%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP384-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:43:26 PM UTC 2026
% Result : Unsatisfiable 45.49s 7.17s
% Output : CNFRefutation 45.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 73
% Number of leaves : 48
% Syntax : Number of clauses : 330 ( 23 unt; 297 nHn; 294 RR)
% Number of literals : 836 ( 835 equ; 142 neg)
% Maximal clause size : 16 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% 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 : 102 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this_61,negated_conjecture,
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c10) != sk_c11
| inverse(X5) != X6
| multiply(X5,X6) != sk_c11
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| inverse(X3) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| inverse(X1) != X2
| multiply(X1,X2) != sk_c10
| multiply(sk_c11,sk_c9) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c11
| inverse(sk_c11) != sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_61) ).
cnf(prove_this_34,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
cnf(prove_this_33,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
cnf(prove_this_32,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
cnf(prove_this_31,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(prove_this_9,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
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_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(prove_this_36,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
cnf(prove_this_35,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
cnf(prove_this_37,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
cnf(prove_this_25,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_15,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_38,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
cnf(prove_this_40,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
cnf(prove_this_26,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_16,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_39,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
cnf(prove_this_49,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_49) ).
cnf(prove_this_47,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_47) ).
cnf(prove_this_42,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_13,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_4,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_14,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_55,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_55) ).
cnf(prove_this_56,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_56) ).
cnf(prove_this_48,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_48) ).
cnf(prove_this_8,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_2,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_50,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_50) ).
cnf(prove_this_46,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
cnf(prove_this_6,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_11,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_23,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_12,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_17,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_51,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_51) ).
cnf(prove_this_21,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_53,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_53) ).
cnf(prove_this_24,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_52,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_52) ).
cnf(prove_this_22,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_54,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_54) ).
cnf(prove_this_45,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_45) ).
cnf(c_0_48,negated_conjecture,
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c10) != sk_c11
| inverse(X5) != X6
| multiply(X5,X6) != sk_c11
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| inverse(X3) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| inverse(X1) != X2
| multiply(X1,X2) != sk_c10
| multiply(sk_c11,sk_c9) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c11
| inverse(sk_c11) != sk_c10 ),
inference(fof_simplification,[status(thm)],[prove_this_61]) ).
cnf(c_0_49,negated_conjecture,
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c10) != sk_c11
| inverse(X5) != X6
| multiply(X5,X6) != sk_c11
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| inverse(X3) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| inverse(X1) != X2
| multiply(X1,X2) != sk_c10
| multiply(sk_c11,sk_c9) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c11
| inverse(sk_c11) != sk_c10 ),
c_0_48 ).
cnf(c_0_50,negated_conjecture,
( inverse(X5) != sk_c11
| inverse(X4) != sk_c10
| inverse(sk_c11) != sk_c10
| multiply(X5,sk_c11) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(X3,inverse(X3)) != sk_c10
| multiply(X2,inverse(X2)) != sk_c11
| multiply(sk_c10,sk_c9) != sk_c11
| multiply(sk_c11,sk_c9) != sk_c10
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(inverse(X3),sk_c9) != sk_c10
| multiply(inverse(X2),sk_c10) != sk_c11
| inverse(multiply(X1,inverse(X2))) != inverse(X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_49])])]) ).
cnf(c_0_51,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
prove_this_34 ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c10 ),
prove_this_33 ).
cnf(c_0_53,negated_conjecture,
( inverse(X4) != sk_c11
| inverse(sk_c11) != sk_c10
| multiply(X4,sk_c11) != sk_c10
| multiply(X3,inverse(X3)) != sk_c10
| multiply(X2,inverse(X2)) != sk_c11
| multiply(sk_c10,sk_c9) != sk_c11
| multiply(sk_c11,sk_c9) != sk_c10
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(inverse(X3),sk_c9) != sk_c10
| multiply(inverse(X2),sk_c10) != sk_c11
| inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
cnf(c_0_54,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c10 ),
prove_this_32 ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
prove_this_31 ).
cnf(c_0_56,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_57,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c11) = sk_c10 ),
prove_this_9 ).
cnf(c_0_58,negated_conjecture,
( inverse(sk_c11) != sk_c10
| multiply(X3,inverse(X3)) != sk_c10
| multiply(X2,inverse(X2)) != sk_c11
| multiply(sk_c10,sk_c9) != sk_c11
| multiply(sk_c11,sk_c9) != sk_c10
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(inverse(X3),sk_c9) != sk_c10
| multiply(inverse(X2),sk_c10) != sk_c11
| inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).
cnf(c_0_59,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c8,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_60,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_61,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_62,negated_conjecture,
( multiply(X3,inverse(X3)) != sk_c10
| multiply(X2,inverse(X2)) != sk_c11
| multiply(sk_c10,sk_c9) != sk_c11
| multiply(sk_c11,sk_c9) != sk_c10
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(inverse(X3),sk_c9) != sk_c10
| multiply(inverse(X2),sk_c10) != sk_c11
| inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c8,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_63,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c10 ),
prove_this_36 ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c10 ),
prove_this_35 ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c10 ),
prove_this_37 ).
cnf(c_0_66,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_56]),c_0_61]) ).
cnf(c_0_67,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
prove_this_25 ).
cnf(c_0_68,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
prove_this_15 ).
cnf(c_0_69,negated_conjecture,
( multiply(X2,inverse(X2)) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c11
| multiply(sk_c11,sk_c9) != sk_c10
| inverse(X1) != multiply(X1,sk_c8)
| multiply(inverse(X2),sk_c9) != sk_c10
| inverse(multiply(X1,sk_c8)) != sk_c8
| multiply(sk_c8,sk_c6) = identity
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]),c_0_65]) ).
cnf(c_0_70,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c10 ),
prove_this_38 ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c10 ),
prove_this_40 ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(inverse(sk_c5),sk_c11) = sk_c8 ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_73,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c11,sk_c9) = sk_c10 ),
prove_this_26 ).
cnf(c_0_74,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(inverse(sk_c5),sk_c11) = sk_c8 ),
inference(spm,[status(thm)],[c_0_66,c_0_68]) ).
cnf(c_0_75,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c10,sk_c9) = sk_c11 ),
prove_this_16 ).
cnf(c_0_76,negated_conjecture,
( multiply(X1,inverse(X1)) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c11
| multiply(sk_c11,sk_c9) != sk_c10
| multiply(inverse(X1),sk_c9) != sk_c10
| inverse(multiply(sk_c7,sk_c8)) != sk_c8
| multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c8,sk_c6) = identity ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]) ).
