TSTP Solution File: GRP338-1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP338-1 : 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 : n016.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 00:18:31 EDT 2023
% Result : Unsatisfiable 1.96s 2.05s
% Output : CNFRefutation 2.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 53
% Syntax : Number of formulae : 264 ( 16 unt; 14 typ; 0 def)
% Number of atoms : 676 ( 675 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 586 ( 160 ~; 426 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 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 : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 103 ( 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_c10: $i ).
tff(decl_26,type,
sk_c11: $i ).
tff(decl_27,type,
sk_c9: $i ).
tff(decl_28,type,
sk_c3: $i ).
tff(decl_29,type,
sk_c4: $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_3,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_4,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_38,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
cnf(prove_this_51,negated_conjecture,
( multiply(sk_c10,sk_c11) != sk_c9
| inverse(X1) != sk_c11
| multiply(X1,sk_c10) != sk_c11
| multiply(X2,sk_c10) != sk_c11
| inverse(X2) != 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_39,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
cnf(prove_this_48,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_48) ).
cnf(prove_this_21,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_31,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_49,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_49) ).
cnf(prove_this_22,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_32,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
cnf(prove_this_18,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_19,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_33,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
cnf(prove_this_34,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
cnf(prove_this_28,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
cnf(prove_this_29,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
cnf(prove_this_46,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
cnf(prove_this_45,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_45) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_35,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_36,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
cnf(prove_this_44,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_44) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_8,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_9,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_7,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c8,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_16,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_42,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
cnf(prove_this_12,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_25,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_14,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_2,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_26,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_11,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
cnf(c_0_39,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_40,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_41,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_42,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_43,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_42,c_0_42]) ).
cnf(c_0_44,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
prove_this_3 ).
cnf(c_0_45,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_40]),c_0_43]) ).
cnf(c_0_46,negated_conjecture,
( multiply(inverse(sk_c4),sk_c9) = sk_c10
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_42,c_0_44]) ).
cnf(c_0_47,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c4) = sk_c10 ),
prove_this_4 ).
cnf(c_0_48,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_45]),c_0_45]) ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| inverse(sk_c7) = sk_c6 ),
prove_this_38 ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c10,sk_c11) != sk_c9
| inverse(X1) != sk_c11
| multiply(X1,sk_c10) != sk_c11
| multiply(X2,sk_c10) != sk_c11
| inverse(X2) != 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_51,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c10,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| inverse(sk_c6) = sk_c8 ),
prove_this_39 ).
cnf(c_0_53,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| inverse(sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c7) = sk_c6 ),
prove_this_48 ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
prove_this_21 ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
prove_this_31 ).
cnf(c_0_57,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(sk_c10,sk_c11) != sk_c9
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X3,sk_c10) != sk_c9
| multiply(X4,sk_c11) != sk_c10
| multiply(X5,sk_c10) != sk_c11
| multiply(X6,sk_c10) != sk_c11
| inverse(X3) != sk_c10
| inverse(X4) != sk_c11
| inverse(X5) != sk_c10
| inverse(X6) != sk_c11 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_50])]) ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| sk_c9 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_51]),c_0_40]) ).
cnf(c_0_59,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_60,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c6) = sk_c8 ),
prove_this_49 ).
cnf(c_0_61,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_48,c_0_54]) ).
cnf(c_0_62,negated_conjecture,
( multiply(inverse(sk_c3),sk_c10) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_42,c_0_55]) ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c11 ),
prove_this_22 ).
cnf(c_0_64,negated_conjecture,
( multiply(inverse(sk_c3),sk_c10) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_42,c_0_56]) ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c11 ),
prove_this_32 ).
cnf(c_0_66,negated_conjecture,
( sk_c9 = identity
| inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X3,sk_c10) != sk_c9
| multiply(X4,sk_c11) != sk_c10
| multiply(X5,sk_c10) != sk_c11
| multiply(X6,sk_c10) != sk_c11
| inverse(X3) != sk_c10
| inverse(X4) != sk_c11
| inverse(X5) != sk_c10
| inverse(X6) != sk_c11 ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_67,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_42,c_0_41]) ).
cnf(c_0_68,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c7) = sk_c6 ),
prove_this_18 ).
cnf(c_0_69,negated_conjecture,
( multiply(inverse(sk_c2),sk_c11) = sk_c10
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_42,c_0_59]) ).
