%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP510-1 : TPTP v9.0.0. Released v2.6.0.
% 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 : n031.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 06:26:23 PM UTC 2025
% Result : Unsatisfiable 4.09s 2.09s
% Output : CNFRefutation 4.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 25 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 24 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 53 ( 53 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > #nlpp > inverse > b2 > a2
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(b2,type,
b2: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(a2,type,
a2: $i ).
tff(f_24,axiom,
! [A,B,C] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B ),
file(unknown,unknown) ).
tff(f_26,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file(unknown,unknown) ).
tff(c_2,plain,
! [A_1,B_2,C_3] : ( multiply(multiply(multiply(A_1,B_2),C_3),inverse(multiply(A_1,C_3))) = B_2 ),
inference(cnfTransformation,[status(thm)],[f_24]) ).
tff(c_5,plain,
! [A_4,B_5,C_6] : ( multiply(multiply(multiply(A_4,B_5),C_6),inverse(multiply(A_4,C_6))) = B_5 ),
inference(cnfTransformation,[status(thm)],[f_24]) ).
tff(c_26,plain,
! [A_1,B_2,C_3,B_5] : ( multiply(multiply(multiply(multiply(multiply(A_1,B_2),C_3),B_5),inverse(multiply(A_1,C_3))),inverse(B_2)) = B_5 ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_5]) ).
tff(c_70,plain,
! [A_10,B_11,C_12,B_13] : ( multiply(multiply(multiply(multiply(multiply(A_10,B_11),C_12),B_13),inverse(multiply(A_10,C_12))),inverse(B_11)) = B_13 ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_5]) ).
tff(c_109,plain,
! [B_5,A_1,B_2,C_3] : ( multiply(multiply(B_5,inverse(multiply(multiply(multiply(A_1,B_2),C_3),inverse(multiply(A_1,C_3))))),inverse(B_5)) = inverse(B_2) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_70]) ).
tff(c_256,plain,
! [B_18,B_19] : ( multiply(multiply(B_18,inverse(B_19)),inverse(B_18)) = inverse(B_19) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_109]) ).
tff(c_144,plain,
! [B_5,B_2] : ( multiply(multiply(B_5,inverse(B_2)),inverse(B_5)) = inverse(B_2) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_109]) ).
tff(c_382,plain,
! [B_22,B_23] : ( multiply(inverse(B_22),inverse(multiply(B_23,inverse(B_22)))) = inverse(B_23) ),
inference(superposition,[status(thm),theory(equality)],[c_256,c_144]) ).
tff(c_11,plain,
! [B_5,A_4,C_6] : ( multiply(B_5,inverse(multiply(multiply(A_4,B_5),inverse(multiply(A_4,C_6))))) = C_6 ),
inference(superposition,[status(thm),theory(equality)],[c_5,c_2]) ).
tff(c_417,plain,
! [A_4,C_6] : ( inverse(multiply(A_4,inverse(multiply(A_4,C_6)))) = C_6 ),
inference(superposition,[status(thm),theory(equality)],[c_382,c_11]) ).
tff(c_259,plain,
! [B_19,B_18] : ( multiply(inverse(B_19),inverse(multiply(B_18,inverse(B_19)))) = inverse(B_18) ),
inference(superposition,[status(thm),theory(equality)],[c_256,c_144]) ).
tff(c_460,plain,
! [A_24,C_25] : ( inverse(multiply(A_24,inverse(multiply(A_24,C_25)))) = C_25 ),
inference(superposition,[status(thm),theory(equality)],[c_382,c_11]) ).
tff(c_548,plain,
! [B_26] : ( inverse(inverse(inverse(B_26))) = inverse(B_26) ),
inference(superposition,[status(thm),theory(equality)],[c_259,c_460]) ).
tff(c_590,plain,
! [A_4,C_6] : ( inverse(multiply(A_4,inverse(multiply(A_4,C_6)))) = inverse(inverse(C_6)) ),
inference(superposition,[status(thm),theory(equality)],[c_417,c_548]) ).
tff(c_601,plain,
! [C_6] : ( inverse(inverse(C_6)) = C_6 ),
inference(demodulation,[status(thm),theory(equality)],[c_417,c_590]) ).
tff(c_484,plain,
! [B_5,C_25,A_24] : ( multiply(multiply(B_5,C_25),inverse(B_5)) = inverse(multiply(A_24,inverse(multiply(A_24,C_25)))) ),
inference(superposition,[status(thm),theory(equality)],[c_460,c_144]) ).
tff(c_649,plain,
! [B_28,C_29] : ( multiply(multiply(B_28,C_29),inverse(B_28)) = C_29 ),
inference(demodulation,[status(thm),theory(equality)],[c_417,c_484]) ).
tff(c_822,plain,
! [C_32,B_33] : ( multiply(C_32,inverse(multiply(B_33,inverse(B_33)))) = C_32 ),
inference(superposition,[status(thm),theory(equality)],[c_649,c_2]) ).
tff(c_544,plain,
! [B_5,C_25] : ( multiply(multiply(B_5,C_25),inverse(B_5)) = C_25 ),
inference(demodulation,[status(thm),theory(equality)],[c_417,c_484]) ).
tff(c_993,plain,
! [B_34,C_35] : ( multiply(multiply(B_34,inverse(B_34)),C_35) = C_35 ),
inference(superposition,[status(thm),theory(equality)],[c_822,c_544]) ).
tff(c_1117,plain,
! [C_6,C_35] : ( multiply(multiply(inverse(C_6),C_6),C_35) = C_35 ),
inference(superposition,[status(thm),theory(equality)],[c_601,c_993]) ).
tff(c_4,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_1387,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1117,c_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP510-1 : TPTP v9.0.0. Released v2.6.0.
% 0.07/0.14 % 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
% 0.13/0.35 % Computer : n031.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 7 21:53:52 EDT 2025
% 0.13/0.35 % CPUTime :
% 4.09/2.09 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.09/2.10
% 4.09/2.10 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------