%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP223-1 : 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 12:39:01 PM UTC 2026
% Result : Unsatisfiable 12.49s 2.26s
% Output : CNFRefutation 12.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 32
% Syntax : Number of clauses : 212 ( 39 unt; 126 nHn; 185 RR)
% Number of literals : 512 ( 511 equ; 176 neg)
% Maximal clause size : 11 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 117 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this_31,negated_conjecture,
( inverse(X7) != sk_c9
| multiply(X7,sk_c9) != X6
| multiply(sk_c9,X6) != sk_c8
| multiply(X5,sk_c8) != sk_c9
| inverse(X4) != X5
| multiply(X4,X5) != sk_c9
| inverse(X3) != sk_c9
| multiply(X3,sk_c9) != X2
| multiply(sk_c9,X2) != sk_c8
| multiply(X1,sk_c8) != sk_c9
| inverse(X1) != sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_28,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
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_c9,sk_c7) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_16,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_13,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_17,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_14,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_18,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_4,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_20,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_23,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_26,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_24,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_29,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
cnf(prove_this_25,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_11,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_6,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_30,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
cnf(prove_this_12,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_27,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_21,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_15,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_7,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_9,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_8,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_2,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
cnf(c_0_32,negated_conjecture,
( inverse(X7) != sk_c9
| multiply(X7,sk_c9) != X6
| multiply(sk_c9,X6) != sk_c8
| multiply(X5,sk_c8) != sk_c9
| inverse(X4) != X5
| multiply(X4,X5) != sk_c9
| inverse(X3) != sk_c9
| multiply(X3,sk_c9) != X2
| multiply(sk_c9,X2) != sk_c8
| multiply(X1,sk_c8) != sk_c9
| inverse(X1) != sk_c9 ),
inference(fof_simplification,[status(thm)],[prove_this_31]) ).
cnf(c_0_33,negated_conjecture,
( inverse(X7) != sk_c9
| multiply(X7,sk_c9) != X6
| multiply(sk_c9,X6) != sk_c8
| multiply(X5,sk_c8) != sk_c9
| inverse(X4) != X5
| multiply(X4,X5) != sk_c9
| inverse(X3) != sk_c9
| multiply(X3,sk_c9) != X2
| multiply(sk_c9,X2) != sk_c8
| multiply(X1,sk_c8) != sk_c9
| inverse(X1) != sk_c9 ),
c_0_32 ).
cnf(c_0_34,negated_conjecture,
( inverse(X4) != sk_c9
| inverse(X2) != sk_c9
| inverse(X1) != sk_c9
| multiply(X4,sk_c8) != sk_c9
| multiply(X3,inverse(X3)) != sk_c9
| multiply(inverse(X3),sk_c8) != sk_c9
| multiply(sk_c9,multiply(X2,sk_c9)) != sk_c8
| multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_33])])]) ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c9 ),
prove_this_28 ).
cnf(c_0_36,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_37,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_38,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_39,negated_conjecture,
( inverse(X3) != sk_c9
| inverse(X1) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| multiply(X2,inverse(X2)) != sk_c9
| multiply(inverse(X2),sk_c8) != sk_c9
| multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8
| multiply(sk_c9,multiply(sk_c2,sk_c9)) != sk_c8
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
prove_this_22 ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
prove_this_16 ).
cnf(c_0_42,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
prove_this_13 ).
cnf(c_0_44,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
prove_this_17 ).
cnf(c_0_45,negated_conjecture,
( inverse(X3) != sk_c9
| inverse(X1) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| multiply(X2,inverse(X2)) != sk_c9
| multiply(inverse(X2),sk_c8) != sk_c9
| multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_46,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(inverse(sk_c4),sk_c9) = sk_c5 ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c9,sk_c3) = sk_c8 ),
prove_this_14 ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(inverse(sk_c6),sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_42,c_0_44]) ).
cnf(c_0_49,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
prove_this_18 ).
cnf(c_0_50,negated_conjecture,
( inverse(X2) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| multiply(X1,inverse(X1)) != sk_c9
| multiply(inverse(X1),sk_c8) != sk_c9
| multiply(sk_c9,multiply(sk_c2,sk_c9)) != sk_c8
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_45,c_0_35]) ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
prove_this_10 ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c4,multiply(sk_c5,X1)) = multiply(sk_c9,X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_43]) ).