cnf(c_0_70,negated_conjecture,
( inverse(sk_c2) = sk_c10
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_73,negated_conjecture,
( sk_c9 = identity
| multiply(inverse(X1),sk_c10) != sk_c11
| inverse(inverse(inverse(X1))) != identity
| multiply(X1,inverse(X1)) != sk_c11
| inverse(identity) != inverse(X1)
| multiply(X2,sk_c10) != sk_c9
| multiply(X3,sk_c11) != sk_c10
| multiply(X4,sk_c10) != sk_c11
| multiply(X5,sk_c10) != sk_c11
| inverse(X2) != sk_c10
| inverse(X3) != sk_c11
| inverse(X4) != sk_c10
| inverse(X5) != sk_c11 ),
inference(spm,[status(thm)],[c_0_66,c_0_40]) ).
cnf(c_0_74,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_67,c_0_45]) ).
cnf(c_0_75,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c6) = sk_c8 ),
prove_this_19 ).
cnf(c_0_76,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_48,c_0_68]) ).
cnf(c_0_77,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c10
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c1,multiply(sk_c10,X1)) = multiply(sk_c11,X1)
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_39,c_0_71]) ).
cnf(c_0_79,negated_conjecture,
( multiply(sk_c10,sk_c2) = identity
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_40,c_0_70]) ).
cnf(c_0_80,negated_conjecture,
( multiply(sk_c2,multiply(sk_c10,X1)) = multiply(sk_c11,X1)
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_39,c_0_72]) ).
cnf(c_0_81,negated_conjecture,
( sk_c9 = identity
| multiply(inverse(X1),sk_c10) != sk_c11
| multiply(X1,inverse(X1)) != sk_c11
| multiply(X2,sk_c10) != sk_c9
| multiply(X3,sk_c11) != sk_c10
| multiply(X4,sk_c10) != sk_c11
| multiply(X5,sk_c10) != sk_c11
| inverse(X1) != identity
| inverse(X2) != sk_c10
| inverse(X3) != sk_c11
| inverse(X4) != sk_c10
| inverse(X5) != sk_c11 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_74]),c_0_48])]) ).
cnf(c_0_82,negated_conjecture,
( inverse(sk_c1) = sk_c11
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_83,negated_conjecture,
( sk_c7 = sk_c8
| sk_c11 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_77]),c_0_40]) ).
cnf(c_0_84,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c11
| multiply(sk_c11,sk_c2) = sk_c1
| sk_c7 = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_45]) ).
cnf(c_0_85,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c11
| multiply(sk_c11,sk_c2) = sk_c2
| sk_c7 = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_79]),c_0_45]) ).
cnf(c_0_86,negated_conjecture,
( sk_c7 = sk_c8
| sk_c9 = identity
| multiply(sk_c11,sk_c10) != sk_c11
| multiply(sk_c1,sk_c11) != sk_c11
| multiply(X1,sk_c10) != sk_c9
| multiply(X2,sk_c11) != sk_c10
| multiply(X3,sk_c10) != sk_c11
| multiply(X4,sk_c10) != sk_c11
| inverse(X1) != sk_c10
| inverse(X2) != sk_c11
| inverse(X3) != sk_c10
| inverse(X4) != sk_c11 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83]) ).
cnf(c_0_87,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c11
| sk_c7 = sk_c8
| sk_c2 = sk_c1 ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_88,negated_conjecture,
( inverse(sk_c11) = sk_c1
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_48,c_0_82]) ).
cnf(c_0_89,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
prove_this_33 ).
cnf(c_0_90,negated_conjecture,
( sk_c2 = sk_c1
| sk_c9 = identity
| sk_c7 = sk_c8
| multiply(sk_c1,sk_c11) != sk_c11
| multiply(X1,sk_c10) != sk_c9
| multiply(X2,sk_c11) != sk_c10
| multiply(X3,sk_c10) != sk_c11
| multiply(X4,sk_c10) != sk_c11
| inverse(X1) != sk_c10
| inverse(X2) != sk_c11
| inverse(X3) != sk_c10
| inverse(X4) != sk_c11 ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_91,negated_conjecture,
( multiply(sk_c1,sk_c11) = identity
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_40,c_0_88]) ).
cnf(c_0_92,negated_conjecture,
( multiply(inverse(sk_c4),sk_c9) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_42,c_0_89]) ).
