%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP320-1 : TPTP v9.2.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:25:33 PM UTC 2026
% Result : Unsatisfiable 45.53s 27.38s
% Output : CNFRefutation 45.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 33
% Syntax : Number of clauses : 357 ( 28 unt; 305 nHn; 296 RR)
% Number of literals : 826 ( 825 equ; 100 neg)
% Maximal clause size : 11 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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_25,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_21,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_2,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_30,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
cnf(prove_this_26,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_20,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_16,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_31,negated_conjecture,
( multiply(sk_c7,sk_c8) != sk_c6
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c7
| multiply(sk_c8,X2) != sk_c7
| multiply(X3,sk_c8) != X2
| inverse(X3) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| inverse(X4) != sk_c8
| multiply(X5,sk_c7) != sk_c6
| inverse(X5) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_15,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_13,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_12,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_8,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_29,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
cnf(prove_this_11,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_7,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_14,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_27,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_18,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_19,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_4,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_22,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_17,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_28,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
cnf(prove_this_23,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_9,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
cnf(c_0_33,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_34,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_35,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_36,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_37,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_34]) ).
cnf(c_0_38,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_36,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c6,sk_c8) = sk_c7 ),
prove_this_25 ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c4,sk_c8) = sk_c7 ),
prove_this_21 ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c6,sk_c8) = sk_c7 ),
prove_this_5 ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c4) = sk_c8 ),
prove_this_2 ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c4,sk_c8) = sk_c7 ),
prove_this_1 ).
cnf(c_0_44,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_45,negated_conjecture,
( multiply(inverse(sk_c2),sk_c3) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_36,c_0_39]) ).
cnf(c_0_46,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
prove_this_30 ).
cnf(c_0_47,negated_conjecture,
( multiply(inverse(sk_c2),sk_c3) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_36,c_0_40]) ).
cnf(c_0_48,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c7 ),
prove_this_26 ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c6,multiply(sk_c8,X1)) = multiply(sk_c7,X1)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_33,c_0_41]) ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_34,c_0_42]) ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c4,multiply(sk_c8,X1)) = multiply(sk_c7,X1)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_33,c_0_43]) ).
cnf(c_0_52,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_44]),c_0_44]) ).
cnf(c_0_53,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
prove_this_20 ).
cnf(c_0_54,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c7 ),
prove_this_16 ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c7,sk_c8) != sk_c6
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c7
| multiply(sk_c8,X2) != sk_c7
| multiply(X3,sk_c8) != X2
| inverse(X3) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| inverse(X4) != sk_c8
| multiply(X5,sk_c7) != sk_c6
| inverse(X5) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7 ),
prove_this_31 ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c4) = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_44]) ).
cnf(c_0_59,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c4) = sk_c4 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_50]),c_0_44]) ).
cnf(c_0_60,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_34,c_0_52]) ).
cnf(c_0_61,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
prove_this_15 ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c6,multiply(sk_c8,X1)) = multiply(sk_c7,X1)
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(spm,[status(thm)],[c_0_33,c_0_53]) ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c4,multiply(sk_c8,X1)) = multiply(sk_c7,X1)
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(spm,[status(thm)],[c_0_33,c_0_54]) ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c6,multiply(sk_c8,X1)) = multiply(sk_c7,X1)
| multiply(sk_c8,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_33,c_0_55]) ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c4,multiply(sk_c8,X1)) = multiply(sk_c7,X1)
| multiply(sk_c8,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_33,c_0_56]) ).
cnf(c_0_66,negated_conjecture,
( multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(sk_c6,sk_c8) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| multiply(X3,sk_c8) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| inverse(X2) != sk_c7
| inverse(X3) != sk_c8
| inverse(X1) != sk_c8
| inverse(X4) != sk_c7 ),
inference(er,[status(thm)],[c_0_57]) ).
cnf(c_0_67,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_68,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
prove_this_10 ).
cnf(c_0_69,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = identity ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_70,negated_conjecture,
( multiply(sk_c7,inverse(sk_c8)) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_60]),c_0_44]) ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c7,inverse(sk_c8)) = sk_c4
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_60]),c_0_44]) ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c7,inverse(sk_c8)) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_60]),c_0_44]) ).
cnf(c_0_73,negated_conjecture,
( multiply(sk_c7,inverse(sk_c8)) = sk_c4
| multiply(sk_c8,sk_c3) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_60]),c_0_44]) ).
cnf(c_0_74,negated_conjecture,
( sk_c4 = sk_c6
| multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| multiply(X3,sk_c8) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| inverse(X2) != sk_c7
| inverse(X3) != sk_c8
| inverse(X1) != sk_c8
| inverse(X4) != sk_c7 ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_75,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| identity = sk_c8 ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_76,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_77,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c8
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_78,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c5,sk_c7) = sk_c6 ),
prove_this_13 ).
cnf(c_0_79,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c8 ),
prove_this_12 ).
cnf(c_0_80,negated_conjecture,
( identity = sk_c8
| sk_c4 = sk_c6
| multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| multiply(X3,sk_c8) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| inverse(X2) != sk_c7
| inverse(X3) != sk_c8
| inverse(X1) != sk_c8
| inverse(X4) != sk_c7 ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_81,negated_conjecture,
( sk_c4 = sk_c6
| sk_c8 = sk_c7 ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_82,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c5,sk_c7) = sk_c6 ),
prove_this_8 ).
cnf(c_0_83,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = identity ),
inference(spm,[status(thm)],[c_0_60,c_0_78]) ).
cnf(c_0_84,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c7) = sk_c1 ),
inference(spm,[status(thm)],[c_0_52,c_0_79]) ).
cnf(c_0_85,negated_conjecture,
( sk_c4 = sk_c6
| identity = sk_c8
| multiply(X1,sk_c7) != sk_c6
| multiply(X2,sk_c8) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X1) != sk_c7
| inverse(X2) != sk_c8
| inverse(X3) != sk_c7 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_34]),c_0_44]),c_0_52])]),c_0_81]) ).
cnf(c_0_86,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| identity = sk_c8 ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_87,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c5) = sk_c7 ),
prove_this_29 ).
cnf(c_0_88,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c7 ),
prove_this_11 ).