cnf(c_0_53,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c5
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_54,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(inverse(sk_c2),sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_42,c_0_40]) ).
cnf(c_0_56,negated_conjecture,
( inverse(X2) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| multiply(X1,inverse(X1)) != sk_c9
| multiply(inverse(X1),sk_c8) != sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_40]),c_0_41]) ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
prove_this_4 ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(inverse(sk_c1),sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_42,c_0_51]) ).
cnf(c_0_59,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c4,sk_c5) = multiply(sk_c9,sk_c9) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_60,negated_conjecture,
( sk_c8 = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_41,c_0_54]) ).
cnf(c_0_61,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_55,c_0_35]) ).
cnf(c_0_62,negated_conjecture,
( multiply(X1,inverse(X1)) != sk_c9
| multiply(inverse(X1),sk_c8) != sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_51]) ).
cnf(c_0_63,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_42,c_0_42]) ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c9,sk_c9) = sk_c8
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_58,c_0_57]) ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c9,sk_c9) = sk_c9 ),
inference(spm,[status(thm)],[c_0_43,c_0_59]) ).
cnf(c_0_66,negated_conjecture,
( sk_c8 = sk_c9
| multiply(inverse(sk_c9),sk_c8) = sk_c3 ),
inference(spm,[status(thm)],[c_0_42,c_0_60]) ).
cnf(c_0_67,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c9
| multiply(inverse(sk_c9),sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_42,c_0_61]) ).
cnf(c_0_68,negated_conjecture,
( inverse(X3) != sk_c9
| inverse(X1) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| multiply(X2,inverse(X2)) != sk_c9
| multiply(inverse(X2),sk_c8) != sk_c9
| multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8
| multiply(sk_c9,multiply(sk_c6,sk_c9)) != sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_34,c_0_49]) ).
cnf(c_0_69,negated_conjecture,
( multiply(X1,sk_c8) != sk_c9
| multiply(inverse(X1),inverse(inverse(X1))) != sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_70,negated_conjecture,
( multiply(sk_c9,sk_c9) = sk_c8
| multiply(inverse(sk_c9),sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_42,c_0_64]) ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c9,sk_c9) = sk_c9
| multiply(inverse(sk_c9),sk_c8) = sk_c3 ),
inference(spm,[status(thm)],[c_0_42,c_0_65]) ).
cnf(c_0_72,negated_conjecture,
( sk_c7 = sk_c3
| sk_c8 = sk_c9
| multiply(sk_c9,sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_73,negated_conjecture,
( inverse(X3) != sk_c9
| inverse(X1) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| multiply(X2,inverse(X2)) != sk_c9
| multiply(inverse(X2),sk_c8) != sk_c9
| multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_44]),c_0_62]) ).
cnf(c_0_74,negated_conjecture,
( multiply(X1,sk_c8) != sk_c9
| multiply(inverse(X1),inverse(inverse(inverse(inverse(X1))))) != sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_63]),c_0_63]) ).
cnf(c_0_75,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_37]),c_0_63]) ).
cnf(c_0_76,negated_conjecture,
( sk_c7 = sk_c3
| multiply(sk_c9,sk_c9) = sk_c8
| multiply(sk_c9,sk_c9) = sk_c9 ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_77,negated_conjecture,
( sk_c8 = sk_c9
| sk_c7 = sk_c3 ),
inference(spm,[status(thm)],[c_0_60,c_0_72]) ).
cnf(c_0_78,negated_conjecture,
( inverse(X2) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| multiply(X1,inverse(X1)) != sk_c9
| multiply(inverse(X1),sk_c8) != sk_c9
| multiply(sk_c9,multiply(sk_c6,sk_c9)) != sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_73,c_0_49]) ).
cnf(c_0_79,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c2,sk_c9) = sk_c3 ),
prove_this_20 ).
cnf(c_0_80,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
prove_this_23 ).
cnf(c_0_81,negated_conjecture,
( sk_c8 != sk_c9
| multiply(inverse(identity),inverse(inverse(inverse(inverse(identity))))) != sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_74,c_0_38]) ).
cnf(c_0_82,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_37,c_0_75]) ).
cnf(c_0_83,negated_conjecture,
( sk_c7 = sk_c3
| multiply(sk_c9,sk_c9) = sk_c9 ),
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_76]),c_0_77]) ).
