%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP228-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 12:39:02 PM UTC 2026
% Result : Unsatisfiable 85.37s 12.84s
% Output : CNFRefutation 85.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 27
% Syntax : Number of clauses : 214 ( 29 unt; 173 nHn; 182 RR)
% Number of literals : 520 ( 519 equ; 119 neg)
% Maximal clause size : 14 ( 2 avg)
% Maximal term depth : 4 ( 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 : 99 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(prove_this_12,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_11,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_22,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_23,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_2,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_46,negated_conjecture,
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c9) != sk_c10
| inverse(X5) != X6
| multiply(X5,X6) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| inverse(X4) != sk_c10
| inverse(sk_c10) != sk_c9
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != X2
| multiply(sk_c10,X2) != sk_c9
| multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_46) ).
cnf(prove_this_10,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_20,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_21,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_42,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
cnf(prove_this_37,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
cnf(prove_this_19,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_1,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_28,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
cnf(prove_this_24,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_31,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_32,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
cnf(prove_this_41,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
cnf(prove_this_5,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_33,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
cnf(prove_this_40,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_40) ).
cnf(prove_this_4,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
cnf(c_0_27,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_28,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_29,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_30,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
prove_this_12 ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| multiply(inverse(sk_c4),sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
prove_this_11 ).
cnf(c_0_34,negated_conjecture,
( multiply(sk_c10,sk_c10) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c10,sk_c10) = sk_c9
| multiply(inverse(sk_c1),sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_30,c_0_34]) ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c10 ),
prove_this_3 ).
cnf(c_0_37,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
prove_this_22 ).
cnf(c_0_38,negated_conjecture,
( multiply(sk_c10,sk_c10) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| multiply(inverse(sk_c5),sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_30,c_0_37]) ).
cnf(c_0_40,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c10,sk_c3) = sk_c9 ),
prove_this_23 ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c10,sk_c10) = sk_c9
| multiply(inverse(sk_c4),sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_30,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
prove_this_2 ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c8
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c10,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,negated_conjecture,
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c9) != sk_c10
| inverse(X5) != X6
| multiply(X5,X6) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| inverse(X4) != sk_c10
| inverse(sk_c10) != sk_c9
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != X2
| multiply(sk_c10,X2) != sk_c9
| multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10 ),
inference(fof_simplification,[status(thm)],[prove_this_46]) ).
cnf(c_0_46,negated_conjecture,
( identity = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_43]),c_0_28]) ).
cnf(c_0_47,negated_conjecture,
multiply(sk_c10,sk_c10) = sk_c9,
inference(spm,[status(thm)],[c_0_35,c_0_44]) ).
cnf(c_0_48,negated_conjecture,
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c9) != sk_c10
| inverse(X5) != X6
| multiply(X5,X6) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| inverse(X4) != sk_c10
| inverse(sk_c10) != sk_c9
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != X2
| multiply(sk_c10,X2) != sk_c9
| multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10 ),
c_0_45 ).
cnf(c_0_49,negated_conjecture,
( identity = sk_c10
| multiply(inverse(sk_c10),sk_c9) = sk_c3 ),
inference(spm,[status(thm)],[c_0_30,c_0_46]) ).
cnf(c_0_50,negated_conjecture,
multiply(inverse(sk_c10),sk_c9) = sk_c10,
inference(spm,[status(thm)],[c_0_30,c_0_47]) ).
cnf(c_0_51,negated_conjecture,
( inverse(X5) != sk_c10
| inverse(X1) != sk_c10
| inverse(X4) != sk_c10
| inverse(sk_c10) != sk_c9
| multiply(X5,sk_c9) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| multiply(X3,inverse(X3)) != sk_c10
| multiply(X2,inverse(X3)) != inverse(X2)
| multiply(inverse(X3),sk_c9) != sk_c10
| inverse(multiply(X2,inverse(X3))) != inverse(X3)
| multiply(sk_c10,multiply(X1,sk_c10)) != sk_c9 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_48])])]) ).
cnf(c_0_52,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
prove_this_10 ).
cnf(c_0_53,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
prove_this_20 ).