cnf(c_0_89,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c8 ),
prove_this_7 ).
cnf(c_0_90,negated_conjecture,
( inverse(sk_c7) = sk_c1
| inverse(sk_c8) = sk_c4 ),
inference(spm,[status(thm)],[c_0_52,c_0_84]) ).
cnf(c_0_91,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c5) = sk_c7 ),
prove_this_14 ).
cnf(c_0_92,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c4) = sk_c8 ),
prove_this_27 ).
cnf(c_0_93,negated_conjecture,
( identity = sk_c8
| sk_c4 = sk_c6
| multiply(X1,sk_c8) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| inverse(sk_c5) != sk_c7
| inverse(X1) != sk_c8
| inverse(X2) != sk_c7 ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_94,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c8) = sk_c2 ),
inference(spm,[status(thm)],[c_0_52,c_0_87]) ).
cnf(c_0_95,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c7 ),
prove_this_6 ).
cnf(c_0_96,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = identity ),
inference(spm,[status(thm)],[c_0_60,c_0_88]) ).
cnf(c_0_97,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c4 ),
inference(spm,[status(thm)],[c_0_52,c_0_89]) ).
cnf(c_0_98,negated_conjecture,
( multiply(sk_c4,multiply(sk_c8,X1)) = X1
| inverse(sk_c7) = sk_c1 ),
inference(spm,[status(thm)],[c_0_36,c_0_90]) ).
cnf(c_0_99,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c7) = sk_c1 ),
inference(spm,[status(thm)],[c_0_52,c_0_91]) ).
cnf(c_0_100,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = sk_c2 ),
inference(spm,[status(thm)],[c_0_52,c_0_92]) ).
cnf(c_0_101,negated_conjecture,
( inverse(sk_c8) = sk_c2
| sk_c4 = sk_c6
| identity = sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| inverse(X2) != sk_c7 ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_102,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| identity = sk_c8 ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_103,negated_conjecture,
( multiply(sk_c4,multiply(sk_c8,X1)) = X1
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_36,c_0_97]) ).
cnf(c_0_104,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c3
| inverse(sk_c7) = sk_c1
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_98,c_0_77]) ).
cnf(c_0_105,negated_conjecture,
( inverse(sk_c7) = sk_c1
| sk_c4 = sk_c6
| identity = sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| inverse(X2) != sk_c7 ),
inference(spm,[status(thm)],[c_0_93,c_0_99]) ).
cnf(c_0_106,negated_conjecture,
( inverse(sk_c8) = sk_c2
| inverse(sk_c8) = sk_c4 ),
inference(spm,[status(thm)],[c_0_52,c_0_100]) ).
cnf(c_0_107,negated_conjecture,
( inverse(sk_c8) = sk_c2
| identity = sk_c8
| sk_c4 = sk_c6
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_100]) ).
cnf(c_0_108,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c3
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_103,c_0_77]) ).
cnf(c_0_109,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c3
| inverse(sk_c1) = sk_c7
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_52,c_0_104]) ).
cnf(c_0_110,negated_conjecture,
( inverse(sk_c7) = sk_c1
| identity = sk_c8
| sk_c4 = sk_c6
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_102]),c_0_84]) ).
cnf(c_0_111,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_35]) ).
cnf(c_0_112,negated_conjecture,
( inverse(sk_c8) = sk_c4
| sk_c2 != sk_c4 ),
inference(ef,[status(thm)],[c_0_106]) ).
cnf(c_0_113,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c3
| inverse(sk_c8) = sk_c2
| sk_c4 = sk_c6
| identity = sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_109]) ).
cnf(c_0_114,negated_conjecture,
( inverse(sk_c7) = sk_c1
| sk_c4 = sk_c6
| identity = sk_c8
| multiply(X1,multiply(X2,sk_c7)) != sk_c8
| inverse(multiply(X1,X2)) != sk_c7 ),
inference(spm,[status(thm)],[c_0_110,c_0_33]) ).
cnf(c_0_115,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_111]) ).
cnf(c_0_116,negated_conjecture,
( multiply(sk_c4,sk_c8) = identity
| sk_c2 != sk_c4 ),
inference(spm,[status(thm)],[c_0_34,c_0_112]) ).
cnf(c_0_117,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c8,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_34,c_0_48]) ).
cnf(c_0_118,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c3
| multiply(sk_c8,sk_c2) = identity
| identity = sk_c8
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_60,c_0_113]) ).
cnf(c_0_119,negated_conjecture,
( inverse(sk_c7) = sk_c1
| identity = sk_c8
| sk_c4 = sk_c6
| inverse(multiply(sk_c4,sk_c8)) != sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_98]),c_0_81]) ).
cnf(c_0_120,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_34,c_0_115]) ).
cnf(c_0_121,negated_conjecture,
( identity = sk_c8
| identity = sk_c7
| sk_c2 != sk_c4 ),
inference(spm,[status(thm)],[c_0_116,c_0_102]) ).
cnf(c_0_122,negated_conjecture,
( multiply(sk_c8,sk_c2) = identity
| sk_c4 = sk_c6
| identity = sk_c8
| sk_c3 = sk_c7 ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_123,negated_conjecture,
( inverse(sk_c7) = sk_c1
| sk_c4 = sk_c6
| identity = sk_c8
| sk_c2 != sk_c4 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_116]),c_0_120]),c_0_121]) ).
cnf(c_0_124,negated_conjecture,
( inverse(sk_c7) = sk_c1
| sk_c3 = sk_c7
| identity = sk_c8
| sk_c4 = sk_c6 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_122]),c_0_44]),c_0_123]) ).
cnf(c_0_125,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c8,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_34,c_0_89]) ).
cnf(c_0_126,negated_conjecture,
( multiply(sk_c1,sk_c7) = identity
| sk_c4 = sk_c6
| identity = sk_c8
| sk_c3 = sk_c7 ),
inference(spm,[status(thm)],[c_0_34,c_0_124]) ).
cnf(c_0_127,negated_conjecture,
( multiply(sk_c8,sk_c4) = identity
| sk_c3 = sk_c7
| sk_c4 = sk_c6
| identity = sk_c8 ),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_128,negated_conjecture,
( inverse(sk_c8) = sk_c2
| sk_c3 = sk_c7
| identity = sk_c8
| sk_c4 = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_122]),c_0_44]) ).
