%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP380-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:43:26 PM UTC 2026
% Result : Unsatisfiable 10.05s 1.77s
% Output : CNFRefutation 10.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 30
% Syntax : Number of clauses : 206 ( 23 unt; 168 nHn; 180 RR)
% Number of literals : 493 ( 492 equ; 122 neg)
% Maximal clause size : 15 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 95 ( 3 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_28,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
cnf(prove_this_29,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
cnf(prove_this_38,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
cnf(prove_this_39,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
cnf(prove_this_18,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_19,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_51,negated_conjecture,
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c10) != sk_c11
| inverse(X5) != X6
| multiply(X5,X6) != sk_c11
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| inverse(X3) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| inverse(X1) != X2
| multiply(X1,X2) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c11
| inverse(sk_c11) != sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_51) ).
cnf(prove_this_8,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_9,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_27,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_22,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_37,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
cnf(prove_this_32,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
cnf(prove_this_15,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_17,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_11,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_12,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_16,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_20,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_4,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_31,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_21,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_2,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_13,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_14,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
cnf(c_0_30,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_31,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_32,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_33,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_34,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_33,c_0_33]) ).
cnf(c_0_35,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_31]),c_0_34]) ).
cnf(c_0_36,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_35]) ).
cnf(c_0_37,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c10 ),
prove_this_28 ).
cnf(c_0_38,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c10 ),
prove_this_29 ).
cnf(c_0_39,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c2 ),
prove_this_38 ).
cnf(c_0_41,negated_conjecture,
( sk_c7 = sk_c8
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c2 ),
prove_this_39 ).
cnf(c_0_43,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c1) = sk_c2 ),
inference(spm,[status(thm)],[c_0_36,c_0_40]) ).
cnf(c_0_44,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c10,sk_c9) = sk_c11 ),
prove_this_18 ).
cnf(c_0_45,negated_conjecture,
( sk_c7 = sk_c8
| multiply(inverse(sk_c1),sk_c10) = sk_c2 ),
inference(spm,[status(thm)],[c_0_33,c_0_41]) ).
cnf(c_0_46,negated_conjecture,
( sk_c7 = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c10,sk_c9) = sk_c11 ),
prove_this_19 ).
cnf(c_0_48,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_36,c_0_44]) ).
cnf(c_0_49,negated_conjecture,
( sk_c7 = sk_c8
| multiply(sk_c2,sk_c10) = sk_c2 ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_50,negated_conjecture,
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c10) != sk_c11
| inverse(X5) != X6
| multiply(X5,X6) != sk_c11
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| inverse(X3) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| inverse(X1) != X2
| multiply(X1,X2) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c11
| inverse(sk_c11) != sk_c10 ),
inference(fof_simplification,[status(thm)],[prove_this_51]) ).
cnf(c_0_51,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c11) = sk_c10 ),
prove_this_8 ).
cnf(c_0_52,negated_conjecture,
( sk_c7 = sk_c8
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_53,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_31,c_0_35]) ).
cnf(c_0_54,negated_conjecture,
( identity = sk_c10
| sk_c7 = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_49]),c_0_31]) ).
cnf(c_0_55,negated_conjecture,
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c10) != sk_c11
| inverse(X5) != X6
| multiply(X5,X6) != sk_c11
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| inverse(X3) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| inverse(X1) != X2
| multiply(X1,X2) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c11
| inverse(sk_c11) != sk_c10 ),
c_0_50 ).
cnf(c_0_56,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c11) = sk_c10 ),
prove_this_9 ).
cnf(c_0_57,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_36,c_0_51]) ).
cnf(c_0_58,negated_conjecture,
( sk_c7 = sk_c8
| multiply(inverse(sk_c10),sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_33,c_0_52]) ).
cnf(c_0_59,negated_conjecture,
( sk_c7 = sk_c8
| inverse(sk_c10) = sk_c10 ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_60,negated_conjecture,
( inverse(X5) != sk_c11
| inverse(X4) != sk_c10
| inverse(sk_c11) != sk_c10
| multiply(X5,sk_c11) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(X3,inverse(X3)) != sk_c10
| multiply(X2,inverse(X2)) != sk_c11
| multiply(sk_c10,sk_c9) != sk_c11
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(inverse(X3),sk_c9) != sk_c10
| multiply(inverse(X2),sk_c10) != sk_c11
| inverse(multiply(X1,inverse(X2))) != inverse(X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_55])])]) ).
