TSTP Solution File: GRP209-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP209-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n002.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 : Thu Aug 31 00:17:44 EDT 2023
% Result : Unsatisfiable 1.15s 1.24s
% Output : CNFRefutation 1.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 39
% Syntax : Number of formulae : 210 ( 18 unt; 13 typ; 0 def)
% Number of atoms : 473 ( 472 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 393 ( 117 ~; 276 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 87 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
identity: $i ).
tff(decl_23,type,
multiply: ( $i * $i ) > $i ).
tff(decl_24,type,
inverse: $i > $i ).
tff(decl_25,type,
sk_c1: $i ).
tff(decl_26,type,
sk_c2: $i ).
tff(decl_27,type,
sk_c10: $i ).
tff(decl_28,type,
sk_c5: $i ).
tff(decl_29,type,
sk_c9: $i ).
tff(decl_30,type,
sk_c6: $i ).
tff(decl_31,type,
sk_c7: $i ).
tff(decl_32,type,
sk_c8: $i ).
tff(decl_33,type,
sk_c4: $i ).
tff(decl_34,type,
sk_c3: $i ).
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(prove_this_23,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c5,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_24,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_26,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_28,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c8,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
cnf(prove_this_27,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_22,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| inverse(sk_c5) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_25,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_43,negated_conjecture,
( multiply(X1,X2) != sk_c10
| inverse(X1) != X2
| multiply(X2,sk_c9) != sk_c10
| multiply(sk_c10,X3) != sk_c9
| multiply(X4,sk_c10) != X3
| inverse(X4) != sk_c10
| inverse(X5) != sk_c10
| multiply(X5,sk_c9) != sk_c10
| multiply(X6,sk_c9) != sk_c10
| inverse(X6) != sk_c9
| multiply(X7,X8) != sk_c9
| inverse(X7) != X8
| multiply(X8,sk_c10) != sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_43) ).
cnf(prove_this_36,negated_conjecture,
( inverse(sk_c3) = sk_c10
| inverse(sk_c5) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
cnf(prove_this_30,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| multiply(sk_c5,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
cnf(prove_this_37,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c5,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
cnf(prove_this_29,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| inverse(sk_c5) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
cnf(prove_this_31,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| multiply(sk_c6,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_32,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| inverse(sk_c5) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_39,negated_conjecture,
( inverse(sk_c3) = sk_c10
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_39) ).
cnf(prove_this_8,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c5) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_19,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_20,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_38,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c6,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_38) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c6,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_4,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_9,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c5,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
cnf(c_0_26,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_27,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_28,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_29,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_30,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_29,c_0_29]) ).
cnf(c_0_31,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_27]),c_0_30]) ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c5,sk_c9) = sk_c10 ),
prove_this_23 ).
cnf(c_0_33,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c10 ),
prove_this_24 ).
cnf(c_0_34,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c7,sk_c8) = sk_c9 ),
prove_this_26 ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c8,sk_c10) = sk_c9 ),
prove_this_28 ).
cnf(c_0_36,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_31]) ).
cnf(c_0_37,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| inverse(sk_c7) = sk_c8 ),
prove_this_27 ).
cnf(c_0_38,negated_conjecture,
( multiply(inverse(sk_c5),sk_c10) = sk_c9
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(spm,[status(thm)],[c_0_29,c_0_32]) ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| inverse(sk_c5) = sk_c10 ),
prove_this_22 ).
cnf(c_0_40,negated_conjecture,
( multiply(inverse(sk_c6),sk_c10) = sk_c9
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(spm,[status(thm)],[c_0_29,c_0_33]) ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c7,multiply(sk_c8,X1)) = multiply(sk_c9,X1)
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(spm,[status(thm)],[c_0_26,c_0_34]) ).
cnf(c_0_42,negated_conjecture,
( multiply(inverse(sk_c8),sk_c9) = sk_c10
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(spm,[status(thm)],[c_0_29,c_0_35]) ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| inverse(sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_44,negated_conjecture,
( multiply(inverse(sk_c5),multiply(sk_c10,X1)) = multiply(sk_c9,X1)
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(spm,[status(thm)],[c_0_26,c_0_38]) ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c10,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_27,c_0_39]) ).
cnf(c_0_46,negated_conjecture,
( multiply(inverse(sk_c6),multiply(sk_c10,X1)) = multiply(sk_c9,X1)
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(spm,[status(thm)],[c_0_26,c_0_40]) ).
