%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP240-1 : 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 : n015.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 12:39:04 PM UTC 2026
% Result : Unsatisfiable 10.18s 6.78s
% Output : CNFRefutation 10.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 35
% Syntax : Number of clauses : 210 ( 19 unt; 182 nHn; 187 RR)
% Number of literals : 549 ( 548 equ; 143 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 : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 96 ( 2 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_22,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_35,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
cnf(prove_this_39,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_39) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_30,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
cnf(prove_this_36,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
cnf(prove_this_40,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_40) ).
cnf(prove_this_46,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_46) ).
cnf(prove_this_34,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_34) ).
cnf(prove_this_38,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_38) ).
cnf(prove_this_54,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_54) ).
cnf(prove_this_57,negated_conjecture,
( inverse(X8) != sk_c10
| multiply(X8,sk_c10) != X7
| multiply(sk_c10,X7) != sk_c9
| multiply(X6,sk_c10) != sk_c9
| inverse(X5) != X6
| multiply(X5,X6) != sk_c9
| multiply(X4,sk_c9) != sk_c10
| inverse(X4) != sk_c10
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != X2
| multiply(sk_c10,X2) != sk_c9
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c10
| inverse(sk_c9) != sk_c10
| inverse(sk_c10) != sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_57) ).
cnf(prove_this_33,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
cnf(prove_this_2,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_32,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
cnf(prove_this_23,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_16,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_14,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_25,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_26,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_31,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_9,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_24,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_15,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_19,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_20,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_37,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
cnf(prove_this_21,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_29,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
cnf(prove_this_13,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c9
| inverse(sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_56,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_56) ).
cnf(c_0_35,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_36,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_37,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_38,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
prove_this_22 ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
prove_this_35 ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c10,sk_c3) = sk_c9 ),
prove_this_39 ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c10) = sk_c9 ),
prove_this_6 ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(inverse(sk_c1),sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
prove_this_30 ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| multiply(inverse(sk_c5),sk_c9) = sk_c6 ),
inference(spm,[status(thm)],[c_0_38,c_0_40]) ).
cnf(c_0_46,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c10,sk_c3) = sk_c9 ),
prove_this_36 ).
cnf(c_0_47,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| multiply(inverse(sk_c7),sk_c8) = sk_c10 ),
inference(spm,[status(thm)],[c_0_38,c_0_41]) ).
cnf(c_0_48,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
prove_this_40 ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c3 ),
prove_this_46 ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c9,sk_c10) = identity
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_36,c_0_42]) ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c9
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c6
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_53,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
prove_this_34 ).
cnf(c_0_54,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c1,multiply(sk_c9,X1)) = multiply(sk_c10,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_39]) ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
prove_this_38 ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(inverse(sk_c2),sk_c3) = sk_c10 ),
inference(spm,[status(thm)],[c_0_38,c_0_49]) ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c10 ),
prove_this_54 ).
cnf(c_0_59,negated_conjecture,
( inverse(X8) != sk_c10
| multiply(X8,sk_c10) != X7
| multiply(sk_c10,X7) != sk_c9
| multiply(X6,sk_c10) != sk_c9
| inverse(X5) != X6
| multiply(X5,X6) != sk_c9
| multiply(X4,sk_c9) != sk_c10
| inverse(X4) != sk_c10
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != X2
| multiply(sk_c10,X2) != sk_c9
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c10
| inverse(sk_c9) != sk_c10
| inverse(sk_c10) != sk_c9 ),
inference(fof_simplification,[status(thm)],[prove_this_57]) ).
cnf(c_0_60,negated_conjecture,
( identity = sk_c9
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_61,negated_conjecture,
( identity = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_52]),c_0_36]) ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| multiply(inverse(sk_c4),sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_38,c_0_53]) ).
cnf(c_0_63,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
prove_this_33 ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = multiply(sk_c10,sk_c10) ),
inference(spm,[status(thm)],[c_0_54,c_0_51]) ).
cnf(c_0_65,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_66,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_67,negated_conjecture,
( inverse(X8) != sk_c10
| multiply(X8,sk_c10) != X7
| multiply(sk_c10,X7) != sk_c9
| multiply(X6,sk_c10) != sk_c9
| inverse(X5) != X6
| multiply(X5,X6) != sk_c9
| multiply(X4,sk_c9) != sk_c10
| inverse(X4) != sk_c10
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != X2
| multiply(sk_c10,X2) != sk_c9
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c10
| inverse(sk_c9) != sk_c10
| inverse(sk_c10) != sk_c9 ),
c_0_59 ).