cnf(c_0_61,negated_conjecture,
( sk_c7 = sk_c8
| inverse(sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_62,negated_conjecture,
( sk_c7 = sk_c8
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_63,negated_conjecture,
( inverse(X5) != sk_c11
| inverse(X4) != sk_c10
| multiply(X5,sk_c11) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(X3,inverse(X3)) != sk_c10
| multiply(X2,inverse(X2)) != sk_c11
| multiply(sk_c10,sk_c9) != sk_c11
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(inverse(X3),sk_c9) != sk_c10
| multiply(inverse(X2),sk_c10) != sk_c11
| inverse(multiply(X1,inverse(X2))) != inverse(X2)
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_64,negated_conjecture,
( sk_c7 = sk_c8
| multiply(inverse(sk_c10),sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_33,c_0_62]) ).
cnf(c_0_65,negated_conjecture,
( sk_c7 = sk_c8
| inverse(sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_36,c_0_61]) ).
cnf(c_0_66,negated_conjecture,
( inverse(X5) != sk_c11
| inverse(X4) != sk_c10
| multiply(X5,sk_c11) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(X3,inverse(X3)) != sk_c10
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(inverse(X3),sk_c9) != sk_c10
| multiply(inverse(X2),sk_c10) != sk_c11
| inverse(multiply(X1,inverse(X2))) != inverse(X2)
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_63,c_0_52]) ).
cnf(c_0_67,negated_conjecture,
( sk_c7 = sk_c8
| multiply(sk_c11,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_68,negated_conjecture,
( identity != sk_c9
| inverse(X4) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| multiply(X3,inverse(X3)) != sk_c10
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(inverse(X3),sk_c9) != sk_c10
| multiply(inverse(X2),sk_c10) != sk_c11
| inverse(multiply(X1,inverse(X2))) != inverse(X2)
| sk_c7 = sk_c8 ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_36])]),c_0_31]) ).
cnf(c_0_69,negated_conjecture,
( identity = sk_c9
| sk_c7 = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_67]),c_0_31]) ).
cnf(c_0_70,negated_conjecture,
( inverse(X4) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| multiply(X3,inverse(X3)) != sk_c10
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(inverse(X3),sk_c9) != sk_c10
| multiply(inverse(X2),sk_c10) != sk_c11
| inverse(multiply(X1,inverse(X2))) != inverse(X2)
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_71,negated_conjecture,
( multiply(X3,inverse(X3)) != sk_c10
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(inverse(X3),sk_c9) != sk_c10
| multiply(inverse(X2),sk_c10) != sk_c11
| inverse(multiply(X1,inverse(X2))) != inverse(X2)
| sk_c7 = sk_c8 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_36])]),c_0_31]),c_0_54]) ).
cnf(c_0_72,negated_conjecture,
( sk_c11 = sk_c10
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_65,c_0_59]) ).
cnf(c_0_73,negated_conjecture,
( identity != sk_c11
| inverse(X2) != X2
| inverse(X2) != identity
| multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X1),sk_c9) != sk_c10
| sk_c7 = sk_c8 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_53]),c_0_35]),c_0_32]),c_0_35]),c_0_35]),c_0_72]) ).
cnf(c_0_74,negated_conjecture,
( inverse(X2) != X2
| inverse(X2) != sk_c10
| multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X1),sk_c9) != sk_c10
| sk_c7 = sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_54]),c_0_72]) ).
cnf(c_0_75,negated_conjecture,
( multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X1),sk_c9) != sk_c10
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_74,c_0_59]) ).
cnf(c_0_76,negated_conjecture,
( sk_c7 = sk_c8
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_54,c_0_69]) ).
cnf(c_0_77,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c6,sk_c7) = identity ),
inference(spm,[status(thm)],[c_0_31,c_0_40]) ).
cnf(c_0_78,negated_conjecture,
sk_c7 = sk_c8,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_53]),c_0_32]),c_0_35]),c_0_54]),c_0_76]) ).
cnf(c_0_79,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c6,sk_c8) = identity ),
inference(rw,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_80,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c10 ),
prove_this_27 ).
cnf(c_0_81,negated_conjecture,
( inverse(sk_c2) = sk_c1
| multiply(sk_c6,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_36,c_0_79]) ).
cnf(c_0_82,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(inverse(sk_c1),sk_c10) = sk_c2 ),
inference(spm,[status(thm)],[c_0_33,c_0_80]) ).