cnf(c_0_54,negated_conjecture,
( sk_c3 = sk_c10
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_55,negated_conjecture,
( inverse(X5) != sk_c10
| inverse(X1) != sk_c10
| inverse(X4) != sk_c10
| multiply(X5,sk_c9) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| multiply(X3,inverse(X3)) != sk_c10
| multiply(X2,inverse(X3)) != inverse(X2)
| multiply(inverse(X3),sk_c9) != sk_c10
| inverse(multiply(X2,inverse(X3))) != inverse(X3)
| multiply(sk_c10,multiply(X1,sk_c10)) != sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c10,sk_c4) = identity
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_28,c_0_53]) ).
cnf(c_0_57,negated_conjecture,
( sk_c3 = sk_c10
| multiply(sk_c10,X1) = X1 ),
inference(spm,[status(thm)],[c_0_29,c_0_54]) ).
cnf(c_0_58,negated_conjecture,
( inverse(X4) != sk_c10
| inverse(X1) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| multiply(X3,inverse(X3)) != sk_c10
| multiply(X2,inverse(X3)) != inverse(X2)
| multiply(inverse(X3),sk_c9) != sk_c10
| inverse(multiply(X2,inverse(X3))) != inverse(X3)
| multiply(sk_c10,multiply(X1,sk_c10)) != sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_33]),c_0_31]) ).
cnf(c_0_59,negated_conjecture,
( identity = sk_c4
| sk_c3 = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_60,negated_conjecture,
( inverse(X3) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| multiply(X2,inverse(X2)) != sk_c10
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(inverse(X2),sk_c9) != sk_c10
| inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(sk_c10,multiply(sk_c4,sk_c10)) != sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_58,c_0_33]) ).
cnf(c_0_61,negated_conjecture,
( sk_c3 = sk_c10
| identity = sk_c4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_59]),c_0_50])]) ).
cnf(c_0_62,negated_conjecture,
( inverse(X3) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| multiply(X2,inverse(X2)) != sk_c10
| multiply(sk_c4,sk_c10) != sk_c9
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(inverse(X2),sk_c9) != sk_c10
| inverse(multiply(X1,inverse(X2))) != inverse(X2)
| sk_c3 = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_60,c_0_57]) ).
cnf(c_0_63,negated_conjecture,
( sk_c4 = sk_c10
| sk_c3 = sk_c10 ),
inference(spm,[status(thm)],[c_0_54,c_0_61]) ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
prove_this_21 ).
cnf(c_0_65,negated_conjecture,
( inverse(X3) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| multiply(X2,inverse(X2)) != sk_c10
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(inverse(X2),sk_c9) != sk_c10
| inverse(multiply(X1,inverse(X2))) != inverse(X2)
| sk_c3 = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_47])]) ).
cnf(c_0_66,negated_conjecture,
( sk_c3 = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9
| multiply(sk_c10,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_64,c_0_63]) ).
cnf(c_0_67,negated_conjecture,
( multiply(X2,inverse(X2)) != sk_c10
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(inverse(X2),sk_c9) != sk_c10
| inverse(multiply(X1,inverse(X2))) != inverse(X2)
| sk_c3 = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_33]),c_0_31]) ).
cnf(c_0_68,negated_conjecture,
( sk_c3 = sk_c10
| inverse(sk_c10) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_33,c_0_63]) ).
cnf(c_0_69,negated_conjecture,
( sk_c9 = sk_c10
| sk_c3 = sk_c10 ),
inference(spm,[status(thm)],[c_0_47,c_0_57]) ).
cnf(c_0_70,negated_conjecture,
( sk_c3 = sk_c10
| multiply(sk_c10,sk_c9) = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_66]),c_0_50])]) ).
cnf(c_0_71,negated_conjecture,
( inverse(X1) != multiply(X1,sk_c10)
| multiply(sk_c10,sk_c9) != sk_c10
| inverse(multiply(X1,sk_c10)) != sk_c10
| sk_c3 = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_47]),c_0_69]) ).
cnf(c_0_72,negated_conjecture,
( identity = sk_c9
| sk_c3 = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_70]),c_0_28]) ).
cnf(c_0_73,negated_conjecture,
( inverse(X1) != multiply(X1,sk_c10)
| inverse(multiply(X1,sk_c10)) != sk_c10
| sk_c3 = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_57]),c_0_69]) ).
cnf(c_0_74,negated_conjecture,
( sk_c4 = sk_c9
| sk_c3 = sk_c10 ),
inference(spm,[status(thm)],[c_0_61,c_0_72]) ).
cnf(c_0_75,negated_conjecture,
( inverse(sk_c9) != sk_c10
| sk_c3 = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_52]),c_0_47]),c_0_47])]) ).