cnf(c_0_77,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c10 ),
prove_this_39 ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c8
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_79,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c8
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_80,negated_conjecture,
( multiply(X1,inverse(X1)) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c11
| multiply(sk_c11,sk_c9) != sk_c10
| multiply(inverse(X1),sk_c9) != sk_c10
| multiply(sk_c8,sk_c6) = identity
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_71]),c_0_77]) ).
cnf(c_0_81,negated_conjecture,
( identity = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_78]),c_0_56]) ).
cnf(c_0_82,negated_conjecture,
( identity = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_79]),c_0_56]) ).
cnf(c_0_83,negated_conjecture,
( multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X1),sk_c9) != sk_c10
| identity = sk_c11
| multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c8,sk_c6) = identity ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]) ).
cnf(c_0_84,negated_conjecture,
( identity = sk_c11
| multiply(sk_c8,sk_c6) = identity
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_54]),c_0_55]),c_0_81]) ).
cnf(c_0_85,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c2 ),
prove_this_49 ).
cnf(c_0_86,negated_conjecture,
( identity = sk_c11
| multiply(sk_c8,sk_c6) = identity
| multiply(inverse(sk_c1),sk_c10) = sk_c2 ),
inference(spm,[status(thm)],[c_0_66,c_0_84]) ).
cnf(c_0_87,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c8,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_56,c_0_85]) ).
cnf(c_0_88,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(inverse(sk_c1),sk_c10) = sk_c2 ),
inference(spm,[status(thm)],[c_0_66,c_0_65]) ).
cnf(c_0_89,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c2 ),
prove_this_47 ).
cnf(c_0_90,negated_conjecture,
( identity = sk_c11
| multiply(sk_c2,sk_c10) = sk_c2
| multiply(sk_c8,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_91,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c2
| multiply(sk_c8,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_92,negated_conjecture,
( identity = sk_c10
| identity = sk_c11
| multiply(sk_c8,sk_c6) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_90]),c_0_56]) ).
cnf(c_0_93,negated_conjecture,
( identity = sk_c10
| multiply(sk_c8,sk_c10) = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_91]),c_0_56]) ).
cnf(c_0_94,negated_conjecture,
( identity = sk_c11
| identity = sk_c10
| multiply(inverse(sk_c8),identity) = sk_c6 ),
inference(spm,[status(thm)],[c_0_66,c_0_92]) ).
cnf(c_0_95,negated_conjecture,
( identity = sk_c10
| multiply(inverse(sk_c8),sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_66,c_0_93]) ).
cnf(c_0_96,negated_conjecture,
( identity = sk_c10
| identity = sk_c11
| multiply(inverse(sk_c8),X1) = multiply(sk_c6,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_94]),c_0_61]) ).
cnf(c_0_97,negated_conjecture,
( identity = sk_c10
| identity = sk_c11
| multiply(sk_c6,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_98,negated_conjecture,
( identity = sk_c11
| identity = sk_c10
| multiply(sk_c6,multiply(sk_c11,X1)) = multiply(sk_c10,X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_97]) ).
cnf(c_0_99,negated_conjecture,
( identity = sk_c11
| identity = sk_c10
| multiply(sk_c8,multiply(sk_c6,X1)) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_92]),c_0_61]) ).
cnf(c_0_100,negated_conjecture,
( identity = sk_c10
| identity = sk_c11
| multiply(sk_c6,sk_c10) = multiply(sk_c10,sk_c9) ),
inference(spm,[status(thm)],[c_0_98,c_0_81]) ).
cnf(c_0_101,negated_conjecture,
( identity = sk_c10
| identity = sk_c11
| multiply(sk_c8,multiply(sk_c10,sk_c9)) = sk_c10 ),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_102,negated_conjecture,
( identity = sk_c11
| identity = sk_c10
| multiply(sk_c6,multiply(sk_c8,X1)) = X1 ),
inference(spm,[status(thm)],[c_0_66,c_0_96]) ).
cnf(c_0_103,negated_conjecture,
( identity = sk_c11
| identity = sk_c10
| multiply(sk_c8,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_101,c_0_82]) ).
cnf(c_0_104,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_56,c_0_54]) ).
cnf(c_0_105,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c2 ),
prove_this_42 ).
cnf(c_0_106,negated_conjecture,
( identity = sk_c10
| identity = sk_c11
| multiply(sk_c6,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_107,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| multiply(inverse(sk_c1),sk_c10) = sk_c2 ),
inference(spm,[status(thm)],[c_0_66,c_0_104]) ).
cnf(c_0_108,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c11,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_56,c_0_105]) ).
cnf(c_0_109,negated_conjecture,
( identity = sk_c11
| identity = sk_c10
| multiply(sk_c6,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_56,c_0_96]) ).
cnf(c_0_110,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_66,c_0_66]) ).
cnf(c_0_111,negated_conjecture,
( identity = sk_c11
| identity = sk_c10
| multiply(inverse(sk_c6),sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_66,c_0_106]) ).
cnf(c_0_112,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c2
| multiply(sk_c11,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_113,negated_conjecture,
( identity = sk_c10
| identity = sk_c11
| multiply(inverse(sk_c6),identity) = sk_c8 ),
inference(spm,[status(thm)],[c_0_66,c_0_109]) ).
cnf(c_0_114,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_56]),c_0_110]) ).
cnf(c_0_115,negated_conjecture,
( identity = sk_c10
| identity = sk_c11
| multiply(inverse(sk_c6),multiply(sk_c11,X1)) = multiply(sk_c10,X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_111]) ).
cnf(c_0_116,negated_conjecture,
( identity = sk_c10
| multiply(sk_c11,sk_c3) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_112]),c_0_56]) ).
cnf(c_0_117,negated_conjecture,
( identity = sk_c10
| multiply(inverse(sk_c8),multiply(sk_c11,X1)) = multiply(sk_c10,X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_95]) ).
cnf(c_0_118,negated_conjecture,
( identity = sk_c11
| identity = sk_c10
| inverse(sk_c6) = sk_c8 ),
inference(rw,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_119,negated_conjecture,
( identity = sk_c11
| identity = sk_c10
| inverse(sk_c6) = multiply(sk_c10,sk_c3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_114]) ).
cnf(c_0_120,negated_conjecture,
( identity = sk_c10
| identity = sk_c11
| inverse(sk_c8) = sk_c6 ),
inference(rw,[status(thm)],[c_0_94,c_0_114]) ).