cnf(c_0_129,negated_conjecture,
( inverse(sk_c8) = sk_c4
| identity = sk_c8
| sk_c4 = sk_c6
| sk_c3 = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_127]),c_0_44]) ).
cnf(c_0_130,negated_conjecture,
( sk_c4 = sk_c6
| identity = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_77]),c_0_34]) ).
cnf(c_0_131,negated_conjecture,
( sk_c4 = sk_c6
| identity = sk_c8
| sk_c3 = sk_c7
| sk_c2 = sk_c4 ),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_132,negated_conjecture,
( sk_c2 = sk_c4
| sk_c3 = sk_c7
| sk_c3 = sk_c8
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_133,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c5,sk_c7) = sk_c6 ),
prove_this_18 ).
cnf(c_0_134,negated_conjecture,
( sk_c4 = sk_c6
| sk_c3 = sk_c7
| sk_c2 = sk_c4 ),
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_132]),c_0_81]) ).
cnf(c_0_135,negated_conjecture,
( multiply(sk_c5,multiply(sk_c7,X1)) = multiply(sk_c6,X1)
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(spm,[status(thm)],[c_0_33,c_0_133]) ).
cnf(c_0_136,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c5) = sk_c7 ),
prove_this_19 ).
cnf(c_0_137,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(spm,[status(thm)],[c_0_33,c_0_60]) ).
cnf(c_0_138,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c7
| sk_c2 = sk_c4
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_76,c_0_134]) ).
cnf(c_0_139,negated_conjecture,
( multiply(sk_c6,inverse(sk_c7)) = sk_c5
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_60]),c_0_44]) ).
cnf(c_0_140,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_52,c_0_136]) ).
cnf(c_0_141,negated_conjecture,
( sk_c4 = sk_c6
| sk_c2 = sk_c4
| identity = sk_c8 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_60]),c_0_44]) ).
cnf(c_0_142,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c5 ),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_143,negated_conjecture,
( multiply(X1,sk_c8) = X1
| sk_c2 = sk_c4
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_44,c_0_141]) ).
cnf(c_0_144,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c5) = sk_c7 ),
prove_this_4 ).
cnf(c_0_145,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c5,sk_c7) = sk_c6 ),
prove_this_3 ).
cnf(c_0_146,negated_conjecture,
( multiply(inverse(sk_c6),sk_c5) = sk_c5
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(spm,[status(thm)],[c_0_36,c_0_142]) ).
cnf(c_0_147,negated_conjecture,
( multiply(sk_c2,multiply(sk_c8,X1)) = multiply(sk_c3,X1)
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_33,c_0_39]) ).
cnf(c_0_148,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c4) = sk_c8 ),
prove_this_22 ).
cnf(c_0_149,negated_conjecture,
( sk_c2 = sk_c4
| sk_c4 = sk_c6
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_67,c_0_143]) ).
cnf(c_0_150,negated_conjecture,
( multiply(inverse(sk_c7),sk_c6) = sk_c4
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_36,c_0_58]) ).
cnf(c_0_151,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_52,c_0_144]) ).
cnf(c_0_152,negated_conjecture,
( multiply(sk_c5,multiply(sk_c7,X1)) = multiply(sk_c6,X1)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_33,c_0_145]) ).
cnf(c_0_153,negated_conjecture,
( multiply(inverse(sk_c6),sk_c7) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(spm,[status(thm)],[c_0_36,c_0_53]) ).
cnf(c_0_154,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c6) = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_146]),c_0_60]),c_0_44]) ).
cnf(c_0_155,negated_conjecture,
( multiply(sk_c3,inverse(sk_c8)) = sk_c2
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_60]),c_0_44]) ).
cnf(c_0_156,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c8) = sk_c2 ),
inference(spm,[status(thm)],[c_0_52,c_0_46]) ).
cnf(c_0_157,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c8,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_34,c_0_148]) ).
cnf(c_0_158,negated_conjecture,
( multiply(sk_c8,sk_c4) = identity
| inverse(sk_c8) = sk_c2 ),
inference(spm,[status(thm)],[c_0_34,c_0_100]) ).
cnf(c_0_159,negated_conjecture,
( sk_c6 = sk_c7
| sk_c4 = sk_c6
| identity = sk_c7
| identity = sk_c8 ),
inference(spm,[status(thm)],[c_0_121,c_0_149]) ).
cnf(c_0_160,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(spm,[status(thm)],[c_0_150,c_0_151]) ).
cnf(c_0_161,negated_conjecture,
( multiply(sk_c5,sk_c6) = multiply(sk_c6,sk_c4)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_152,c_0_58]) ).
cnf(c_0_162,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| sk_c8 = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_154]),c_0_35]) ).
cnf(c_0_163,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c3,sk_c2) = sk_c2 ),
inference(spm,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_164,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c4) = sk_c8 ),
prove_this_17 ).
cnf(c_0_165,negated_conjecture,
( multiply(inverse(sk_c2),sk_c3) = sk_c8
| multiply(sk_c8,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_36,c_0_157]) ).
cnf(c_0_166,negated_conjecture,
( multiply(sk_c8,sk_c4) = identity
| inverse(sk_c2) = sk_c8 ),
inference(spm,[status(thm)],[c_0_52,c_0_158]) ).
cnf(c_0_167,negated_conjecture,
( identity = sk_c7
| sk_c4 = sk_c6
| sk_c6 = sk_c7 ),
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_159]),c_0_81]) ).
cnf(c_0_168,negated_conjecture,
( multiply(sk_c6,sk_c4) = sk_c4
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_160,c_0_161]) ).
cnf(c_0_169,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_137]),c_0_44]) ).
cnf(c_0_170,negated_conjecture,
( multiply(inverse(sk_c8),sk_c7) = sk_c3
| sk_c8 = sk_c7 ),
inference(spm,[status(thm)],[c_0_36,c_0_162]) ).
cnf(c_0_171,negated_conjecture,
( multiply(inverse(sk_c3),sk_c2) = sk_c2
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_36,c_0_163]) ).