cnf(c_0_76,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c10 ),
prove_this_42 ).
cnf(c_0_77,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
prove_this_37 ).
cnf(c_0_78,negated_conjecture,
( sk_c3 = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_74]),c_0_75]) ).
cnf(c_0_79,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
prove_this_19 ).
cnf(c_0_80,negated_conjecture,
( multiply(sk_c10,sk_c2) = identity
| multiply(sk_c8,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_28,c_0_76]) ).
cnf(c_0_81,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c10,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_28,c_0_77]) ).
cnf(c_0_82,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_30,c_0_30]) ).
cnf(c_0_83,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c10 ),
prove_this_6 ).
cnf(c_0_84,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
prove_this_1 ).
cnf(c_0_85,negated_conjecture,
( sk_c3 = sk_c10
| multiply(sk_c1,multiply(sk_c9,X1)) = multiply(sk_c10,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_78]) ).
cnf(c_0_86,negated_conjecture,
( multiply(sk_c9,sk_c10) = identity
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_28,c_0_79]) ).
cnf(c_0_87,negated_conjecture,
( multiply(sk_c10,sk_c2) = identity
| multiply(sk_c8,multiply(sk_c9,X1)) = multiply(sk_c10,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_80]) ).
cnf(c_0_88,negated_conjecture,
( multiply(sk_c9,sk_c10) = identity
| multiply(sk_c10,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_28,c_0_81]) ).
cnf(c_0_89,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_28]),c_0_82]) ).
cnf(c_0_90,negated_conjecture,
( multiply(sk_c10,sk_c1) = identity
| multiply(sk_c8,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_28,c_0_83]) ).
cnf(c_0_91,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c10,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_28,c_0_84]) ).
cnf(c_0_92,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| multiply(sk_c5,multiply(sk_c8,X1)) = multiply(sk_c10,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_37]) ).
cnf(c_0_93,negated_conjecture,
( sk_c3 = sk_c10
| multiply(sk_c1,identity) = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_47]) ).
cnf(c_0_94,negated_conjecture,
( sk_c8 = sk_c9
| multiply(sk_c10,sk_c2) = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89]),c_0_47]) ).
cnf(c_0_95,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c3 ),
prove_this_28 ).
cnf(c_0_96,negated_conjecture,
( multiply(sk_c10,sk_c1) = identity
| multiply(sk_c8,multiply(sk_c9,X1)) = multiply(sk_c10,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_90]) ).
cnf(c_0_97,negated_conjecture,
( multiply(sk_c9,sk_c10) = identity
| multiply(sk_c10,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_28,c_0_91]) ).
cnf(c_0_98,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_43]),c_0_47]) ).
cnf(c_0_99,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
prove_this_24 ).
cnf(c_0_100,negated_conjecture,
( sk_c3 = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_93,c_0_54]) ).
cnf(c_0_101,negated_conjecture,
( sk_c3 = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9
| multiply(sk_c1,X1) = multiply(sk_c9,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_93]),c_0_29]) ).
cnf(c_0_102,negated_conjecture,
( sk_c8 = sk_c9
| inverse(sk_c10) = sk_c2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_94]),c_0_89]) ).
cnf(c_0_103,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c3
| multiply(sk_c9,multiply(sk_c10,X1)) = X1 ),
inference(spm,[status(thm)],[c_0_30,c_0_95]) ).
cnf(c_0_104,negated_conjecture,
( sk_c8 = sk_c9
| multiply(sk_c10,sk_c1) = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_89]),c_0_47]) ).
cnf(c_0_105,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| multiply(inverse(sk_c5),sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_30,c_0_98]) ).
cnf(c_0_106,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| multiply(sk_c8,multiply(sk_c9,X1)) = multiply(sk_c10,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_99]) ).
cnf(c_0_107,negated_conjecture,
( sk_c3 = sk_c10
| multiply(sk_c9,sk_c10) = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_108,negated_conjecture,
( sk_c8 = sk_c9
| multiply(sk_c2,sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_28,c_0_102]) ).
cnf(c_0_109,negated_conjecture,
( sk_c1 = sk_c9
| sk_c8 = sk_c9
| multiply(sk_c2,sk_c10) = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_89]) ).
cnf(c_0_110,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c8
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_105,c_0_40]) ).
cnf(c_0_111,negated_conjecture,
( sk_c3 = sk_c10
| multiply(sk_c8,sk_c9) = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_47]) ).
cnf(c_0_112,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c3 ),
prove_this_31 ).