cnf(c_0_68,negated_conjecture,
( identity = sk_c9
| multiply(inverse(sk_c10),sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_38,c_0_60]) ).
cnf(c_0_69,negated_conjecture,
( identity = sk_c9
| multiply(inverse(sk_c10),sk_c9) = sk_c3 ),
inference(spm,[status(thm)],[c_0_38,c_0_61]) ).
cnf(c_0_70,negated_conjecture,
( multiply(sk_c10,sk_c10) = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c10,sk_c10) = sk_c10 ),
inference(spm,[status(thm)],[c_0_39,c_0_64]) ).
cnf(c_0_72,negated_conjecture,
( sk_c9 = sk_c10
| multiply(inverse(sk_c10),sk_c9) = sk_c3 ),
inference(spm,[status(thm)],[c_0_38,c_0_65]) ).
cnf(c_0_73,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c10
| multiply(inverse(sk_c10),sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_38,c_0_66]) ).
cnf(c_0_74,negated_conjecture,
( inverse(X5) != sk_c9
| inverse(X2) != sk_c10
| inverse(X4) != sk_c10
| inverse(X1) != sk_c10
| inverse(sk_c9) != sk_c10
| inverse(sk_c10) != sk_c9
| multiply(X5,sk_c9) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| multiply(X3,inverse(X3)) != sk_c9
| multiply(inverse(X3),sk_c10) != sk_c9
| multiply(sk_c10,multiply(X2,sk_c10)) != sk_c9
| multiply(sk_c10,multiply(X1,sk_c10)) != sk_c9 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_67])])]) ).
cnf(c_0_75,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c10) = sk_c9 ),
prove_this_2 ).
cnf(c_0_76,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c9) = sk_c10 ),
prove_this_10 ).
cnf(c_0_77,negated_conjecture,
( sk_c8 = sk_c3
| identity = sk_c9 ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c10,sk_c10) = sk_c9
| multiply(inverse(sk_c10),sk_c9) = sk_c3 ),
inference(spm,[status(thm)],[c_0_38,c_0_70]) ).
cnf(c_0_79,negated_conjecture,
( multiply(sk_c10,sk_c10) = sk_c10
| multiply(inverse(sk_c10),sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_38,c_0_71]) ).
cnf(c_0_80,negated_conjecture,
( sk_c8 = sk_c3
| sk_c9 = sk_c10
| multiply(sk_c10,sk_c3) = sk_c10 ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_81,negated_conjecture,
( inverse(X5) != sk_c9
| inverse(X2) != sk_c10
| inverse(X4) != sk_c10
| inverse(X1) != sk_c10
| multiply(X5,sk_c9) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| multiply(X3,inverse(X3)) != sk_c9
| multiply(inverse(X3),sk_c10) != sk_c9
| multiply(sk_c10,multiply(X2,sk_c10)) != sk_c9
| multiply(sk_c10,multiply(X1,sk_c10)) != sk_c9
| multiply(sk_c4,sk_c9) = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]) ).
cnf(c_0_82,negated_conjecture,
( sk_c8 = sk_c3
| multiply(sk_c9,X1) = X1 ),
inference(spm,[status(thm)],[c_0_37,c_0_77]) ).
cnf(c_0_83,negated_conjecture,
( sk_c8 = sk_c3
| multiply(sk_c10,sk_c10) = sk_c9
| multiply(sk_c10,sk_c10) = sk_c10 ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_84,negated_conjecture,
( sk_c9 = sk_c10
| sk_c8 = sk_c3 ),
inference(spm,[status(thm)],[c_0_65,c_0_80]) ).
cnf(c_0_85,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_38,c_0_38]) ).
cnf(c_0_86,negated_conjecture,
( inverse(X4) != sk_c9
| inverse(X1) != sk_c10
| inverse(X3) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| multiply(X2,inverse(X2)) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| multiply(inverse(X2),sk_c10) != sk_c9
| multiply(sk_c10,multiply(X1,sk_c10)) != sk_c9
| sk_c8 = sk_c3
| multiply(sk_c4,sk_c9) = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_76]) ).
cnf(c_0_87,negated_conjecture,
( sk_c8 = sk_c3
| multiply(sk_c10,sk_c10) = sk_c10 ),
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_83]),c_0_84]) ).