cnf(c_0_47,negated_conjecture,
( multiply(inverse(sk_c7),sk_c9) = sk_c8
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(spm,[status(thm)],[c_0_29,c_0_34]) ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| inverse(sk_c6) = sk_c9 ),
prove_this_25 ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c7,sk_c9) = multiply(sk_c9,sk_c10)
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(spm,[status(thm)],[c_0_41,c_0_35]) ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c7,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_51,negated_conjecture,
( inverse(sk_c5) = multiply(sk_c9,sk_c5)
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_31]) ).
cnf(c_0_52,negated_conjecture,
( inverse(sk_c6) = multiply(sk_c9,sk_c5)
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_45]),c_0_31]) ).
cnf(c_0_53,negated_conjecture,
( multiply(inverse(sk_c7),multiply(sk_c9,X1)) = multiply(sk_c8,X1)
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(spm,[status(thm)],[c_0_26,c_0_47]) ).
cnf(c_0_54,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c9,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_27,c_0_48]) ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c9,sk_c10) = sk_c10 ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_56,negated_conjecture,
( inverse(multiply(sk_c9,sk_c5)) = sk_c5
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(spm,[status(thm)],[c_0_36,c_0_51]) ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c9,sk_c5) = sk_c9
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(spm,[status(thm)],[c_0_48,c_0_52]) ).
cnf(c_0_58,negated_conjecture,
( inverse(sk_c7) = multiply(sk_c8,sk_c6)
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_31]) ).
cnf(c_0_59,negated_conjecture,
( multiply(inverse(sk_c9),sk_c10) = sk_c10
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(spm,[status(thm)],[c_0_29,c_0_55]) ).
cnf(c_0_60,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| inverse(sk_c9) = sk_c5 ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_61,negated_conjecture,
( multiply(sk_c9,sk_c5) = sk_c10
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(spm,[status(thm)],[c_0_39,c_0_51]) ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c8
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(spm,[status(thm)],[c_0_37,c_0_58]) ).
cnf(c_0_63,negated_conjecture,
( multiply(X1,X2) != sk_c10
| inverse(X1) != X2
| multiply(X2,sk_c9) != sk_c10
| multiply(sk_c10,X3) != sk_c9
| multiply(X4,sk_c10) != X3
| inverse(X4) != sk_c10
| inverse(X5) != sk_c10
| multiply(X5,sk_c9) != sk_c10
| multiply(X6,sk_c9) != sk_c10
| inverse(X6) != sk_c9
| multiply(X7,X8) != sk_c9
| inverse(X7) != X8
| multiply(X8,sk_c10) != sk_c9 ),
prove_this_43 ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c5,sk_c10) = sk_c10 ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_65,negated_conjecture,
( multiply(inverse(sk_c9),sk_c10) = sk_c5
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(spm,[status(thm)],[c_0_29,c_0_61]) ).
cnf(c_0_66,negated_conjecture,
( multiply(sk_c7,sk_c8) = multiply(sk_c9,sk_c6)
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(spm,[status(thm)],[c_0_41,c_0_62]) ).
cnf(c_0_67,negated_conjecture,
( multiply(sk_c10,multiply(X1,sk_c10)) != sk_c9
| multiply(inverse(X2),sk_c10) != sk_c9
| multiply(inverse(X3),sk_c9) != sk_c10
| multiply(X2,inverse(X2)) != sk_c9
| multiply(X3,inverse(X3)) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| multiply(X5,sk_c9) != sk_c10
| inverse(X4) != sk_c9
| inverse(X5) != sk_c10
| inverse(X1) != sk_c10 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_63])])]) ).
cnf(c_0_68,negated_conjecture,
( multiply(inverse(sk_c5),sk_c10) = sk_c10
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(spm,[status(thm)],[c_0_29,c_0_64]) ).
cnf(c_0_69,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| sk_c5 = sk_c10 ),
inference(spm,[status(thm)],[c_0_59,c_0_65]) ).
cnf(c_0_70,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c10,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_47,c_0_37]) ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c9,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_40,c_0_48]) ).
cnf(c_0_73,negated_conjecture,
( multiply(inverse(sk_c8),multiply(sk_c9,X1)) = multiply(sk_c10,X1)
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(spm,[status(thm)],[c_0_26,c_0_42]) ).