cnf(c_0_113,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_28,c_0_89]) ).
cnf(c_0_114,negated_conjecture,
( identity = sk_c3
| sk_c8 = sk_c9
| sk_c1 = sk_c9 ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_115,negated_conjecture,
( sk_c8 = sk_c9
| sk_c3 = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_116,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c3
| multiply(inverse(sk_c5),sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_30,c_0_112]) ).
cnf(c_0_117,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c3 ),
prove_this_32 ).
cnf(c_0_118,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_30,c_0_27]) ).
cnf(c_0_119,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c10 ),
prove_this_41 ).
cnf(c_0_120,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c10 ),
prove_this_5 ).
cnf(c_0_121,negated_conjecture,
( sk_c1 = sk_c9
| sk_c8 = sk_c9
| inverse(sk_c3) = sk_c3 ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_122,negated_conjecture,
( sk_c3 = sk_c10
| sk_c8 = sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_115]),c_0_50])]) ).
cnf(c_0_123,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c3 ),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_124,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c3 ),
prove_this_33 ).
cnf(c_0_125,negated_conjecture,
multiply(inverse(multiply(X1,sk_c10)),multiply(X1,sk_c9)) = sk_c10,
inference(spm,[status(thm)],[c_0_118,c_0_47]) ).
cnf(c_0_126,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_89]),c_0_89]) ).
cnf(c_0_127,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c8,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_28,c_0_119]) ).
cnf(c_0_128,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c8,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_28,c_0_120]) ).
cnf(c_0_129,negated_conjecture,
( sk_c8 = sk_c9
| sk_c1 = sk_c9
| inverse(sk_c10) = sk_c10 ),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_130,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c8
| multiply(inverse(sk_c2),sk_c3) = sk_c10 ),
inference(spm,[status(thm)],[c_0_30,c_0_123]) ).
cnf(c_0_131,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| multiply(inverse(sk_c2),sk_c3) = sk_c10 ),
inference(spm,[status(thm)],[c_0_30,c_0_124]) ).
cnf(c_0_132,negated_conjecture,
inverse(multiply(inverse(sk_c9),sk_c10)) = sk_c10,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_28]),c_0_89]) ).
cnf(c_0_133,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c10
| inverse(sk_c2) = sk_c10 ),
prove_this_40 ).
cnf(c_0_134,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c10
| inverse(sk_c1) = sk_c10 ),
prove_this_4 ).
cnf(c_0_135,negated_conjecture,
( inverse(sk_c10) = sk_c2
| multiply(sk_c8,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_136,negated_conjecture,
( inverse(sk_c10) = sk_c1
| multiply(sk_c8,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_126,c_0_128]) ).
cnf(c_0_137,negated_conjecture,
( sk_c2 = sk_c10
| sk_c8 = sk_c9
| sk_c1 = sk_c9 ),
inference(spm,[status(thm)],[c_0_102,c_0_129]) ).
cnf(c_0_138,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c8,sk_c10) = sk_c8
| multiply(inverse(sk_c2),sk_c10) = sk_c10 ),
inference(spm,[status(thm)],[c_0_130,c_0_69]) ).
cnf(c_0_139,negated_conjecture,
( sk_c8 = sk_c9
| inverse(sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_126,c_0_102]) ).
cnf(c_0_140,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c10
| multiply(sk_c8,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_131,c_0_76]) ).
cnf(c_0_141,negated_conjecture,
multiply(inverse(sk_c9),sk_c10) = inverse(sk_c10),
inference(spm,[status(thm)],[c_0_126,c_0_132]) ).
cnf(c_0_142,negated_conjecture,
( inverse(sk_c10) = sk_c2
| multiply(sk_c5,sk_c8) = sk_c10 ),
inference(spm,[status(thm)],[c_0_126,c_0_133]) ).
cnf(c_0_143,negated_conjecture,
( inverse(sk_c10) = sk_c1
| multiply(sk_c5,sk_c8) = sk_c10 ),
inference(spm,[status(thm)],[c_0_126,c_0_134]) ).
cnf(c_0_144,negated_conjecture,
( sk_c2 = sk_c1
| multiply(sk_c8,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
cnf(c_0_145,negated_conjecture,
( inverse(sk_c10) = sk_c2
| inverse(sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_126,c_0_77]) ).
cnf(c_0_146,negated_conjecture,
( sk_c3 = sk_c9
| sk_c8 = sk_c9
| sk_c1 = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_137]),c_0_47]) ).
