%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP515-1 : 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 : n022.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 06:26:24 PM UTC 2025
% Result : Unsatisfiable 20.49s 9.50s
% Output : CNFRefutation 20.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of formulae : 34 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 34 ( 33 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 8 ( 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 78 ( 78 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > #nlpp > inverse > c3 > b3 > a3
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a3,type,
a3: $i ).
tff(c3,type,
c3: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(b3,type,
b3: $i ).
tff(f_23,axiom,
! [A,B,C] : ( multiply(A,multiply(multiply(B,C),inverse(multiply(A,C)))) = B ),
file(unknown,unknown) ).
tff(f_25,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file(unknown,unknown) ).
tff(c_2,plain,
! [A_1,B_2,C_3] : ( multiply(A_1,multiply(multiply(B_2,C_3),inverse(multiply(A_1,C_3)))) = B_2 ),
inference(cnfTransformation,[status(thm)],[f_23]) ).
tff(c_5,plain,
! [A_4,B_5,C_6] : ( multiply(A_4,multiply(multiply(B_5,C_6),inverse(multiply(A_4,C_6)))) = B_5 ),
inference(cnfTransformation,[status(thm)],[f_23]) ).
tff(c_26,plain,
! [A_7,B_8,C_9,A_10] : ( multiply(A_7,multiply(B_8,inverse(multiply(A_7,multiply(multiply(B_8,C_9),inverse(multiply(A_10,C_9))))))) = A_10 ),
inference(superposition,[status(thm),theory(equality)],[c_5,c_2]) ).
tff(c_62,plain,
! [A_11,B_12] : ( multiply(A_11,multiply(B_12,inverse(B_12))) = A_11 ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_26]) ).
tff(c_8,plain,
! [A_1,B_5,C_6,A_4] : ( multiply(A_1,multiply(B_5,inverse(multiply(A_1,multiply(multiply(B_5,C_6),inverse(multiply(A_4,C_6))))))) = A_4 ),
inference(superposition,[status(thm),theory(equality)],[c_5,c_2]) ).
tff(c_101,plain,
! [A_13,B_14] : ( multiply(A_13,multiply(B_14,inverse(A_13))) = B_14 ),
inference(superposition,[status(thm),theory(equality)],[c_62,c_8]) ).
tff(c_220,plain,
! [A_19,C_20,B_21] : ( multiply(multiply(A_19,C_20),multiply(B_21,inverse(multiply(B_21,C_20)))) = A_19 ),
inference(superposition,[status(thm),theory(equality)],[c_101,c_8]) ).
tff(c_497,plain,
! [A_28,C_29,B_30] : ( multiply(multiply(A_28,C_29),multiply(B_30,inverse(A_28))) = multiply(B_30,C_29) ),
inference(superposition,[status(thm),theory(equality)],[c_220,c_8]) ).
tff(c_75,plain,
! [A_11,B_5] : ( multiply(A_11,multiply(B_5,inverse(A_11))) = B_5 ),
inference(superposition,[status(thm),theory(equality)],[c_62,c_8]) ).
tff(c_136,plain,
! [A_15,B_16,B_17,C_18] : ( multiply(A_15,multiply(multiply(B_16,multiply(multiply(B_17,C_18),inverse(multiply(A_15,C_18)))),inverse(B_17))) = B_16 ),
inference(superposition,[status(thm),theory(equality)],[c_5,c_2]) ).
tff(c_180,plain,
! [A_15,B_17,C_18] : ( multiply(A_15,multiply(multiply(B_17,C_18),inverse(B_17))) = multiply(A_15,C_18) ),
inference(superposition,[status(thm),theory(equality)],[c_75,c_136]) ).
tff(c_614,plain,
! [A_31,C_33,C_32] : ( multiply(multiply(A_31,C_33),C_32) = multiply(multiply(A_31,C_32),C_33) ),
inference(superposition,[status(thm),theory(equality)],[c_497,c_180]) ).
tff(c_880,plain,
! [A_34,A_35,C_36] : ( multiply(A_34,multiply(multiply(A_35,inverse(A_34)),C_36)) = multiply(A_35,C_36) ),
inference(superposition,[status(thm),theory(equality)],[c_614,c_75]) ).
