TSTP Solution File: GRP402-1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP402-1 : TPTP v8.1.2. Released v2.5.0.
% 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 : n017.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 : Tue Aug 22 10:41:10 EDT 2023
% Result : Unsatisfiable 18.43s 7.07s
% Output : CNFRefutation 18.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 60 ( 42 unt; 5 typ; 0 def)
% Number of atoms : 68 ( 67 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 31 ( 18 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 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 : 124 (; 124 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > commutator > #nlpp > c > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(commutator,type,
commutator: ( $i * $i ) > $i ).
tff(b,type,
b: $i ).
tff(c,type,
c: $i ).
tff(f_91,axiom,
! [A,B] : ( multiply(A,B) = multiply(B,multiply(A,commutator(A,B))) ),
file(unknown,unknown) ).
tff(f_86,axiom,
! [A,B,C] :
( ( multiply(A,B) != multiply(A,C) )
| ( B = C ) ),
file(unknown,unknown) ).
tff(f_94,axiom,
! [A,B,C] : ( multiply(commutator(A,B),C) = multiply(C,commutator(A,B)) ),
file(unknown,unknown) ).
tff(f_53,axiom,
! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_81,axiom,
! [A,B,C] :
( ( multiply(A,B) != multiply(C,B) )
| ( A = C ) ),
file(unknown,unknown) ).
tff(f_97,axiom,
commutator(commutator(a,b),c) != commutator(a,commutator(b,c)),
file(unknown,unknown) ).
tff(c_84,plain,
! [B_24,A_25] : ( multiply(B_24,multiply(A_25,commutator(A_25,B_24))) = multiply(A_25,B_24) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_6,plain,
! [C_9,B_8,A_7] :
( ( C_9 = B_8 )
| ( multiply(A_7,C_9) != multiply(A_7,B_8) ) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_96,plain,
! [A_25,B_24,B_8] :
( ( multiply(A_25,commutator(A_25,B_24)) = B_8 )
| ( multiply(B_24,B_8) != multiply(A_25,B_24) ) ),
inference(superposition,[status(thm),theory(equality)],[c_84,c_6]) ).
tff(c_254,plain,
! [A_25] : ( multiply(A_25,commutator(A_25,A_25)) = A_25 ),
inference(reflexivity,[status(thm),theory(equality)],[c_96]) ).
tff(c_10,plain,
! [A_12,B_13,C_14] : ( multiply(commutator(A_12,B_13),C_14) = multiply(C_14,commutator(A_12,B_13)) ),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_105,plain,
! [X_26,Y_27,Z_28] : ( multiply(multiply(X_26,Y_27),Z_28) = multiply(X_26,multiply(Y_27,Z_28)) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_1185,plain,
! [A_76,B_77,X_78,Y_79] : ( multiply(commutator(A_76,B_77),multiply(X_78,Y_79)) = multiply(X_78,multiply(Y_79,commutator(A_76,B_77))) ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_105]) ).
tff(c_1497,plain,
! [A_80,X_81] : ( multiply(commutator(A_80,A_80),multiply(X_81,A_80)) = multiply(X_81,A_80) ),
inference(superposition,[status(thm),theory(equality)],[c_254,c_1185]) ).
tff(c_274,plain,
! [A_44] : ( multiply(A_44,commutator(A_44,A_44)) = A_44 ),
inference(reflexivity,[status(thm),theory(equality)],[c_96]) ).
tff(c_23,plain,
! [A_21,B_22,C_23] : ( multiply(commutator(A_21,B_22),C_23) = multiply(C_23,commutator(A_21,B_22)) ),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_4,plain,
! [C_6,A_4,B_5] :
( ( C_6 = A_4 )
| ( multiply(C_6,B_5) != multiply(A_4,B_5) ) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_46,plain,
! [A_21,B_22,A_4,C_23] :
( ( commutator(A_21,B_22) = A_4 )
| ( multiply(C_23,commutator(A_21,B_22)) != multiply(A_4,C_23) ) ),
inference(superposition,[status(thm),theory(equality)],[c_23,c_4]) ).