cnf(c_0_93,negated_conjecture,
( sk_c7 = sk_c8
| sk_c9 = identity
| sk_c2 = sk_c1
| multiply(X1,sk_c10) != sk_c9
| multiply(X2,sk_c11) != sk_c10
| multiply(X3,sk_c10) != sk_c11
| multiply(X4,sk_c10) != sk_c11
| inverse(X1) != sk_c10
| inverse(X2) != sk_c11
| inverse(X3) != sk_c10
| inverse(X4) != sk_c11 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_83]) ).
cnf(c_0_94,negated_conjecture,
( multiply(inverse(inverse(sk_c4)),sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_42,c_0_92]) ).
cnf(c_0_95,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| inverse(sk_c4) = sk_c10 ),
prove_this_34 ).
cnf(c_0_96,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c7) = sk_c6 ),
prove_this_28 ).
cnf(c_0_97,negated_conjecture,
( sk_c2 = sk_c1
| sk_c9 = identity
| sk_c7 = sk_c8
| multiply(X1,multiply(X2,sk_c10)) != sk_c9
| inverse(multiply(X1,X2)) != sk_c10
| multiply(X3,sk_c11) != sk_c10
| multiply(X4,sk_c10) != sk_c11
| multiply(X5,sk_c10) != sk_c11
| inverse(X3) != sk_c11
| inverse(X4) != sk_c10
| inverse(X5) != sk_c11 ),
inference(spm,[status(thm)],[c_0_93,c_0_39]) ).
cnf(c_0_98,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| sk_c9 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_40]) ).
cnf(c_0_99,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c6) = sk_c8 ),
prove_this_29 ).
cnf(c_0_100,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_48,c_0_96]) ).
cnf(c_0_101,negated_conjecture,
( sk_c7 = sk_c8
| sk_c9 = identity
| sk_c2 = sk_c1
| inverse(multiply(X1,sk_c2)) != sk_c10
| multiply(X1,sk_c11) != sk_c9
| multiply(X2,sk_c11) != sk_c10
| multiply(X3,sk_c10) != sk_c11
| multiply(X4,sk_c10) != sk_c11
| inverse(X2) != sk_c11
| inverse(X3) != sk_c10
| inverse(X4) != sk_c11 ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_102,negated_conjecture,
( sk_c2 = sk_c1
| sk_c7 = sk_c8
| sk_c10 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_87]),c_0_40]) ).
cnf(c_0_103,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_104,negated_conjecture,
( sk_c2 = sk_c1
| sk_c9 = identity
| sk_c7 = sk_c8
| multiply(X1,sk_c11) != sk_c10
| multiply(X2,sk_c10) != sk_c11
| multiply(X3,sk_c10) != sk_c11
| inverse(X1) != sk_c11
| inverse(X2) != sk_c10
| inverse(X3) != sk_c11 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_79]),c_0_74]),c_0_102]),c_0_58]) ).
cnf(c_0_105,negated_conjecture,
( multiply(inverse(sk_c1),sk_c11) = sk_c10
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_42,c_0_103]) ).
cnf(c_0_106,negated_conjecture,
( sk_c7 = sk_c8
| sk_c9 = identity
| sk_c2 = sk_c1
| multiply(X1,sk_c10) != sk_c11
| multiply(X2,sk_c10) != sk_c11
| inverse(X1) != sk_c10
| inverse(X2) != sk_c11 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_40]),c_0_48])]),c_0_102]) ).
cnf(c_0_107,negated_conjecture,
( multiply(sk_c11,sk_c11) = sk_c10
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_105,c_0_82]) ).
cnf(c_0_108,negated_conjecture,
( sk_c2 = sk_c1
| sk_c9 = identity
| sk_c7 = sk_c8
| multiply(X1,sk_c10) != sk_c11
| inverse(X1) != sk_c11 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_40]),c_0_48])]),c_0_83]) ).
cnf(c_0_109,negated_conjecture,
( multiply(inverse(sk_c11),sk_c10) = sk_c11
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_42,c_0_107]) ).
cnf(c_0_110,negated_conjecture,
( multiply(sk_c6,multiply(sk_c7,X1)) = X1
| inverse(sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_42,c_0_54]) ).
cnf(c_0_111,negated_conjecture,
( sk_c7 = sk_c8
| sk_c9 = identity
| sk_c2 = sk_c1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_48])]) ).
cnf(c_0_112,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c5) = sk_c8 ),
prove_this_46 ).