cnf(c_0_121,negated_conjecture,
( identity = sk_c10
| inverse(sk_c8) = multiply(sk_c10,sk_c3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_116]),c_0_114]) ).
cnf(c_0_122,negated_conjecture,
( identity = sk_c10
| identity = sk_c11
| multiply(sk_c10,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_123,negated_conjecture,
( identity = sk_c11
| identity = sk_c10
| multiply(sk_c10,sk_c3) = sk_c6 ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_124,negated_conjecture,
( sk_c6 = sk_c8
| identity = sk_c11
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_125,negated_conjecture,
( identity = sk_c10
| sk_c6 = sk_c8
| multiply(X1,sk_c11) = X1 ),
inference(spm,[status(thm)],[c_0_114,c_0_124]) ).
cnf(c_0_126,negated_conjecture,
( identity = sk_c10
| sk_c6 = sk_c8
| multiply(sk_c11,X1) = X1 ),
inference(spm,[status(thm)],[c_0_61,c_0_124]) ).
cnf(c_0_127,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c11) = sk_c10 ),
prove_this_1 ).
cnf(c_0_128,negated_conjecture,
( sk_c6 = sk_c8
| identity = sk_c10
| inverse(sk_c11) = identity ),
inference(spm,[status(thm)],[c_0_56,c_0_125]) ).
cnf(c_0_129,negated_conjecture,
( identity = sk_c3
| identity = sk_c10
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_116,c_0_126]) ).
cnf(c_0_130,negated_conjecture,
( identity = sk_c10
| sk_c6 = sk_c8
| multiply(sk_c3,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_131,negated_conjecture,
( sk_c3 != sk_c10
| sk_c6 = sk_c8
| identity = sk_c10 ),
inference(ef,[status(thm)],[c_0_129]) ).
cnf(c_0_132,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c10,sk_c9) = sk_c11 ),
prove_this_13 ).
cnf(c_0_133,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_114]),c_0_114]) ).
cnf(c_0_134,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c11) = sk_c10 ),
prove_this_4 ).
cnf(c_0_135,negated_conjecture,
( sk_c6 = sk_c8
| identity = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_130]),c_0_131]) ).
cnf(c_0_136,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_66,c_0_61]) ).
cnf(c_0_137,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(inverse(sk_c4),sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_66,c_0_132]) ).
cnf(c_0_138,negated_conjecture,
( inverse(sk_c10) = sk_c4
| inverse(sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_139,negated_conjecture,
( sk_c6 = sk_c8
| multiply(X1,sk_c10) = X1 ),
inference(spm,[status(thm)],[c_0_114,c_0_135]) ).
cnf(c_0_140,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c11) = sk_c10 ),
prove_this_3 ).
cnf(c_0_141,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_136,c_0_114]) ).
cnf(c_0_142,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(inverse(inverse(sk_c4)),sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_66,c_0_137]) ).
cnf(c_0_143,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
prove_this_14 ).
cnf(c_0_144,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(inverse(sk_c3),sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_66,c_0_55]) ).
cnf(c_0_145,negated_conjecture,
( inverse(sk_c10) = sk_c11
| inverse(sk_c10) = sk_c4 ),
inference(spm,[status(thm)],[c_0_133,c_0_138]) ).
cnf(c_0_146,negated_conjecture,
( sk_c6 = sk_c8
| inverse(sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_56,c_0_139]) ).
cnf(c_0_147,negated_conjecture,
( inverse(sk_c10) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_133,c_0_140]) ).
cnf(c_0_148,negated_conjecture,
( sk_c6 = sk_c8
| inverse(sk_c10) = sk_c10 ),
inference(spm,[status(thm)],[c_0_141,c_0_135]) ).
cnf(c_0_149,negated_conjecture,
( sk_c6 = sk_c8
| multiply(sk_c10,X1) = X1 ),
inference(spm,[status(thm)],[c_0_61,c_0_135]) ).
cnf(c_0_150,negated_conjecture,
( identity = sk_c9
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_56]) ).
cnf(c_0_151,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
prove_this_55 ).
cnf(c_0_152,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(inverse(inverse(sk_c3)),sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_66,c_0_144]) ).
cnf(c_0_153,negated_conjecture,
( identity = sk_c4
| identity = sk_c11
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_154,negated_conjecture,
( sk_c11 = sk_c10
| sk_c6 = sk_c8
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_155,negated_conjecture,
( sk_c9 = sk_c11
| identity = sk_c11
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_82,c_0_149]) ).
cnf(c_0_156,negated_conjecture,
( sk_c9 = sk_c11
| identity = sk_c9
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_150,c_0_149]) ).
cnf(c_0_157,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(inverse(sk_c5),sk_c11) = sk_c8 ),
inference(spm,[status(thm)],[c_0_66,c_0_151]) ).
cnf(c_0_158,negated_conjecture,
( identity = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_54]),c_0_56]) ).
cnf(c_0_159,negated_conjecture,
( sk_c4 != sk_c11
| sk_c6 = sk_c8
| identity = sk_c11 ),
inference(ef,[status(thm)],[c_0_153]) ).
cnf(c_0_160,negated_conjecture,
( sk_c4 = sk_c9
| sk_c6 = sk_c8
| sk_c11 = sk_c10 ),
inference(spm,[status(thm)],[c_0_139,c_0_154]) ).
cnf(c_0_161,negated_conjecture,
( sk_c6 = sk_c8
| sk_c9 = sk_c11 ),
inference(spm,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_162,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(inverse(inverse(sk_c5)),sk_c8) = sk_c11 ),
inference(spm,[status(thm)],[c_0_66,c_0_157]) ).
cnf(c_0_163,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c10 ),
prove_this_56 ).
cnf(c_0_164,negated_conjecture,
( identity = sk_c11
| multiply(inverse(sk_c11),sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_66,c_0_81]) ).
cnf(c_0_165,negated_conjecture,
( identity = sk_c10
| multiply(inverse(sk_c1),sk_c10) = sk_c2 ),
inference(spm,[status(thm)],[c_0_66,c_0_158]) ).
cnf(c_0_166,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c2 ),
prove_this_48 ).
cnf(c_0_167,negated_conjecture,
( identity = sk_c11
| sk_c6 = sk_c8
| sk_c11 = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_161]) ).
cnf(c_0_168,negated_conjecture,
( identity = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_163]),c_0_56]) ).
cnf(c_0_169,negated_conjecture,
( identity = sk_c11
| multiply(inverse(sk_c11),multiply(sk_c10,X1)) = multiply(sk_c9,X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_164]) ).