cnf(c_0_88,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_36]),c_0_85]) ).
cnf(c_0_89,negated_conjecture,
( inverse(X4) != sk_c9
| inverse(X1) != sk_c10
| inverse(X3) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| multiply(X2,inverse(X2)) != sk_c9
| multiply(inverse(X2),sk_c10) != sk_c9
| multiply(sk_c10,multiply(X1,sk_c10)) != sk_c9
| sk_c8 = sk_c3
| multiply(sk_c4,sk_c9) = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_84]) ).
cnf(c_0_90,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_88]),c_0_88]) ).
cnf(c_0_91,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c1) = sk_c9 ),
prove_this_32 ).
cnf(c_0_92,negated_conjecture,
( inverse(X3) != sk_c9
| inverse(X2) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| multiply(X1,inverse(X1)) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| multiply(inverse(X1),sk_c10) != sk_c9
| sk_c8 = sk_c3
| multiply(sk_c4,sk_c9) = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_82]),c_0_76]) ).
cnf(c_0_93,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c10 ),
prove_this_23 ).
cnf(c_0_94,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c9) = sk_c10 ),
prove_this_16 ).
cnf(c_0_95,negated_conjecture,
( inverse(sk_c10) = sk_c7
| inverse(sk_c1) = sk_c9 ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_96,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c9) = sk_c10 ),
prove_this_14 ).
cnf(c_0_97,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c9 ),
prove_this_25 ).
cnf(c_0_98,negated_conjecture,
( inverse(X3) != sk_c9
| inverse(X2) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| multiply(X1,inverse(X1)) != sk_c9
| multiply(inverse(X1),sk_c10) != sk_c9
| sk_c8 = sk_c3
| multiply(sk_c4,sk_c9) = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_87]),c_0_84]) ).
cnf(c_0_99,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c9 ),
prove_this_26 ).
cnf(c_0_100,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| multiply(inverse(sk_c7),sk_c8) = sk_c10 ),
inference(spm,[status(thm)],[c_0_38,c_0_93]) ).
cnf(c_0_101,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c1) = sk_c9 ),
prove_this_31 ).
cnf(c_0_102,negated_conjecture,
( inverse(sk_c10) = sk_c7
| inverse(sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_90,c_0_94]) ).
cnf(c_0_103,negated_conjecture,
( inverse(sk_c9) = sk_c1
| inverse(sk_c10) = sk_c7 ),
inference(spm,[status(thm)],[c_0_90,c_0_95]) ).
cnf(c_0_104,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c10,multiply(sk_c9,X1)) = X1 ),
inference(spm,[status(thm)],[c_0_38,c_0_96]) ).
cnf(c_0_105,negated_conjecture,
( multiply(sk_c9,sk_c1) = identity
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_36,c_0_44]) ).
cnf(c_0_106,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c9) = sk_c10 ),
prove_this_9 ).
cnf(c_0_107,negated_conjecture,
( inverse(sk_c10) = sk_c4
| inverse(sk_c1) = sk_c9 ),
inference(spm,[status(thm)],[c_0_90,c_0_97]) ).
cnf(c_0_108,negated_conjecture,
( inverse(X2) != sk_c9
| inverse(X1) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| multiply(X1,sk_c9) != sk_c10
| multiply(sk_c1,sk_c9) != sk_c9
| multiply(sk_c9,sk_c10) != sk_c9
| sk_c8 = sk_c3
| multiply(sk_c4,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_109,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| multiply(inverse(inverse(sk_c7)),sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_38,c_0_100]) ).
cnf(c_0_110,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
prove_this_24 ).
cnf(c_0_111,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c9) = sk_c10 ),
prove_this_15 ).
cnf(c_0_112,negated_conjecture,
( inverse(sk_c9) = sk_c1
| multiply(sk_c7,sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_90,c_0_101]) ).
cnf(c_0_113,negated_conjecture,
( sk_c1 = sk_c10
| inverse(sk_c10) = sk_c7 ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_114,negated_conjecture,
( sk_c1 = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_88]) ).
cnf(c_0_115,negated_conjecture,
( inverse(sk_c10) = sk_c4
| inverse(sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_90,c_0_106]) ).
cnf(c_0_116,negated_conjecture,
( inverse(sk_c9) = sk_c1
| inverse(sk_c10) = sk_c4 ),
inference(spm,[status(thm)],[c_0_90,c_0_107]) ).