cnf(c_0_113,negated_conjecture,
( multiply(sk_c6,multiply(sk_c8,X1)) = X1
| inverse(sk_c2) = sk_c10
| sk_c2 = sk_c1
| sk_c9 = identity ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_114,negated_conjecture,
( multiply(sk_c8,multiply(sk_c5,X1)) = X1
| inverse(sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_42,c_0_112]) ).
cnf(c_0_115,negated_conjecture,
( multiply(sk_c6,sk_c7) = identity
| inverse(sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_40,c_0_54]) ).
cnf(c_0_116,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
prove_this_45 ).
cnf(c_0_117,negated_conjecture,
( multiply(sk_c5,X1) = multiply(sk_c6,X1)
| inverse(sk_c2) = sk_c10
| sk_c9 = identity
| sk_c2 = sk_c1 ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_118,negated_conjecture,
( multiply(sk_c6,sk_c7) = identity
| multiply(sk_c10,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_40,c_0_115]) ).
cnf(c_0_119,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c10,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_40,c_0_116]) ).
cnf(c_0_120,negated_conjecture,
( multiply(sk_c5,X1) = multiply(sk_c6,X1)
| multiply(sk_c10,sk_c2) = identity
| sk_c2 = sk_c1
| sk_c9 = identity ),
inference(spm,[status(thm)],[c_0_40,c_0_117]) ).
cnf(c_0_121,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c11 ),
prove_this_5 ).
cnf(c_0_122,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
prove_this_35 ).
cnf(c_0_123,negated_conjecture,
( multiply(sk_c10,sk_c2) = identity
| multiply(sk_c6,sk_c8) = identity
| sk_c2 = sk_c1
| sk_c9 = identity ),
inference(spm,[status(thm)],[c_0_118,c_0_111]) ).
cnf(c_0_124,negated_conjecture,
( multiply(sk_c10,sk_c2) = identity
| multiply(sk_c6,sk_c8) = sk_c11
| sk_c9 = identity
| sk_c2 = sk_c1 ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_125,negated_conjecture,
( multiply(inverse(sk_c5),sk_c11) = sk_c8
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_42,c_0_121]) ).
cnf(c_0_126,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c5) = sk_c8 ),
prove_this_6 ).
cnf(c_0_127,negated_conjecture,
( multiply(inverse(sk_c5),sk_c11) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_42,c_0_122]) ).
cnf(c_0_128,negated_conjecture,
( multiply(sk_c10,sk_c2) = identity
| sk_c9 = identity
| sk_c2 = sk_c1
| sk_c11 = identity ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_129,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c8,sk_c11) = sk_c8 ),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_130,negated_conjecture,
( multiply(inverse(inverse(sk_c5)),sk_c8) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_42,c_0_127]) ).
cnf(c_0_131,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| inverse(sk_c5) = sk_c8 ),
prove_this_36 ).
cnf(c_0_132,negated_conjecture,
( inverse(sk_c10) = sk_c2
| sk_c11 = identity
| sk_c2 = sk_c1
| sk_c9 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_128]),c_0_45]) ).
cnf(c_0_133,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c4) = sk_c10 ),
prove_this_44 ).
cnf(c_0_134,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| sk_c11 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_129]),c_0_40]) ).
cnf(c_0_135,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| sk_c11 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_40]) ).
cnf(c_0_136,negated_conjecture,
( multiply(sk_c2,sk_c10) = identity
| sk_c9 = identity
| sk_c2 = sk_c1
| sk_c11 = identity ),
inference(spm,[status(thm)],[c_0_40,c_0_132]) ).
cnf(c_0_137,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c10) = sk_c4 ),
inference(spm,[status(thm)],[c_0_48,c_0_133]) ).
cnf(c_0_138,negated_conjecture,
( multiply(inverse(sk_c10),sk_c9) = sk_c11
| sk_c11 = identity ),
inference(spm,[status(thm)],[c_0_42,c_0_134]) ).
cnf(c_0_139,negated_conjecture,
( sk_c2 = sk_c1
| sk_c9 = identity
| sk_c11 = identity ),
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
cnf(c_0_140,negated_conjecture,
( multiply(sk_c10,sk_c2) = identity
| inverse(sk_c10) = sk_c4 ),
inference(spm,[status(thm)],[c_0_40,c_0_137]) ).
cnf(c_0_141,negated_conjecture,
( inverse(sk_c10) = sk_c11
| sk_c2 = sk_c1
| sk_c11 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_45]) ).