cnf(c_0_170,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c11) = sk_c10 ),
prove_this_8 ).
cnf(c_0_171,negated_conjecture,
( identity = sk_c10
| multiply(sk_c2,sk_c10) = sk_c2
| multiply(sk_c8,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_165,c_0_87]) ).
cnf(c_0_172,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_66,c_0_60]) ).
cnf(c_0_173,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c1) = sk_c2 ),
inference(spm,[status(thm)],[c_0_133,c_0_166]) ).
cnf(c_0_174,negated_conjecture,
( sk_c11 = sk_c10
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_135,c_0_167]) ).
cnf(c_0_175,negated_conjecture,
( identity = sk_c11
| multiply(sk_c2,multiply(sk_c9,X1)) = multiply(sk_c10,X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_168]) ).
cnf(c_0_176,negated_conjecture,
( identity = sk_c11
| multiply(sk_c9,sk_c9) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_82]),c_0_56]) ).
cnf(c_0_177,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_133,c_0_170]) ).
cnf(c_0_178,negated_conjecture,
( identity = sk_c10
| multiply(sk_c8,sk_c6) = identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_171]),c_0_56])]) ).
cnf(c_0_179,negated_conjecture,
( identity = sk_c10
| multiply(inverse(multiply(X1,inverse(sk_c1))),multiply(X1,sk_c2)) = sk_c10 ),
inference(spm,[status(thm)],[c_0_172,c_0_165]) ).
cnf(c_0_180,negated_conjecture,
( sk_c11 = sk_c10
| inverse(sk_c1) = sk_c2
| inverse(sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_173,c_0_174]) ).
cnf(c_0_181,negated_conjecture,
( identity = sk_c11
| multiply(sk_c10,sk_c9) = sk_c2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_176]),c_0_114]) ).
cnf(c_0_182,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_133,c_0_57]) ).
cnf(c_0_183,negated_conjecture,
( sk_c11 = sk_c10
| inverse(sk_c11) = sk_c10
| inverse(sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_177,c_0_174]) ).
cnf(c_0_184,negated_conjecture,
( identity = sk_c10
| inverse(sk_c8) = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_178]),c_0_114]) ).
cnf(c_0_185,negated_conjecture,
( identity = sk_c10
| sk_c11 = sk_c10
| inverse(sk_c8) = sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_180]),c_0_56])]) ).
cnf(c_0_186,negated_conjecture,
( sk_c2 = sk_c11
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_82,c_0_181]) ).
cnf(c_0_187,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c11) = sk_c10 ),
prove_this_2 ).
cnf(c_0_188,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c11) = sk_c10 ),
prove_this_10 ).
cnf(c_0_189,negated_conjecture,
( sk_c7 = sk_c6
| sk_c11 = sk_c10
| inverse(sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_182,c_0_183]) ).
cnf(c_0_190,negated_conjecture,
( sk_c7 = sk_c6
| identity = sk_c10
| sk_c11 = sk_c10 ),
inference(spm,[status(thm)],[c_0_184,c_0_185]) ).
cnf(c_0_191,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c2 ),
prove_this_50 ).
cnf(c_0_192,negated_conjecture,
( sk_c2 = sk_c11
| inverse(sk_c11) = sk_c11 ),
inference(spm,[status(thm)],[c_0_141,c_0_186]) ).
cnf(c_0_193,negated_conjecture,
( inverse(sk_c11) = sk_c3
| inverse(sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_133,c_0_187]) ).
cnf(c_0_194,negated_conjecture,
( multiply(sk_c10,sk_c11) = identity
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_56,c_0_188]) ).
cnf(c_0_195,negated_conjecture,
( sk_c11 = sk_c10
| sk_c7 = sk_c6
| inverse(sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_133,c_0_189]) ).
cnf(c_0_196,negated_conjecture,
( sk_c11 = sk_c10
| sk_c7 = sk_c6
| inverse(sk_c10) = sk_c10 ),
inference(spm,[status(thm)],[c_0_141,c_0_190]) ).
cnf(c_0_197,negated_conjecture,
( multiply(sk_c2,sk_c1) = identity
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_56,c_0_191]) ).
cnf(c_0_198,negated_conjecture,
( sk_c11 = sk_c10
| sk_c2 = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_127,c_0_192]) ).
cnf(c_0_199,negated_conjecture,
( sk_c11 = sk_c10
| sk_c3 = sk_c11
| sk_c2 = sk_c11 ),
inference(spm,[status(thm)],[c_0_193,c_0_192]) ).
cnf(c_0_200,negated_conjecture,
( multiply(sk_c10,sk_c11) = identity
| multiply(inverse(sk_c7),sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_66,c_0_194]) ).
cnf(c_0_201,negated_conjecture,
( sk_c11 = sk_c10
| sk_c7 = sk_c6 ),
inference(spm,[status(thm)],[c_0_195,c_0_196]) ).
cnf(c_0_202,negated_conjecture,
( multiply(sk_c2,sk_c1) = identity
| multiply(inverse(sk_c7),sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_66,c_0_197]) ).
cnf(c_0_203,negated_conjecture,
( sk_c2 = sk_c11
| multiply(sk_c11,sk_c11) = identity ),
inference(spm,[status(thm)],[c_0_56,c_0_192]) ).
cnf(c_0_204,negated_conjecture,
( sk_c2 = sk_c11
| sk_c11 = sk_c10
| multiply(sk_c11,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_198,c_0_199]) ).
cnf(c_0_205,negated_conjecture,
( identity = sk_c8
| sk_c11 = sk_c10
| multiply(sk_c10,sk_c11) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_201]),c_0_56]) ).
cnf(c_0_206,negated_conjecture,
( identity = sk_c8
| sk_c11 = sk_c10
| multiply(sk_c2,sk_c1) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_201]),c_0_56]) ).
cnf(c_0_207,negated_conjecture,
( identity = sk_c10
| sk_c2 = sk_c11
| sk_c11 = sk_c10 ),
inference(spm,[status(thm)],[c_0_203,c_0_204]) ).
cnf(c_0_208,negated_conjecture,
( sk_c11 = sk_c10
| identity = sk_c8
| inverse(sk_c10) = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_205]),c_0_114]) ).
cnf(c_0_209,negated_conjecture,
( sk_c11 = sk_c10
| identity = sk_c8
| inverse(sk_c2) = sk_c1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_206]),c_0_114]) ).
cnf(c_0_210,negated_conjecture,
( sk_c11 = sk_c10
| sk_c2 = sk_c11 ),
inference(spm,[status(thm)],[c_0_186,c_0_207]) ).
