TSTP Solution File: GRP380-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP380-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n020.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 00:18:45 EDT 2023
% Result : Unsatisfiable 2.78s 2.86s
% Output : CNFRefutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 36
% Syntax : Number of formulae : 196 ( 21 unt; 14 typ; 0 def)
% Number of atoms : 436 ( 435 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 367 ( 113 ~; 254 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 5 ( 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 : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 90 ( 4 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_c11: $i ).
tff(decl_26,type,
sk_c10: $i ).
tff(decl_27,type,
sk_c3: $i ).
tff(decl_28,type,
sk_c4: $i ).
tff(decl_29,type,
sk_c9: $i ).
tff(decl_30,type,
sk_c5: $i ).
tff(decl_31,type,
sk_c8: $i ).
tff(decl_32,type,
sk_c7: $i ).
tff(decl_33,type,
sk_c6: $i ).
tff(decl_34,type,
sk_c1: $i ).
tff(decl_35,type,
sk_c2: $i ).
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(prove_this_15,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_20,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_16,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_17,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c8,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_18,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_19,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_12,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_11,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_14,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_25,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_26,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_35,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
cnf(prove_this_36,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
cnf(prove_this_4,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_13,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_1,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_51,negated_conjecture,
( inverse(sk_c11) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c11
| multiply(X1,X2) != sk_c10
| inverse(X1) != X2
| multiply(X2,sk_c9) != sk_c10
| multiply(X3,sk_c11) != sk_c10
| inverse(X3) != sk_c11
| multiply(X4,sk_c10) != sk_c9
| inverse(X4) != sk_c10
| multiply(X5,X6) != sk_c11
| inverse(X5) != X6
| multiply(X6,sk_c10) != sk_c11
| inverse(X7) != X8
| inverse(X8) != X6
| multiply(X7,X6) != X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_51) ).
cnf(prove_this_3,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_2,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
cnf(c_0_22,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_23,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_24,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_25,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_26,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
prove_this_15 ).
cnf(c_0_27,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c7,sk_c8) = sk_c6 ),
prove_this_20 ).
cnf(c_0_28,negated_conjecture,
( multiply(inverse(sk_c5),sk_c11) = sk_c8
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c5) = sk_c8 ),
prove_this_16 ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c5,multiply(sk_c8,X1)) = multiply(sk_c11,X1)
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_22,c_0_26]) ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c8,sk_c10) = sk_c11 ),
prove_this_17 ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c7,multiply(sk_c8,X1)) = multiply(sk_c6,X1)
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_22,c_0_27]) ).
cnf(c_0_33,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c8,sk_c11) = sk_c8 ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,negated_conjecture,
( multiply(inverse(sk_c7),sk_c6) = sk_c8
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_25,c_0_27]) ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c7) = sk_c6 ),
prove_this_18 ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c5,sk_c11) = multiply(sk_c11,sk_c10)
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c6) = sk_c8 ),
prove_this_19 ).
cnf(c_0_38,negated_conjecture,
( multiply(sk_c7,sk_c8) = multiply(sk_c6,sk_c11)
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c6,sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_25,c_0_25]) ).
cnf(c_0_41,negated_conjecture,
( multiply(inverse(sk_c8),sk_c11) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_25,c_0_31]) ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c3) = sk_c11 ),
prove_this_12 ).
cnf(c_0_43,negated_conjecture,
( multiply(inverse(sk_c5),multiply(sk_c11,sk_c10)) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_25,c_0_36]) ).
cnf(c_0_44,negated_conjecture,
( multiply(sk_c8,multiply(sk_c6,X1)) = X1
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_25,c_0_37]) ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c6
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_27,c_0_38]) ).
cnf(c_0_46,negated_conjecture,
( multiply(inverse(sk_c6),sk_c8) = sk_c6
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_25,c_0_39]) ).
cnf(c_0_47,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_23]),c_0_40]) ).
cnf(c_0_48,negated_conjecture,
( multiply(inverse(sk_c8),multiply(sk_c11,X1)) = multiply(sk_c10,X1)
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_22,c_0_41]) ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c11,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_23,c_0_42]) ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
prove_this_11 ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c8,multiply(sk_c11,sk_c10)) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_43,c_0_29]) ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c8,sk_c6) = sk_c11 ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_53,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c8,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_46,c_0_37]) ).