cnf(c_0_142,negated_conjecture,
( multiply(sk_c10,sk_c2) = identity
| sk_c11 = identity
| sk_c2 = sk_c1
| sk_c4 = sk_c11 ),
inference(spm,[status(thm)],[c_0_140,c_0_141]) ).
cnf(c_0_143,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c8) = sk_c5 ),
inference(spm,[status(thm)],[c_0_48,c_0_112]) ).
cnf(c_0_144,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c7,sk_c8) = sk_c6 ),
prove_this_10 ).
cnf(c_0_145,negated_conjecture,
( inverse(sk_c10) = sk_c4
| inverse(sk_c10) = sk_c2 ),
inference(spm,[status(thm)],[c_0_48,c_0_137]) ).
cnf(c_0_146,negated_conjecture,
( inverse(sk_c10) = sk_c2
| sk_c4 = sk_c11
| sk_c2 = sk_c1
| sk_c11 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_142]),c_0_45]) ).
cnf(c_0_147,negated_conjecture,
( inverse(sk_c8) = sk_c5
| inverse(sk_c10) = sk_c2 ),
inference(spm,[status(thm)],[c_0_48,c_0_143]) ).
cnf(c_0_148,negated_conjecture,
( multiply(sk_c7,multiply(sk_c8,X1)) = multiply(sk_c6,X1)
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_39,c_0_144]) ).
cnf(c_0_149,negated_conjecture,
( multiply(inverse(sk_c7),sk_c6) = sk_c8
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_42,c_0_144]) ).
cnf(c_0_150,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c7) = sk_c6 ),
prove_this_8 ).
cnf(c_0_151,negated_conjecture,
( inverse(sk_c10) = sk_c2
| sk_c4 != sk_c2 ),
inference(ef,[status(thm)],[c_0_145]) ).
cnf(c_0_152,negated_conjecture,
( multiply(inverse(sk_c2),sk_c11) = sk_c10
| sk_c11 = identity ),
inference(spm,[status(thm)],[c_0_42,c_0_135]) ).
cnf(c_0_153,negated_conjecture,
( inverse(sk_c2) = sk_c10
| sk_c11 = identity
| sk_c2 = sk_c1
| sk_c4 = sk_c11 ),
inference(spm,[status(thm)],[c_0_48,c_0_146]) ).
cnf(c_0_154,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c10) = sk_c2 ),
inference(spm,[status(thm)],[c_0_48,c_0_116]) ).
cnf(c_0_155,negated_conjecture,
( multiply(sk_c5,sk_c8) = identity
| inverse(sk_c10) = sk_c2 ),
inference(spm,[status(thm)],[c_0_40,c_0_147]) ).
cnf(c_0_156,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c6) = sk_c8 ),
prove_this_9 ).
cnf(c_0_157,negated_conjecture,
( multiply(sk_c7,sk_c8) = multiply(sk_c6,sk_c11)
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_148,c_0_129]) ).
cnf(c_0_158,negated_conjecture,
( multiply(inverse(sk_c7),multiply(sk_c6,X1)) = multiply(sk_c8,X1)
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_39,c_0_149]) ).
cnf(c_0_159,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c6,sk_c7) = identity ),
inference(spm,[status(thm)],[c_0_40,c_0_150]) ).
cnf(c_0_160,negated_conjecture,
( multiply(sk_c2,sk_c10) = identity
| sk_c4 != sk_c2 ),
inference(spm,[status(thm)],[c_0_40,c_0_151]) ).
cnf(c_0_161,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c10
| sk_c4 = sk_c11
| sk_c2 = sk_c1
| sk_c11 = identity ),
inference(spm,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_162,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| sk_c11 = identity
| sk_c2 = sk_c1
| sk_c2 = sk_c11 ),
inference(spm,[status(thm)],[c_0_154,c_0_141]) ).
cnf(c_0_163,negated_conjecture,
( multiply(sk_c5,sk_c8) = identity
| sk_c11 = identity
| sk_c2 = sk_c1
| sk_c2 = sk_c11 ),
inference(spm,[status(thm)],[c_0_155,c_0_141]) ).
cnf(c_0_164,negated_conjecture,
( multiply(sk_c8,multiply(sk_c6,X1)) = X1
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_42,c_0_156]) ).
cnf(c_0_165,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c6
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_144,c_0_157]) ).
cnf(c_0_166,negated_conjecture,
( inverse(sk_c7) = multiply(sk_c8,sk_c7)
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_159]),c_0_45]) ).