cnf(c_0_84,negated_conjecture,
( inverse(X2) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| multiply(X1,inverse(X1)) != sk_c9
| multiply(inverse(X1),sk_c8) != sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_44]),c_0_62]) ).
cnf(c_0_85,negated_conjecture,
( identity = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_53]),c_0_37]) ).
cnf(c_0_86,negated_conjecture,
( multiply(sk_c5,sk_c4) = identity
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(spm,[status(thm)],[c_0_37,c_0_79]) ).
cnf(c_0_87,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c2) = sk_c9 ),
prove_this_26 ).
cnf(c_0_88,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(inverse(sk_c6),sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_42,c_0_80]) ).
cnf(c_0_89,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
prove_this_24 ).
cnf(c_0_90,negated_conjecture,
( sk_c8 != sk_c9
| identity != sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
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_81,c_0_82]),c_0_82]),c_0_82]),c_0_82]),c_0_82]),c_0_75]) ).
cnf(c_0_91,negated_conjecture,
( identity = sk_c9
| sk_c7 = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_83]),c_0_37]) ).
cnf(c_0_92,negated_conjecture,
( multiply(X1,inverse(X1)) != sk_c9
| multiply(inverse(X1),sk_c8) != sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_82]),c_0_38]),c_0_85]),c_0_60]) ).
cnf(c_0_93,negated_conjecture,
( multiply(sk_c5,sk_c4) = identity
| multiply(inverse(sk_c2),sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_42,c_0_86]) ).
cnf(c_0_94,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c5,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_37,c_0_87]) ).
cnf(c_0_95,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_96,negated_conjecture,
( sk_c7 = sk_c3
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_77]) ).
cnf(c_0_97,negated_conjecture,
multiply(sk_c9,sk_c3) = sk_c8,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_82]),c_0_38]),c_0_75]),c_0_85]),c_0_60]) ).
cnf(c_0_98,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c9
| multiply(sk_c5,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_99,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c9
| multiply(inverse(sk_c2),sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_42,c_0_95]) ).
cnf(c_0_100,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c9 ),
prove_this_29 ).
cnf(c_0_101,negated_conjecture,
( sk_c7 = sk_c3
| multiply(inverse(sk_c9),sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_42,c_0_96]) ).
cnf(c_0_102,negated_conjecture,
multiply(inverse(sk_c9),sk_c8) = sk_c3,
inference(spm,[status(thm)],[c_0_42,c_0_97]) ).
cnf(c_0_103,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| inverse(sk_c2) = sk_c9 ),
prove_this_25 ).
cnf(c_0_104,negated_conjecture,
( inverse(sk_c5) = sk_c4
| multiply(sk_c9,sk_c3) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_98]),c_0_75]) ).
cnf(c_0_105,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c9 ),
prove_this_11 ).
cnf(c_0_106,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9 ),
prove_this_6 ).
cnf(c_0_107,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_108,negated_conjecture,
sk_c7 = sk_c3,
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_109,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c9
| multiply(sk_c4,sk_c5) = sk_c9 ),
inference(spm,[status(thm)],[c_0_99,c_0_103]) ).
cnf(c_0_110,negated_conjecture,
( sk_c8 = sk_c9
| inverse(sk_c5) = sk_c4 ),
inference(rw,[status(thm)],[c_0_104,c_0_97]) ).
cnf(c_0_111,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c9 ),
prove_this_30 ).
cnf(c_0_112,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(inverse(sk_c6),sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_42,c_0_105]) ).
cnf(c_0_113,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
prove_this_12 ).
cnf(c_0_114,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c9,multiply(sk_c6,X1)) = X1 ),
inference(spm,[status(thm)],[c_0_42,c_0_106]) ).
cnf(c_0_115,negated_conjecture,
( sk_c8 = sk_c9
| multiply(sk_c6,sk_c9) = sk_c3 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_97]),c_0_108]),c_0_108]),c_0_97])]) ).
cnf(c_0_116,negated_conjecture,
( sk_c8 = sk_c9
| multiply(sk_c4,sk_c5) = sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_97]),c_0_108]),c_0_97])]) ).
cnf(c_0_117,negated_conjecture,
( sk_c8 = sk_c9
| multiply(sk_c4,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_37,c_0_110]) ).
cnf(c_0_118,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c9,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_37,c_0_111]) ).
cnf(c_0_119,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_42,c_0_36]) ).