cnf(c_0_147,negated_conjecture,
( inverse(sk_c10) = sk_c1
| inverse(sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_126,c_0_84]) ).
cnf(c_0_148,negated_conjecture,
( sk_c9 = sk_c10
| sk_c8 = sk_c9
| multiply(sk_c8,sk_c10) = sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_47])]) ).
cnf(c_0_149,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c10
| multiply(inverse(sk_c8),sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_30,c_0_140]) ).
cnf(c_0_150,negated_conjecture,
multiply(inverse(sk_c10),multiply(sk_c9,X1)) = multiply(sk_c10,X1),
inference(spm,[status(thm)],[c_0_27,c_0_50]) ).
cnf(c_0_151,negated_conjecture,
multiply(sk_c9,inverse(sk_c10)) = sk_c10,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_141]),c_0_126]) ).
cnf(c_0_152,negated_conjecture,
( multiply(sk_c8,sk_c5) = identity
| multiply(sk_c10,multiply(sk_c2,X1)) = X1 ),
inference(spm,[status(thm)],[c_0_30,c_0_127]) ).
cnf(c_0_153,negated_conjecture,
( multiply(sk_c8,sk_c5) = identity
| multiply(sk_c2,sk_c10) = sk_c3 ),
inference(spm,[status(thm)],[c_0_28,c_0_117]) ).
cnf(c_0_154,negated_conjecture,
( sk_c2 = sk_c1
| multiply(sk_c5,sk_c8) = sk_c10 ),
inference(spm,[status(thm)],[c_0_142,c_0_143]) ).
cnf(c_0_155,negated_conjecture,
( sk_c2 = sk_c1
| inverse(sk_c8) = sk_c5 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_144]),c_0_89]) ).
cnf(c_0_156,negated_conjecture,
( sk_c2 != sk_c9
| inverse(sk_c10) = sk_c9 ),
inference(ef,[status(thm)],[c_0_145]) ).
cnf(c_0_157,negated_conjecture,
( sk_c9 = sk_c10
| sk_c1 = sk_c9
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_69,c_0_146]) ).
cnf(c_0_158,negated_conjecture,
( sk_c1 != sk_c9
| inverse(sk_c10) = sk_c9 ),
inference(ef,[status(thm)],[c_0_147]) ).
cnf(c_0_159,negated_conjecture,
( identity = sk_c10
| sk_c8 = sk_c9
| sk_c9 = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_148]),c_0_28]) ).
cnf(c_0_160,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c10
| multiply(inverse(sk_c8),multiply(sk_c10,X1)) = multiply(sk_c9,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_149]) ).
cnf(c_0_161,negated_conjecture,
multiply(sk_c10,inverse(sk_c10)) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_28]) ).
cnf(c_0_162,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c10
| multiply(sk_c8,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_163,negated_conjecture,
( sk_c2 = sk_c1
| multiply(inverse(sk_c5),sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_30,c_0_154]) ).
cnf(c_0_164,negated_conjecture,
( sk_c2 = sk_c1
| inverse(sk_c5) = sk_c8 ),
inference(spm,[status(thm)],[c_0_126,c_0_155]) ).
cnf(c_0_165,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c8,sk_c9) = sk_c10
| multiply(inverse(sk_c2),sk_c10) = sk_c10 ),
inference(spm,[status(thm)],[c_0_131,c_0_69]) ).
cnf(c_0_166,negated_conjecture,
( sk_c8 = sk_c9
| inverse(sk_c10) = sk_c9 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_137]),c_0_157]),c_0_158]) ).
cnf(c_0_167,negated_conjecture,
( sk_c9 = sk_c10
| sk_c8 = sk_c9
| inverse(sk_c10) = sk_c10 ),
inference(spm,[status(thm)],[c_0_113,c_0_159]) ).
cnf(c_0_168,negated_conjecture,
( multiply(sk_c10,sk_c1) = identity
| multiply(sk_c5,sk_c8) = sk_c10 ),
inference(spm,[status(thm)],[c_0_28,c_0_134]) ).
cnf(c_0_169,negated_conjecture,
( inverse(sk_c8) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c10 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_89]),c_0_151]) ).
cnf(c_0_170,negated_conjecture,
( inverse(sk_c8) = sk_c5
| multiply(sk_c10,sk_c3) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_162]),c_0_89]) ).