cnf(c_0_117,negated_conjecture,
( inverse(X2) != sk_c9
| inverse(X1) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| multiply(X1,sk_c9) != sk_c10
| multiply(sk_c1,sk_c9) != sk_c9
| sk_c8 = sk_c3
| multiply(sk_c4,sk_c9) = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_82]),c_0_84]) ).
cnf(c_0_118,negated_conjecture,
( identity = sk_c8
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_36]) ).
cnf(c_0_119,negated_conjecture,
( sk_c1 = sk_c10
| multiply(sk_c7,sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_120,negated_conjecture,
( sk_c1 = sk_c10
| multiply(sk_c7,sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_36,c_0_113]) ).
cnf(c_0_121,negated_conjecture,
( inverse(sk_c9) = sk_c1
| multiply(sk_c4,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_90,c_0_99]) ).
cnf(c_0_122,negated_conjecture,
( sk_c1 = sk_c10
| multiply(inverse(sk_c10),sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_38,c_0_114]) ).
cnf(c_0_123,negated_conjecture,
( sk_c1 = sk_c10
| inverse(sk_c10) = sk_c4 ),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_124,negated_conjecture,
( inverse(X2) != sk_c9
| inverse(X1) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| multiply(X1,sk_c9) != sk_c10
| sk_c8 = sk_c3
| identity = sk_c8
| multiply(sk_c4,sk_c9) = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_84]) ).
cnf(c_0_125,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_36,c_0_88]) ).
cnf(c_0_126,negated_conjecture,
( identity = sk_c8
| sk_c1 = sk_c10 ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_127,negated_conjecture,
( sk_c1 = sk_c10
| multiply(sk_c4,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_76,c_0_121]) ).
cnf(c_0_128,negated_conjecture,
( sk_c1 = sk_c10
| multiply(sk_c4,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_129,negated_conjecture,
( inverse(X1) != sk_c9
| inverse(sk_c1) != sk_c10
| multiply(X1,sk_c9) != sk_c10
| identity = sk_c8
| sk_c8 = sk_c3
| multiply(sk_c4,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_124,c_0_118]) ).
cnf(c_0_130,negated_conjecture,
( sk_c1 = sk_c10
| inverse(sk_c8) = sk_c8 ),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_131,negated_conjecture,
( sk_c8 = sk_c10
| sk_c1 = sk_c10 ),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_132,negated_conjecture,
( inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c10
| sk_c8 = sk_c3
| identity = sk_c8
| multiply(sk_c4,sk_c9) = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_99]),c_0_84]) ).
cnf(c_0_133,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
prove_this_19 ).
cnf(c_0_134,negated_conjecture,
( sk_c1 = sk_c10
| inverse(sk_c10) = sk_c10 ),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_135,negated_conjecture,
( identity = sk_c8
| sk_c8 = sk_c3
| multiply(sk_c4,sk_c9) = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_118]),c_0_99]) ).
cnf(c_0_136,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| multiply(inverse(sk_c5),sk_c9) = sk_c6 ),
inference(spm,[status(thm)],[c_0_38,c_0_133]) ).
cnf(c_0_137,negated_conjecture,
( sk_c7 = sk_c10
| sk_c1 = sk_c10 ),
inference(spm,[status(thm)],[c_0_113,c_0_134]) ).
cnf(c_0_138,negated_conjecture,
( sk_c8 = sk_c3
| identity = sk_c8
| multiply(sk_c4,multiply(sk_c9,X1)) = multiply(sk_c10,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_135]) ).
cnf(c_0_139,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| multiply(inverse(inverse(sk_c5)),sk_c6) = sk_c9 ),
inference(spm,[status(thm)],[c_0_38,c_0_136]) ).
cnf(c_0_140,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c9) = sk_c10 ),
prove_this_20 ).
cnf(c_0_141,negated_conjecture,
( sk_c1 = sk_c10
| multiply(sk_c10,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_114,c_0_131]) ).
cnf(c_0_142,negated_conjecture,
( sk_c1 = sk_c10
| multiply(sk_c10,sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_119,c_0_137]) ).
cnf(c_0_143,negated_conjecture,
( identity = sk_c8
| sk_c8 = sk_c3
| multiply(sk_c4,X1) = multiply(sk_c10,X1) ),
inference(spm,[status(thm)],[c_0_138,c_0_82]) ).