cnf(c_0_167,negated_conjecture,
( sk_c11 = identity
| sk_c4 != sk_c2 ),
inference(spm,[status(thm)],[c_0_135,c_0_160]) ).
cnf(c_0_168,negated_conjecture,
( sk_c2 = sk_c1
| sk_c4 = sk_c11
| sk_c11 = identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_161]),c_0_40])]) ).
cnf(c_0_169,negated_conjecture,
( sk_c2 = sk_c11
| sk_c2 = sk_c1
| sk_c11 = identity ),
inference(spm,[status(thm)],[c_0_162,c_0_163]) ).
cnf(c_0_170,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c8,sk_c10) = sk_c11 ),
prove_this_7 ).
cnf(c_0_171,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c8,sk_c6) = sk_c11 ),
inference(spm,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_172,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_150,c_0_166]) ).
cnf(c_0_173,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c5) = sk_c8 ),
prove_this_16 ).
cnf(c_0_174,negated_conjecture,
( sk_c2 = sk_c1
| sk_c11 = identity ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_168]),c_0_169]) ).
cnf(c_0_175,negated_conjecture,
( multiply(sk_c7,sk_c11) = multiply(sk_c6,sk_c10)
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_148,c_0_170]) ).
cnf(c_0_176,negated_conjecture,
( multiply(sk_c7,sk_c11) = multiply(sk_c6,sk_c6)
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_148,c_0_171]) ).
cnf(c_0_177,negated_conjecture,
( multiply(inverse(sk_c8),sk_c6) = sk_c7
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_42,c_0_172]) ).
cnf(c_0_178,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_48,c_0_156]) ).
cnf(c_0_179,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c8) = sk_c5 ),
inference(spm,[status(thm)],[c_0_48,c_0_173]) ).
cnf(c_0_180,negated_conjecture,
( inverse(sk_c8) = sk_c5
| inverse(sk_c1) = sk_c10
| sk_c11 = identity ),
inference(spm,[status(thm)],[c_0_143,c_0_174]) ).
cnf(c_0_181,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c3) = sk_c11 ),
prove_this_42 ).
cnf(c_0_182,negated_conjecture,
( multiply(inverse(sk_c8),sk_c11) = sk_c10
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_42,c_0_170]) ).
cnf(c_0_183,negated_conjecture,
( multiply(sk_c6,sk_c6) = multiply(sk_c6,sk_c10)
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_175,c_0_176]) ).
cnf(c_0_184,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c6,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_177,c_0_178]) ).
cnf(c_0_185,negated_conjecture,
( inverse(sk_c8) = sk_c5
| sk_c11 = identity
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_179,c_0_180]) ).
cnf(c_0_186,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| inverse(sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_40,c_0_181]) ).
cnf(c_0_187,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c6,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_182,c_0_178]) ).
cnf(c_0_188,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c6,sk_c10) = sk_c7 ),
inference(spm,[status(thm)],[c_0_183,c_0_184]) ).
cnf(c_0_189,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c3) = sk_c11 ),
prove_this_12 ).
cnf(c_0_190,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
prove_this_25 ).
cnf(c_0_191,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c4) = sk_c10 ),
prove_this_14 ).
cnf(c_0_192,negated_conjecture,
( multiply(sk_c5,sk_c8) = identity
| sk_c10 = sk_c11
| sk_c11 = identity ),
inference(spm,[status(thm)],[c_0_40,c_0_185]) ).
cnf(c_0_193,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c3) = sk_c11 ),
prove_this_2 ).
cnf(c_0_194,negated_conjecture,
( multiply(sk_c10,multiply(sk_c2,X1)) = X1
| multiply(sk_c11,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_42,c_0_186]) ).
cnf(c_0_195,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| multiply(sk_c11,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_40,c_0_65]) ).
cnf(c_0_196,negated_conjecture,
( multiply(inverse(sk_c6),sk_c10) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_42,c_0_187]) ).
cnf(c_0_197,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_48,c_0_150]) ).
cnf(c_0_198,negated_conjecture,
( inverse(multiply(sk_c8,sk_c7)) = sk_c7
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_48,c_0_166]) ).
cnf(c_0_199,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c10 ),
inference(spm,[status(thm)],[c_0_164,c_0_188]) ).
cnf(c_0_200,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c11) = sk_c3 ),
inference(spm,[status(thm)],[c_0_48,c_0_189]) ).