cnf(c_0_83,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c10 ),
prove_this_22 ).
cnf(c_0_84,negated_conjecture,
( multiply(sk_c1,sk_c2) = identity
| multiply(sk_c6,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_31,c_0_81]) ).
cnf(c_0_85,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(inverse(inverse(sk_c1)),sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_33,c_0_82]) ).
cnf(c_0_86,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c2 ),
prove_this_37 ).
cnf(c_0_87,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_31,c_0_83]) ).
cnf(c_0_88,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c2 ),
prove_this_32 ).
cnf(c_0_89,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c1,sk_c2) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_84]),c_0_35]) ).
cnf(c_0_90,negated_conjecture,
( identity = sk_c10
| multiply(sk_c8,sk_c10) = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_31]) ).
cnf(c_0_91,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| multiply(inverse(sk_c1),sk_c10) = sk_c2 ),
inference(spm,[status(thm)],[c_0_33,c_0_87]) ).
cnf(c_0_92,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c11,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_31,c_0_88]) ).
cnf(c_0_93,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
prove_this_15 ).
cnf(c_0_94,negated_conjecture,
( multiply(sk_c8,sk_c6) = identity
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_31,c_0_38]) ).
cnf(c_0_95,negated_conjecture,
( multiply(sk_c8,sk_c6) = identity
| multiply(sk_c1,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_31,c_0_89]) ).
cnf(c_0_96,negated_conjecture,
( identity = sk_c10
| multiply(inverse(sk_c8),sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_33,c_0_90]) ).
cnf(c_0_97,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c2
| multiply(sk_c11,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_98,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c5,multiply(sk_c8,X1)) = multiply(sk_c11,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_93]) ).
cnf(c_0_99,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
prove_this_17 ).
cnf(c_0_100,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
prove_this_11 ).
cnf(c_0_101,negated_conjecture,
( identity = sk_c10
| multiply(sk_c8,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_102,negated_conjecture,
( identity = sk_c10
| multiply(inverse(sk_c8),multiply(sk_c11,X1)) = multiply(sk_c10,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_96]) ).
cnf(c_0_103,negated_conjecture,
( identity = sk_c10
| multiply(sk_c11,sk_c3) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_97]),c_0_31]) ).
cnf(c_0_104,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c5,sk_c11) = multiply(sk_c11,sk_c10) ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_105,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(inverse(sk_c3),sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_33,c_0_100]) ).
cnf(c_0_106,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
prove_this_12 ).
cnf(c_0_107,negated_conjecture,
( identity = sk_c10
| inverse(sk_c8) = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_101]),c_0_35]) ).
cnf(c_0_108,negated_conjecture,
( identity = sk_c10
| inverse(sk_c8) = multiply(sk_c10,sk_c3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_35]) ).
cnf(c_0_109,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(inverse(sk_c5),multiply(sk_c11,sk_c10)) = sk_c11 ),
inference(spm,[status(thm)],[c_0_33,c_0_104]) ).
cnf(c_0_110,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_111,negated_conjecture,
( identity = sk_c10
| multiply(sk_c8,multiply(sk_c10,X1)) = multiply(sk_c11,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_90]) ).
cnf(c_0_112,negated_conjecture,
( identity = sk_c10
| multiply(sk_c10,sk_c3) = sk_c6 ),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_113,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(inverse(sk_c5),sk_c11) = sk_c11 ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_114,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c10,sk_c9) = sk_c11 ),
prove_this_16 ).
cnf(c_0_115,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c10,sk_c9) = sk_c11 ),
prove_this_20 ).
cnf(c_0_116,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(inverse(sk_c5),sk_c11) = sk_c8 ),
inference(spm,[status(thm)],[c_0_33,c_0_93]) ).
cnf(c_0_117,negated_conjecture,
( identity = sk_c10
| multiply(sk_c6,multiply(sk_c8,X1)) = X1 ),
inference(spm,[status(thm)],[c_0_33,c_0_107]) ).
cnf(c_0_118,negated_conjecture,
( identity = sk_c10
| multiply(sk_c8,sk_c6) = multiply(sk_c11,sk_c3) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_119,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_120,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c7,multiply(sk_c8,X1)) = multiply(sk_c6,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_115]) ).
cnf(c_0_121,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c8
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_116,c_0_114]) ).
cnf(c_0_122,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_33,c_0_30]) ).