cnf(c_0_144,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(inverse(inverse(sk_c2)),sk_c10) = sk_c3 ),
inference(spm,[status(thm)],[c_0_38,c_0_57]) ).
cnf(c_0_145,negated_conjecture,
( identity = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_36]) ).
cnf(c_0_146,negated_conjecture,
( sk_c8 = sk_c9
| sk_c1 = sk_c10 ),
inference(spm,[status(thm)],[c_0_141,c_0_142]) ).
cnf(c_0_147,negated_conjecture,
( sk_c8 = sk_c3
| identity = sk_c8
| multiply(inverse(sk_c4),multiply(sk_c10,X1)) = X1 ),
inference(spm,[status(thm)],[c_0_38,c_0_143]) ).
cnf(c_0_148,negated_conjecture,
( identity = sk_c8
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_56]),c_0_36]) ).
cnf(c_0_149,negated_conjecture,
( identity = sk_c3
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_58]),c_0_36]) ).
cnf(c_0_150,negated_conjecture,
( identity = sk_c9
| multiply(inverse(sk_c1),sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_38,c_0_145]) ).
cnf(c_0_151,negated_conjecture,
( sk_c1 = sk_c10
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_131,c_0_146]) ).
cnf(c_0_152,negated_conjecture,
( identity = sk_c8
| sk_c8 = sk_c3
| multiply(inverse(sk_c4),sk_c9) = sk_c3 ),
inference(spm,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_153,negated_conjecture,
( identity = sk_c8
| sk_c8 = sk_c3
| identity = sk_c3
| multiply(inverse(sk_c4),sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_147,c_0_149]) ).
cnf(c_0_154,negated_conjecture,
( identity = sk_c9
| sk_c9 = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_36])]) ).
cnf(c_0_155,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
prove_this_37 ).
cnf(c_0_156,negated_conjecture,
( identity = sk_c10
| sk_c8 = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_87]),c_0_36]) ).
cnf(c_0_157,negated_conjecture,
( sk_c8 = sk_c3
| identity = sk_c8
| identity = sk_c3 ),
inference(spm,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_158,negated_conjecture,
( sk_c9 = sk_c10
| inverse(sk_c9) = sk_c9 ),
inference(spm,[status(thm)],[c_0_125,c_0_154]) ).
cnf(c_0_159,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| multiply(sk_c6,multiply(sk_c10,X1)) = multiply(sk_c9,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_155]) ).
cnf(c_0_160,negated_conjecture,
( sk_c8 = sk_c3
| sk_c8 = sk_c10
| identity = sk_c3 ),
inference(spm,[status(thm)],[c_0_156,c_0_157]) ).
cnf(c_0_161,negated_conjecture,
( sk_c9 = sk_c10
| inverse(sk_c10) = sk_c4 ),
inference(spm,[status(thm)],[c_0_115,c_0_158]) ).
cnf(c_0_162,negated_conjecture,
( sk_c9 = sk_c10
| inverse(sk_c10) = sk_c7 ),
inference(spm,[status(thm)],[c_0_102,c_0_158]) ).
cnf(c_0_163,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| multiply(sk_c6,sk_c9) = multiply(sk_c9,sk_c8) ),
inference(spm,[status(thm)],[c_0_159,c_0_55]) ).
cnf(c_0_164,negated_conjecture,
( sk_c3 = sk_c9
| sk_c8 = sk_c3
| sk_c8 = sk_c10 ),
inference(spm,[status(thm)],[c_0_77,c_0_160]) ).
cnf(c_0_165,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c4,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_76,c_0_158]) ).
cnf(c_0_166,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c4,sk_c9) = sk_c3 ),
inference(spm,[status(thm)],[c_0_72,c_0_161]) ).
cnf(c_0_167,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c7,sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_111,c_0_158]) ).
cnf(c_0_168,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c7,sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_36,c_0_162]) ).
cnf(c_0_169,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_52,c_0_163]) ).
cnf(c_0_170,negated_conjecture,
( sk_c3 != sk_c10
| sk_c8 = sk_c10
| sk_c3 = sk_c9 ),
inference(ef,[status(thm)],[c_0_164]) ).
cnf(c_0_171,negated_conjecture,
( sk_c3 = sk_c10
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_165,c_0_166]) ).
cnf(c_0_172,negated_conjecture,
( identity = sk_c8
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_167,c_0_168]) ).
cnf(c_0_173,negated_conjecture,
( sk_c8 = sk_c6
| sk_c8 = sk_c3
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_82,c_0_169]) ).