cnf(c_0_120,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_121,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_75]),c_0_75]) ).
cnf(c_0_122,negated_conjecture,
( sk_c8 = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_97])]) ).
cnf(c_0_123,negated_conjecture,
( identity = sk_c9
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_124,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
prove_this_27 ).
cnf(c_0_125,negated_conjecture,
( inverse(X3) != sk_c9
| inverse(X1) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| multiply(X2,inverse(X2)) != sk_c9
| multiply(inverse(X2),sk_c8) != sk_c9
| multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8
| multiply(sk_c9,multiply(sk_c2,sk_c9)) != sk_c8
| multiply(sk_c9,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_34,c_0_118]) ).
cnf(c_0_126,negated_conjecture,
( multiply(sk_c9,sk_c6) = identity
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(spm,[status(thm)],[c_0_37,c_0_89]) ).
cnf(c_0_127,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c9
| multiply(inverse(multiply(X1,sk_c1)),multiply(X1,sk_c9)) = sk_c8 ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_128,negated_conjecture,
( sk_c8 = sk_c9
| inverse(sk_c9) = sk_c1 ),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_129,negated_conjecture,
( sk_c8 = sk_c9
| inverse(sk_c9) = sk_c9 ),
inference(spm,[status(thm)],[c_0_82,c_0_123]) ).
cnf(c_0_130,negated_conjecture,
( inverse(X3) != sk_c9
| inverse(X1) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| multiply(X2,inverse(X2)) != sk_c9
| multiply(inverse(X2),sk_c8) != sk_c9
| multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8
| multiply(sk_c9,multiply(sk_c2,sk_c9)) != sk_c8
| multiply(sk_c5,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_34,c_0_124]) ).
cnf(c_0_131,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
prove_this_21 ).
cnf(c_0_132,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
prove_this_15 ).
cnf(c_0_133,negated_conjecture,
( inverse(X3) != sk_c9
| inverse(X1) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| multiply(X2,inverse(X2)) != sk_c9
| multiply(inverse(X2),sk_c8) != sk_c9
| multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8
| multiply(sk_c9,sk_c6) = identity ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_84]) ).
cnf(c_0_134,negated_conjecture,
( sk_c8 = sk_c9
| multiply(inverse(multiply(X1,sk_c1)),multiply(X1,sk_c9)) = sk_c8 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_127,c_0_108]),c_0_97]) ).
cnf(c_0_135,negated_conjecture,
( sk_c1 = sk_c9
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_136,negated_conjecture,
( inverse(X3) != sk_c9
| inverse(X1) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| multiply(X2,inverse(X2)) != sk_c9
| multiply(inverse(X2),sk_c8) != sk_c9
| multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8
| multiply(sk_c5,sk_c8) = sk_c9 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_132]) ).
cnf(c_0_137,negated_conjecture,
( inverse(X2) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| multiply(X1,inverse(X1)) != sk_c9
| multiply(inverse(X1),sk_c8) != sk_c9
| multiply(sk_c9,multiply(sk_c2,sk_c9)) != sk_c8
| multiply(sk_c9,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_133,c_0_118]) ).
cnf(c_0_138,negated_conjecture,
( identity = sk_c8
| sk_c8 = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_37]) ).
cnf(c_0_139,negated_conjecture,
( inverse(X2) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| multiply(X1,inverse(X1)) != sk_c9
| multiply(inverse(X1),sk_c8) != sk_c9
| multiply(sk_c9,multiply(sk_c2,sk_c9)) != sk_c8
| multiply(sk_c5,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_136,c_0_124]) ).
cnf(c_0_140,negated_conjecture,
( inverse(X2) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| multiply(X1,inverse(X1)) != sk_c9
| multiply(inverse(X1),sk_c8) != sk_c9
| multiply(sk_c9,sk_c6) = identity ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_126]),c_0_84]) ).
cnf(c_0_141,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c9,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_37,c_0_106]) ).
cnf(c_0_142,negated_conjecture,
( multiply(sk_c9,sk_c6) = identity
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_37,c_0_113]) ).
cnf(c_0_143,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
prove_this_7 ).
cnf(c_0_144,negated_conjecture,
sk_c8 = sk_c9,
inference(spm,[status(thm)],[c_0_123,c_0_138]) ).