cnf(c_0_54,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_47]),c_0_47]) ).
cnf(c_0_55,negated_conjecture,
( inverse(sk_c8) = multiply(sk_c10,sk_c3)
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_47]) ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c3,multiply(sk_c11,X1)) = multiply(sk_c10,X1)
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_22,c_0_50]) ).
cnf(c_0_57,negated_conjecture,
( multiply(inverse(sk_c8),sk_c11) = multiply(sk_c11,sk_c10)
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_25,c_0_51]) ).
cnf(c_0_58,negated_conjecture,
( multiply(inverse(sk_c8),sk_c11) = sk_c6
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_25,c_0_52]) ).
cnf(c_0_59,negated_conjecture,
( multiply(inverse(sk_c8),sk_c6) = sk_c8
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_25,c_0_53]) ).
cnf(c_0_60,negated_conjecture,
( inverse(multiply(sk_c10,sk_c3)) = sk_c8
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_61,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c10,sk_c3) = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_49]),c_0_47]) ).
cnf(c_0_62,negated_conjecture,
( multiply(inverse(sk_c3),sk_c10) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_25,c_0_50]) ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c6 ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_64,negated_conjecture,
( multiply(inverse(sk_c7),multiply(sk_c6,X1)) = multiply(sk_c8,X1)
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_22,c_0_34]) ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c6,sk_c7) = identity ),
inference(spm,[status(thm)],[c_0_23,c_0_35]) ).
cnf(c_0_66,negated_conjecture,
( multiply(inverse(sk_c8),multiply(sk_c6,X1)) = multiply(sk_c8,X1)
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_22,c_0_59]) ).
cnf(c_0_67,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_68,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_62,c_0_42]) ).
cnf(c_0_69,negated_conjecture,
( multiply(inverse(sk_c11),sk_c6) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_25,c_0_63]) ).
cnf(c_0_70,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c11) = sk_c3 ),
inference(spm,[status(thm)],[c_0_54,c_0_42]) ).
cnf(c_0_71,negated_conjecture,
( inverse(sk_c7) = multiply(sk_c8,sk_c7)
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_47]) ).
cnf(c_0_72,negated_conjecture,
( inverse(sk_c8) = multiply(sk_c8,sk_c7)
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_65]),c_0_47]) ).
cnf(c_0_73,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c8) = sk_c3 ),
inference(spm,[status(thm)],[c_0_54,c_0_67]) ).
cnf(c_0_74,negated_conjecture,
( multiply(inverse(sk_c5),sk_c11) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_43,c_0_68]) ).
cnf(c_0_75,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c3,sk_c6) = sk_c10 ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_76,negated_conjecture,
( inverse(multiply(sk_c8,sk_c7)) = sk_c7
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_54,c_0_71]) ).
cnf(c_0_77,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c8,sk_c7) = sk_c3 ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c8,sk_c11) = sk_c11 ),
inference(spm,[status(thm)],[c_0_74,c_0_29]) ).
cnf(c_0_79,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c8) = sk_c5 ),
inference(spm,[status(thm)],[c_0_54,c_0_29]) ).
cnf(c_0_80,negated_conjecture,
( multiply(inverse(sk_c6),multiply(sk_c8,X1)) = multiply(sk_c6,X1)
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_22,c_0_46]) ).
cnf(c_0_81,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c8,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_23,c_0_37]) ).
cnf(c_0_82,negated_conjecture,
( multiply(inverse(sk_c3),sk_c10) = sk_c6
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_25,c_0_75]) ).
cnf(c_0_83,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c3) = sk_c7 ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_84,negated_conjecture,
( multiply(sk_c5,sk_c11) = multiply(sk_c11,sk_c11)
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_30,c_0_78]) ).
cnf(c_0_85,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c5,sk_c11) = sk_c6 ),
inference(spm,[status(thm)],[c_0_58,c_0_79]) ).
cnf(c_0_86,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_54,c_0_37]) ).
cnf(c_0_87,negated_conjecture,
( inverse(sk_c6) = multiply(sk_c6,sk_c6)
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_47]) ).