cnf(c_0_74,negated_conjecture,
( multiply(sk_c5,multiply(sk_c9,X1)) = multiply(sk_c10,X1)
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(spm,[status(thm)],[c_0_26,c_0_32]) ).
cnf(c_0_75,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c9
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(spm,[status(thm)],[c_0_34,c_0_66]) ).
cnf(c_0_76,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(inverse(X1),sk_c10) != sk_c9
| multiply(inverse(X2),sk_c9) != sk_c10
| multiply(X1,inverse(X1)) != sk_c9
| multiply(X2,inverse(X2)) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| inverse(X3) != sk_c9
| inverse(X4) != sk_c10 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_36]),c_0_69]),c_0_70]) ).
cnf(c_0_77,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_27,c_0_31]) ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| sk_c9 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_71]),c_0_27]) ).
cnf(c_0_79,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_72,c_0_55]) ).
cnf(c_0_80,negated_conjecture,
( inverse(sk_c8) = multiply(sk_c10,sk_c6)
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_54]),c_0_31]) ).
cnf(c_0_81,negated_conjecture,
( multiply(sk_c5,sk_c9) = multiply(sk_c10,sk_c6)
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_82,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(inverse(X1),sk_c9) != sk_c10
| multiply(X1,inverse(X1)) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| inverse(X2) != sk_c9
| inverse(X3) != sk_c10 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_28]),c_0_28]),c_0_78]),c_0_79]) ).
cnf(c_0_83,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| sk_c10 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_72]),c_0_27]) ).
cnf(c_0_84,negated_conjecture,
( inverse(multiply(sk_c10,sk_c6)) = sk_c8
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(spm,[status(thm)],[c_0_36,c_0_80]) ).
cnf(c_0_85,negated_conjecture,
( multiply(sk_c10,sk_c6) = sk_c10
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(spm,[status(thm)],[c_0_32,c_0_81]) ).
cnf(c_0_86,negated_conjecture,
( multiply(inverse(inverse(sk_c5)),sk_c9) = sk_c10
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(spm,[status(thm)],[c_0_29,c_0_38]) ).
cnf(c_0_87,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(X1,sk_c9) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| inverse(X1) != sk_c9
| inverse(X2) != sk_c10 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_77]),c_0_28]),c_0_28]),c_0_83]),c_0_79]) ).
cnf(c_0_88,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| inverse(sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_89,negated_conjecture,
( multiply(inverse(sk_c10),sk_c9) = sk_c10
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(spm,[status(thm)],[c_0_86,c_0_39]) ).
cnf(c_0_90,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_27]),c_0_36])]),c_0_83]) ).
cnf(c_0_91,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| inverse(sk_c8) = sk_c10 ),
inference(spm,[status(thm)],[c_0_36,c_0_88]) ).
cnf(c_0_92,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_89,c_0_88]) ).
cnf(c_0_93,negated_conjecture,
( inverse(sk_c3) = sk_c10
| inverse(sk_c5) = sk_c10 ),
prove_this_36 ).
cnf(c_0_94,negated_conjecture,
multiply(sk_c10,sk_c4) = sk_c9,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]) ).
cnf(c_0_95,negated_conjecture,
( inverse(sk_c3) = sk_c10
| inverse(sk_c10) = sk_c5 ),
inference(spm,[status(thm)],[c_0_36,c_0_93]) ).
cnf(c_0_96,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| multiply(sk_c5,sk_c9) = sk_c10 ),
prove_this_30 ).
cnf(c_0_97,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c5,sk_c9) = sk_c10 ),
prove_this_37 ).
cnf(c_0_98,negated_conjecture,
multiply(inverse(sk_c10),sk_c9) = sk_c4,
inference(spm,[status(thm)],[c_0_29,c_0_94]) ).
cnf(c_0_99,negated_conjecture,
( multiply(sk_c10,sk_c3) = identity
| inverse(sk_c10) = sk_c5 ),
inference(spm,[status(thm)],[c_0_27,c_0_95]) ).
cnf(c_0_100,negated_conjecture,
( multiply(inverse(sk_c5),sk_c10) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(spm,[status(thm)],[c_0_29,c_0_96]) ).
cnf(c_0_101,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c10,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_27,c_0_97]) ).