cnf(c_0_211,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c2 ),
prove_this_46 ).
cnf(c_0_212,negated_conjecture,
( identity = sk_c8
| sk_c11 = sk_c10
| inverse(sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_133,c_0_208]) ).
cnf(c_0_213,negated_conjecture,
( identity = sk_c8
| sk_c11 = sk_c10
| inverse(sk_c11) = sk_c1 ),
inference(spm,[status(thm)],[c_0_209,c_0_210]) ).
cnf(c_0_214,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c8,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_56,c_0_211]) ).
cnf(c_0_215,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(inverse(sk_c5),sk_c11) = sk_c8 ),
inference(spm,[status(thm)],[c_0_66,c_0_64]) ).
cnf(c_0_216,negated_conjecture,
( sk_c1 = sk_c10
| sk_c11 = sk_c10
| identity = sk_c8 ),
inference(spm,[status(thm)],[c_0_212,c_0_213]) ).
cnf(c_0_217,negated_conjecture,
( identity = sk_c10
| multiply(sk_c2,sk_c10) = sk_c2
| multiply(sk_c8,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_165,c_0_214]) ).
cnf(c_0_218,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(inverse(inverse(sk_c5)),sk_c8) = sk_c11 ),
inference(spm,[status(thm)],[c_0_66,c_0_215]) ).
cnf(c_0_219,negated_conjecture,
( identity = sk_c10
| multiply(inverse(multiply(X1,sk_c8)),multiply(X1,sk_c11)) = sk_c10 ),
inference(spm,[status(thm)],[c_0_172,c_0_93]) ).
cnf(c_0_220,negated_conjecture,
( sk_c11 = sk_c10
| sk_c1 = sk_c10
| multiply(sk_c8,X1) = X1 ),
inference(spm,[status(thm)],[c_0_61,c_0_216]) ).
cnf(c_0_221,negated_conjecture,
( identity = sk_c10
| multiply(sk_c8,sk_c5) = identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_217]),c_0_56])]) ).
cnf(c_0_222,negated_conjecture,
( identity = sk_c11
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_63]),c_0_56]) ).
cnf(c_0_223,negated_conjecture,
( sk_c11 = sk_c10
| identity = sk_c10
| sk_c1 = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_219,c_0_220]),c_0_66])]) ).
cnf(c_0_224,negated_conjecture,
( identity = sk_c10
| inverse(sk_c8) = sk_c5 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_221]),c_0_114]) ).
cnf(c_0_225,negated_conjecture,
( identity = sk_c11
| multiply(inverse(sk_c1),sk_c10) = sk_c2 ),
inference(spm,[status(thm)],[c_0_66,c_0_222]) ).
cnf(c_0_226,negated_conjecture,
( sk_c8 = sk_c10
| sk_c11 = sk_c10
| sk_c1 = sk_c10 ),
inference(spm,[status(thm)],[c_0_216,c_0_223]) ).
cnf(c_0_227,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c11) = sk_c10 ),
prove_this_6 ).
cnf(c_0_228,negated_conjecture,
( identity = sk_c10
| multiply(sk_c10,sk_c3) = sk_c5 ),
inference(spm,[status(thm)],[c_0_121,c_0_224]) ).
cnf(c_0_229,negated_conjecture,
( identity = sk_c2
| identity = sk_c11
| sk_c11 = sk_c10
| sk_c8 = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_226]),c_0_56]) ).
cnf(c_0_230,negated_conjecture,
( inverse(sk_c8) = sk_c5
| inverse(sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_133,c_0_227]) ).
cnf(c_0_231,negated_conjecture,
( sk_c11 = sk_c10
| inverse(sk_c11) = sk_c10
| inverse(sk_c8) = sk_c8 ),
inference(spm,[status(thm)],[c_0_57,c_0_174]) ).
cnf(c_0_232,negated_conjecture,
( sk_c5 = sk_c8
| identity = sk_c11
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_122,c_0_228]) ).
cnf(c_0_233,negated_conjecture,
( sk_c8 = sk_c10
| sk_c11 = sk_c10
| identity = sk_c11 ),
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_229]),c_0_186]) ).
cnf(c_0_234,negated_conjecture,
( sk_c5 = sk_c8
| sk_c11 = sk_c10
| inverse(sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_230,c_0_231]) ).
cnf(c_0_235,negated_conjecture,
( identity = sk_c10
| sk_c5 = sk_c8
| inverse(sk_c11) = sk_c11 ),
inference(spm,[status(thm)],[c_0_141,c_0_232]) ).
cnf(c_0_236,negated_conjecture,
( sk_c11 != sk_c10
| identity = sk_c10
| sk_c5 = sk_c8 ),
inference(ef,[status(thm)],[c_0_232]) ).
cnf(c_0_237,negated_conjecture,
( sk_c11 = sk_c10
| sk_c8 = sk_c10
| inverse(sk_c11) = sk_c11 ),
inference(spm,[status(thm)],[c_0_141,c_0_233]) ).
cnf(c_0_238,negated_conjecture,
( sk_c5 = sk_c8
| identity = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_235]),c_0_236]) ).
cnf(c_0_239,negated_conjecture,
( sk_c11 = sk_c10
| identity = sk_c8
| sk_c8 = sk_c10 ),
inference(spm,[status(thm)],[c_0_212,c_0_237]) ).
cnf(c_0_240,negated_conjecture,
( sk_c11 = sk_c10
| sk_c5 = sk_c8
| inverse(sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_133,c_0_234]) ).
cnf(c_0_241,negated_conjecture,
( sk_c5 = sk_c8
| inverse(sk_c10) = sk_c10 ),
inference(spm,[status(thm)],[c_0_141,c_0_238]) ).
cnf(c_0_242,negated_conjecture,
( sk_c8 = sk_c11
| sk_c11 = sk_c10
| sk_c8 = sk_c10 ),
inference(spm,[status(thm)],[c_0_233,c_0_239]) ).
cnf(c_0_243,negated_conjecture,
( identity = sk_c10
| inverse(sk_c5) = sk_c8 ),
inference(spm,[status(thm)],[c_0_133,c_0_224]) ).
cnf(c_0_244,negated_conjecture,
( sk_c11 = sk_c10
| sk_c5 = sk_c8 ),
inference(spm,[status(thm)],[c_0_240,c_0_241]) ).
cnf(c_0_245,negated_conjecture,
( identity = sk_c10
| sk_c8 = sk_c10
| sk_c11 = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_242]),c_0_56])]) ).