cnf(c_0_145,negated_conjecture,
( inverse(X2) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| multiply(X1,inverse(X1)) != sk_c9
| multiply(inverse(X1),sk_c8) != sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_131]),c_0_132]) ).
cnf(c_0_146,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
prove_this_3 ).
cnf(c_0_147,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
prove_this_9 ).
cnf(c_0_148,negated_conjecture,
( multiply(X1,inverse(X1)) != sk_c9
| multiply(inverse(X1),sk_c8) != sk_c9
| multiply(sk_c9,sk_c6) = identity ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_142]) ).
cnf(c_0_149,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(inverse(sk_c4),sk_c9) = sk_c5 ),
inference(spm,[status(thm)],[c_0_42,c_0_143]) ).
cnf(c_0_150,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c9 ),
prove_this_8 ).
cnf(c_0_151,negated_conjecture,
identity = sk_c3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_144]),c_0_37]) ).
cnf(c_0_152,negated_conjecture,
( multiply(X1,inverse(X1)) != sk_c9
| multiply(inverse(X1),sk_c8) != sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_147]) ).
cnf(c_0_153,negated_conjecture,
( multiply(X1,sk_c8) != sk_c9
| multiply(inverse(X1),inverse(inverse(X1))) != sk_c9
| multiply(sk_c9,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_148,c_0_63]) ).
cnf(c_0_154,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_155,plain,
multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,X3)) = multiply(X2,X3),
inference(spm,[status(thm)],[c_0_119,c_0_42]) ).
cnf(c_0_156,plain,
multiply(inverse(X1),X1) = sk_c3,
inference(rw,[status(thm)],[c_0_37,c_0_151]) ).
cnf(c_0_157,negated_conjecture,
( multiply(X1,sk_c8) != sk_c9
| multiply(inverse(X1),inverse(inverse(X1))) != sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_152,c_0_63]) ).
cnf(c_0_158,negated_conjecture,
( multiply(inverse(sk_c1),inverse(inverse(sk_c1))) != sk_c9
| multiply(sk_c9,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_153,c_0_142]) ).
cnf(c_0_159,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c5
| multiply(sk_c1,multiply(sk_c8,X1)) = multiply(sk_c9,X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_154]) ).
cnf(c_0_160,plain,
multiply(X1,inverse(X1)) = sk_c3,
inference(spm,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_161,plain,
multiply(X1,sk_c3) = X1,
inference(rw,[status(thm)],[c_0_75,c_0_151]) ).
cnf(c_0_162,negated_conjecture,
( multiply(X1,sk_c8) != sk_c9
| multiply(inverse(X1),inverse(inverse(inverse(inverse(X1))))) != sk_c9
| multiply(sk_c9,sk_c6) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_63]),c_0_63]) ).
cnf(c_0_163,negated_conjecture,
( multiply(inverse(sk_c1),inverse(inverse(sk_c1))) != sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_157,c_0_147]) ).
cnf(c_0_164,negated_conjecture,
( multiply(X1,sk_c8) != sk_c9
| multiply(inverse(X1),inverse(inverse(inverse(inverse(X1))))) != sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_63]),c_0_63]) ).
cnf(c_0_165,negated_conjecture,
( multiply(sk_c9,inverse(sk_c9)) != sk_c9
| multiply(sk_c9,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_158,c_0_141]) ).
cnf(c_0_166,negated_conjecture,
( inverse(sk_c9) = sk_c1
| multiply(sk_c9,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_121,c_0_141]) ).
cnf(c_0_167,negated_conjecture,
( sk_c3 = sk_c1
| multiply(sk_c5,sk_c9) = sk_c5 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_161]),c_0_144]),c_0_160]) ).
cnf(c_0_168,negated_conjecture,
( multiply(inverse(sk_c1),inverse(inverse(inverse(inverse(sk_c1))))) != sk_c9
| multiply(sk_c9,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_162,c_0_142]) ).
cnf(c_0_169,negated_conjecture,
( multiply(sk_c9,inverse(sk_c9)) != sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_163,c_0_146]) ).
cnf(c_0_170,negated_conjecture,
( inverse(sk_c9) = sk_c1
| multiply(sk_c5,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_121,c_0_146]) ).
cnf(c_0_171,negated_conjecture,
( multiply(inverse(sk_c1),inverse(inverse(inverse(inverse(sk_c1))))) != sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_164,c_0_147]) ).