cnf(c_0_171,negated_conjecture,
( sk_c2 = sk_c1
| multiply(sk_c8,sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_163,c_0_164]) ).
cnf(c_0_172,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c8,sk_c9) = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_76]),c_0_47])]) ).
cnf(c_0_173,negated_conjecture,
( sk_c9 = sk_c10
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_166,c_0_167]) ).
cnf(c_0_174,negated_conjecture,
( multiply(sk_c10,sk_c1) = identity
| multiply(sk_c5,multiply(sk_c8,X1)) = multiply(sk_c10,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_168]) ).
cnf(c_0_175,negated_conjecture,
( multiply(sk_c10,sk_c1) = identity
| multiply(sk_c8,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_28,c_0_128]) ).
cnf(c_0_176,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_37,c_0_98]) ).
cnf(c_0_177,negated_conjecture,
( sk_c5 = sk_c10
| multiply(sk_c10,sk_c3) = sk_c10 ),
inference(spm,[status(thm)],[c_0_169,c_0_170]) ).
cnf(c_0_178,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c3
| multiply(sk_c5,multiply(sk_c8,X1)) = multiply(sk_c10,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_112]) ).
cnf(c_0_179,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c3
| multiply(sk_c8,multiply(sk_c5,X1)) = X1 ),
inference(spm,[status(thm)],[c_0_30,c_0_117]) ).
cnf(c_0_180,negated_conjecture,
( identity = sk_c10
| sk_c2 = sk_c1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_171]),c_0_28]) ).
cnf(c_0_181,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c9,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_172,c_0_173]) ).
cnf(c_0_182,negated_conjecture,
( multiply(sk_c10,sk_c5) = sk_c5
| multiply(sk_c10,sk_c1) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_175]),c_0_89]) ).
cnf(c_0_183,negated_conjecture,
( sk_c9 = sk_c10
| sk_c5 = sk_c10 ),
inference(spm,[status(thm)],[c_0_176,c_0_177]) ).
cnf(c_0_184,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c3
| multiply(sk_c10,multiply(sk_c5,X1)) = multiply(sk_c5,X1) ),
inference(spm,[status(thm)],[c_0_178,c_0_179]) ).
cnf(c_0_185,negated_conjecture,
( sk_c2 = sk_c1
| inverse(sk_c10) = sk_c9 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_147]),c_0_158]) ).
cnf(c_0_186,negated_conjecture,
( sk_c2 = sk_c1
| inverse(sk_c10) = sk_c10 ),
inference(spm,[status(thm)],[c_0_113,c_0_180]) ).
cnf(c_0_187,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c10,sk_c9) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_181]),c_0_28]) ).
cnf(c_0_188,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c10,sk_c1) = identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_183]),c_0_47])]) ).
cnf(c_0_189,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c2,sk_c10) = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_112]),c_0_47]) ).
cnf(c_0_190,negated_conjecture,
( sk_c9 = sk_c10
| sk_c2 = sk_c1 ),
inference(spm,[status(thm)],[c_0_185,c_0_186]) ).
cnf(c_0_191,negated_conjecture,
( sk_c9 = sk_c10
| inverse(sk_c10) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_187]),c_0_89]) ).
cnf(c_0_192,negated_conjecture,
( sk_c9 = sk_c10
| inverse(sk_c10) = sk_c1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_188]),c_0_89]) ).
cnf(c_0_193,negated_conjecture,
multiply(sk_c10,multiply(sk_c10,X1)) = multiply(sk_c9,X1),
inference(spm,[status(thm)],[c_0_27,c_0_47]) ).
cnf(c_0_194,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c1,sk_c10) = sk_c3 ),
inference(spm,[status(thm)],[c_0_189,c_0_190]) ).
cnf(c_0_195,negated_conjecture,
( sk_c1 = sk_c9
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_191,c_0_192]) ).
cnf(c_0_196,negated_conjecture,
multiply(sk_c9,sk_c10) = multiply(sk_c10,sk_c9),
inference(spm,[status(thm)],[c_0_193,c_0_47]) ).
cnf(c_0_197,negated_conjecture,
( sk_c9 = sk_c10
| multiply(inverse(multiply(X1,sk_c10)),multiply(X1,sk_c9)) = sk_c3 ),
inference(spm,[status(thm)],[c_0_118,c_0_176]) ).
cnf(c_0_198,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c10,sk_c9) = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_195]),c_0_196]) ).