cnf(c_0_88,negated_conjecture,
( multiply(sk_c6,multiply(sk_c7,X1)) = X1
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_25,c_0_35]) ).
cnf(c_0_89,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c7,sk_c10) = sk_c6 ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_90,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c11,sk_c11) = sk_c6 ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_91,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c6
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_86,c_0_55]) ).
cnf(c_0_92,negated_conjecture,
( inverse(multiply(sk_c6,sk_c6)) = sk_c6
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_54,c_0_87]) ).
cnf(c_0_93,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c6,sk_c6) = sk_c10 ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_94,negated_conjecture,
( multiply(inverse(sk_c11),sk_c6) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_25,c_0_90]) ).
cnf(c_0_95,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c4) = sk_c10 ),
prove_this_14 ).
cnf(c_0_96,negated_conjecture,
( multiply(inverse(sk_c10),sk_c6) = sk_c3
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_25,c_0_91]) ).
cnf(c_0_97,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c10) = sk_c6 ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_98,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c3,sk_c6) = sk_c11 ),
inference(spm,[status(thm)],[c_0_94,c_0_70]) ).
cnf(c_0_99,negated_conjecture,
( multiply(inverse(sk_c3),multiply(sk_c10,X1)) = multiply(sk_c11,X1)
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_22,c_0_62]) ).
cnf(c_0_100,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c10,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_23,c_0_95]) ).
cnf(c_0_101,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c6,sk_c6) = sk_c3 ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_102,negated_conjecture,
( multiply(inverse(sk_c3),sk_c11) = sk_c6
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_25,c_0_98]) ).
cnf(c_0_103,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
prove_this_25 ).
cnf(c_0_104,negated_conjecture,
( inverse(sk_c3) = multiply(sk_c11,sk_c4)
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_47]) ).
cnf(c_0_105,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c3) = sk_c6 ),
inference(spm,[status(thm)],[c_0_92,c_0_101]) ).
cnf(c_0_106,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c7,sk_c11) = sk_c6 ),
inference(spm,[status(thm)],[c_0_102,c_0_83]) ).
cnf(c_0_107,negated_conjecture,
( multiply(inverse(sk_c5),sk_c11) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_25,c_0_103]) ).
cnf(c_0_108,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| inverse(sk_c5) = sk_c8 ),
prove_this_26 ).
cnf(c_0_109,negated_conjecture,
( multiply(sk_c5,sk_c6) = multiply(sk_c11,sk_c8)
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_30,c_0_53]) ).
cnf(c_0_110,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c11,sk_c4) = sk_c6 ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_111,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c6,sk_c6) = sk_c11 ),
inference(spm,[status(thm)],[c_0_88,c_0_106]) ).
cnf(c_0_112,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c8,sk_c11) = sk_c8 ),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_113,negated_conjecture,
( multiply(inverse(sk_c5),multiply(sk_c11,sk_c8)) = sk_c6
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_25,c_0_109]) ).
cnf(c_0_114,negated_conjecture,
( multiply(inverse(sk_c11),sk_c6) = sk_c4
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_25,c_0_110]) ).
cnf(c_0_115,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c11) = sk_c6 ),
inference(spm,[status(thm)],[c_0_92,c_0_111]) ).
cnf(c_0_116,negated_conjecture,
( multiply(inverse(sk_c1),sk_c10) = sk_c2
| multiply(sk_c8,sk_c11) = sk_c8 ),
inference(spm,[status(thm)],[c_0_25,c_0_112]) ).
cnf(c_0_117,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c5,sk_c8) = sk_c11 ),
prove_this_35 ).
cnf(c_0_118,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c5) = sk_c8 ),
prove_this_36 ).
cnf(c_0_119,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c4) = sk_c10 ),
prove_this_4 ).
cnf(c_0_120,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
prove_this_13 ).
cnf(c_0_121,negated_conjecture,
( multiply(sk_c8,multiply(sk_c11,sk_c8)) = sk_c6
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_113,c_0_29]) ).
cnf(c_0_122,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c6,sk_c6) = sk_c4 ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_123,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_25,c_0_22]) ).