cnf(c_0_123,negated_conjecture,
( identity = sk_c10
| multiply(sk_c6,multiply(sk_c11,sk_c3)) = sk_c6 ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_124,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(inverse(sk_c8),sk_c11) = sk_c11 ),
inference(spm,[status(thm)],[c_0_33,c_0_119]) ).
cnf(c_0_125,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_36,c_0_47]) ).
cnf(c_0_126,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c7,sk_c8) = multiply(sk_c6,sk_c11) ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_127,negated_conjecture,
( identity = sk_c10
| multiply(sk_c11,multiply(sk_c3,X1)) = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_30]),c_0_33]) ).
cnf(c_0_128,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_129,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c6,sk_c11) = multiply(sk_c8,sk_c8) ),
inference(rw,[status(thm)],[c_0_126,c_0_78]) ).
cnf(c_0_130,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c11) = sk_c10 ),
prove_this_1 ).
cnf(c_0_131,negated_conjecture,
( identity = sk_c10
| multiply(inverse(sk_c11),X1) = multiply(sk_c3,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_127]) ).
cnf(c_0_132,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(inverse(sk_c8),sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_33,c_0_99]) ).
cnf(c_0_133,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c8,sk_c8) = sk_c11 ),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_134,negated_conjecture,
( multiply(sk_c10,sk_c11) = identity
| multiply(sk_c3,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_31,c_0_130]) ).
cnf(c_0_135,negated_conjecture,
( identity = sk_c10
| multiply(sk_c3,sk_c11) = identity ),
inference(spm,[status(thm)],[c_0_31,c_0_131]) ).
cnf(c_0_136,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_132,c_0_125]) ).
cnf(c_0_137,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(inverse(sk_c7),sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_33,c_0_115]) ).
cnf(c_0_138,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(inverse(sk_c8),sk_c11) = sk_c8 ),
inference(spm,[status(thm)],[c_0_33,c_0_133]) ).
cnf(c_0_139,negated_conjecture,
( identity = sk_c10
| multiply(sk_c10,sk_c11) = identity ),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_140,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c8,sk_c8) = sk_c10 ),
inference(spm,[status(thm)],[c_0_136,c_0_129]) ).
cnf(c_0_141,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(inverse(sk_c8),multiply(sk_c6,X1)) = multiply(sk_c8,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_137]),c_0_78]) ).
cnf(c_0_142,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c8
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_138,c_0_125]) ).
cnf(c_0_143,negated_conjecture,
( identity = sk_c10
| inverse(sk_c10) = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_139]),c_0_35]) ).
cnf(c_0_144,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(inverse(sk_c8),sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_33,c_0_140]) ).
cnf(c_0_145,negated_conjecture,
( multiply(sk_c8,sk_c11) = identity
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_31]) ).
cnf(c_0_146,negated_conjecture,
( identity = sk_c10
| inverse(sk_c11) = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_131]),c_0_35]) ).
cnf(c_0_147,negated_conjecture,
( identity = sk_c10
| inverse(sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_36,c_0_143]) ).
cnf(c_0_148,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c8
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_144,c_0_125]) ).
cnf(c_0_149,negated_conjecture,
( inverse(sk_c8) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_145]),c_0_35]) ).
cnf(c_0_150,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c11) = sk_c10 ),
prove_this_4 ).
cnf(c_0_151,negated_conjecture,
( sk_c3 = sk_c10
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_152,negated_conjecture,
( multiply(sk_c8,sk_c10) = identity
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_148]),c_0_31]) ).
cnf(c_0_153,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(inverse(sk_c8),multiply(sk_c11,X1)) = multiply(sk_c10,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_132]) ).
cnf(c_0_154,negated_conjecture,
( multiply(sk_c11,sk_c8) = identity
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_31,c_0_149]) ).
cnf(c_0_155,negated_conjecture,
( inverse(sk_c10) = sk_c4
| inverse(sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_36,c_0_150]) ).
cnf(c_0_156,negated_conjecture,
( sk_c3 = sk_c10
| multiply(X1,sk_c10) = X1 ),
inference(spm,[status(thm)],[c_0_35,c_0_151]) ).
cnf(c_0_157,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c11) = sk_c10 ),
prove_this_3 ).
cnf(c_0_158,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c3,multiply(sk_c11,X1)) = multiply(sk_c10,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_100]) ).