cnf(c_0_102,negated_conjecture,
( multiply(sk_c10,sk_c3) = identity
| multiply(sk_c5,sk_c9) = sk_c4 ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_103,negated_conjecture,
( multiply(inverse(inverse(sk_c5)),sk_c9) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(spm,[status(thm)],[c_0_29,c_0_100]) ).
cnf(c_0_104,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| inverse(sk_c5) = sk_c10 ),
prove_this_29 ).
cnf(c_0_105,negated_conjecture,
( multiply(sk_c10,sk_c3) = identity
| sk_c4 = sk_c10 ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_106,negated_conjecture,
( multiply(inverse(sk_c10),sk_c9) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_107,negated_conjecture,
( inverse(sk_c10) = sk_c3
| sk_c4 = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_105]),c_0_31]) ).
cnf(c_0_108,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| sk_c4 = sk_c10 ),
inference(spm,[status(thm)],[c_0_106,c_0_98]) ).
cnf(c_0_109,negated_conjecture,
( multiply(sk_c3,sk_c10) = identity
| sk_c4 = sk_c10 ),
inference(spm,[status(thm)],[c_0_27,c_0_107]) ).
cnf(c_0_110,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| multiply(sk_c6,sk_c9) = sk_c10 ),
prove_this_31 ).
cnf(c_0_111,negated_conjecture,
( sk_c4 = sk_c10
| sk_c4 = identity ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_112,negated_conjecture,
( multiply(inverse(sk_c6),sk_c10) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(spm,[status(thm)],[c_0_29,c_0_110]) ).
cnf(c_0_113,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| inverse(sk_c6) = sk_c9 ),
prove_this_32 ).
cnf(c_0_114,negated_conjecture,
( sk_c4 = identity
| sk_c10 != identity ),
inference(ef,[status(thm)],[c_0_111]) ).
cnf(c_0_115,negated_conjecture,
( multiply(inverse(inverse(sk_c6)),sk_c9) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(spm,[status(thm)],[c_0_29,c_0_112]) ).
cnf(c_0_116,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| inverse(sk_c9) = sk_c6 ),
inference(spm,[status(thm)],[c_0_36,c_0_113]) ).
cnf(c_0_117,negated_conjecture,
( sk_c9 = sk_c10
| sk_c10 != identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_114]),c_0_31]) ).
cnf(c_0_118,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| sk_c10 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_113]),c_0_27]) ).
cnf(c_0_119,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| inverse(sk_c5) = sk_c10 ),
prove_this_1 ).
cnf(c_0_120,negated_conjecture,
( inverse(sk_c3) = sk_c10
| inverse(sk_c6) = sk_c9 ),
prove_this_39 ).
cnf(c_0_121,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| inverse(sk_c10) = sk_c6 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_118]) ).
cnf(c_0_122,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c10,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_27,c_0_119]) ).
cnf(c_0_123,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c5) = sk_c10 ),
prove_this_8 ).
cnf(c_0_124,negated_conjecture,
( multiply(sk_c9,sk_c6) = identity
| inverse(sk_c3) = sk_c10 ),
inference(spm,[status(thm)],[c_0_27,c_0_120]) ).
cnf(c_0_125,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| inverse(sk_c6) = sk_c10 ),
inference(spm,[status(thm)],[c_0_36,c_0_121]) ).
cnf(c_0_126,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c7,sk_c8) = sk_c9 ),
prove_this_19 ).
cnf(c_0_127,negated_conjecture,
( multiply(inverse(sk_c1),sk_c10) = sk_c2
| multiply(sk_c10,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_29,c_0_122]) ).
cnf(c_0_128,negated_conjecture,
( multiply(sk_c10,sk_c5) = identity
| inverse(sk_c1) = sk_c2 ),
inference(spm,[status(thm)],[c_0_27,c_0_123]) ).
cnf(c_0_129,negated_conjecture,
( multiply(sk_c10,multiply(sk_c3,X1)) = X1
| multiply(sk_c9,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_29,c_0_124]) ).
cnf(c_0_130,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_113,c_0_125]) ).
cnf(c_0_131,negated_conjecture,
( multiply(inverse(sk_c7),sk_c9) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_29,c_0_126]) ).
cnf(c_0_132,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| inverse(sk_c7) = sk_c8 ),
prove_this_20 ).
cnf(c_0_133,negated_conjecture,
( multiply(sk_c10,sk_c5) = identity
| multiply(sk_c2,sk_c10) = sk_c2 ),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_134,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c6,sk_c9) = sk_c10 ),
prove_this_38 ).