tff(c_291,plain,
! [A_44,A_4] :
( ( commutator(A_44,A_44) = A_4 )
| ( multiply(A_4,A_44) != A_44 ) ),
inference(superposition,[status(thm),theory(equality)],[c_274,c_46]) ).
tff(c_1649,plain,
! [X_81,A_80] : ( commutator(multiply(X_81,A_80),multiply(X_81,A_80)) = commutator(A_80,A_80) ),
inference(superposition,[status(thm),theory(equality)],[c_1497,c_291]) ).
tff(c_2,plain,
! [X_1,Y_2,Z_3] : ( multiply(multiply(X_1,Y_2),Z_3) = multiply(X_1,multiply(Y_2,Z_3)) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_456,plain,
! [A_57,Z_58] : ( multiply(A_57,multiply(commutator(A_57,A_57),Z_58)) = multiply(A_57,Z_58) ),
inference(superposition,[status(thm),theory(equality)],[c_274,c_2]) ).
tff(c_535,plain,
! [A_57] : ( multiply(A_57,commutator(commutator(A_57,A_57),commutator(A_57,A_57))) = multiply(A_57,commutator(A_57,A_57)) ),
inference(superposition,[status(thm),theory(equality)],[c_254,c_456]) ).
tff(c_687,plain,
! [A_61] : ( multiply(A_61,commutator(commutator(A_61,A_61),commutator(A_61,A_61))) = A_61 ),
inference(demodulation,[status(thm),theory(equality)],[c_254,c_535]) ).
tff(c_323,plain,
! [A_44,C_9] :
( ( commutator(A_44,A_44) = C_9 )
| ( multiply(A_44,C_9) != A_44 ) ),
inference(superposition,[status(thm),theory(equality)],[c_274,c_6]) ).
tff(c_764,plain,
! [A_61] : ( commutator(commutator(A_61,A_61),commutator(A_61,A_61)) = commutator(A_61,A_61) ),
inference(superposition,[status(thm),theory(equality)],[c_687,c_323]) ).
tff(c_555,plain,
! [B_13,C_14] : ( multiply(B_13,multiply(C_14,commutator(B_13,B_13))) = multiply(B_13,C_14) ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_456]) ).
tff(c_1664,plain,
! [X_82,A_83] : ( commutator(multiply(X_82,A_83),multiply(X_82,A_83)) = commutator(A_83,A_83) ),
inference(superposition,[status(thm),theory(equality)],[c_1497,c_291]) ).
tff(c_1763,plain,
! [C_14,B_13] : ( commutator(multiply(C_14,commutator(B_13,B_13)),multiply(C_14,commutator(B_13,B_13))) = commutator(multiply(B_13,C_14),multiply(B_13,multiply(C_14,commutator(B_13,B_13)))) ),
inference(superposition,[status(thm),theory(equality)],[c_555,c_1664]) ).
tff(c_1831,plain,
! [C_14,B_13] : ( commutator(C_14,C_14) = commutator(B_13,B_13) ),
inference(demodulation,[status(thm),theory(equality)],[c_1649,c_764,c_1649,c_555,c_1763]) ).
tff(c_1841,plain,
! [C_84,B_85] : ( commutator(C_84,C_84) = commutator(B_85,B_85) ),
inference(demodulation,[status(thm),theory(equality)],[c_1649,c_764,c_1649,c_555,c_1763]) ).
tff(c_1927,plain,
! [C_84,B_85] : ( multiply(C_84,commutator(B_85,B_85)) = C_84 ),
inference(superposition,[status(thm),theory(equality)],[c_1841,c_254]) ).