cnf(c_0_174,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
prove_this_21 ).
cnf(c_0_175,negated_conjecture,
( sk_c9 = sk_c10
| sk_c8 = sk_c10 ),
inference(spm,[status(thm)],[c_0_170,c_0_171]) ).
cnf(c_0_176,negated_conjecture,
( sk_c9 = sk_c10
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_154,c_0_172]) ).
cnf(c_0_177,negated_conjecture,
( sk_c8 = sk_c3
| sk_c8 = sk_c6
| multiply(inverse(sk_c10),sk_c9) = sk_c3 ),
inference(spm,[status(thm)],[c_0_38,c_0_173]) ).
cnf(c_0_178,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c9
| multiply(inverse(sk_c1),sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_38,c_0_174]) ).
cnf(c_0_179,negated_conjecture,
sk_c9 = sk_c10,
inference(spm,[status(thm)],[c_0_175,c_0_176]) ).
cnf(c_0_180,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c9 ),
prove_this_29 ).
cnf(c_0_181,negated_conjecture,
( sk_c8 = sk_c3
| sk_c8 = sk_c6
| multiply(sk_c10,sk_c3) = sk_c10 ),
inference(spm,[status(thm)],[c_0_73,c_0_177]) ).
cnf(c_0_182,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c9
| multiply(inverse(inverse(sk_c1)),sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_38,c_0_178]) ).
cnf(c_0_183,negated_conjecture,
( identity = sk_c3
| identity = sk_c10 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_179]),c_0_36]),c_0_179]) ).
cnf(c_0_184,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c9
| inverse(sk_c9) = sk_c10 ),
prove_this_13 ).
cnf(c_0_185,negated_conjecture,
( inverse(sk_c9) = sk_c1
| multiply(sk_c6,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_90,c_0_180]) ).
cnf(c_0_186,negated_conjecture,
( identity = sk_c3
| sk_c8 = sk_c6
| sk_c8 = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_181]),c_0_36]) ).
cnf(c_0_187,negated_conjecture,
( identity = sk_c10
| multiply(sk_c6,sk_c10) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_180]),c_0_36]) ).
cnf(c_0_188,negated_conjecture,
( sk_c3 != sk_c10
| identity = sk_c10 ),
inference(ef,[status(thm)],[c_0_183]) ).
cnf(c_0_189,negated_conjecture,
( sk_c1 = sk_c10
| multiply(sk_c6,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_184,c_0_185]) ).
cnf(c_0_190,negated_conjecture,
( sk_c8 = sk_c3
| sk_c3 = sk_c10
| sk_c8 = sk_c6 ),
inference(spm,[status(thm)],[c_0_156,c_0_186]) ).
cnf(c_0_191,negated_conjecture,
( identity = sk_c10
| multiply(sk_c6,multiply(sk_c10,X1)) = multiply(sk_c9,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_187]) ).
cnf(c_0_192,negated_conjecture,
( sk_c3 != sk_c10
| multiply(X1,sk_c10) = X1 ),
inference(spm,[status(thm)],[c_0_88,c_0_188]) ).
cnf(c_0_193,negated_conjecture,
( sk_c1 = sk_c10
| multiply(sk_c6,sk_c10) = sk_c10 ),
inference(rw,[status(thm)],[c_0_189,c_0_179]) ).
cnf(c_0_194,negated_conjecture,
( sk_c6 = sk_c10
| sk_c3 = sk_c10
| sk_c1 = sk_c10 ),
inference(spm,[status(thm)],[c_0_190,c_0_131]) ).
cnf(c_0_195,negated_conjecture,
( identity = sk_c10
| multiply(sk_c6,multiply(sk_c10,X1)) = multiply(sk_c10,X1) ),
inference(rw,[status(thm)],[c_0_191,c_0_179]) ).
cnf(c_0_196,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_36,c_0_90]) ).
cnf(c_0_197,negated_conjecture,
( identity = sk_c10
| multiply(inverse(sk_c1),sk_c10) = sk_c10 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_150,c_0_179]),c_0_179]) ).
cnf(c_0_198,negated_conjecture,
( sk_c6 = sk_c10
| sk_c1 = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_193]),c_0_194]) ).
cnf(c_0_199,negated_conjecture,
( identity = sk_c6
| identity = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_196]),c_0_88]) ).
