%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP170-2 : 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/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 : n021.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 06:25:25 PM UTC 2025
% Result : Unsatisfiable 48.52s 35.07s
% Output : CNFRefutation 48.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 56 ( 56 unt; 0 typ; 0 def)
% Number of atoms : 56 ( 55 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 90 ( 90 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > least_upper_bound > greatest_lower_bound > #nlpp > inverse > identity > d > c > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(greatest_lower_bound,type,
greatest_lower_bound: ( $i * $i ) > $i ).
tff(least_upper_bound,type,
least_upper_bound: ( $i * $i ) > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(b,type,
b: $i ).
tff(d,type,
d: $i ).
tff(identity,type,
identity: $i ).
tff(c,type,
c: $i ).
tff(f_118,axiom,
greatest_lower_bound(multiply(a,c),multiply(b,d)) != multiply(a,c),
file(unknown,unknown) ).
tff(f_60,axiom,
! [X] : ( multiply(inverse(X),X) = identity ),
file(unknown,unknown) ).
tff(f_56,axiom,
! [X] : ( multiply(identity,X) = X ),
file(unknown,unknown) ).
tff(f_63,axiom,
! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_91,axiom,
! [X,Y] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
file(unknown,unknown) ).
tff(f_116,axiom,
greatest_lower_bound(c,d) = c,
file(unknown,unknown) ).
tff(f_89,axiom,
! [X,Y] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
file(unknown,unknown) ).
tff(f_101,axiom,
! [X,Y] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
file(unknown,unknown) ).
tff(f_115,axiom,
greatest_lower_bound(a,b) = a,
file(unknown,unknown) ).
tff(f_108,axiom,
! [X,Y,Z] : ( multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ),
file(unknown,unknown) ).
tff(f_112,axiom,
! [Y,Z,X] : ( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ),
file(unknown,unknown) ).
tff(f_95,axiom,
! [X,Y,Z] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ),
file(unknown,unknown) ).
tff(f_106,axiom,
! [X,Y,Z] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ),
file(unknown,unknown) ).
tff(f_103,axiom,
! [X,Y] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
file(unknown,unknown) ).
tff(c_36,plain,
greatest_lower_bound(multiply(a,c),multiply(b,d)) != multiply(a,c),
inference(cnfTransformation,[status(thm)],[f_118]) ).
tff(c_4,plain,
! [X_2] : ( multiply(inverse(X_2),X_2) = identity ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_2,plain,
! [X_1] : ( multiply(identity,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_432,plain,
! [X_53,Y_54,Z_55] : ( multiply(multiply(X_53,Y_54),Z_55) = multiply(X_53,multiply(Y_54,Z_55)) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_447,plain,
! [X_2,Z_55] : ( multiply(inverse(X_2),multiply(X_2,Z_55)) = multiply(identity,Z_55) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_432]) ).
tff(c_474,plain,
! [X_56,Z_57] : ( multiply(inverse(X_56),multiply(X_56,Z_57)) = Z_57 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_447]) ).
tff(c_495,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_474]) ).
tff(c_455,plain,
! [X_2,Z_55] : ( multiply(inverse(X_2),multiply(X_2,Z_55)) = Z_55 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_447]) ).
tff(c_1991,plain,
! [X_93,Z_94] : ( multiply(inverse(inverse(X_93)),Z_94) = multiply(X_93,Z_94) ),
inference(superposition,[status(thm),theory(equality)],[c_474,c_455]) ).
tff(c_2078,plain,
! [X_95] : ( multiply(X_95,identity) = X_95 ),
inference(superposition,[status(thm),theory(equality)],[c_1991,c_495]) ).
tff(c_2156,plain,
! [X_2] : ( inverse(inverse(X_2)) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_495,c_2078]) ).
tff(c_10,plain,
! [Y_9,X_8] : ( least_upper_bound(Y_9,X_8) = least_upper_bound(X_8,Y_9) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_34,plain,
greatest_lower_bound(c,d) = c,
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_8,plain,
! [Y_7,X_6] : ( greatest_lower_bound(Y_7,X_6) = greatest_lower_bound(X_6,Y_7) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_164,plain,
! [X_44,Y_45] : ( least_upper_bound(X_44,greatest_lower_bound(X_44,Y_45)) = X_44 ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_238,plain,
! [X_48,Y_49] : ( least_upper_bound(X_48,greatest_lower_bound(Y_49,X_48)) = X_48 ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_164]) ).
tff(c_279,plain,
least_upper_bound(d,c) = d,
inference(superposition,[status(thm),theory(equality)],[c_34,c_238]) ).
tff(c_328,plain,
least_upper_bound(c,d) = d,
inference(superposition,[status(thm),theory(equality)],[c_10,c_279]) ).
tff(c_6,plain,
! [X_3,Y_4,Z_5] : ( multiply(multiply(X_3,Y_4),Z_5) = multiply(X_3,multiply(Y_4,Z_5)) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_32,plain,
greatest_lower_bound(a,b) = a,
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_1151,plain,
! [X_76,Y_77,Z_78] : ( greatest_lower_bound(multiply(X_76,Y_77),multiply(X_76,Z_78)) = multiply(X_76,greatest_lower_bound(Y_77,Z_78)) ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_1212,plain,
! [X_2,Y_77] : ( multiply(inverse(X_2),greatest_lower_bound(Y_77,X_2)) = greatest_lower_bound(multiply(inverse(X_2),Y_77),identity) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_1151]) ).