tff(c_8,plain,
! [B_11,A_10] : ( multiply(B_11,multiply(A_10,commutator(A_10,B_11))) = multiply(A_10,B_11) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_512,plain,
! [A_57] : ( multiply(A_57,commutator(commutator(A_57,A_57),A_57)) = multiply(commutator(A_57,A_57),A_57) ),
inference(superposition,[status(thm),theory(equality)],[c_456,c_8]) ).
tff(c_571,plain,
! [A_59] : ( multiply(A_59,commutator(commutator(A_59,A_59),A_59)) = A_59 ),
inference(demodulation,[status(thm),theory(equality)],[c_254,c_10,c_512]) ).
tff(c_645,plain,
! [A_59] : ( commutator(commutator(A_59,A_59),A_59) = commutator(A_59,A_59) ),
inference(superposition,[status(thm),theory(equality)],[c_571,c_323]) ).
tff(c_1900,plain,
! [C_84,B_85] : ( commutator(commutator(C_84,C_84),B_85) = commutator(B_85,B_85) ),
inference(superposition,[status(thm),theory(equality)],[c_1841,c_645]) ).
tff(c_2667,plain,
! [C_96,B_97] : ( commutator(commutator(C_96,C_96),B_97) = commutator(B_97,B_97) ),
inference(superposition,[status(thm),theory(equality)],[c_1841,c_645]) ).
tff(c_6285,plain,
! [C_155,B_156,B_157] : ( commutator(commutator(commutator(C_155,C_155),B_156),B_157) = commutator(B_157,B_157) ),
inference(superposition,[status(thm),theory(equality)],[c_1900,c_2667]) ).
tff(c_6483,plain,
! [C_155,B_156,B_157,C_14] : ( multiply(commutator(commutator(commutator(C_155,C_155),B_156),B_157),C_14) = multiply(C_14,commutator(B_157,B_157)) ),
inference(superposition,[status(thm),theory(equality)],[c_6285,c_10]) ).
tff(c_6630,plain,
! [C_155,B_156,B_157,C_14] : ( multiply(commutator(commutator(commutator(C_155,C_155),B_156),B_157),C_14) = C_14 ),
inference(demodulation,[status(thm),theory(equality)],[c_1927,c_6483]) ).
tff(c_155,plain,
! [A_12,B_13,X_26,Y_27] : ( multiply(commutator(A_12,B_13),multiply(X_26,Y_27)) = multiply(X_26,multiply(Y_27,commutator(A_12,B_13))) ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_105]) ).
tff(c_135,plain,
! [Z_28,C_9,X_26,Y_27] :
( ( Z_28 = C_9 )
| ( multiply(multiply(X_26,Y_27),C_9) != multiply(X_26,multiply(Y_27,Z_28)) ) ),
inference(superposition,[status(thm),theory(equality)],[c_105,c_6]) ).
tff(c_349,plain,
! [Z_47,C_48,X_49,Y_50] :
( ( Z_47 = C_48 )
| ( multiply(X_49,multiply(Y_50,Z_47)) != multiply(X_49,multiply(Y_50,C_48)) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_135]) ).
tff(c_29227,plain,
! [A_431,Z_432,X_433] :
( ( commutator(A_431,A_431) = Z_432 )
| ( multiply(X_433,multiply(A_431,Z_432)) != multiply(X_433,A_431) ) ),
inference(superposition,[status(thm),theory(equality)],[c_254,c_349]) ).
tff(c_31125,plain,
! [A_439,B_440] :
( ( commutator(A_439,B_440) = commutator(A_439,A_439) )
| ( multiply(B_440,A_439) != multiply(A_439,B_440) ) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_29227]) ).
tff(c_31181,plain,
! [A_12,B_13,X_26,Y_27] :
( ( commutator(commutator(A_12,B_13),multiply(X_26,Y_27)) = commutator(commutator(A_12,B_13),commutator(A_12,B_13)) )
| ( multiply(multiply(X_26,Y_27),commutator(A_12,B_13)) != multiply(X_26,multiply(Y_27,commutator(A_12,B_13))) ) ),
inference(superposition,[status(thm),theory(equality)],[c_155,c_31125]) ).