cnf(c_0_246,negated_conjecture,
( identity = sk_c10
| sk_c11 = sk_c10
| inverse(sk_c8) = sk_c8 ),
inference(spm,[status(thm)],[c_0_243,c_0_244]) ).
cnf(c_0_247,negated_conjecture,
( sk_c11 = sk_c10
| sk_c8 = sk_c10 ),
inference(spm,[status(thm)],[c_0_233,c_0_245]) ).
cnf(c_0_248,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
prove_this_11 ).
cnf(c_0_249,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c11,sk_c9) = sk_c10 ),
prove_this_23 ).
cnf(c_0_250,negated_conjecture,
( sk_c11 = sk_c10
| identity = sk_c10
| inverse(sk_c10) = sk_c10 ),
inference(spm,[status(thm)],[c_0_246,c_0_247]) ).
cnf(c_0_251,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(inverse(sk_c3),sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_66,c_0_248]) ).
cnf(c_0_252,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
prove_this_12 ).
cnf(c_0_253,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(inverse(sk_c4),sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_66,c_0_249]) ).
cnf(c_0_254,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
prove_this_17 ).
cnf(c_0_255,negated_conjecture,
( sk_c11 = sk_c10
| identity = sk_c8
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_208,c_0_250]) ).
cnf(c_0_256,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
prove_this_51 ).
cnf(c_0_257,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_251,c_0_252]) ).
cnf(c_0_258,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c11,sk_c9) = sk_c10 ),
prove_this_21 ).
cnf(c_0_259,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
prove_this_53 ).
cnf(c_0_260,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(inverse(inverse(sk_c4)),sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_66,c_0_253]) ).
cnf(c_0_261,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c11,sk_c9) = sk_c10 ),
prove_this_24 ).
cnf(c_0_262,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c5,multiply(sk_c8,X1)) = multiply(sk_c11,X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_68]) ).
cnf(c_0_263,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(inverse(sk_c8),sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_66,c_0_254]) ).
cnf(c_0_264,negated_conjecture,
( inverse(sk_c8) = sk_c5
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_133,c_0_75]) ).
cnf(c_0_265,negated_conjecture,
( identity = sk_c10
| sk_c11 = sk_c10 ),
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_255]),c_0_247]) ).
cnf(c_0_266,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(inverse(sk_c3),sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_66,c_0_256]) ).
cnf(c_0_267,negated_conjecture,
( identity = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_257]),c_0_56]) ).
cnf(c_0_268,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(inverse(sk_c3),sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_66,c_0_258]) ).
cnf(c_0_269,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(inverse(sk_c4),sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_66,c_0_259]) ).
cnf(c_0_270,negated_conjecture,
( identity = sk_c9
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_260,c_0_261]),c_0_56]) ).
cnf(c_0_271,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c5,sk_c11) = multiply(sk_c11,sk_c10) ),
inference(spm,[status(thm)],[c_0_262,c_0_254]) ).
cnf(c_0_272,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_263,c_0_264]) ).
cnf(c_0_273,negated_conjecture,
( sk_c11 = sk_c10
| inverse(sk_c10) = sk_c10 ),
inference(spm,[status(thm)],[c_0_141,c_0_265]) ).
cnf(c_0_274,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(inverse(inverse(sk_c3)),sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_66,c_0_266]) ).
cnf(c_0_275,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
prove_this_52 ).
cnf(c_0_276,negated_conjecture,
( identity = sk_c10
| multiply(inverse(sk_c10),sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_66,c_0_267]) ).
cnf(c_0_277,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(inverse(inverse(sk_c3)),sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_66,c_0_268]) ).
cnf(c_0_278,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
prove_this_22 ).
cnf(c_0_279,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(inverse(inverse(sk_c4)),sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_66,c_0_269]) ).
cnf(c_0_280,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
prove_this_54 ).
cnf(c_0_281,negated_conjecture,
( identity = sk_c9
| multiply(inverse(sk_c11),sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_66,c_0_270]) ).
cnf(c_0_282,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_271,c_0_272]) ).
cnf(c_0_283,negated_conjecture,
( sk_c11 = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_147,c_0_273]) ).
cnf(c_0_284,negated_conjecture,
( sk_c4 = sk_c10
| sk_c11 = sk_c10 ),
inference(spm,[status(thm)],[c_0_145,c_0_273]) ).
cnf(c_0_285,negated_conjecture,
( identity = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_274,c_0_275]),c_0_56]) ).
cnf(c_0_286,negated_conjecture,
( identity = sk_c10
| multiply(inverse(sk_c10),multiply(sk_c11,X1)) = multiply(sk_c9,X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_276]) ).
cnf(c_0_287,negated_conjecture,
( identity = sk_c10
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_277,c_0_278]),c_0_56]) ).
cnf(c_0_288,negated_conjecture,
( identity = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_279,c_0_280]),c_0_56]) ).
cnf(c_0_289,negated_conjecture,
( identity = sk_c9
| multiply(inverse(sk_c11),multiply(sk_c10,X1)) = multiply(sk_c9,X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_281]) ).
cnf(c_0_290,negated_conjecture,
( sk_c11 = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_257,c_0_282]) ).
cnf(c_0_291,negated_conjecture,
( sk_c11 = sk_c10
| multiply(sk_c10,X1) = X1 ),
inference(spm,[status(thm)],[c_0_61,c_0_265]) ).
cnf(c_0_292,negated_conjecture,
( sk_c11 = sk_c10
| multiply(sk_c10,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_283,c_0_284]) ).
cnf(c_0_293,negated_conjecture,
( identity = sk_c10
| multiply(sk_c2,multiply(sk_c9,X1)) = multiply(sk_c10,X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_285]) ).
cnf(c_0_294,negated_conjecture,
( identity = sk_c10
| multiply(sk_c9,sk_c9) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_286,c_0_287]),c_0_56]) ).
cnf(c_0_295,negated_conjecture,
( identity = sk_c9
| multiply(sk_c2,multiply(sk_c9,X1)) = multiply(sk_c10,X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_288]) ).
cnf(c_0_296,negated_conjecture,
( identity = sk_c9
| multiply(sk_c9,sk_c9) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_289,c_0_150]),c_0_56]) ).
cnf(c_0_297,negated_conjecture,
( sk_c9 = sk_c11
| sk_c11 = sk_c10 ),
inference(spm,[status(thm)],[c_0_290,c_0_291]) ).