cnf(c_0_200,negated_conjecture,
( identity = sk_c10
| sk_c6 = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_198]),c_0_36])]) ).
cnf(c_0_201,negated_conjecture,
( inverse(X5) != sk_c10
| inverse(X2) != sk_c10
| inverse(X4) != sk_c10
| inverse(X1) != sk_c10
| inverse(sk_c10) != sk_c10
| multiply(X5,sk_c10) != sk_c10
| multiply(X4,sk_c10) != sk_c10
| multiply(X3,inverse(X3)) != sk_c10
| multiply(inverse(X3),sk_c10) != sk_c10
| multiply(sk_c10,multiply(X2,sk_c10)) != sk_c10
| multiply(sk_c10,multiply(X1,sk_c10)) != sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_179]),c_0_179]),c_0_179]),c_0_179]),c_0_179]),c_0_179]),c_0_179]),c_0_179]),c_0_179])]) ).
cnf(c_0_202,negated_conjecture,
identity = sk_c10,
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_199]),c_0_200]) ).
cnf(c_0_203,negated_conjecture,
( identity != sk_c10
| inverse(X5) != sk_c10
| inverse(X2) != sk_c10
| inverse(X4) != sk_c10
| inverse(X1) != sk_c10
| inverse(sk_c10) != sk_c10
| multiply(X5,sk_c10) != sk_c10
| multiply(X4,sk_c10) != sk_c10
| multiply(inverse(X3),sk_c10) != sk_c10
| multiply(sk_c10,multiply(X2,sk_c10)) != sk_c10
| multiply(sk_c10,multiply(X1,sk_c10)) != sk_c10 ),
inference(rw,[status(thm)],[c_0_201,c_0_196]) ).
cnf(c_0_204,plain,
multiply(X1,sk_c10) = X1,
inference(rw,[status(thm)],[c_0_88,c_0_202]) ).
cnf(c_0_205,plain,
multiply(sk_c10,X1) = X1,
inference(rw,[status(thm)],[c_0_37,c_0_202]) ).
cnf(c_0_206,plain,
inverse(sk_c10) = sk_c10,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_125,c_0_202]),c_0_202]) ).
cnf(c_0_207,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c2) = sk_c10 ),
prove_this_56 ).
cnf(c_0_208,negated_conjecture,
inverse(X1) != sk_c10,
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(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_203,c_0_202])]),c_0_204]),c_0_205]),c_0_204]),c_0_205]),c_0_204]),c_0_204]),c_0_204]),c_0_206])])])])])]),c_0_206])]) ).
cnf(c_0_209,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_207,c_0_208]),c_0_208]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP240-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/5.37 % Computer : n015.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sun Sep 20 20:10:26 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 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
% 10.18/6.78 % Version: 3.5.1
% 10.18/6.78 % Preprocessing class: FSMSSMSMSSSNFFN.
% 10.18/6.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.18/6.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 10.18/6.78 % Starting new_bool_3 with 300s (1) cores
% 10.18/6.78 % Starting new_bool_1 with 300s (1) cores
% 10.18/6.78 % Starting sh5l with 300s (1) cores
% 10.18/6.78 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 3817802 completed with status 0
% 10.18/6.78 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 10.18/6.78 % Preprocessing class: FSMSSMSMSSSNFFN.
% 10.18/6.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.18/6.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 10.18/6.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 10.18/6.78 % No SInE strategy applied
% 10.18/6.78 % Search class: FGHPS-FFMM21-SFFFFFNN
% 10.18/6.78 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 10.18/6.78 % Starting SubtermCWHack with 136s (1) cores
% 10.18/6.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 10.18/6.78 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 10.18/6.78 % Starting new_bool_3 with 136s (1) cores
% 10.18/6.78 % Starting new_bool_1 with 136s (1) cores
% 10.18/6.78 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 3817809 completed with status 0
% 10.18/6.78 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 10.18/6.78 % Preprocessing class: FSMSSMSMSSSNFFN.
% 10.18/6.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.18/6.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 10.18/6.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 10.18/6.78 % No SInE strategy applied
% 10.18/6.78 % Search class: FGHPS-FFMM21-SFFFFFNN
% 10.18/6.78 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 10.18/6.78 % Starting SubtermCWHack with 136s (1) cores
% 10.18/6.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 10.18/6.78 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 10.18/6.78 % Preprocessing time : 0.001 s
% 10.18/6.78 % Presaturation interreduction done
% 10.18/6.78
% 10.18/6.78 % Proof found!