cnf(c_0_124,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c8,sk_c11) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c2 ),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_125,negated_conjecture,
( multiply(sk_c8,sk_c5) = identity
| inverse(sk_c1) = sk_c2 ),
inference(spm,[status(thm)],[c_0_23,c_0_118]) ).
cnf(c_0_126,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c10) = sk_c4 ),
inference(spm,[status(thm)],[c_0_54,c_0_119]) ).
cnf(c_0_127,negated_conjecture,
( multiply(inverse(sk_c4),sk_c9) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_25,c_0_120]) ).
cnf(c_0_128,negated_conjecture,
( multiply(inverse(sk_c8),sk_c6) = multiply(sk_c11,sk_c8)
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_25,c_0_121]) ).
cnf(c_0_129,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c4) = sk_c6 ),
inference(spm,[status(thm)],[c_0_92,c_0_122]) ).
cnf(c_0_130,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
prove_this_1 ).
cnf(c_0_131,negated_conjecture,
( multiply(inverse(multiply(X1,sk_c5)),multiply(X1,sk_c11)) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c2
| multiply(sk_c8,sk_c11) = sk_c8 ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_132,negated_conjecture,
( multiply(sk_c8,sk_c5) = identity
| multiply(sk_c8,sk_c11) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c2 ),
inference(spm,[status(thm)],[c_0_116,c_0_125]) ).
cnf(c_0_133,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_23,c_0_47]) ).
cnf(c_0_134,negated_conjecture,
( inverse(sk_c11) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c11
| multiply(X1,X2) != sk_c10
| inverse(X1) != X2
| multiply(X2,sk_c9) != sk_c10
| multiply(X3,sk_c11) != sk_c10
| inverse(X3) != sk_c11
| multiply(X4,sk_c10) != sk_c9
| inverse(X4) != sk_c10
| multiply(X5,X6) != sk_c11
| inverse(X5) != X6
| multiply(X6,sk_c10) != sk_c11
| inverse(X7) != X8
| inverse(X8) != X6
| multiply(X7,X6) != X8 ),
prove_this_51 ).
cnf(c_0_135,negated_conjecture,
( inverse(sk_c10) = sk_c4
| inverse(sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_54,c_0_126]) ).
cnf(c_0_136,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_127,c_0_95]) ).
cnf(c_0_137,negated_conjecture,
( multiply(inverse(sk_c8),sk_c11) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_25,c_0_78]) ).
cnf(c_0_138,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c11,sk_c8) = sk_c8 ),
inference(spm,[status(thm)],[c_0_59,c_0_128]) ).
cnf(c_0_139,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c6,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_127,c_0_129]) ).
cnf(c_0_140,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c10,sk_c11) = identity ),
inference(spm,[status(thm)],[c_0_23,c_0_130]) ).
cnf(c_0_141,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c2
| multiply(sk_c8,sk_c11) = sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_133]),c_0_24])]) ).
cnf(c_0_142,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(inverse(X3),sk_c9) != sk_c10
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(sk_c10,sk_c9) != sk_c11
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X3,inverse(X3)) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(X5,sk_c11) != sk_c10
| inverse(sk_c11) != sk_c10
| inverse(X4) != sk_c10
| inverse(X5) != sk_c11 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_134])])]) ).
cnf(c_0_143,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
prove_this_3 ).
cnf(c_0_144,negated_conjecture,
( inverse(sk_c10) = sk_c11
| sk_c4 != sk_c11 ),
inference(ef,[status(thm)],[c_0_135]) ).
cnf(c_0_145,negated_conjecture,
( multiply(sk_c11,multiply(sk_c10,X1)) = multiply(sk_c11,X1)
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_22,c_0_68]) ).
cnf(c_0_146,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c10
| sk_c11 != sk_c10 ),
inference(ef,[status(thm)],[c_0_136]) ).
cnf(c_0_147,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| sk_c11 = sk_c10 ),
inference(spm,[status(thm)],[c_0_41,c_0_137]) ).
cnf(c_0_148,negated_conjecture,
( multiply(sk_c11,multiply(sk_c8,X1)) = multiply(sk_c8,X1)
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_22,c_0_138]) ).