cnf(c_0_298,negated_conjecture,
( sk_c9 = sk_c10
| sk_c11 = sk_c10 ),
inference(spm,[status(thm)],[c_0_291,c_0_292]) ).
cnf(c_0_299,negated_conjecture,
( identity = sk_c10
| multiply(sk_c10,sk_c9) = sk_c2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_293,c_0_294]),c_0_114]) ).
cnf(c_0_300,negated_conjecture,
( identity = sk_c9
| multiply(sk_c10,sk_c9) = sk_c2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_295,c_0_296]),c_0_114]) ).
cnf(c_0_301,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c1) = sk_c2 ),
prove_this_45 ).
cnf(c_0_302,negated_conjecture,
( identity = sk_c9
| multiply(inverse(sk_c10),sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_66,c_0_150]) ).
cnf(c_0_303,negated_conjecture,
sk_c11 = sk_c10,
inference(spm,[status(thm)],[c_0_297,c_0_298]) ).
cnf(c_0_304,negated_conjecture,
( sk_c2 = sk_c11
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_267,c_0_299]) ).
cnf(c_0_305,negated_conjecture,
( sk_c2 = sk_c11
| identity = sk_c9 ),
inference(spm,[status(thm)],[c_0_150,c_0_300]) ).
cnf(c_0_306,negated_conjecture,
( identity = sk_c11
| multiply(inverse(sk_c2),sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_66,c_0_168]) ).
cnf(c_0_307,negated_conjecture,
( inverse(sk_c2) = sk_c1
| multiply(sk_c5,sk_c8) = sk_c11 ),
inference(spm,[status(thm)],[c_0_133,c_0_301]) ).
cnf(c_0_308,negated_conjecture,
identity = sk_c9,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_302,c_0_303]),c_0_56])]) ).
cnf(c_0_309,negated_conjecture,
( sk_c9 = sk_c10
| sk_c2 = sk_c11 ),
inference(spm,[status(thm)],[c_0_304,c_0_305]) ).
cnf(c_0_310,negated_conjecture,
( identity = sk_c10
| multiply(sk_c5,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_56,c_0_224]) ).
cnf(c_0_311,negated_conjecture,
( identity = sk_c11
| multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c11 ),
inference(spm,[status(thm)],[c_0_306,c_0_307]) ).
cnf(c_0_312,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(rw,[status(thm)],[c_0_158,c_0_308]) ).
cnf(c_0_313,negated_conjecture,
( sk_c2 = sk_c10
| sk_c9 = sk_c10 ),
inference(rw,[status(thm)],[c_0_309,c_0_303]) ).
cnf(c_0_314,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c5,sk_c8) = sk_c9 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_310,c_0_308]),c_0_308]) ).
cnf(c_0_315,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c5,sk_c8) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_311,c_0_303]),c_0_303]),c_0_308]) ).
cnf(c_0_316,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c1,sk_c10) = sk_c10 ),
inference(spm,[status(thm)],[c_0_312,c_0_313]) ).
cnf(c_0_317,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_314,c_0_315]) ).
cnf(c_0_318,negated_conjecture,
( identity != sk_c10
| sk_c9 != sk_c10
| inverse(X4) != sk_c11
| inverse(sk_c11) != sk_c10
| multiply(X4,sk_c11) != sk_c10
| multiply(X3,inverse(X3)) != sk_c10
| multiply(X2,inverse(X2)) != sk_c11
| multiply(sk_c10,sk_c9) != sk_c11
| multiply(sk_c11,sk_c9) != sk_c10
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(inverse(X3),sk_c9) != sk_c10
| multiply(inverse(X2),sk_c10) != sk_c11
| inverse(multiply(X1,inverse(X2))) != inverse(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_141]),c_0_61]) ).
cnf(c_0_319,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_56,c_0_133]) ).
cnf(c_0_320,plain,
multiply(X1,sk_c9) = X1,
inference(rw,[status(thm)],[c_0_114,c_0_308]) ).
cnf(c_0_321,negated_conjecture,
sk_c9 = sk_c10,
inference(spm,[status(thm)],[c_0_316,c_0_317]) ).
cnf(c_0_322,plain,
inverse(sk_c9) = sk_c9,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_141,c_0_308]),c_0_308]) ).
cnf(c_0_323,negated_conjecture,
( sk_c9 != sk_c10
| identity != sk_c10
| identity != sk_c11
| inverse(X4) != sk_c11
| inverse(sk_c11) != sk_c10
| multiply(X4,sk_c11) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c11
| multiply(sk_c11,sk_c9) != sk_c10
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(inverse(X3),sk_c9) != sk_c10
| multiply(inverse(X2),sk_c10) != sk_c11
| inverse(multiply(X1,inverse(X2))) != inverse(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_318,c_0_319]),c_0_319])]) ).
cnf(c_0_324,plain,
multiply(X1,sk_c10) = X1,
inference(rw,[status(thm)],[c_0_320,c_0_321]) ).
cnf(c_0_325,plain,
inverse(sk_c10) = sk_c10,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_322,c_0_321]),c_0_321]) ).
cnf(c_0_326,negated_conjecture,
( inverse(X3) != sk_c10
| inverse(X2) != sk_c10
| multiply(X1,inverse(X2)) != inverse(X1)
| inverse(multiply(X1,inverse(X2))) != inverse(X2) ),
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(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)],[c_0_323,c_0_303]),c_0_303]),c_0_303]),c_0_303]),c_0_303]),c_0_303]),c_0_303])]),c_0_324]),c_0_321]),c_0_324]),c_0_320]),c_0_324]),c_0_325]),c_0_308]),c_0_321]),c_0_321])])]),c_0_325])]) ).
cnf(c_0_327,negated_conjecture,
( inverse(X1) != X1
| inverse(X2) != sk_c10
| inverse(X1) != sk_c10 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_326,c_0_325]),c_0_324]),c_0_324]) ).
cnf(c_0_328,negated_conjecture,
inverse(X1) != sk_c10,
inference(spm,[status(thm)],[c_0_327,c_0_325]) ).
cnf(c_0_329,plain,
$false,
inference(sr,[status(thm)],[c_0_325,c_0_328]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP384-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.51 % Computer : n001.cluster.edu
% 0.10/0.51 % Model : x86_64 x86_64
% 0.10/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.51 % Memory : 8046.5625MB
% 0.10/0.51 % OS : Linux 6.8.0-71-generic
% 0.10/0.51 % CPULimit : 300
% 0.10/0.51 % WCLimit : 300
% 0.10/0.51 % DateTime : Sun Sep 20 20:16:28 UTC 2026
% 0.10/0.51 % CPUTime :
% 0.10/0.51 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.55 Running first-order theorem proving
% 0.17/0.56 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 45.49/7.17 % Version: 3.5.1
% 45.49/7.17 % Preprocessing class: FSMSSMSMSSSNFFN.