tff(c_1060,plain,
! [A_37,A_38] : ( multiply(A_37,inverse(multiply(A_38,inverse(A_38)))) = A_37 ),
inference(superposition,[status(thm),theory(equality)],[c_880,c_2]) ).
tff(c_118,plain,
! [A_4,C_6,B_5] : ( multiply(multiply(A_4,C_6),multiply(B_5,inverse(multiply(B_5,C_6)))) = A_4 ),
inference(superposition,[status(thm),theory(equality)],[c_101,c_8]) ).
tff(c_1179,plain,
! [A_39,A_40] : ( multiply(multiply(A_39,inverse(A_40)),A_40) = A_39 ),
inference(superposition,[status(thm),theory(equality)],[c_1060,c_118]) ).
tff(c_718,plain,
! [A_11,A_31,C_33] : ( multiply(A_11,multiply(multiply(A_31,inverse(A_11)),C_33)) = multiply(A_31,C_33) ),
inference(superposition,[status(thm),theory(equality)],[c_614,c_75]) ).
tff(c_1197,plain,
! [A_40,A_39] : ( multiply(A_40,A_39) = multiply(A_39,A_40) ),
inference(superposition,[status(thm),theory(equality)],[c_1179,c_718]) ).
tff(c_510,plain,
! [A_28,C_29,C_18] : ( multiply(multiply(A_28,C_29),C_18) = multiply(multiply(A_28,C_18),C_29) ),
inference(superposition,[status(thm),theory(equality)],[c_497,c_180]) ).
tff(c_1829,plain,
! [A_45,A_46] : ( multiply(multiply(A_45,A_46),inverse(A_46)) = A_45 ),
inference(superposition,[status(thm),theory(equality)],[c_1179,c_510]) ).
tff(c_1117,plain,
! [A_38,A_37] : ( multiply(multiply(A_38,inverse(A_38)),A_37) = A_37 ),
inference(superposition,[status(thm),theory(equality)],[c_1060,c_75]) ).
tff(c_1839,plain,
! [A_45] : ( inverse(inverse(A_45)) = A_45 ),
inference(superposition,[status(thm),theory(equality)],[c_1829,c_1117]) ).
tff(c_1580,plain,
! [A_43,A_44] : ( multiply(multiply(A_43,inverse(A_43)),A_44) = A_44 ),
inference(superposition,[status(thm),theory(equality)],[c_1060,c_75]) ).
tff(c_1792,plain,
! [B_2,C_3,A_43] : ( multiply(multiply(B_2,C_3),inverse(multiply(multiply(A_43,inverse(A_43)),C_3))) = B_2 ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1580]) ).
tff(c_2476,plain,
! [C_54,B_55] : ( multiply(inverse(C_54),multiply(B_55,C_54)) = B_55 ),
inference(demodulation,[status(thm),theory(equality)],[c_1197,c_1117,c_1792]) ).
tff(c_253,plain,
! [A_19,C_20,B_5] : ( multiply(multiply(A_19,C_20),multiply(B_5,inverse(A_19))) = multiply(B_5,C_20) ),
inference(superposition,[status(thm),theory(equality)],[c_220,c_8]) ).
tff(c_2511,plain,
! [B_55,B_5,C_54] : ( multiply(B_55,multiply(B_5,inverse(inverse(C_54)))) = multiply(B_5,multiply(B_55,C_54)) ),
inference(superposition,[status(thm),theory(equality)],[c_2476,c_253]) ).
tff(c_2622,plain,
! [B_55,B_5,C_54] : ( multiply(B_55,multiply(B_5,C_54)) = multiply(B_5,multiply(B_55,C_54)) ),
inference(demodulation,[status(thm),theory(equality)],[c_1839,c_2511]) ).
tff(c_4,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cnfTransformation,[status(thm)],[f_25]) ).
tff(c_1318,plain,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(demodulation,[status(thm),theory(equality)],[c_1197,c_4]) ).
tff(c_48756,plain,
multiply(a3,multiply(c3,b3)) != multiply(a3,multiply(b3,c3)),
inference(demodulation,[status(thm),theory(equality)],[c_2622,c_1318]) ).
tff(c_48759,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1197,c_48756]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP515-1 : TPTP v9.0.0. Released v2.6.0.
% 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 : n022.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 21:54:21 EDT 2025
% 0.13/0.34 % CPUTime :
% 20.49/9.50 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.49/9.50
% 20.49/9.50 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------