cnf(c_0_159,negated_conjecture,
( inverse(sk_c8) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_152]),c_0_35]) ).
cnf(c_0_160,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c8) = multiply(sk_c10,sk_c8) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_154]),c_0_35]) ).
cnf(c_0_161,negated_conjecture,
( inverse(sk_c10) = sk_c11
| inverse(sk_c10) = sk_c4 ),
inference(spm,[status(thm)],[c_0_36,c_0_155]) ).
cnf(c_0_162,negated_conjecture,
( sk_c3 = sk_c10
| inverse(sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_31,c_0_156]) ).
cnf(c_0_163,negated_conjecture,
( inverse(sk_c10) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_36,c_0_157]) ).
cnf(c_0_164,negated_conjecture,
( sk_c3 = sk_c10
| inverse(sk_c10) = sk_c10 ),
inference(spm,[status(thm)],[c_0_53,c_0_151]) ).
cnf(c_0_165,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c3
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_154]),c_0_35]) ).
cnf(c_0_166,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c10,sk_c8) = sk_c10 ),
inference(spm,[status(thm)],[c_0_159,c_0_160]) ).
cnf(c_0_167,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c2 ),
prove_this_31 ).
cnf(c_0_168,negated_conjecture,
( identity = sk_c4
| identity = sk_c11
| sk_c3 = sk_c10 ),
inference(spm,[status(thm)],[c_0_161,c_0_162]) ).
cnf(c_0_169,negated_conjecture,
( sk_c11 = sk_c10
| sk_c3 = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_163,c_0_164]) ).
cnf(c_0_170,negated_conjecture,
( sk_c3 = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_165,c_0_166]) ).
cnf(c_0_171,negated_conjecture,
( sk_c3 = sk_c10
| multiply(sk_c10,X1) = X1 ),
inference(spm,[status(thm)],[c_0_32,c_0_151]) ).
cnf(c_0_172,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
prove_this_21 ).
cnf(c_0_173,negated_conjecture,
( multiply(sk_c2,sk_c1) = identity
| multiply(sk_c3,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_31,c_0_167]) ).
cnf(c_0_174,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c11) = sk_c10 ),
prove_this_2 ).
cnf(c_0_175,negated_conjecture,
( sk_c4 != sk_c11
| sk_c3 = sk_c10
| identity = sk_c11 ),
inference(ef,[status(thm)],[c_0_168]) ).
cnf(c_0_176,negated_conjecture,
( sk_c4 = sk_c9
| sk_c3 = sk_c10
| sk_c11 = sk_c10 ),
inference(spm,[status(thm)],[c_0_169,c_0_156]) ).
cnf(c_0_177,negated_conjecture,
( sk_c9 = sk_c11
| sk_c3 = sk_c10 ),
inference(spm,[status(thm)],[c_0_170,c_0_171]) ).
cnf(c_0_178,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(inverse(sk_c3),sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_33,c_0_172]) ).
cnf(c_0_179,negated_conjecture,
( identity = sk_c10
| multiply(sk_c2,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_173,c_0_135]) ).
cnf(c_0_180,negated_conjecture,
( inverse(sk_c11) = sk_c3
| inverse(sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_36,c_0_174]) ).
cnf(c_0_181,negated_conjecture,
( identity = sk_c11
| sk_c3 = sk_c10
| sk_c11 = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_176]),c_0_177]) ).
cnf(c_0_182,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(inverse(inverse(sk_c3)),sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_33,c_0_178]) ).
cnf(c_0_183,negated_conjecture,
( identity = sk_c10
| inverse(sk_c2) = sk_c1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_179]),c_0_35]) ).
cnf(c_0_184,negated_conjecture,
( sk_c3 != sk_c10
| inverse(sk_c11) = sk_c10 ),
inference(ef,[status(thm)],[c_0_180]) ).
cnf(c_0_185,negated_conjecture,
( sk_c11 = sk_c10
| sk_c3 = sk_c10 ),
inference(spm,[status(thm)],[c_0_151,c_0_181]) ).
cnf(c_0_186,negated_conjecture,
( identity = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_83]),c_0_31]) ).
cnf(c_0_187,negated_conjecture,
( identity = sk_c10
| multiply(sk_c1,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_31,c_0_183]) ).
cnf(c_0_188,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c10,sk_c9) = sk_c11 ),
prove_this_13 ).
cnf(c_0_189,negated_conjecture,
( sk_c11 = sk_c10
| inverse(sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_184,c_0_185]) ).