tff(c_38797,plain,
! [X_319,Y_320] : ( multiply(inverse(X_319),greatest_lower_bound(Y_320,X_319)) = greatest_lower_bound(identity,multiply(inverse(X_319),Y_320)) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_1212]) ).
tff(c_39110,plain,
greatest_lower_bound(identity,multiply(inverse(b),a)) = multiply(inverse(b),a),
inference(superposition,[status(thm),theory(equality)],[c_32,c_38797]) ).
tff(c_1298,plain,
! [Y_80,X_81,Z_82] : ( greatest_lower_bound(multiply(Y_80,X_81),multiply(Z_82,X_81)) = multiply(greatest_lower_bound(Y_80,Z_82),X_81) ),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_20,plain,
! [X_18,Y_19] : ( least_upper_bound(X_18,greatest_lower_bound(X_18,Y_19)) = X_18 ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_1314,plain,
! [Y_80,X_81,Z_82] : ( least_upper_bound(multiply(Y_80,X_81),multiply(greatest_lower_bound(Y_80,Z_82),X_81)) = multiply(Y_80,X_81) ),
inference(superposition,[status(thm),theory(equality)],[c_1298,c_20]) ).
tff(c_101440,plain,
! [X_81] : ( least_upper_bound(multiply(identity,X_81),multiply(multiply(inverse(b),a),X_81)) = multiply(identity,X_81) ),
inference(superposition,[status(thm),theory(equality)],[c_39110,c_1314]) ).
tff(c_104241,plain,
! [X_517] : ( least_upper_bound(X_517,multiply(inverse(b),multiply(a,X_517))) = X_517 ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_2,c_2,c_101440]) ).
tff(c_538,plain,
! [X_59,Y_60,Z_61] : ( least_upper_bound(least_upper_bound(X_59,Y_60),Z_61) = least_upper_bound(X_59,least_upper_bound(Y_60,Z_61)) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_4919,plain,
! [Z_128,X_129,Y_130] : ( least_upper_bound(Z_128,least_upper_bound(X_129,Y_130)) = least_upper_bound(X_129,least_upper_bound(Y_130,Z_128)) ),
inference(superposition,[status(thm),theory(equality)],[c_538,c_10]) ).
tff(c_5234,plain,
! [Z_128] : ( least_upper_bound(d,least_upper_bound(c,Z_128)) = least_upper_bound(Z_128,d) ),
inference(superposition,[status(thm),theory(equality)],[c_279,c_4919]) ).
tff(c_104432,plain,
least_upper_bound(multiply(inverse(b),multiply(a,c)),d) = least_upper_bound(d,c),
inference(superposition,[status(thm),theory(equality)],[c_104241,c_5234]) ).
tff(c_104675,plain,
least_upper_bound(multiply(inverse(b),multiply(a,c)),d) = d,
inference(demodulation,[status(thm),theory(equality)],[c_328,c_10,c_104432]) ).
tff(c_735,plain,
! [X_65,Y_66,Z_67] : ( least_upper_bound(multiply(X_65,Y_66),multiply(X_65,Z_67)) = multiply(X_65,least_upper_bound(Y_66,Z_67)) ),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_22,plain,
! [X_20,Y_21] : ( greatest_lower_bound(X_20,least_upper_bound(X_20,Y_21)) = X_20 ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_42578,plain,
! [X_332,Y_333,Z_334] : ( greatest_lower_bound(multiply(X_332,Y_333),multiply(X_332,least_upper_bound(Y_333,Z_334))) = multiply(X_332,Y_333) ),
inference(superposition,[status(thm),theory(equality)],[c_735,c_22]) ).
tff(c_42983,plain,
! [Z_55,X_2,Z_334] : ( greatest_lower_bound(Z_55,multiply(inverse(X_2),least_upper_bound(multiply(X_2,Z_55),Z_334))) = multiply(inverse(X_2),multiply(X_2,Z_55)) ),
inference(superposition,[status(thm),theory(equality)],[c_455,c_42578]) ).
tff(c_210967,plain,
! [Z_730,X_731,Z_732] : ( greatest_lower_bound(Z_730,multiply(inverse(X_731),least_upper_bound(multiply(X_731,Z_730),Z_732))) = Z_730 ),
inference(demodulation,[status(thm),theory(equality)],[c_455,c_42983]) ).
tff(c_211597,plain,
greatest_lower_bound(multiply(a,c),multiply(inverse(inverse(b)),d)) = multiply(a,c),
inference(superposition,[status(thm),theory(equality)],[c_104675,c_210967]) ).
tff(c_212195,plain,
greatest_lower_bound(multiply(a,c),multiply(b,d)) = multiply(a,c),
inference(demodulation,[status(thm),theory(equality)],[c_2156,c_211597]) ).
tff(c_212197,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_36,c_212195]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP170-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.06/0.13 % 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
% 0.13/0.34 % Computer : n021.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 21:31:13 EDT 2025
% 0.13/0.34 % CPUTime :
% 48.52/35.07 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 48.52/35.09
% 48.52/35.09 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------