cnf(c_0_172,negated_conjecture,
( multiply(sk_c9,sk_c1) != sk_c9
| multiply(sk_c9,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_165,c_0_166]) ).
cnf(c_0_173,negated_conjecture,
( sk_c3 = sk_c9
| sk_c3 = sk_c1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_167]),c_0_37]),c_0_151]) ).
cnf(c_0_174,negated_conjecture,
( identity != sk_c9
| multiply(sk_c9,sk_c6) = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_168,c_0_121]),c_0_121]),c_0_37]) ).
cnf(c_0_175,negated_conjecture,
( multiply(sk_c9,sk_c1) != sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_169,c_0_170]) ).
cnf(c_0_176,negated_conjecture,
( identity != sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_171,c_0_121]),c_0_121]),c_0_37]) ).
cnf(c_0_177,negated_conjecture,
( multiply(sk_c9,sk_c1) != sk_c9
| multiply(sk_c9,sk_c6) = sk_c3 ),
inference(rw,[status(thm)],[c_0_172,c_0_151]) ).
cnf(c_0_178,negated_conjecture,
( sk_c3 = sk_c9
| multiply(X1,sk_c1) = X1 ),
inference(spm,[status(thm)],[c_0_161,c_0_173]) ).
cnf(c_0_179,negated_conjecture,
( sk_c3 != sk_c9
| multiply(sk_c9,sk_c6) = sk_c3 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_174,c_0_151]),c_0_151]) ).
cnf(c_0_180,negated_conjecture,
( multiply(sk_c9,sk_c1) != sk_c9
| multiply(sk_c5,sk_c9) = sk_c9 ),
inference(rw,[status(thm)],[c_0_175,c_0_144]) ).
cnf(c_0_181,negated_conjecture,
( sk_c3 != sk_c9
| multiply(sk_c5,sk_c9) = sk_c9 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_176,c_0_144]),c_0_151]) ).
cnf(c_0_182,negated_conjecture,
multiply(sk_c9,sk_c6) = sk_c3,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_179]) ).
cnf(c_0_183,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c9 ),
prove_this_2 ).
cnf(c_0_184,plain,
inverse(multiply(inverse(multiply(X1,X2)),X1)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_37]),c_0_75]) ).
cnf(c_0_185,negated_conjecture,
multiply(sk_c5,sk_c9) = sk_c9,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_178]),c_0_181]) ).
cnf(c_0_186,negated_conjecture,
inverse(sk_c9) = sk_c6,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_182]),c_0_161]) ).
cnf(c_0_187,negated_conjecture,
( inverse(sk_c5) = sk_c4
| inverse(sk_c1) = sk_c9 ),
inference(spm,[status(thm)],[c_0_121,c_0_183]) ).
cnf(c_0_188,negated_conjecture,
( sk_c3 = sk_c9
| inverse(sk_c1) = sk_c3 ),
inference(spm,[status(thm)],[c_0_156,c_0_178]) ).
cnf(c_0_189,negated_conjecture,
inverse(multiply(sk_c6,sk_c5)) = sk_c9,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_185]),c_0_186]) ).
cnf(c_0_190,plain,
inverse(sk_c3) = sk_c3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_151]),c_0_151]) ).
cnf(c_0_191,negated_conjecture,
( sk_c3 = sk_c9
| inverse(sk_c5) = sk_c4 ),
inference(spm,[status(thm)],[c_0_187,c_0_188]) ).
cnf(c_0_192,negated_conjecture,
sk_c3 = sk_c5,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_189]),c_0_182]),c_0_190]) ).
cnf(c_0_193,negated_conjecture,
( sk_c3 = sk_c9
| inverse(sk_c4) = sk_c5 ),
inference(spm,[status(thm)],[c_0_121,c_0_191]) ).
cnf(c_0_194,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| inverse(sk_c1) = sk_c9 ),
prove_this_1 ).
cnf(c_0_195,plain,
multiply(X1,sk_c5) = X1,
inference(rw,[status(thm)],[c_0_161,c_0_192]) ).
cnf(c_0_196,negated_conjecture,
( sk_c5 = sk_c9
| inverse(sk_c4) = sk_c5 ),
inference(rw,[status(thm)],[c_0_193,c_0_192]) ).
cnf(c_0_197,plain,
inverse(sk_c5) = sk_c5,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_190,c_0_192]),c_0_192]) ).