cnf(c_0_201,negated_conjecture,
( multiply(inverse(sk_c5),sk_c11) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_42,c_0_190]) ).
cnf(c_0_202,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c10) = sk_c4 ),
inference(spm,[status(thm)],[c_0_48,c_0_191]) ).
cnf(c_0_203,negated_conjecture,
( inverse(sk_c10) = sk_c4
| inverse(sk_c1) = sk_c10
| sk_c11 = identity ),
inference(spm,[status(thm)],[c_0_137,c_0_174]) ).
cnf(c_0_204,negated_conjecture,
( multiply(sk_c10,sk_c2) = identity
| sk_c10 = sk_c11
| sk_c11 = identity ),
inference(spm,[status(thm)],[c_0_119,c_0_192]) ).
cnf(c_0_205,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c11,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_40,c_0_193]) ).
cnf(c_0_206,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| multiply(sk_c10,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_194,c_0_195]) ).
cnf(c_0_207,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c7,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_196,c_0_197]) ).
cnf(c_0_208,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c10) = sk_c7 ),
inference(spm,[status(thm)],[c_0_198,c_0_199]) ).
cnf(c_0_209,negated_conjecture,
( inverse(sk_c11) = sk_c3
| inverse(sk_c11) = sk_c1 ),
inference(spm,[status(thm)],[c_0_48,c_0_200]) ).
cnf(c_0_210,negated_conjecture,
( multiply(inverse(inverse(sk_c5)),sk_c8) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_42,c_0_201]) ).
cnf(c_0_211,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c5) = sk_c8 ),
prove_this_26 ).
cnf(c_0_212,negated_conjecture,
( inverse(sk_c10) = sk_c4
| sk_c11 = identity
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_202,c_0_203]) ).
cnf(c_0_213,negated_conjecture,
( inverse(sk_c10) = sk_c2
| sk_c11 = identity
| sk_c10 = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_204]),c_0_45]) ).
cnf(c_0_214,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
prove_this_11 ).
cnf(c_0_215,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_205,c_0_206]) ).
cnf(c_0_216,negated_conjecture,
( multiply(inverse(sk_c7),sk_c11) = sk_c10
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_42,c_0_207]) ).
cnf(c_0_217,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c7) = sk_c10 ),
inference(spm,[status(thm)],[c_0_48,c_0_208]) ).
cnf(c_0_218,negated_conjecture,
( inverse(sk_c11) = sk_c1
| sk_c3 != sk_c1 ),
inference(ef,[status(thm)],[c_0_209]) ).
cnf(c_0_219,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| sk_c11 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_210,c_0_211]),c_0_40]) ).
cnf(c_0_220,negated_conjecture,
( sk_c10 = sk_c11
| sk_c11 = identity ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_213]),c_0_167]) ).
cnf(c_0_221,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c11) = sk_c1 ),
inference(spm,[status(thm)],[c_0_48,c_0_214]) ).
cnf(c_0_222,negated_conjecture,
( inverse(sk_c11) = sk_c3
| sk_c9 = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_215]),c_0_45]) ).
cnf(c_0_223,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c10,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_216,c_0_217]) ).
cnf(c_0_224,negated_conjecture,
( multiply(sk_c1,sk_c11) = identity
| sk_c3 != sk_c1 ),
inference(spm,[status(thm)],[c_0_40,c_0_218]) ).
cnf(c_0_225,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c11
| sk_c11 = identity ),
inference(spm,[status(thm)],[c_0_219,c_0_220]) ).
cnf(c_0_226,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| sk_c9 = sk_c10
| sk_c3 = sk_c1 ),
inference(spm,[status(thm)],[c_0_221,c_0_222]) ).
cnf(c_0_227,negated_conjecture,
( multiply(sk_c3,sk_c11) = identity
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_40,c_0_222]) ).
cnf(c_0_228,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c10
| sk_c9 != sk_c10 ),
inference(ef,[status(thm)],[c_0_223]) ).
cnf(c_0_229,negated_conjecture,
( sk_c11 = identity
| sk_c3 != sk_c1 ),
inference(spm,[status(thm)],[c_0_224,c_0_225]) ).
cnf(c_0_230,negated_conjecture,
( sk_c3 = sk_c1
| sk_c9 = sk_c10
| sk_c10 = identity ),
inference(spm,[status(thm)],[c_0_226,c_0_227]) ).
