0.08 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.09/0.27 % Computer : n032.cluster.edu
% 0.09/0.27 % Model : x86_64 x86_64
% 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27 % Memory : 8042.1875MB
% 0.09/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.27 % CPULimit : 300
% 0.09/0.27 % WCLimit : 300
% 0.09/0.27 % DateTime : Mon Apr 7 19:19:16 EDT 2025
% 0.09/0.28 % CPUTime :
% 9.08/3.15 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.08/3.16
% 9.08/3.16 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------