% 45.49/7.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 45.49/7.17 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 45.49/7.17 % Starting new_bool_3 with 300s (1) cores
% 45.49/7.17 % Starting new_bool_1 with 300s (1) cores
% 45.49/7.17 % Starting sh5l with 300s (1) cores
% 45.49/7.17 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 1305463 completed with status 0
% 45.49/7.17 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 45.49/7.17 % Preprocessing class: FSMSSMSMSSSNFFN.
% 45.49/7.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 45.49/7.17 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 45.49/7.17 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 45.49/7.17 % No SInE strategy applied
% 45.49/7.17 % Search class: FGHPS-FFMM21-SFFFFFNN
% 45.49/7.17 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 45.49/7.17 % Starting SubtermCWHack with 136s (1) cores
% 45.49/7.17 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 45.49/7.17 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 45.49/7.17 % Starting new_bool_3 with 136s (1) cores
% 45.49/7.17 % Starting new_bool_1 with 136s (1) cores
% 45.49/7.17 % new_bool_1 with pid 1305471 completed with status 0
% 45.49/7.17 % Result found by new_bool_1
% 45.49/7.17 % Preprocessing class: FSMSSMSMSSSNFFN.
% 45.49/7.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 45.49/7.17 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 45.49/7.17 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 45.49/7.17 % No SInE strategy applied
% 45.49/7.17 % Search class: FGHPS-FFMM21-SFFFFFNN
% 45.49/7.17 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 45.49/7.17 % Starting SubtermCWHack with 136s (1) cores
% 45.49/7.17 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 45.49/7.17 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 45.49/7.17 % Starting new_bool_3 with 136s (1) cores
% 45.49/7.17 % Starting new_bool_1 with 136s (1) cores
% 45.49/7.17 % Preprocessing time : 0.001 s
% 45.49/7.17 % Presaturation interreduction done
% 45.49/7.17
% 45.49/7.17 % Proof found!
% 45.49/7.17 % SZS status Unsatisfiable
% 45.49/7.17 % SZS output start CNFRefutation
% See solution above
% 45.49/7.17 % Parsed axioms : 64
% 45.49/7.17 % Removed by relevancy pruning/SinE : 0
% 45.49/7.17 % Initial clauses : 64
% 45.49/7.17 % Removed in clause preprocessing : 0
% 45.49/7.17 % Initial clauses in saturation : 64
% 45.49/7.17 % Processed clauses : 55386
% 45.49/7.17 % ...of these trivial : 717
% 45.49/7.17 % ...subsumed : 48813
% 45.49/7.17 % ...remaining for further processing : 5856
% 45.49/7.17 % Other redundant clauses eliminated : 78
% 45.49/7.17 % Clauses deleted for lack of memory : 0
% 45.49/7.17 % Backward-subsumed : 1793
% 45.49/7.17 % Backward-rewritten : 3966
% 45.49/7.17 % Generated clauses : 969499
% 45.49/7.17 % ...of the previous two non-redundant : 956356
% 45.49/7.17 % ...aggressively subsumed : 0
% 45.49/7.17 % Contextual simplify-reflections : 126
% 45.49/7.17 % Paramodulations : 969354
% 45.49/7.17 % Factorizations : 69
% 45.49/7.17 % NegExts : 0
% 45.49/7.17 % Equation resolutions : 78
% 45.49/7.17 % Disequality decompositions : 0
% 45.49/7.17 % Total rewrite steps : 254977
% 45.49/7.17 % ...of those cached : 250678
% 45.49/7.17 % Propositional unsat checks : 1
% 45.49/7.17 % Propositional check models : 0
% 45.49/7.17 % Propositional check unsatisfiable : 0
% 45.49/7.17 % Propositional clauses : 0
% 45.49/7.17 % Propositional clauses after purity: 0
% 45.49/7.17 % Propositional unsat core size : 0
% 45.49/7.17 % Propositional preprocessing time : 0.000
% 45.49/7.17 % Propositional encoding time : 0.413
% 45.49/7.17 % Propositional solver time : 0.114
% 45.49/7.17 % Success case prop preproc time : 0.000
% 45.49/7.17 % Success case prop encoding time : 0.000
% 45.49/7.17 % Success case prop solver time : 0.000
% 45.49/7.17 % Current number of processed clauses : 25
% 45.49/7.17 % Positive orientable unit clauses : 23
% 45.49/7.17 % Positive unorientable unit clauses: 0
% 45.49/7.17 % Negative unit clauses : 1
% 45.49/7.17 % Non-unit-clauses : 1
% 45.49/7.17 % Current number of unprocessed clauses: 888104
% 45.49/7.17 % ...number of literals in the above : 3299303
% 45.49/7.17 % Current number of archived formulas : 0
% 45.49/7.17 % Current number of archived clauses : 5824
% 45.49/7.17 % Clause-clause subsumption calls (NU) : 1141912
% 45.49/7.17 % Rec. Clause-clause subsumption calls : 450494
% 45.49/7.17 % Non-unit clause-clause subsumptions : 50677
% 45.49/7.17 % Unit Clause-clause subsumption calls : 3866
% 45.49/7.17 % Rewrite failures with RHS unbound : 0
% 45.49/7.17 % BW rewrite match attempts : 370
% 45.49/7.17 % BW rewrite match successes : 105
% 45.49/7.17 % Condensation attempts : 0
% 45.49/7.17 % Condensation successes : 0
% 45.49/7.17 % Termbank termtop insertions : 16719821
% 45.49/7.17 % Search garbage collected termcells : 44
% 45.49/7.17
% 45.49/7.17 % -------------------------------------------------
% 45.49/7.17 % User time : 6.031 s
% 45.49/7.17 % System time : 0.414 s
% 45.49/7.17 % Total time : 6.445 s
% 45.49/7.17 % Maximum resident set size: 3664 pages
% 45.49/7.17
% 45.49/7.17 % -------------------------------------------------
% 45.49/7.17 % User time : 30.585 s
% 45.49/7.17 % System time : 1.695 s
% 45.49/7.17 % Total time : 32.279 s
% 45.49/7.17 % Maximum resident set size: 4864 pages
% 45.49/7.17 % E exiting
%------------------------------------------------------------------------------