cnf(c_0_135,negated_conjecture,
( multiply(sk_c9,sk_c6) = identity
| sk_c9 = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_94])]) ).
cnf(c_0_136,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c8,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_137,negated_conjecture,
( inverse(sk_c10) = sk_c5
| inverse(sk_c10) = sk_c3 ),
inference(spm,[status(thm)],[c_0_36,c_0_95]) ).
cnf(c_0_138,negated_conjecture,
( multiply(sk_c10,sk_c5) = identity
| sk_c10 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_133]),c_0_27]) ).
cnf(c_0_139,negated_conjecture,
( multiply(sk_c10,multiply(sk_c3,X1)) = X1
| multiply(sk_c6,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_29,c_0_134]) ).
cnf(c_0_140,negated_conjecture,
( inverse(sk_c9) = sk_c6
| sk_c9 = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_135]),c_0_31]) ).
cnf(c_0_141,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| sk_c9 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_136]),c_0_27]) ).
cnf(c_0_142,negated_conjecture,
( inverse(sk_c10) = sk_c3
| sk_c5 != sk_c3 ),
inference(ef,[status(thm)],[c_0_137]) ).
cnf(c_0_143,negated_conjecture,
( multiply(inverse(sk_c10),sk_c9) = sk_c4
| sk_c10 = identity ),
inference(spm,[status(thm)],[c_0_29,c_0_83]) ).
cnf(c_0_144,negated_conjecture,
( inverse(sk_c10) = sk_c5
| sk_c10 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_138]),c_0_31]) ).
cnf(c_0_145,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| inverse(sk_c10) = sk_c3 ),
inference(spm,[status(thm)],[c_0_36,c_0_97]) ).
cnf(c_0_146,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| sk_c9 = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_130]),c_0_94])]) ).
cnf(c_0_147,negated_conjecture,
( multiply(sk_c6,sk_c9) = identity
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_27,c_0_140]) ).
cnf(c_0_148,negated_conjecture,
( multiply(inverse(sk_c2),sk_c10) = sk_c9
| sk_c9 = identity ),
inference(spm,[status(thm)],[c_0_29,c_0_141]) ).
cnf(c_0_149,negated_conjecture,
( inverse(sk_c3) = sk_c10
| sk_c5 != sk_c3 ),
inference(spm,[status(thm)],[c_0_36,c_0_142]) ).
cnf(c_0_150,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c4
| sk_c10 = identity ),
inference(spm,[status(thm)],[c_0_143,c_0_144]) ).
cnf(c_0_151,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| sk_c10 = identity
| sk_c5 = sk_c3 ),
inference(spm,[status(thm)],[c_0_145,c_0_144]) ).
cnf(c_0_152,negated_conjecture,
sk_c9 = sk_c10,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_117]) ).
cnf(c_0_153,negated_conjecture,
( multiply(inverse(sk_c2),multiply(sk_c10,X1)) = multiply(sk_c9,X1)
| sk_c9 = identity ),
inference(spm,[status(thm)],[c_0_26,c_0_148]) ).
cnf(c_0_154,negated_conjecture,
( multiply(sk_c10,sk_c3) = identity
| sk_c5 != sk_c3 ),
inference(spm,[status(thm)],[c_0_27,c_0_149]) ).
cnf(c_0_155,negated_conjecture,
( sk_c5 = sk_c3
| sk_c10 = identity
| sk_c4 = sk_c10 ),
inference(spm,[status(thm)],[c_0_150,c_0_151]) ).
cnf(c_0_156,negated_conjecture,
sk_c4 = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_152]),c_0_27]) ).
cnf(c_0_157,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c6,sk_c9) = sk_c10 ),
prove_this_3 ).
cnf(c_0_158,negated_conjecture,
( inverse(sk_c2) = multiply(sk_c9,sk_c3)
| sk_c9 = identity
| sk_c5 != sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_154]),c_0_31]) ).
cnf(c_0_159,negated_conjecture,
( sk_c10 = identity
| sk_c5 = sk_c3 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_155,c_0_156])]) ).
cnf(c_0_160,negated_conjecture,
( multiply(inverse(sk_c10),sk_c9) = sk_c4
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_29,c_0_79]) ).