cnf(c_0_172,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_36,c_0_33]) ).
cnf(c_0_173,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c8,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_34,c_0_164]) ).
cnf(c_0_174,negated_conjecture,
( multiply(sk_c8,sk_c4) = identity
| multiply(sk_c8,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_165,c_0_166]) ).
cnf(c_0_175,negated_conjecture,
( sk_c6 = sk_c7
| sk_c3 = sk_c7
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_130,c_0_167]) ).
cnf(c_0_176,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c4 ),
inference(spm,[status(thm)],[c_0_52,c_0_42]) ).
cnf(c_0_177,negated_conjecture,
( multiply(inverse(sk_c6),sk_c4) = sk_c4
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_36,c_0_168]) ).
cnf(c_0_178,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c6) = sk_c8
| sk_c8 = sk_c7 ),
inference(spm,[status(thm)],[c_0_42,c_0_81]) ).
cnf(c_0_179,negated_conjecture,
( multiply(sk_c7,inverse(sk_c3)) = sk_c8
| sk_c8 = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_52]) ).
cnf(c_0_180,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c3) = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_171]),c_0_60]),c_0_44]) ).
cnf(c_0_181,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_60]),c_0_44]) ).
cnf(c_0_182,negated_conjecture,
( multiply(sk_c8,sk_c4) = identity
| sk_c8 = sk_c7 ),
inference(spm,[status(thm)],[c_0_173,c_0_174]) ).
cnf(c_0_183,negated_conjecture,
( multiply(sk_c4,multiply(sk_c8,X1)) = X1
| sk_c2 != sk_c4 ),
inference(spm,[status(thm)],[c_0_36,c_0_112]) ).
cnf(c_0_184,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c7
| sk_c6 = sk_c7
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_76,c_0_175]) ).
cnf(c_0_185,negated_conjecture,
( multiply(sk_c4,multiply(sk_c8,X1)) = X1
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_36,c_0_176]) ).
cnf(c_0_186,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c4) = sk_c4
| sk_c8 = sk_c7 ),
inference(spm,[status(thm)],[c_0_177,c_0_178]) ).
cnf(c_0_187,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| sk_c8 = sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_180]),c_0_44])]) ).
cnf(c_0_188,negated_conjecture,
( inverse(sk_c4) = sk_c8
| sk_c8 = sk_c7 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_182]),c_0_120]),c_0_35]) ).
cnf(c_0_189,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c7
| sk_c4 = sk_c6
| sk_c6 = sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_184]),c_0_149]) ).
cnf(c_0_190,negated_conjecture,
( multiply(inverse(multiply(X1,sk_c4)),multiply(X1,sk_c7)) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_172,c_0_43]) ).
cnf(c_0_191,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c4,sk_c4) = sk_c4
| sk_c8 = sk_c7 ),
inference(spm,[status(thm)],[c_0_185,c_0_186]) ).
cnf(c_0_192,negated_conjecture,
( multiply(inverse(sk_c6),sk_c7) = sk_c8
| sk_c8 = sk_c7 ),
inference(spm,[status(thm)],[c_0_36,c_0_187]) ).
cnf(c_0_193,negated_conjecture,
( inverse(sk_c6) = sk_c8
| sk_c8 = sk_c7 ),
inference(spm,[status(thm)],[c_0_188,c_0_81]) ).
cnf(c_0_194,negated_conjecture,
( sk_c4 = sk_c6
| sk_c6 = sk_c7
| identity = sk_c8 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_184]),c_0_60]),c_0_44]) ).
cnf(c_0_195,negated_conjecture,
( sk_c6 = sk_c7
| sk_c4 = sk_c6
| identity = sk_c4 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_189]),c_0_60]),c_0_44]) ).
cnf(c_0_196,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c8 = sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_191]),c_0_36])]) ).
cnf(c_0_197,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c8
| sk_c8 = sk_c7 ),
inference(spm,[status(thm)],[c_0_192,c_0_193]) ).
cnf(c_0_198,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c5,sk_c7) = sk_c6 ),
prove_this_28 ).
cnf(c_0_199,negated_conjecture,
( multiply(sk_c8,sk_c2) = identity
| inverse(sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_34,c_0_87]) ).
cnf(c_0_200,negated_conjecture,
( sk_c4 = sk_c8
| sk_c6 = sk_c7
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_194,c_0_195]) ).
cnf(c_0_201,negated_conjecture,
( multiply(inverse(sk_c7),sk_c6) = sk_c8
| sk_c8 = sk_c7 ),
inference(spm,[status(thm)],[c_0_36,c_0_196]) ).
cnf(c_0_202,negated_conjecture,
( inverse(sk_c7) = identity
| sk_c8 = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_197]),c_0_34]) ).
cnf(c_0_203,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c5,sk_c7) = sk_c6 ),
prove_this_23 ).
cnf(c_0_204,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c8,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_34,c_0_198]) ).
cnf(c_0_205,negated_conjecture,
( multiply(sk_c8,sk_c2) = identity
| multiply(sk_c5,sk_c7) = identity ),
inference(spm,[status(thm)],[c_0_60,c_0_199]) ).
cnf(c_0_206,negated_conjecture,
( sk_c6 = sk_c7
| sk_c4 = sk_c8
| sk_c6 != sk_c8 ),
inference(ef,[status(thm)],[c_0_200]) ).
cnf(c_0_207,negated_conjecture,
( sk_c8 = sk_c7
| sk_c6 = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_202]),c_0_35]) ).
cnf(c_0_208,negated_conjecture,
( multiply(sk_c2,multiply(sk_c8,X1)) = multiply(sk_c3,X1)
| multiply(sk_c5,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_33,c_0_203]) ).
cnf(c_0_209,negated_conjecture,
( multiply(sk_c8,sk_c2) = identity
| identity = sk_c6 ),
inference(spm,[status(thm)],[c_0_204,c_0_205]) ).
cnf(c_0_210,negated_conjecture,
( sk_c4 = sk_c8
| sk_c8 = sk_c7 ),
inference(spm,[status(thm)],[c_0_206,c_0_207]) ).