cnf(c_0_190,negated_conjecture,
identity = sk_c10,
inference(spm,[status(thm)],[c_0_186,c_0_187]) ).
cnf(c_0_191,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(inverse(sk_c4),sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_33,c_0_188]) ).
cnf(c_0_192,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
prove_this_14 ).
cnf(c_0_193,negated_conjecture,
( sk_c11 = sk_c10
| inverse(sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_36,c_0_189]) ).
cnf(c_0_194,plain,
inverse(sk_c10) = sk_c10,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_190]),c_0_190]) ).
cnf(c_0_195,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_191,c_0_192]) ).
cnf(c_0_196,negated_conjecture,
sk_c11 = sk_c10,
inference(spm,[status(thm)],[c_0_193,c_0_194]) ).
cnf(c_0_197,negated_conjecture,
multiply(sk_c10,sk_c9) = sk_c10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_195,c_0_196])]) ).
cnf(c_0_198,plain,
multiply(inverse(X1),X1) = sk_c10,
inference(rw,[status(thm)],[c_0_31,c_0_190]) ).
cnf(c_0_199,plain,
multiply(X1,sk_c10) = X1,
inference(rw,[status(thm)],[c_0_35,c_0_190]) ).
cnf(c_0_200,negated_conjecture,
sk_c9 = sk_c10,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_197]),c_0_31]),c_0_190]) ).
cnf(c_0_201,plain,
multiply(X1,inverse(X1)) = sk_c10,
inference(spm,[status(thm)],[c_0_198,c_0_36]) ).
cnf(c_0_202,negated_conjecture,
( inverse(X3) != sk_c10
| inverse(X2) != sk_c10
| multiply(X1,inverse(X2)) != inverse(X1)
| inverse(multiply(X1,inverse(X2))) != inverse(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_196]),c_0_196]),c_0_196]),c_0_196]),c_0_196]),c_0_194]),c_0_196])]),c_0_199]),c_0_200]),c_0_199]),c_0_200]),c_0_199]),c_0_201]),c_0_201]),c_0_199]),c_0_200]),c_0_199])])])]),c_0_194])]) ).
cnf(c_0_203,negated_conjecture,
( inverse(X1) != X1
| inverse(X2) != sk_c10
| inverse(X1) != sk_c10 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_194]),c_0_199]),c_0_199]) ).
cnf(c_0_204,negated_conjecture,
inverse(X1) != sk_c10,
inference(spm,[status(thm)],[c_0_203,c_0_194]) ).
cnf(c_0_205,plain,
$false,
inference(sr,[status(thm)],[c_0_194,c_0_204]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP380-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 20:15:23 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.05/1.77 % Version: 3.5.1
% 10.05/1.77 % Preprocessing class: FSMSSMSMSSSNFFN.
% 10.05/1.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.05/1.77 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 10.05/1.77 % Starting new_bool_3 with 300s (1) cores
% 10.05/1.77 % Starting new_bool_1 with 300s (1) cores
% 10.05/1.77 % Starting sh5l with 300s (1) cores
% 10.05/1.77 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 701013 completed with status 0
% 10.05/1.77 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 10.05/1.77 % Preprocessing class: FSMSSMSMSSSNFFN.
% 10.05/1.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.05/1.77 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 10.05/1.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 10.05/1.77 % No SInE strategy applied
% 10.05/1.77 % Search class: FGHPS-FFMM21-SFFFFFNN
% 10.05/1.77 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 10.05/1.77 % Starting SubtermCWHack with 136s (1) cores
% 10.05/1.77 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 10.05/1.77 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 10.05/1.77 % Starting new_bool_3 with 136s (1) cores
% 10.05/1.77 % Starting new_bool_1 with 136s (1) cores
% 10.05/1.77 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 701019 completed with status 0
% 10.05/1.77 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 10.05/1.77 % Preprocessing class: FSMSSMSMSSSNFFN.
% 10.05/1.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.05/1.77 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 10.05/1.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 10.05/1.77 % No SInE strategy applied
% 10.05/1.77 % Search class: FGHPS-FFMM21-SFFFFFNN
% 10.05/1.77 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 10.05/1.77 % Starting SubtermCWHack with 136s (1) cores
% 10.05/1.77 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 10.05/1.77 % Preprocessing time : 0.002 s
% 10.05/1.77 % Presaturation interreduction done
% 10.05/1.77
% 10.05/1.77 % Proof found!