cnf(c_0_161,negated_conjecture,
( multiply(inverse(sk_c6),sk_c10) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_29,c_0_157]) ).
cnf(c_0_162,negated_conjecture,
( inverse(sk_c2) = multiply(sk_c10,sk_c3)
| sk_c10 = identity ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_158,c_0_152]),c_0_152]),c_0_159]) ).
cnf(c_0_163,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c4
| inverse(sk_c10) = sk_c3
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_160,c_0_137]) ).
cnf(c_0_164,negated_conjecture,
( multiply(inverse(inverse(sk_c6)),sk_c9) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_29,c_0_161]) ).
cnf(c_0_165,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| inverse(sk_c6) = sk_c9 ),
prove_this_4 ).
cnf(c_0_166,negated_conjecture,
( inverse(multiply(sk_c10,sk_c3)) = sk_c2
| sk_c10 = identity ),
inference(spm,[status(thm)],[c_0_36,c_0_162]) ).
cnf(c_0_167,negated_conjecture,
( multiply(sk_c10,sk_c3) = identity
| sk_c10 = identity ),
inference(rw,[status(thm)],[c_0_105,c_0_156]) ).
cnf(c_0_168,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c4
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_160,c_0_145]) ).
cnf(c_0_169,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c4
| multiply(sk_c3,sk_c9) = sk_c4
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_160,c_0_163]) ).
cnf(c_0_170,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| sk_c10 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_27]) ).
cnf(c_0_171,negated_conjecture,
( sk_c10 = identity
| sk_c2 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_167]),c_0_77]) ).
cnf(c_0_172,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c5,sk_c9) = sk_c10 ),
prove_this_9 ).
cnf(c_0_173,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| sk_c9 = sk_c10
| sk_c4 = sk_c10 ),
inference(spm,[status(thm)],[c_0_106,c_0_160]) ).
cnf(c_0_174,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c4
| sk_c9 = sk_c10
| sk_c4 = sk_c10 ),
inference(spm,[status(thm)],[c_0_168,c_0_169]) ).
cnf(c_0_175,negated_conjecture,
( multiply(sk_c10,multiply(X1,multiply(X2,sk_c10))) != sk_c9
| multiply(inverse(X3),sk_c10) != sk_c9
| multiply(inverse(X4),sk_c9) != sk_c10
| multiply(X3,inverse(X3)) != sk_c9
| multiply(X4,inverse(X4)) != sk_c10
| inverse(multiply(X1,X2)) != sk_c10
| multiply(X5,sk_c9) != sk_c10
| multiply(X6,sk_c9) != sk_c10
| inverse(X5) != sk_c9
| inverse(X6) != sk_c10 ),
inference(spm,[status(thm)],[c_0_67,c_0_26]) ).
cnf(c_0_176,negated_conjecture,
( sk_c10 = identity
| sk_c1 = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_171]),c_0_31]) ).
cnf(c_0_177,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c2,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_27,c_0_172]) ).
cnf(c_0_178,negated_conjecture,
( multiply(inverse(sk_c3),sk_c4) = sk_c10
| sk_c4 = sk_c10
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_29,c_0_173]) ).
cnf(c_0_179,negated_conjecture,
( multiply(inverse(sk_c3),sk_c4) = sk_c9
| sk_c4 = sk_c10
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_29,c_0_174]) ).
cnf(c_0_180,negated_conjecture,
( multiply(sk_c10,multiply(X1,identity)) != sk_c9
| inverse(multiply(X1,inverse(sk_c10))) != sk_c10
| multiply(inverse(X2),sk_c10) != sk_c9
| multiply(inverse(X3),sk_c9) != sk_c10
| multiply(X2,inverse(X2)) != sk_c9
| multiply(X3,inverse(X3)) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| multiply(X5,sk_c9) != sk_c10
| inverse(X4) != sk_c9
| inverse(X5) != sk_c10 ),
inference(spm,[status(thm)],[c_0_175,c_0_27]) ).
cnf(c_0_181,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_29,c_0_26]) ).
cnf(c_0_182,negated_conjecture,
( multiply(sk_c10,sk_c2) = sk_c10
| sk_c10 = identity ),
inference(spm,[status(thm)],[c_0_170,c_0_176]) ).
cnf(c_0_183,negated_conjecture,
( multiply(sk_c5,sk_c10) = identity
| sk_c10 = identity ),
inference(spm,[status(thm)],[c_0_27,c_0_144]) ).