cnf(c_0_198,negated_conjecture,
( sk_c5 = sk_c9
| inverse(sk_c1) = sk_c5 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_188,c_0_192]),c_0_192]) ).
cnf(c_0_199,negated_conjecture,
( sk_c4 = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(rw,[status(thm)],[c_0_194,c_0_195]) ).
cnf(c_0_200,negated_conjecture,
( sk_c4 = sk_c5
| sk_c5 = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_196]),c_0_197]) ).
cnf(c_0_201,negated_conjecture,
( sk_c5 = sk_c9
| sk_c4 = sk_c9 ),
inference(spm,[status(thm)],[c_0_198,c_0_199]) ).
cnf(c_0_202,plain,
multiply(sk_c3,X1) = X1,
inference(rw,[status(thm)],[c_0_38,c_0_151]) ).
cnf(c_0_203,negated_conjecture,
sk_c5 = sk_c9,
inference(spm,[status(thm)],[c_0_200,c_0_201]) ).
cnf(c_0_204,plain,
multiply(sk_c5,X1) = X1,
inference(rw,[status(thm)],[c_0_202,c_0_192]) ).
cnf(c_0_205,plain,
sk_c6 = sk_c9,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_197,c_0_203]),c_0_186]),c_0_203]) ).
cnf(c_0_206,negated_conjecture,
( identity != sk_c9
| inverse(X3) != sk_c9
| inverse(X1) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| multiply(X2,inverse(X2)) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8
| multiply(inverse(X2),sk_c8) != sk_c9
| multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_82]),c_0_38]) ).
cnf(c_0_207,plain,
multiply(X1,sk_c9) = X1,
inference(rw,[status(thm)],[c_0_195,c_0_203]) ).
cnf(c_0_208,plain,
multiply(sk_c9,X1) = X1,
inference(rw,[status(thm)],[c_0_204,c_0_203]) ).
cnf(c_0_209,negated_conjecture,
inverse(sk_c9) = sk_c9,
inference(rw,[status(thm)],[c_0_186,c_0_205]) ).
cnf(c_0_210,negated_conjecture,
inverse(X1) != sk_c9,
inference(cn,[status(thm)],[inference(rw,[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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_206,c_0_144]),c_0_144]),c_0_144]),c_0_144]),c_0_207]),c_0_208]),c_0_207]),c_0_208]),c_0_160]),c_0_192]),c_0_203]),c_0_207]),c_0_151]),c_0_192]),c_0_203])])])]),c_0_186]),c_0_205])]) ).
cnf(c_0_211,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_209,c_0_210]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP223-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n009.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 20:06:57 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 12.49/2.26 % Version: 3.5.1
% 12.49/2.26 % Preprocessing class: FSMSSMSMSSSNFFN.
% 12.49/2.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 12.49/2.26 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 12.49/2.26 % Starting new_bool_3 with 300s (1) cores
% 12.49/2.26 % Starting new_bool_1 with 300s (1) cores
% 12.49/2.26 % Starting sh5l with 300s (1) cores
% 12.49/2.26 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 4125122 completed with status 0
% 12.49/2.26 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 12.49/2.26 % Preprocessing class: FSMSSMSMSSSNFFN.
% 12.49/2.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 12.49/2.26 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 12.49/2.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 12.49/2.26 % No SInE strategy applied
% 12.49/2.26 % Search class: FGHPS-FFMM21-SFFFFFNN
% 12.49/2.26 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 12.49/2.26 % Starting SubtermCWHack with 136s (1) cores
% 12.49/2.26 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 12.49/2.26 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 12.49/2.26 % Starting new_bool_3 with 136s (1) cores
% 12.49/2.26 % Starting new_bool_1 with 136s (1) cores
% 12.49/2.26 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 4125128 completed with status 0
% 12.49/2.26 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 12.49/2.26 % Preprocessing class: FSMSSMSMSSSNFFN.
% 12.49/2.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 12.49/2.26 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 12.49/2.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 12.49/2.26 % No SInE strategy applied
% 12.49/2.26 % Search class: FGHPS-FFMM21-SFFFFFNN
% 12.49/2.26 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 12.49/2.26 % Starting SubtermCWHack with 136s (1) cores
% 12.49/2.26 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 12.49/2.26 % Preprocessing time : 0.002 s
% 12.49/2.26 % Presaturation interreduction done
% 12.49/2.26
% 12.49/2.26 % Proof found!