cnf(c_0_211,negated_conjecture,
( multiply(sk_c3,inverse(sk_c8)) = sk_c2
| multiply(sk_c5,sk_c7) = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_60]),c_0_44]) ).
cnf(c_0_212,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c8) = sk_c2 ),
inference(spm,[status(thm)],[c_0_52,c_0_198]) ).
cnf(c_0_213,negated_conjecture,
( multiply(sk_c6,inverse(sk_c8)) = sk_c7
| sk_c8 = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_201]),c_0_52]) ).
cnf(c_0_214,negated_conjecture,
( inverse(sk_c8) = sk_c4
| sk_c8 = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_182]),c_0_44]) ).
cnf(c_0_215,negated_conjecture,
( inverse(sk_c8) = sk_c2
| identity = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_209]),c_0_44]) ).
cnf(c_0_216,negated_conjecture,
( inverse(sk_c8) = sk_c8
| sk_c8 = sk_c7 ),
inference(spm,[status(thm)],[c_0_188,c_0_210]) ).
cnf(c_0_217,negated_conjecture,
( multiply(inverse(sk_c4),sk_c7) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_36,c_0_43]) ).
cnf(c_0_218,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c3,sk_c2) = sk_c2 ),
inference(spm,[status(thm)],[c_0_211,c_0_212]) ).
cnf(c_0_219,negated_conjecture,
( multiply(sk_c6,sk_c4) = sk_c7
| sk_c8 = sk_c7 ),
inference(spm,[status(thm)],[c_0_213,c_0_214]) ).
cnf(c_0_220,negated_conjecture,
( sk_c8 = sk_c7
| identity = sk_c6
| sk_c2 = sk_c8 ),
inference(spm,[status(thm)],[c_0_215,c_0_216]) ).
cnf(c_0_221,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_217,c_0_42]) ).
cnf(c_0_222,negated_conjecture,
( multiply(inverse(sk_c3),sk_c2) = sk_c2
| multiply(sk_c5,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_36,c_0_218]) ).
cnf(c_0_223,negated_conjecture,
( multiply(sk_c8,sk_c4) = sk_c7
| sk_c8 = sk_c7 ),
inference(spm,[status(thm)],[c_0_219,c_0_207]) ).
cnf(c_0_224,negated_conjecture,
( multiply(sk_c6,X1) = X1
| sk_c2 = sk_c8
| sk_c8 = sk_c7 ),
inference(spm,[status(thm)],[c_0_35,c_0_220]) ).
cnf(c_0_225,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,X1) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_221]),c_0_36]) ).
cnf(c_0_226,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c3) = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_222]),c_0_60]),c_0_44]) ).
cnf(c_0_227,negated_conjecture,
( inverse(sk_c3) = sk_c3
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_120,c_0_130]) ).
cnf(c_0_228,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_36,c_0_52]) ).
cnf(c_0_229,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c4
| sk_c8 = sk_c7
| sk_c2 != sk_c4 ),
inference(spm,[status(thm)],[c_0_183,c_0_223]) ).
cnf(c_0_230,negated_conjecture,
( sk_c2 = sk_c8
| sk_c8 = sk_c7 ),
inference(spm,[status(thm)],[c_0_187,c_0_224]) ).
cnf(c_0_231,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c8
| sk_c6 != sk_c8 ),
inference(ef,[status(thm)],[c_0_225]) ).
cnf(c_0_232,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| sk_c8 = sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_226]),c_0_44])]) ).
cnf(c_0_233,negated_conjecture,
( multiply(inverse(sk_c7),sk_c6) = sk_c8
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_36,c_0_67]) ).
cnf(c_0_234,negated_conjecture,
( inverse(sk_c7) = sk_c7
| sk_c2 = sk_c4
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_227,c_0_134]) ).
cnf(c_0_235,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c8
| sk_c2 = sk_c4
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_77,c_0_134]) ).
cnf(c_0_236,negated_conjecture,
( multiply(sk_c1,multiply(sk_c7,X1)) = multiply(sk_c8,X1)
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_33,c_0_68]) ).
cnf(c_0_237,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(X2),X3),
inference(spm,[status(thm)],[c_0_172,c_0_228]) ).
cnf(c_0_238,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c4
| sk_c8 = sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_230]),c_0_210]) ).
cnf(c_0_239,negated_conjecture,
( identity = sk_c7
| sk_c6 != sk_c8 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_231]),c_0_60]),c_0_44]) ).
cnf(c_0_240,negated_conjecture,
( multiply(inverse(sk_c5),sk_c6) = sk_c7
| sk_c8 = sk_c7 ),
inference(spm,[status(thm)],[c_0_36,c_0_232]) ).
cnf(c_0_241,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c2 = sk_c4
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_233,c_0_234]) ).
cnf(c_0_242,negated_conjecture,
( multiply(sk_c7,X1) = X1
| sk_c4 = sk_c6
| sk_c2 = sk_c4 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_235]),c_0_36]) ).
cnf(c_0_243,negated_conjecture,
( multiply(sk_c2,multiply(sk_c8,X1)) = X1
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_36,c_0_156]) ).
cnf(c_0_244,negated_conjecture,
( multiply(sk_c8,inverse(sk_c7)) = sk_c1
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_236,c_0_60]),c_0_44]) ).
cnf(c_0_245,negated_conjecture,
( multiply(inverse(sk_c7),X1) = X1
| sk_c8 = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_237,c_0_238]),c_0_36]) ).
cnf(c_0_246,negated_conjecture,
( inverse(sk_c7) = sk_c7
| sk_c6 != sk_c8 ),
inference(spm,[status(thm)],[c_0_120,c_0_239]) ).
cnf(c_0_247,negated_conjecture,
( inverse(sk_c8) = sk_c6
| sk_c8 = sk_c7 ),
inference(spm,[status(thm)],[c_0_52,c_0_193]) ).
cnf(c_0_248,negated_conjecture,
( multiply(sk_c6,inverse(sk_c7)) = sk_c5
| sk_c8 = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_240]),c_0_52]) ).
cnf(c_0_249,negated_conjecture,
( sk_c4 = sk_c6
| sk_c2 = sk_c4
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_241,c_0_242]) ).