cnf(c_0_199,negated_conjecture,
( sk_c9 = sk_c10
| inverse(sk_c9) = sk_c3 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_187]),c_0_47]),c_0_89]) ).
cnf(c_0_200,negated_conjecture,
( identity = sk_c3
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_187,c_0_198]) ).
cnf(c_0_201,negated_conjecture,
( sk_c9 = sk_c10
| inverse(sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_126,c_0_199]) ).
cnf(c_0_202,negated_conjecture,
( sk_c9 = sk_c10
| inverse(sk_c3) = sk_c3 ),
inference(spm,[status(thm)],[c_0_113,c_0_200]) ).
cnf(c_0_203,negated_conjecture,
( sk_c3 = sk_c9
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_201,c_0_202]) ).
cnf(c_0_204,negated_conjecture,
sk_c9 = sk_c10,
inference(spm,[status(thm)],[c_0_69,c_0_203]) ).
cnf(c_0_205,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_28,c_0_126]) ).
cnf(c_0_206,negated_conjecture,
identity = sk_c10,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_151,c_0_204]),c_0_205]) ).
cnf(c_0_207,negated_conjecture,
( identity != sk_c10
| inverse(X5) != sk_c10
| inverse(X1) != sk_c10
| inverse(X4) != sk_c10
| inverse(sk_c10) != sk_c9
| multiply(X5,sk_c9) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| multiply(X2,inverse(X3)) != inverse(X2)
| multiply(inverse(X3),sk_c9) != sk_c10
| inverse(multiply(X2,inverse(X3))) != inverse(X3)
| multiply(sk_c10,multiply(X1,sk_c10)) != sk_c9 ),
inference(rw,[status(thm)],[c_0_51,c_0_205]) ).
cnf(c_0_208,plain,
multiply(X1,sk_c10) = X1,
inference(rw,[status(thm)],[c_0_89,c_0_206]) ).
cnf(c_0_209,plain,
multiply(sk_c10,X1) = X1,
inference(rw,[status(thm)],[c_0_29,c_0_206]) ).
cnf(c_0_210,plain,
inverse(sk_c10) = sk_c10,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_206]),c_0_206]) ).
cnf(c_0_211,negated_conjecture,
( 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(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)],[c_0_207,c_0_204]),c_0_204]),c_0_204]),c_0_204]),c_0_204]),c_0_208]),c_0_209]),c_0_208]),c_0_208]),c_0_208]),c_0_210]),c_0_206])])])])]),c_0_210])]) ).
cnf(c_0_212,negated_conjecture,
( inverse(X1) != X1
| inverse(X1) != sk_c10 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_211,c_0_210]),c_0_208]),c_0_208]) ).
cnf(c_0_213,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_212,c_0_210]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP228-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:07:27 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 85.37/12.84 % Version: 3.5.1
% 85.37/12.84 % Preprocessing class: FSMSSMSMSSSNFFN.
% 85.37/12.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 85.37/12.84 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 85.37/12.84 % Starting new_bool_3 with 300s (1) cores
% 85.37/12.84 % Starting new_bool_1 with 300s (1) cores
% 85.37/12.84 % Starting sh5l with 300s (1) cores
% 85.37/12.84 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 4126758 completed with status 0
% 85.37/12.84 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 85.37/12.84 % Preprocessing class: FSMSSMSMSSSNFFN.
% 85.37/12.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 85.37/12.84 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 85.37/12.84 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 85.37/12.84 % No SInE strategy applied
% 85.37/12.84 % Search class: FGHPS-FFMM21-SFFFFFNN
% 85.37/12.84 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 85.37/12.84 % Starting SubtermCWHack with 136s (1) cores
% 85.37/12.84 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 85.37/12.84 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 85.37/12.84 % Starting new_bool_3 with 136s (1) cores
% 85.37/12.84 % Starting new_bool_1 with 136s (1) cores
% 85.37/12.84 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 4126763 completed with status 0
% 85.37/12.84 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 85.37/12.84 % Preprocessing class: FSMSSMSMSSSNFFN.
% 85.37/12.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 85.37/12.84 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 85.37/12.84 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 85.37/12.84 % No SInE strategy applied
% 85.37/12.84 % Search class: FGHPS-FFMM21-SFFFFFNN
% 85.37/12.84 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 85.37/12.84 % Starting SubtermCWHack with 136s (1) cores
% 85.37/12.84 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 85.37/12.84 % Preprocessing time : 0.002 s
% 85.37/12.84 % Presaturation interreduction done
% 85.37/12.84
% 85.37/12.84 % Proof found!