cnf(c_0_149,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c8,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_44,c_0_139]) ).
cnf(c_0_150,negated_conjecture,
( multiply(inverse(sk_c3),sk_c10) = sk_c11
| multiply(sk_c10,sk_c11) = identity ),
inference(spm,[status(thm)],[c_0_25,c_0_140]) ).
cnf(c_0_151,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c3) = sk_c11 ),
prove_this_2 ).
cnf(c_0_152,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c2
| sk_c11 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_141]),c_0_23]) ).
cnf(c_0_153,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(inverse(X3),sk_c9) != sk_c10
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X3,inverse(X3)) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(X5,sk_c11) != sk_c10
| inverse(X4) != sk_c10
| inverse(X5) != sk_c11 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_120]) ).
cnf(c_0_154,negated_conjecture,
( inverse(sk_c11) = sk_c10
| sk_c4 != sk_c11 ),
inference(spm,[status(thm)],[c_0_54,c_0_144]) ).
cnf(c_0_155,negated_conjecture,
( multiply(sk_c11,sk_c9) = multiply(sk_c11,sk_c10)
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_147]) ).
cnf(c_0_156,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c9 ),
inference(spm,[status(thm)],[c_0_148,c_0_149]) ).
cnf(c_0_157,negated_conjecture,
( multiply(sk_c10,sk_c11) = identity
| multiply(sk_c11,sk_c10) = sk_c11
| inverse(sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_150,c_0_151]) ).
cnf(c_0_158,negated_conjecture,
( sk_c11 = identity
| sk_c10 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_152]),c_0_23]) ).
cnf(c_0_159,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(inverse(X1),sk_c10) != sk_c11
| multiply(inverse(X2),sk_c9) != sk_c10
| inverse(inverse(inverse(X1))) != identity
| multiply(X1,inverse(X1)) != sk_c11
| multiply(X2,inverse(X2)) != sk_c10
| inverse(identity) != inverse(X1)
| multiply(X3,sk_c10) != sk_c9
| multiply(X4,sk_c11) != sk_c10
| inverse(X3) != sk_c10
| inverse(X4) != sk_c11 ),
inference(spm,[status(thm)],[c_0_153,c_0_23]) ).
cnf(c_0_160,negated_conjecture,
( multiply(inverse(multiply(X1,sk_c10)),multiply(X1,sk_c11)) = sk_c9
| sk_c11 = sk_c10 ),
inference(spm,[status(thm)],[c_0_123,c_0_147]) ).
cnf(c_0_161,negated_conjecture,
( multiply(sk_c10,sk_c11) = identity
| sk_c4 != sk_c11 ),
inference(spm,[status(thm)],[c_0_23,c_0_154]) ).
cnf(c_0_162,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_163,negated_conjecture,
sk_c10 = identity,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_47]),c_0_24]),c_0_133])]) ).
cnf(c_0_164,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(inverse(X1),sk_c10) != sk_c11
| multiply(inverse(X2),sk_c9) != sk_c10
| multiply(X1,inverse(X1)) != sk_c11
| multiply(X2,inverse(X2)) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| multiply(X4,sk_c11) != sk_c10
| inverse(X1) != identity
| inverse(X3) != sk_c10
| inverse(X4) != sk_c11 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_159,c_0_133]),c_0_54])]) ).
cnf(c_0_165,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_54,c_0_143]) ).
cnf(c_0_166,negated_conjecture,
( inverse(multiply(sk_c10,sk_c10)) = sk_c9
| sk_c11 = sk_c10
| sk_c4 != sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_47]) ).
cnf(c_0_167,negated_conjecture,
sk_c9 = sk_c11,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_162,c_0_163]),c_0_24]),c_0_163]),c_0_47])]) ).
cnf(c_0_168,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(inverse(X1),sk_c9) != sk_c10
| multiply(sk_c11,sk_c10) != sk_c11
| multiply(sk_c10,sk_c11) != sk_c11
| multiply(X1,inverse(X1)) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| multiply(X3,sk_c11) != sk_c10
| inverse(X2) != sk_c10
| inverse(X3) != sk_c11
| sk_c11 != identity ),
inference(spm,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_169,negated_conjecture,
( sk_c11 = identity
| sk_c4 != sk_c11 ),
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)],[c_0_166,c_0_163]),c_0_163]),c_0_47]),c_0_133]),c_0_163]),c_0_167])]) ).