cnf(c_0_250,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c7) = sk_c1 ),
inference(spm,[status(thm)],[c_0_52,c_0_61]) ).
cnf(c_0_251,negated_conjecture,
( inverse(sk_c7) = multiply(sk_c2,sk_c1)
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_243,c_0_244]) ).
cnf(c_0_252,negated_conjecture,
( multiply(sk_c7,X1) = X1
| sk_c8 = sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_245,c_0_246]),c_0_207]) ).
cnf(c_0_253,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c3
| sk_c8 = sk_c7 ),
inference(spm,[status(thm)],[c_0_170,c_0_247]) ).
cnf(c_0_254,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c8 = sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_248,c_0_246]),c_0_207]) ).
cnf(c_0_255,negated_conjecture,
( sk_c6 = sk_c8
| sk_c4 = sk_c6
| identity = sk_c7
| identity = sk_c8 ),
inference(spm,[status(thm)],[c_0_121,c_0_249]) ).
cnf(c_0_256,negated_conjecture,
( multiply(sk_c2,sk_c1) = sk_c1
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_250,c_0_251]) ).
cnf(c_0_257,negated_conjecture,
( inverse(sk_c3) = sk_c8
| sk_c8 = sk_c7 ),
inference(spm,[status(thm)],[c_0_179,c_0_252]) ).
cnf(c_0_258,negated_conjecture,
( sk_c8 = sk_c7
| sk_c3 = sk_c5 ),
inference(spm,[status(thm)],[c_0_253,c_0_254]) ).
cnf(c_0_259,negated_conjecture,
( multiply(sk_c5,multiply(sk_c7,X1)) = X1
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(spm,[status(thm)],[c_0_36,c_0_140]) ).
cnf(c_0_260,negated_conjecture,
( identity = sk_c7
| sk_c4 = sk_c6
| sk_c6 = sk_c8 ),
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_255]),c_0_81]) ).
cnf(c_0_261,negated_conjecture,
( multiply(inverse(sk_c2),sk_c1) = sk_c1
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_36,c_0_256]) ).
cnf(c_0_262,negated_conjecture,
( multiply(inverse(sk_c5),sk_c6) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_36,c_0_145]) ).
cnf(c_0_263,negated_conjecture,
( inverse(sk_c5) = sk_c8
| sk_c8 = sk_c7 ),
inference(spm,[status(thm)],[c_0_257,c_0_258]) ).
cnf(c_0_264,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c8) = sk_c4 ),
inference(spm,[status(thm)],[c_0_52,c_0_164]) ).
cnf(c_0_265,negated_conjecture,
( inverse(sk_c8) = multiply(sk_c5,sk_c4)
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(spm,[status(thm)],[c_0_259,c_0_71]) ).
cnf(c_0_266,negated_conjecture,
( multiply(sk_c7,multiply(sk_c1,X1)) = X1
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_36,c_0_61]) ).
cnf(c_0_267,negated_conjecture,
( multiply(sk_c7,X1) = X1
| sk_c6 = sk_c8
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_35,c_0_260]) ).
cnf(c_0_268,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c2) = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_261]),c_0_60]),c_0_44]) ).
cnf(c_0_269,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_262,c_0_144]) ).
cnf(c_0_270,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c4,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_60,c_0_164]) ).
cnf(c_0_271,negated_conjecture,
( inverse(sk_c7) = sk_c1
| sk_c8 = sk_c7 ),
inference(spm,[status(thm)],[c_0_99,c_0_263]) ).
cnf(c_0_272,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c5) = sk_c7 ),
prove_this_9 ).
cnf(c_0_273,negated_conjecture,
( multiply(sk_c5,sk_c4) = sk_c4
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(spm,[status(thm)],[c_0_264,c_0_265]) ).
cnf(c_0_274,negated_conjecture,
( multiply(sk_c3,multiply(X1,inverse(multiply(sk_c8,X1)))) = sk_c2
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_137]),c_0_44]) ).
cnf(c_0_275,negated_conjecture,
( multiply(sk_c8,multiply(sk_c1,X1)) = multiply(sk_c1,X1)
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_236,c_0_266]) ).
cnf(c_0_276,negated_conjecture,
( sk_c4 = sk_c6
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_67,c_0_267]) ).
cnf(c_0_277,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| identity = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_221]),c_0_34]) ).
cnf(c_0_278,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| sk_c3 = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_268]),c_0_35]) ).
cnf(c_0_279,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| identity = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_269]),c_0_34]) ).
cnf(c_0_280,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_269,c_0_225]) ).
cnf(c_0_281,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| identity = sk_c7 ),
inference(spm,[status(thm)],[c_0_54,c_0_270]) ).
cnf(c_0_282,negated_conjecture,
( multiply(sk_c1,X1) = X1
| sk_c8 = sk_c7 ),
inference(spm,[status(thm)],[c_0_245,c_0_271]) ).
cnf(c_0_283,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| sk_c8 = sk_c7 ),
inference(spm,[status(thm)],[c_0_272,c_0_263]) ).
cnf(c_0_284,negated_conjecture,
( multiply(inverse(sk_c5),sk_c4) = sk_c4
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(spm,[status(thm)],[c_0_36,c_0_273]) ).
cnf(c_0_285,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| sk_c3 = sk_c2 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_274,c_0_275]),c_0_33]),c_0_137]),c_0_44]) ).
cnf(c_0_286,negated_conjecture,
( inverse(sk_c8) = sk_c2
| inverse(sk_c6) = sk_c8
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_100,c_0_276]) ).
cnf(c_0_287,negated_conjecture,
( multiply(inverse(multiply(X1,sk_c7)),multiply(X1,sk_c6)) = sk_c8
| identity = sk_c7 ),
inference(spm,[status(thm)],[c_0_172,c_0_277]) ).
cnf(c_0_288,negated_conjecture,
( multiply(inverse(sk_c6),sk_c7) = sk_c8
| sk_c3 = sk_c8 ),
inference(spm,[status(thm)],[c_0_36,c_0_278]) ).
cnf(c_0_289,negated_conjecture,
( multiply(inverse(multiply(X1,sk_c7)),multiply(X1,sk_c6)) = sk_c8
| identity = sk_c6 ),
inference(spm,[status(thm)],[c_0_172,c_0_279]) ).