% 85.37/12.84 % SZS status Unsatisfiable
% 85.37/12.84 % SZS output start CNFRefutation
% See solution above
% 85.37/12.84 % Parsed axioms : 49
% 85.37/12.84 % Removed by relevancy pruning/SinE : 0
% 85.37/12.84 % Initial clauses : 49
% 85.37/12.84 % Removed in clause preprocessing : 0
% 85.37/12.84 % Initial clauses in saturation : 49
% 85.37/12.84 % Processed clauses : 68945
% 85.37/12.84 % ...of these trivial : 402
% 85.37/12.84 % ...subsumed : 63247
% 85.37/12.84 % ...remaining for further processing : 5296
% 85.37/12.84 % Other redundant clauses eliminated : 78
% 85.37/12.84 % Clauses deleted for lack of memory : 0
% 85.37/12.84 % Backward-subsumed : 1111
% 85.37/12.84 % Backward-rewritten : 2628
% 85.37/12.84 % Generated clauses : 1197472
% 85.37/12.84 % ...of the previous two non-redundant : 1181558
% 85.37/12.84 % ...aggressively subsumed : 0
% 85.37/12.84 % Contextual simplify-reflections : 43
% 85.37/12.84 % Paramodulations : 1197385
% 85.37/12.84 % Factorizations : 26
% 85.37/12.84 % NegExts : 0
% 85.37/12.84 % Equation resolutions : 78
% 85.37/12.84 % Disequality decompositions : 0
% 85.37/12.84 % Total rewrite steps : 515184
% 85.37/12.84 % ...of those cached : 503742
% 85.37/12.84 % Propositional unsat checks : 0
% 85.37/12.84 % Propositional check models : 0
% 85.37/12.84 % Propositional check unsatisfiable : 0
% 85.37/12.84 % Propositional clauses : 0
% 85.37/12.84 % Propositional clauses after purity: 0
% 85.37/12.84 % Propositional unsat core size : 0
% 85.37/12.84 % Propositional preprocessing time : 0.000
% 85.37/12.84 % Propositional encoding time : 0.000
% 85.37/12.84 % Propositional solver time : 0.000
% 85.37/12.84 % Success case prop preproc time : 0.000
% 85.37/12.84 % Success case prop encoding time : 0.000
% 85.37/12.84 % Success case prop solver time : 0.000
% 85.37/12.84 % Current number of processed clauses : 1493
% 85.37/12.84 % Positive orientable unit clauses : 17
% 85.37/12.84 % Positive unorientable unit clauses: 0
% 85.37/12.84 % Negative unit clauses : 0
% 85.37/12.84 % Non-unit-clauses : 1476
% 85.37/12.84 % Current number of unprocessed clauses: 1108670
% 85.37/12.84 % ...number of literals in the above : 3609680
% 85.37/12.84 % Current number of archived formulas : 0
% 85.37/12.84 % Current number of archived clauses : 3788
% 85.37/12.84 % Clause-clause subsumption calls (NU) : 1220186
% 85.37/12.84 % Rec. Clause-clause subsumption calls : 636907
% 85.37/12.84 % Non-unit clause-clause subsumptions : 64382
% 85.37/12.84 % Unit Clause-clause subsumption calls : 6649
% 85.37/12.84 % Rewrite failures with RHS unbound : 0
% 85.37/12.84 % BW rewrite match attempts : 326
% 85.37/12.84 % BW rewrite match successes : 83
% 85.37/12.84 % Condensation attempts : 0
% 85.37/12.84 % Condensation successes : 0
% 85.37/12.84 % Termbank termtop insertions : 14157208
% 85.37/12.84 % Search garbage collected termcells : 40
% 85.37/12.84
% 85.37/12.84 % -------------------------------------------------
% 85.37/12.84 % User time : 11.281 s
% 85.37/12.84 % System time : 0.685 s
% 85.37/12.84 % Total time : 11.965 s
% 85.37/12.84 % Maximum resident set size: 3400 pages
% 85.37/12.84
% 85.37/12.84 % -------------------------------------------------
% 85.37/12.84 % User time : 57.423 s
% 85.37/12.84 % System time : 3.508 s
% 85.37/12.84 % Total time : 60.931 s
% 85.37/12.84 % Maximum resident set size: 4608 pages
% 85.37/12.84 % E exiting
%------------------------------------------------------------------------------