cnf(c_0_170,negated_conjecture,
( sk_c4 = sk_c11
| multiply(inverse(X1),sk_c11) != identity
| multiply(X1,inverse(X1)) != identity
| multiply(X2,sk_c11) != identity
| inverse(sk_c11) != identity
| inverse(X2) != sk_c11
| sk_c11 != identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[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)],[c_0_168,c_0_163]),c_0_47]),c_0_163]),c_0_163]),c_0_47]),c_0_163]),c_0_24]),c_0_163]),c_0_163]),c_0_47]),c_0_163]),c_0_163])])]),c_0_167]),c_0_167]),c_0_167]) ).
cnf(c_0_171,negated_conjecture,
sk_c11 = identity,
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_165,c_0_163]),c_0_47]),c_0_163]),c_0_133]),c_0_167]),c_0_169]) ).
cnf(c_0_172,plain,
multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,X3)) = multiply(X2,X3),
inference(spm,[status(thm)],[c_0_123,c_0_25]) ).
cnf(c_0_173,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_23,c_0_54]) ).
cnf(c_0_174,negated_conjecture,
( sk_c4 = identity
| multiply(X1,inverse(X1)) != identity
| inverse(X1) != identity ),
inference(cn,[status(thm)],[inference(rw,[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)],[c_0_170,c_0_171]),c_0_171]),c_0_47]),c_0_171]),c_0_47]),c_0_171]),c_0_133]),c_0_171]),c_0_171])])]),c_0_133])]) ).
cnf(c_0_175,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(inverse(X3),sk_c9) != sk_c10
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(sk_c10,sk_c9) != sk_c11
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X3,inverse(X3)) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(X5,sk_c11) != sk_c10
| inverse(X4) != sk_c10
| inverse(X5) != sk_c11
| sk_c4 != sk_c11 ),
inference(spm,[status(thm)],[c_0_142,c_0_154]) ).
cnf(c_0_176,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173]),c_0_47]) ).
cnf(c_0_177,negated_conjecture,
sk_c4 = identity,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_133]),c_0_47])]) ).
cnf(c_0_178,negated_conjecture,
( multiply(X1,inverse(X2)) != inverse(X1)
| multiply(X2,inverse(X1)) != inverse(X2)
| inverse(X1) != identity
| inverse(X3) != identity ),
inference(cn,[status(thm)],[inference(rw,[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(er,[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_175,c_0_163]),c_0_47]),c_0_163]),c_0_163]),c_0_24]),c_0_163]),c_0_163]),c_0_47]),c_0_163]),c_0_163])]),c_0_176]),c_0_171]),c_0_167]),c_0_171]),c_0_47]),c_0_167]),c_0_171]),c_0_171]),c_0_173]),c_0_171]),c_0_173]),c_0_171]),c_0_47]),c_0_167]),c_0_171]),c_0_133]),c_0_171]),c_0_177]),c_0_171])])]),c_0_133])]) ).
cnf(c_0_179,negated_conjecture,
( inverse(X1) != identity
| inverse(X2) != identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_23]),c_0_54]),c_0_54]),c_0_173])]) ).
cnf(c_0_180,negated_conjecture,
inverse(X1) != identity,
inference(spm,[status(thm)],[c_0_179,c_0_133]) ).
cnf(c_0_181,plain,
$false,
inference(sr,[status(thm)],[c_0_133,c_0_180]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP380-1 : TPTP v8.1.2. Released v2.5.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 22:14:28 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 2.78/2.86 % Version : CSE_E---1.5
% 2.78/2.86 % Problem : theBenchmark.p
% 2.78/2.86 % Proof found
% 2.78/2.86 % SZS status Theorem for theBenchmark.p
% 2.78/2.86 % SZS output start Proof
% See solution above
% 2.78/2.87 % Total time : 2.299000 s
% 2.78/2.87 % SZS output end Proof
% 2.78/2.87 % Total time : 2.303000 s
%------------------------------------------------------------------------------