cnf(c_0_290,negated_conjecture,
( multiply(inverse(sk_c7),sk_c6) = sk_c8
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_36,c_0_280]) ).
cnf(c_0_291,negated_conjecture,
( multiply(inverse(sk_c8),sk_c7) = sk_c3
| identity = sk_c7 ),
inference(spm,[status(thm)],[c_0_36,c_0_281]) ).
cnf(c_0_292,negated_conjecture,
sk_c8 = sk_c7,
inference(spm,[status(thm)],[c_0_282,c_0_283]) ).
cnf(c_0_293,negated_conjecture,
( multiply(inverse(sk_c5),sk_c6) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(spm,[status(thm)],[c_0_36,c_0_133]) ).
cnf(c_0_294,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c5) = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_284]),c_0_60]),c_0_44]) ).
cnf(c_0_295,negated_conjecture,
( multiply(inverse(sk_c6),sk_c7) = sk_c8
| sk_c3 = sk_c2 ),
inference(spm,[status(thm)],[c_0_36,c_0_285]) ).
cnf(c_0_296,negated_conjecture,
( inverse(sk_c8) = sk_c2
| inverse(sk_c8) = sk_c6
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_52,c_0_286]) ).
cnf(c_0_297,negated_conjecture,
( inverse(sk_c8) = sk_c8
| sk_c3 = sk_c8
| identity = sk_c7 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_287,c_0_288]),c_0_34]),c_0_44]) ).
cnf(c_0_298,negated_conjecture,
( inverse(sk_c8) = sk_c8
| sk_c3 = sk_c8
| identity = sk_c6 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_289,c_0_288]),c_0_34]),c_0_44]) ).
cnf(c_0_299,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| identity = sk_c6 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_142]),c_0_60]),c_0_44]) ).
cnf(c_0_300,negated_conjecture,
( multiply(sk_c6,inverse(sk_c8)) = sk_c7
| sk_c6 = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_290]),c_0_52]) ).
cnf(c_0_301,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c8) = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_275]),c_0_33]),c_0_137]) ).
cnf(c_0_302,negated_conjecture,
( identity = sk_c7
| identity = sk_c3 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_291,c_0_292]),c_0_34]) ).
cnf(c_0_303,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| sk_c6 = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_293,c_0_294]),c_0_35]) ).
cnf(c_0_304,negated_conjecture,
( multiply(sk_c7,inverse(sk_c8)) = sk_c6
| sk_c3 = sk_c2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_295]),c_0_52]) ).
cnf(c_0_305,negated_conjecture,
( identity = sk_c7
| sk_c3 = sk_c8
| sk_c2 = sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_296,c_0_297]),c_0_239]) ).
cnf(c_0_306,negated_conjecture,
( identity = sk_c6
| sk_c3 = sk_c8
| sk_c2 = sk_c8 ),
inference(spm,[status(thm)],[c_0_298,c_0_215]) ).
cnf(c_0_307,negated_conjecture,
( multiply(inverse(sk_c8),sk_c7) = sk_c3
| identity = sk_c6 ),
inference(spm,[status(thm)],[c_0_36,c_0_299]) ).
cnf(c_0_308,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| sk_c6 = sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_300,c_0_301]),c_0_44])]) ).
cnf(c_0_309,negated_conjecture,
( identity = sk_c7
| sk_c3 != sk_c7 ),
inference(ef,[status(thm)],[c_0_302]) ).
cnf(c_0_310,negated_conjecture,
( multiply(inverse(sk_c8),sk_c7) = sk_c3
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_36,c_0_303]) ).
cnf(c_0_311,negated_conjecture,
( sk_c3 = sk_c2
| identity = sk_c6 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_304,c_0_292]),c_0_60]) ).
cnf(c_0_312,negated_conjecture,
( sk_c2 = sk_c8
| sk_c3 = sk_c8
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_305,c_0_306]) ).
cnf(c_0_313,negated_conjecture,
( multiply(sk_c1,multiply(sk_c7,X1)) = multiply(sk_c8,X1)
| multiply(sk_c4,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_33,c_0_95]) ).
cnf(c_0_314,negated_conjecture,
( multiply(sk_c7,multiply(sk_c1,X1)) = X1
| multiply(sk_c4,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_36,c_0_88]) ).
cnf(c_0_315,negated_conjecture,
( multiply(sk_c8,sk_c4) = identity
| inverse(sk_c7) = sk_c1 ),
inference(spm,[status(thm)],[c_0_34,c_0_84]) ).
cnf(c_0_316,negated_conjecture,
( identity = sk_c6
| identity = sk_c3 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_307,c_0_292]),c_0_34]) ).
cnf(c_0_317,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c7
| sk_c6 = sk_c7 ),
inference(rw,[status(thm)],[c_0_308,c_0_292]) ).
cnf(c_0_318,negated_conjecture,
( multiply(X1,sk_c7) = X1
| sk_c3 != sk_c7 ),
inference(spm,[status(thm)],[c_0_44,c_0_309]) ).
cnf(c_0_319,negated_conjecture,
( sk_c6 = sk_c7
| identity = sk_c3 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_310,c_0_292]),c_0_34]) ).
cnf(c_0_320,negated_conjecture,
( sk_c6 = sk_c7
| sk_c3 = sk_c2
| sk_c3 != sk_c7 ),
inference(spm,[status(thm)],[c_0_311,c_0_309]) ).
cnf(c_0_321,negated_conjecture,
( sk_c6 = sk_c7
| sk_c3 = sk_c7
| sk_c2 = sk_c7 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_312,c_0_292]),c_0_292]) ).
cnf(c_0_322,negated_conjecture,
( multiply(sk_c8,multiply(sk_c1,X1)) = multiply(sk_c1,X1)
| multiply(sk_c4,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_313,c_0_314]) ).
cnf(c_0_323,negated_conjecture,
( multiply(inverse(sk_c1),sk_c8) = sk_c7
| multiply(sk_c8,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_36,c_0_125]) ).
cnf(c_0_324,negated_conjecture,
( multiply(sk_c8,sk_c4) = identity
| inverse(sk_c1) = sk_c7 ),
inference(spm,[status(thm)],[c_0_52,c_0_315]) ).