cnf(c_0_184,negated_conjecture,
( multiply(sk_c2,sk_c1) = identity
| multiply(sk_c5,sk_c10) = sk_c10 ),
inference(rw,[status(thm)],[c_0_177,c_0_152]) ).
cnf(c_0_185,negated_conjecture,
( sk_c4 = sk_c10
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_178,c_0_179]) ).
cnf(c_0_186,negated_conjecture,
( inverse(multiply(X1,inverse(sk_c10))) != sk_c10
| multiply(inverse(X2),sk_c10) != sk_c9
| multiply(inverse(X3),sk_c9) != sk_c10
| multiply(X2,inverse(X2)) != sk_c9
| multiply(X3,inverse(X3)) != sk_c10
| multiply(sk_c10,X1) != sk_c9
| multiply(X4,sk_c9) != sk_c10
| multiply(X5,sk_c9) != sk_c10
| inverse(X4) != sk_c9
| inverse(X5) != sk_c10 ),
inference(rw,[status(thm)],[c_0_180,c_0_31]) ).
cnf(c_0_187,negated_conjecture,
( multiply(sk_c2,X1) = X1
| sk_c10 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_182]),c_0_29]) ).
cnf(c_0_188,negated_conjecture,
( multiply(sk_c2,sk_c1) = identity
| sk_c10 = identity ),
inference(spm,[status(thm)],[c_0_183,c_0_184]) ).
cnf(c_0_189,negated_conjecture,
( multiply(sk_c10,sk_c10) = sk_c9
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_70,c_0_185]) ).
cnf(c_0_190,negated_conjecture,
( multiply(inverse(X1),sk_c10) != sk_c9
| multiply(inverse(X2),sk_c9) != sk_c10
| multiply(X1,inverse(X1)) != sk_c9
| multiply(X2,inverse(X2)) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| inverse(X3) != sk_c9
| inverse(X4) != sk_c10
| sk_c9 != sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_28]),c_0_36]),c_0_31])]) ).
cnf(c_0_191,negated_conjecture,
( sk_c10 = identity
| sk_c1 = identity ),
inference(spm,[status(thm)],[c_0_187,c_0_188]) ).
cnf(c_0_192,negated_conjecture,
( multiply(inverse(X1),sk_c10) != sk_c9
| multiply(inverse(X2),sk_c9) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c9
| multiply(X1,inverse(X1)) != sk_c9
| multiply(X2,inverse(X2)) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| inverse(sk_c10) != sk_c10
| inverse(X3) != sk_c9
| inverse(X4) != sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_189]),c_0_190]) ).
cnf(c_0_193,negated_conjecture,
sk_c10 = identity,
inference(spm,[status(thm)],[c_0_176,c_0_191]) ).
cnf(c_0_194,negated_conjecture,
( multiply(X1,inverse(X1)) != identity
| multiply(X2,inverse(X2)) != identity
| inverse(X1) != identity
| inverse(X2) != identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_192,c_0_152]),c_0_152]),c_0_152]),c_0_152]),c_0_152]),c_0_152]),c_0_152]),c_0_152]),c_0_193]),c_0_31]),c_0_193]),c_0_193]),c_0_31]),c_0_193]),c_0_193]),c_0_193]),c_0_28]),c_0_193]),c_0_193]),c_0_193]),c_0_193]),c_0_31]),c_0_193]),c_0_193]),c_0_31]),c_0_193]),c_0_193]),c_0_77]),c_0_193]),c_0_193]),c_0_193])])])]),c_0_77])]) ).
cnf(c_0_195,negated_conjecture,
( multiply(X1,inverse(X1)) != identity
| inverse(X1) != identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_77]),c_0_28])]) ).
cnf(c_0_196,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_77]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP209-1 : TPTP v8.1.2. Released v2.5.0.
% 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 01:26:50 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 1.15/1.24 % Version : CSE_E---1.5
% 1.15/1.24 % Problem : theBenchmark.p
% 1.15/1.24 % Proof found
% 1.15/1.24 % SZS status Theorem for theBenchmark.p
% 1.15/1.24 % SZS output start Proof
% See solution above
% 1.15/1.25 % Total time : 0.670000 s
% 1.15/1.25 % SZS output end Proof
% 1.15/1.25 % Total time : 0.674000 s
%------------------------------------------------------------------------------