% 10.18/6.78 % SZS status Unsatisfiable
% 10.18/6.78 % SZS output start CNFRefutation
% See solution above
% 10.18/6.78 % Parsed axioms : 60
% 10.18/6.78 % Removed by relevancy pruning/SinE : 0
% 10.18/6.78 % Initial clauses : 60
% 10.18/6.78 % Removed in clause preprocessing : 0
% 10.18/6.78 % Initial clauses in saturation : 60
% 10.18/6.78 % Processed clauses : 23493
% 10.18/6.78 % ...of these trivial : 419
% 10.18/6.78 % ...subsumed : 19107
% 10.18/6.78 % ...remaining for further processing : 3967
% 10.18/6.78 % Other redundant clauses eliminated : 54
% 10.18/6.78 % Clauses deleted for lack of memory : 0
% 10.18/6.78 % Backward-subsumed : 1093
% 10.18/6.78 % Backward-rewritten : 2688
% 10.18/6.78 % Generated clauses : 166722
% 10.18/6.78 % ...of the previous two non-redundant : 162699
% 10.18/6.78 % ...aggressively subsumed : 0
% 10.18/6.78 % Contextual simplify-reflections : 140
% 10.18/6.78 % Paramodulations : 166557
% 10.18/6.78 % Factorizations : 105
% 10.18/6.78 % NegExts : 0
% 10.18/6.78 % Equation resolutions : 54
% 10.18/6.78 % Disequality decompositions : 0
% 10.18/6.78 % Total rewrite steps : 21646
% 10.18/6.78 % ...of those cached : 21362
% 10.18/6.78 % Propositional unsat checks : 0
% 10.18/6.78 % Propositional check models : 0
% 10.18/6.78 % Propositional check unsatisfiable : 0
% 10.18/6.78 % Propositional clauses : 0
% 10.18/6.78 % Propositional clauses after purity: 0
% 10.18/6.78 % Propositional unsat core size : 0
% 10.18/6.78 % Propositional preprocessing time : 0.000
% 10.18/6.78 % Propositional encoding time : 0.000
% 10.18/6.78 % Propositional solver time : 0.000
% 10.18/6.78 % Success case prop preproc time : 0.000
% 10.18/6.78 % Success case prop encoding time : 0.000
% 10.18/6.78 % Success case prop solver time : 0.000
% 10.18/6.78 % Current number of processed clauses : 107
% 10.18/6.78 % Positive orientable unit clauses : 15
% 10.18/6.78 % Positive unorientable unit clauses: 0
% 10.18/6.78 % Negative unit clauses : 1
% 10.18/6.78 % Non-unit-clauses : 91
% 10.18/6.78 % Current number of unprocessed clauses: 132709
% 10.18/6.78 % ...number of literals in the above : 592616
% 10.18/6.78 % Current number of archived formulas : 0
% 10.18/6.78 % Current number of archived clauses : 3856
% 10.18/6.78 % Clause-clause subsumption calls (NU) : 435229
% 10.18/6.78 % Rec. Clause-clause subsumption calls : 194308
% 10.18/6.78 % Non-unit clause-clause subsumptions : 20271
% 10.18/6.78 % Unit Clause-clause subsumption calls : 2241
% 10.18/6.78 % Rewrite failures with RHS unbound : 0
% 10.18/6.78 % BW rewrite match attempts : 57
% 10.18/6.78 % BW rewrite match successes : 54
% 10.18/6.78 % Condensation attempts : 0
% 10.18/6.78 % Condensation successes : 0
% 10.18/6.78 % Termbank termtop insertions : 1692203
% 10.18/6.78 % Search garbage collected termcells : 42
% 10.18/6.78
% 10.18/6.78 % -------------------------------------------------
% 10.18/6.78 % User time : 1.253 s
% 10.18/6.78 % System time : 0.051 s
% 10.18/6.78 % Total time : 1.304 s
% 10.18/6.78 % Maximum resident set size: 3660 pages
% 10.18/6.78
% 10.18/6.78 % -------------------------------------------------
% 10.18/6.78 % User time : 6.307 s
% 10.18/6.78 % System time : 0.264 s
% 10.18/6.78 % Total time : 6.571 s
% 10.18/6.78 % Maximum resident set size: 4864 pages
% 10.18/6.78 % E exiting
%------------------------------------------------------------------------------