% 12.49/2.26 % SZS status Unsatisfiable
% 12.49/2.26 % SZS output start CNFRefutation
% See solution above
% 12.49/2.26 % Parsed axioms : 34
% 12.49/2.26 % Removed by relevancy pruning/SinE : 0
% 12.49/2.26 % Initial clauses : 34
% 12.49/2.26 % Removed in clause preprocessing : 0
% 12.49/2.26 % Initial clauses in saturation : 34
% 12.49/2.26 % Processed clauses : 14628
% 12.49/2.26 % ...of these trivial : 384
% 12.49/2.26 % ...subsumed : 12057
% 12.49/2.26 % ...remaining for further processing : 2187
% 12.49/2.26 % Other redundant clauses eliminated : 45
% 12.49/2.26 % Clauses deleted for lack of memory : 0
% 12.49/2.26 % Backward-subsumed : 419
% 12.49/2.26 % Backward-rewritten : 1700
% 12.49/2.26 % Generated clauses : 156968
% 12.49/2.26 % ...of the previous two non-redundant : 155225
% 12.49/2.26 % ...aggressively subsumed : 0
% 12.49/2.26 % Contextual simplify-reflections : 80
% 12.49/2.26 % Paramodulations : 156883
% 12.49/2.26 % Factorizations : 41
% 12.49/2.26 % NegExts : 0
% 12.49/2.26 % Equation resolutions : 45
% 12.49/2.26 % Disequality decompositions : 0
% 12.49/2.26 % Total rewrite steps : 39256
% 12.49/2.26 % ...of those cached : 37548
% 12.49/2.26 % Propositional unsat checks : 0
% 12.49/2.26 % Propositional check models : 0
% 12.49/2.26 % Propositional check unsatisfiable : 0
% 12.49/2.26 % Propositional clauses : 0
% 12.49/2.26 % Propositional clauses after purity: 0
% 12.49/2.26 % Propositional unsat core size : 0
% 12.49/2.26 % Propositional preprocessing time : 0.000
% 12.49/2.26 % Propositional encoding time : 0.000
% 12.49/2.26 % Propositional solver time : 0.000
% 12.49/2.26 % Success case prop preproc time : 0.000
% 12.49/2.26 % Success case prop encoding time : 0.000
% 12.49/2.26 % Success case prop solver time : 0.000
% 12.49/2.26 % Current number of processed clauses : 30
% 12.49/2.26 % Positive orientable unit clauses : 26
% 12.49/2.26 % Positive unorientable unit clauses: 0
% 12.49/2.26 % Negative unit clauses : 1
% 12.49/2.26 % Non-unit-clauses : 3
% 12.49/2.26 % Current number of unprocessed clauses: 48150
% 12.49/2.26 % ...number of literals in the above : 164034
% 12.49/2.26 % Current number of archived formulas : 0
% 12.49/2.26 % Current number of archived clauses : 2155
% 12.49/2.26 % Clause-clause subsumption calls (NU) : 123238
% 12.49/2.26 % Rec. Clause-clause subsumption calls : 86526
% 12.49/2.26 % Non-unit clause-clause subsumptions : 12449
% 12.49/2.26 % Unit Clause-clause subsumption calls : 1319
% 12.49/2.26 % Rewrite failures with RHS unbound : 0
% 12.49/2.26 % BW rewrite match attempts : 227
% 12.49/2.26 % BW rewrite match successes : 102
% 12.49/2.26 % Condensation attempts : 0
% 12.49/2.26 % Condensation successes : 0
% 12.49/2.26 % Termbank termtop insertions : 1865952
% 12.49/2.26 % Search garbage collected termcells : 32
% 12.49/2.26
% 12.49/2.26 % -------------------------------------------------
% 12.49/2.26 % User time : 1.692 s
% 12.49/2.26 % System time : 0.093 s
% 12.49/2.26 % Total time : 1.785 s
% 12.49/2.26 % Maximum resident set size: 3648 pages
% 12.49/2.26
% 12.49/2.26 % -------------------------------------------------
% 12.49/2.26 % User time : 8.570 s
% 12.49/2.26 % System time : 0.427 s
% 12.49/2.26 % Total time : 8.998 s
% 12.49/2.26 % Maximum resident set size: 4608 pages
% 12.49/2.26 % E exiting
%------------------------------------------------------------------------------