cnf(c_0_231,negated_conjecture,
( sk_c11 = identity
| sk_c9 != sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_228]),c_0_40]) ).
cnf(c_0_232,negated_conjecture,
( multiply(sk_c8,multiply(sk_c10,X1)) = multiply(sk_c11,X1)
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_39,c_0_170]) ).
cnf(c_0_233,negated_conjecture,
( multiply(inverse(sk_c1),sk_c11) = sk_c10
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_42,c_0_71]) ).
cnf(c_0_234,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| inverse(sk_c1) = sk_c11 ),
inference(spm,[status(thm)],[c_0_40,c_0_189]) ).
cnf(c_0_235,negated_conjecture,
( sk_c10 = identity
| sk_c11 = identity ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_230]),c_0_231]) ).
cnf(c_0_236,negated_conjecture,
( multiply(sk_c8,sk_c10) = multiply(sk_c11,sk_c9)
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_232,c_0_51]) ).
cnf(c_0_237,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| multiply(sk_c11,sk_c10) = sk_c11
| multiply(sk_c11,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_233,c_0_234]) ).
cnf(c_0_238,negated_conjecture,
sk_c11 = identity,
inference(spm,[status(thm)],[c_0_220,c_0_235]) ).
cnf(c_0_239,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c11,sk_c10) = sk_c11
| multiply(sk_c11,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_233,c_0_214]) ).
cnf(c_0_240,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_170,c_0_236]) ).
cnf(c_0_241,negated_conjecture,
( sk_c10 = identity
| sk_c3 = identity ),
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)],[c_0_237,c_0_238]),c_0_41]),c_0_238]),c_0_41]),c_0_238]),c_0_238]),c_0_238]),c_0_45])]) ).
cnf(c_0_242,negated_conjecture,
( sk_c10 = identity
| sk_c3 = sk_c10 ),
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)],[c_0_239,c_0_238]),c_0_45]),c_0_238]),c_0_41]),c_0_238]),c_0_238]),c_0_238]),c_0_45])]) ).
cnf(c_0_243,negated_conjecture,
( sk_c9 = sk_c10
| sk_c9 = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_240,c_0_238]),c_0_41]),c_0_238]),c_0_238]),c_0_45]) ).
cnf(c_0_244,negated_conjecture,
sk_c10 = identity,
inference(spm,[status(thm)],[c_0_241,c_0_242]) ).
cnf(c_0_245,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X3,sk_c10) != sk_c9
| multiply(X4,sk_c11) != sk_c10
| multiply(X5,sk_c10) != sk_c11
| multiply(X6,sk_c10) != sk_c11
| inverse(X3) != sk_c10
| inverse(X4) != sk_c11
| inverse(X5) != sk_c10
| inverse(X6) != sk_c11
| sk_c9 != sk_c10 ),
inference(spm,[status(thm)],[c_0_57,c_0_228]) ).
cnf(c_0_246,negated_conjecture,
sk_c9 = identity,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_243,c_0_244])]) ).
cnf(c_0_247,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(X2,inverse(X2)) != identity
| inverse(X2) != identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[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(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)],[c_0_245,c_0_238]),c_0_238]),c_0_238]),c_0_45]),c_0_238]),c_0_238]),c_0_238]),c_0_238])]),c_0_244]),c_0_45]),c_0_244]),c_0_45]),c_0_246]),c_0_244]),c_0_45]),c_0_244]),c_0_45]),c_0_244]),c_0_244]),c_0_74]),c_0_244]),c_0_246]),c_0_244])])])])]),c_0_74])]) ).
cnf(c_0_248,negated_conjecture,
( inverse(X1) != identity
| inverse(X1) != X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_247,c_0_74]),c_0_45]),c_0_45]),c_0_45])]) ).
cnf(c_0_249,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_248,c_0_74]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP338-1 : TPTP v8.1.2. Released v2.5.0.
% 0.03/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 02:08:30 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.65/0.67 start to proof: theBenchmark
% 1.96/2.05 % Version : CSE_E---1.5
% 1.96/2.05 % Problem : theBenchmark.p
% 1.96/2.05 % Proof found
% 1.96/2.05 % SZS status Theorem for theBenchmark.p
% 1.96/2.05 % SZS output start Proof
% See solution above
% 2.06/2.06 % Total time : 1.373000 s
% 2.06/2.06 % SZS output end Proof
% 2.06/2.06 % Total time : 1.376000 s
%------------------------------------------------------------------------------