% 10.05/1.77 % SZS status Unsatisfiable
% 10.05/1.77 % SZS output start CNFRefutation
% See solution above
% 10.05/1.77 % Parsed axioms : 54
% 10.05/1.77 % Removed by relevancy pruning/SinE : 0
% 10.05/1.77 % Initial clauses : 54
% 10.05/1.77 % Removed in clause preprocessing : 0
% 10.05/1.77 % Initial clauses in saturation : 54
% 10.05/1.77 % Processed clauses : 11318
% 10.05/1.77 % ...of these trivial : 697
% 10.05/1.77 % ...subsumed : 8553
% 10.05/1.77 % ...remaining for further processing : 2068
% 10.05/1.77 % Other redundant clauses eliminated : 120
% 10.05/1.77 % Clauses deleted for lack of memory : 0
% 10.05/1.77 % Backward-subsumed : 193
% 10.05/1.77 % Backward-rewritten : 1337
% 10.05/1.77 % Generated clauses : 52311
% 10.05/1.77 % ...of the previous two non-redundant : 52548
% 10.05/1.77 % ...aggressively subsumed : 0
% 10.05/1.77 % Contextual simplify-reflections : 48
% 10.05/1.77 % Paramodulations : 52156
% 10.05/1.77 % Factorizations : 8
% 10.05/1.77 % NegExts : 0
% 10.05/1.77 % Equation resolutions : 120
% 10.05/1.77 % Disequality decompositions : 0
% 10.05/1.77 % Total rewrite steps : 13508
% 10.05/1.77 % ...of those cached : 12945
% 10.05/1.77 % Propositional unsat checks : 0
% 10.05/1.77 % Propositional check models : 0
% 10.05/1.77 % Propositional check unsatisfiable : 0
% 10.05/1.77 % Propositional clauses : 0
% 10.05/1.77 % Propositional clauses after purity: 0
% 10.05/1.77 % Propositional unsat core size : 0
% 10.05/1.77 % Propositional preprocessing time : 0.000
% 10.05/1.77 % Propositional encoding time : 0.000
% 10.05/1.77 % Propositional solver time : 0.000
% 10.05/1.77 % Success case prop preproc time : 0.000
% 10.05/1.77 % Success case prop encoding time : 0.000
% 10.05/1.77 % Success case prop solver time : 0.000
% 10.05/1.77 % Current number of processed clauses : 372
% 10.05/1.77 % Positive orientable unit clauses : 12
% 10.05/1.77 % Positive unorientable unit clauses: 0
% 10.05/1.77 % Negative unit clauses : 1
% 10.05/1.77 % Non-unit-clauses : 359
% 10.05/1.77 % Current number of unprocessed clauses: 39146
% 10.05/1.77 % ...number of literals in the above : 178608
% 10.05/1.77 % Current number of archived formulas : 0
% 10.05/1.77 % Current number of archived clauses : 1626
% 10.05/1.77 % Clause-clause subsumption calls (NU) : 228861
% 10.05/1.77 % Rec. Clause-clause subsumption calls : 153130
% 10.05/1.77 % Non-unit clause-clause subsumptions : 8780
% 10.05/1.77 % Unit Clause-clause subsumption calls : 1655
% 10.05/1.77 % Rewrite failures with RHS unbound : 0
% 10.05/1.77 % BW rewrite match attempts : 43
% 10.05/1.77 % BW rewrite match successes : 31
% 10.05/1.77 % Condensation attempts : 0
% 10.05/1.77 % Condensation successes : 0
% 10.05/1.77 % Termbank termtop insertions : 691575
% 10.05/1.77 % Search garbage collected termcells : 42
% 10.05/1.77
% 10.05/1.77 % -------------------------------------------------
% 10.05/1.77 % User time : 1.245 s
% 10.05/1.77 % System time : 0.049 s
% 10.05/1.77 % Total time : 1.295 s
% 10.05/1.77 % Maximum resident set size: 3660 pages
% 10.05/1.77
% 10.05/1.77 % -------------------------------------------------
% 10.05/1.77 % User time : 6.140 s
% 10.05/1.77 % System time : 0.246 s
% 10.05/1.77 % Total time : 6.386 s
% 10.05/1.77 % Maximum resident set size: 4608 pages
% 10.05/1.77 % E exiting
%------------------------------------------------------------------------------