tff(c_39254,plain,
! [A_502,B_503,X_504,Y_505] : ( commutator(commutator(A_502,B_503),multiply(X_504,Y_505)) = commutator(B_503,B_503) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1831,c_31181]) ).
tff(c_39937,plain,
! [A_502,B_503,C_14] : ( commutator(commutator(A_502,B_503),C_14) = commutator(B_503,B_503) ),
inference(superposition,[status(thm),theory(equality)],[c_6630,c_39254]) ).
tff(c_31239,plain,
! [C_14,A_12,B_13] : ( commutator(C_14,commutator(A_12,B_13)) = commutator(C_14,C_14) ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_31125]) ).
tff(c_12,plain,
commutator(commutator(a,b),c) != commutator(a,commutator(b,c)),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_31242,plain,
commutator(commutator(a,b),c) != commutator(a,a),
inference(demodulation,[status(thm),theory(equality)],[c_31239,c_12]) ).
tff(c_40127,plain,
commutator(b,b) != commutator(a,a),
inference(demodulation,[status(thm),theory(equality)],[c_39937,c_31242]) ).
tff(c_41041,plain,
! [C_14] : ( commutator(a,a) != commutator(C_14,C_14) ),
inference(superposition,[status(thm),theory(equality)],[c_1831,c_40127]) ).
tff(c_41047,plain,
$false,
inference(reflexivity,[status(thm),theory(equality)],[c_41041]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP402-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.14 % 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
% 0.15/0.35 % Computer : n017.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 3 21:28:52 EDT 2023
% 0.15/0.35 % CPUTime :
% 18.43/7.07 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.43/7.08
% 18.43/7.08 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 18.53/7.11
% 18.53/7.11 Inference rules
% 18.53/7.11 ----------------------
% 18.53/7.11 #Ref : 42
% 18.53/7.11 #Sup : 11457
% 18.53/7.11 #Fact : 0
% 18.53/7.11 #Define : 0
% 18.53/7.11 #Split : 0
% 18.53/7.11 #Chain : 0
% 18.53/7.11 #Close : 0
% 18.53/7.11
% 18.53/7.11 Ordering : KBO
% 18.53/7.11
% 18.53/7.11 Simplification rules
% 18.53/7.11 ----------------------
% 18.53/7.11 #Subsume : 2973
% 18.53/7.11 #Demod : 7574
% 18.53/7.11 #Tautology : 2520
% 18.53/7.11 #SimpNegUnit : 0
% 18.53/7.11 #BackRed : 14
% 18.53/7.11
% 18.53/7.11 #Partial instantiations: 0
% 18.53/7.11 #Strategies tried : 1
% 18.53/7.11
% 18.53/7.11 Timing (in seconds)
% 18.53/7.11 ----------------------
% 18.53/7.11 Preprocessing : 0.41
% 18.53/7.11 Parsing : 0.21
% 18.53/7.11 CNF conversion : 0.02
% 18.53/7.11 Main loop : 5.60
% 18.53/7.11 Inferencing : 1.28
% 18.53/7.11 Reduction : 2.80
% 18.53/7.11 Demodulation : 2.54
% 18.53/7.11 BG Simplification : 0.17
% 18.53/7.11 Subsumption : 1.04
% 18.53/7.11 Abstraction : 0.32
% 18.53/7.12 MUC search : 0.00
% 18.53/7.12 Cooper : 0.00
% 18.53/7.12 Total : 6.07
% 18.53/7.12 Index Insertion : 0.00
% 18.53/7.12 Index Deletion : 0.00
% 18.53/7.12 Index Matching : 0.00
% 18.53/7.12 BG Taut test : 0.00
%------------------------------------------------------------------------------