cnf(c_0_325,negated_conjecture,
( identity = sk_c6
| sk_c3 != sk_c6 ),
inference(ef,[status(thm)],[c_0_316]) ).
cnf(c_0_326,negated_conjecture,
( sk_c6 = sk_c7
| sk_c3 != sk_c7 ),
inference(spm,[status(thm)],[c_0_317,c_0_318]) ).
cnf(c_0_327,negated_conjecture,
( sk_c6 = sk_c7
| sk_c3 = sk_c6
| sk_c3 = sk_c2 ),
inference(spm,[status(thm)],[c_0_311,c_0_319]) ).
cnf(c_0_328,negated_conjecture,
( sk_c2 = sk_c7
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_320,c_0_321]) ).
cnf(c_0_329,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c8) = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_322]),c_0_33]),c_0_137]) ).
cnf(c_0_330,negated_conjecture,
( multiply(sk_c8,sk_c4) = identity
| multiply(sk_c7,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_323,c_0_324]) ).
cnf(c_0_331,negated_conjecture,
( multiply(sk_c6,X1) = X1
| sk_c3 != sk_c6 ),
inference(spm,[status(thm)],[c_0_35,c_0_325]) ).
cnf(c_0_332,negated_conjecture,
( multiply(sk_c6,inverse(sk_c7)) = sk_c7
| sk_c6 = sk_c7 ),
inference(rw,[status(thm)],[c_0_300,c_0_292]) ).
cnf(c_0_333,negated_conjecture,
( sk_c3 = sk_c6
| sk_c6 = sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_326,c_0_327]),c_0_328]) ).
cnf(c_0_334,negated_conjecture,
( inverse(sk_c7) = sk_c7
| sk_c6 != sk_c7 ),
inference(rw,[status(thm)],[c_0_246,c_0_292]) ).
cnf(c_0_335,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| sk_c6 = sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_300,c_0_329]),c_0_44])]) ).
cnf(c_0_336,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_330]),c_0_120]),c_0_35]) ).
cnf(c_0_337,negated_conjecture,
inverse(sk_c7) = sk_c7,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_331,c_0_332]),c_0_333]),c_0_334]) ).
cnf(c_0_338,negated_conjecture,
( identity = sk_c7
| sk_c2 != sk_c4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_292])]) ).
cnf(c_0_339,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c7
| sk_c6 = sk_c7 ),
inference(rw,[status(thm)],[c_0_335,c_0_292]) ).
cnf(c_0_340,negated_conjecture,
( multiply(sk_c7,sk_c7) = sk_c7
| inverse(sk_c4) = sk_c7 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_336,c_0_292]),c_0_292]) ).
cnf(c_0_341,negated_conjecture,
multiply(sk_c7,sk_c7) = identity,
inference(spm,[status(thm)],[c_0_34,c_0_337]) ).
cnf(c_0_342,negated_conjecture,
( multiply(X1,sk_c7) = X1
| sk_c2 != sk_c4 ),
inference(spm,[status(thm)],[c_0_44,c_0_338]) ).
cnf(c_0_343,negated_conjecture,
( multiply(inverse(sk_c7),sk_c8) = sk_c8
| sk_c6 != sk_c8 ),
inference(spm,[status(thm)],[c_0_36,c_0_231]) ).
cnf(c_0_344,negated_conjecture,
( inverse(sk_c4) = identity
| sk_c6 = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_339]),c_0_60]) ).
cnf(c_0_345,negated_conjecture,
( inverse(sk_c4) = sk_c7
| identity = sk_c7 ),
inference(rw,[status(thm)],[c_0_340,c_0_341]) ).
cnf(c_0_346,negated_conjecture,
( sk_c6 = sk_c7
| sk_c2 != sk_c4 ),
inference(spm,[status(thm)],[c_0_317,c_0_342]) ).
cnf(c_0_347,negated_conjecture,
( identity = sk_c7
| sk_c6 != sk_c7 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_343,c_0_292]),c_0_34]),c_0_292]),c_0_292]) ).
cnf(c_0_348,negated_conjecture,
( sk_c6 = sk_c7
| identity = sk_c4 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_344]),c_0_35]) ).
cnf(c_0_349,negated_conjecture,
( identity = sk_c7
| sk_c4 = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_345]),c_0_337]) ).
cnf(c_0_350,negated_conjecture,
( sk_c6 = sk_c7
| sk_c4 != sk_c7 ),
inference(spm,[status(thm)],[c_0_346,c_0_328]) ).
cnf(c_0_351,negated_conjecture,
( multiply(X1,sk_c7) = X1
| sk_c6 != sk_c7 ),
inference(spm,[status(thm)],[c_0_44,c_0_347]) ).
cnf(c_0_352,negated_conjecture,
sk_c6 = sk_c7,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_348,c_0_349]),c_0_350]) ).
cnf(c_0_353,negated_conjecture,
( multiply(sk_c7,X1) = X1
| sk_c6 != sk_c7 ),
inference(spm,[status(thm)],[c_0_35,c_0_347]) ).
cnf(c_0_354,negated_conjecture,
multiply(X1,sk_c7) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_351,c_0_352])]) ).
cnf(c_0_355,negated_conjecture,
multiply(sk_c7,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_353,c_0_352])]) ).
cnf(c_0_356,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_292]),c_0_292]),c_0_292]),c_0_292]),c_0_292]),c_0_292]),c_0_292]),c_0_292]),c_0_354]),c_0_355]),c_0_355]),c_0_352]),c_0_352]),c_0_355]),c_0_354]),c_0_352]),c_0_354]),c_0_354])])])])])]),c_0_337])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP320-1 : TPTP v9.2.1. Released v2.5.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n022.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:32:36 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 45.53/27.38 % Version : CSE_E---1.7
% 45.53/27.38 % Problem : theBenchmark.p
% 45.53/27.38 % SZS status Unsatisfiable for theBenchmark.p
% 45.53/27.38 % SZS output start CNFRefutation
% See solution above
% 45.72/27.58 % Total time : 20.403s
%------------------------------------------------------------------------------