%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP045-2 : 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 : n016.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 06:24:52 PM UTC 2025
% Result : Unsatisfiable 8.98s 3.28s
% Output : CNFRefutation 8.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 36 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 72 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 75 ( 39 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 75 ( 75 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > equalish > multiply > #nlpp > inverse > result > identity > c > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $i ).
tff(product,type,
product: ( $i * $i * $i ) > $o ).
tff(inverse,type,
inverse: $i > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(b,type,
b: $i ).
tff(identity,type,
identity: $i ).
tff(equalish,type,
equalish: ( $i * $i ) > $o ).
tff(result,type,
result: $i ).
tff(c,type,
c: $i ).
tff(f_98,axiom,
equalish(a,b),
file(unknown,unknown) ).
tff(f_51,axiom,
! [X] : product(identity,X,X),
file(unknown,unknown) ).
tff(f_65,axiom,
! [X,Y,Z,W] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| equalish(Z,W) ),
file(unknown,unknown) ).
tff(f_53,axiom,
! [X] : product(inverse(X),X,identity),
file(unknown,unknown) ).
tff(f_95,axiom,
! [X,Y,W,Z] :
( ~ equalish(X,Y)
| ~ product(W,Z,X)
| product(W,Z,Y) ),
file(unknown,unknown) ).
tff(f_76,axiom,
! [W,U,Z,X,Y,V] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W)
| product(X,V,W) ),
file(unknown,unknown) ).
tff(f_87,axiom,
! [W,U,Z,X,Y,V] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) ),
file(unknown,unknown) ).
tff(f_99,axiom,
product(c,a,result),
file(unknown,unknown) ).
tff(f_101,axiom,
~ product(c,b,result),
file(unknown,unknown) ).
tff(c_16,plain,
equalish(a,b),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_2,plain,
! [X_1] : product(identity,X_1,X_1),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_24,plain,
! [Z_29,W_30,X_31,Y_32] :
( equalish(Z_29,W_30)
| ~ product(X_31,Y_32,W_30)
| ~ product(X_31,Y_32,Z_29) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_37,plain,
! [Z_33,X_34] :
( equalish(Z_33,X_34)
| ~ product(identity,X_34,Z_33) ),
inference(resolution,[status(thm)],[c_2,c_24]) ).
tff(c_46,plain,
! [X_1] : equalish(X_1,X_1),
inference(resolution,[status(thm)],[c_2,c_37]) ).
tff(c_4,plain,
! [X_2] : product(inverse(X_2),X_2,identity),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_48,plain,
! [W_36,Z_37,Y_38,X_39] :
( product(W_36,Z_37,Y_38)
| ~ product(W_36,Z_37,X_39)
| ~ equalish(X_39,Y_38) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_58,plain,
! [X_2,Y_38] :
( product(inverse(X_2),X_2,Y_38)
| ~ equalish(identity,Y_38) ),
inference(resolution,[status(thm)],[c_4,c_48]) ).
tff(c_137,plain,
! [V_57,W_54,X_55,Z_59,U_58,Y_56] :
( product(X_55,V_57,W_54)
| ~ product(U_58,Z_59,W_54)
| ~ product(Y_56,Z_59,V_57)
| ~ product(X_55,Y_56,U_58) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_803,plain,
! [X_106,V_107,X_108,Y_109] :
( product(X_106,V_107,X_108)
| ~ product(Y_109,X_108,V_107)
| ~ product(X_106,Y_109,identity) ),
inference(resolution,[status(thm)],[c_2,c_137]) ).
tff(c_1902,plain,
! [X_157,X_158] :
( product(X_157,identity,X_158)
| ~ product(X_157,inverse(X_158),identity) ),
inference(resolution,[status(thm)],[c_4,c_803]) ).
tff(c_1922,plain,
! [X_158] :
( product(inverse(inverse(X_158)),identity,X_158)
| ~ equalish(identity,identity) ),
inference(resolution,[status(thm)],[c_58,c_1902]) ).
tff(c_1940,plain,
! [X_159] : product(inverse(inverse(X_159)),identity,X_159),
inference(demodulation,[status(thm),theory(equality)],[c_46,c_1922]) ).
tff(c_93,plain,
! [W_46,Z_47,X_48,Y_51,U_49,V_50] :
( product(U_49,Z_47,W_46)
| ~ product(X_48,V_50,W_46)
| ~ product(Y_51,Z_47,V_50)
| ~ product(X_48,Y_51,U_49) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_1250,plain,
! [U_127,Z_128,Y_129,X_130] :
( product(U_127,Z_128,identity)
| ~ product(Y_129,Z_128,X_130)
| ~ product(inverse(X_130),Y_129,U_127) ),
inference(resolution,[status(thm)],[c_4,c_93]) ).
tff(c_1318,plain,
! [U_127,X_1] :
( product(U_127,X_1,identity)
| ~ product(inverse(X_1),identity,U_127) ),
inference(resolution,[status(thm)],[c_2,c_1250]) ).
tff(c_1994,plain,
! [X_160] : product(X_160,inverse(X_160),identity),
inference(resolution,[status(thm)],[c_1940,c_1318]) ).
tff(c_855,plain,
! [X_106,X_2] :
( product(X_106,identity,X_2)
| ~ product(X_106,inverse(X_2),identity) ),
inference(resolution,[status(thm)],[c_4,c_803]) ).
tff(c_2030,plain,
! [X_160] : product(X_160,identity,X_160),
inference(resolution,[status(thm)],[c_1994,c_855]) ).
tff(c_59,plain,
! [X_1,Y_38] :
( product(identity,X_1,Y_38)
| ~ equalish(X_1,Y_38) ),
inference(resolution,[status(thm)],[c_2,c_48]) ).
tff(c_18,plain,
product(c,a,result),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_470,plain,
! [X_88,V_89,Y_90] :
( product(X_88,V_89,result)
| ~ product(Y_90,a,V_89)
| ~ product(X_88,Y_90,c) ),
inference(resolution,[status(thm)],[c_18,c_137]) ).
tff(c_8809,plain,
! [X_281,Y_282] :
( product(X_281,Y_282,result)
| ~ product(X_281,identity,c)
| ~ equalish(a,Y_282) ),
inference(resolution,[status(thm)],[c_59,c_470]) ).
tff(c_8876,plain,
! [Y_283] :
( product(c,Y_283,result)
| ~ equalish(a,Y_283) ),
inference(resolution,[status(thm)],[c_2030,c_8809]) ).
tff(c_20,plain,
~ product(c,b,result),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_8924,plain,
~ equalish(a,b),
inference(resolution,[status(thm)],[c_8876,c_20]) ).
tff(c_8953,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_8924]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP045-2 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.13 % 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
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 7 21:13:38 EDT 2025
% 0.12/0.34 % CPUTime :
% 8.98/3.28 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.98/3.28
% 8.98/3.28 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------