%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP322-1 : TPTP v9.2.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:25:33 PM UTC 2026
% Result : Unsatisfiable 2.04s 1.95s
% Output : CNFRefutation 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 65
% Number of leaves : 36
% Syntax : Number of clauses : 235 ( 21 unt; 203 nHn; 215 RR)
% Number of literals : 567 ( 566 equ; 97 neg)
% Maximal clause size : 12 ( 2 avg)
% Maximal term depth : 4 ( 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 : 69 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(prove_this_25,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_37,negated_conjecture,
( multiply(sk_c8,sk_c9) != sk_c7
| multiply(X1,sk_c8) != sk_c9
| inverse(X1) != sk_c8
| multiply(sk_c9,X2) != sk_c8
| multiply(X3,sk_c9) != X2
| inverse(X3) != sk_c9
| multiply(sk_c9,sk_c8) != sk_c7
| multiply(X4,sk_c9) != sk_c8
| inverse(X4) != sk_c9
| multiply(sk_c9,X5) != sk_c8
| multiply(X6,sk_c9) != X5
| inverse(X6) != sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
cnf(prove_this_31,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_4,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c9,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_19,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_28,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c9,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
cnf(prove_this_34,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c9,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
cnf(prove_this_22,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c9,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_23,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c5,sk_c9) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_24,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c9,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_16,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c9,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_33,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
cnf(prove_this_36,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
cnf(prove_this_29,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c5,sk_c9) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
cnf(prove_this_30,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
cnf(prove_this_35,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c5,sk_c9) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
cnf(prove_this_32,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c5,sk_c9) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_27,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_26,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_18,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_15,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_17,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c9) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_20,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_8,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_14,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_7,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_21,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_13,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_9,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
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,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_40,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c9,sk_c8) = sk_c7 ),
prove_this_25 ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c8,sk_c9) != sk_c7
| multiply(X1,sk_c8) != sk_c9
| inverse(X1) != sk_c8
| multiply(sk_c9,X2) != sk_c8
| multiply(X3,sk_c9) != X2
| inverse(X3) != sk_c9
| multiply(sk_c9,sk_c8) != sk_c7
| multiply(X4,sk_c9) != sk_c8
| inverse(X4) != sk_c9
| multiply(sk_c9,X5) != sk_c8
| multiply(X6,sk_c9) != X5
| inverse(X6) != sk_c9 ),
prove_this_37 ).
cnf(c_0_42,negated_conjecture,
( multiply(inverse(sk_c2),sk_c3) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
prove_this_31 ).
cnf(c_0_44,negated_conjecture,
( multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8
| multiply(sk_c9,multiply(X2,sk_c9)) != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7
| multiply(sk_c9,sk_c8) != sk_c7
| multiply(X3,sk_c9) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| inverse(X1) != sk_c9
| inverse(X3) != sk_c9
| inverse(X2) != sk_c9
| inverse(X4) != sk_c8 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_41])]) ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c9,sk_c6) = sk_c8 ),
prove_this_4 ).
cnf(c_0_46,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c9,sk_c8) = sk_c7 ),
prove_this_19 ).
cnf(c_0_47,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c8
| multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8
| multiply(sk_c9,multiply(X2,sk_c9)) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7
| multiply(X3,sk_c9) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| inverse(X1) != sk_c9
| inverse(X3) != sk_c9
| inverse(X2) != sk_c9
| inverse(X4) != sk_c8 ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c7
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c8
| sk_c8 = sk_c9
| multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8
| multiply(sk_c9,multiply(X2,sk_c9)) != sk_c8
| multiply(X3,sk_c9) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| inverse(X1) != sk_c9
| inverse(X3) != sk_c9
| inverse(X2) != sk_c9
| inverse(X4) != sk_c8 ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c9,sk_c6) = sk_c8 ),
prove_this_28 ).
cnf(c_0_52,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c9,sk_c6) = sk_c8 ),
prove_this_34 ).
cnf(c_0_53,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c9,sk_c6) = sk_c8 ),
prove_this_22 ).
cnf(c_0_54,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c8
| sk_c8 = sk_c9
| multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8
| multiply(X2,sk_c9) != sk_c8
| multiply(X3,sk_c8) != sk_c9
| inverse(X2) != sk_c9
| inverse(X1) != sk_c9
| inverse(X3) != sk_c8 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_53]) ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c8
| sk_c8 = sk_c9
| multiply(X1,sk_c9) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| inverse(X1) != sk_c9
| inverse(X2) != sk_c8 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_51]),c_0_52]),c_0_53]) ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c8
| sk_c8 = sk_c9
| multiply(X1,multiply(X2,sk_c9)) != sk_c8
| inverse(multiply(X1,X2)) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| inverse(X3) != sk_c8 ),
inference(spm,[status(thm)],[c_0_55,c_0_36]) ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c8
| sk_c8 = sk_c9
| inverse(multiply(X1,sk_c2)) != sk_c9
| multiply(X1,sk_c3) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| inverse(X2) != sk_c8 ),
inference(spm,[status(thm)],[c_0_56,c_0_51]) ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c5,sk_c9) = sk_c6 ),
prove_this_23 ).
cnf(c_0_59,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c8
| sk_c8 = sk_c9
| inverse(multiply(X1,multiply(X2,sk_c2))) != sk_c9
| multiply(X1,multiply(X2,sk_c3)) != sk_c8
| multiply(X3,sk_c8) != sk_c9
| inverse(X3) != sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_36]),c_0_36]) ).
cnf(c_0_60,negated_conjecture,
( multiply(inverse(sk_c5),sk_c6) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_39,c_0_58]) ).
cnf(c_0_61,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| inverse(sk_c5) = sk_c9 ),
prove_this_24 ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c9,sk_c6) = sk_c8 ),
prove_this_10 ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c8
| sk_c8 = sk_c9
| multiply(X1,multiply(inverse(sk_c2),sk_c3)) != sk_c8
| inverse(multiply(X1,identity)) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| inverse(X2) != sk_c8 ),
inference(spm,[status(thm)],[c_0_59,c_0_37]) ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c9,sk_c6) = sk_c9 ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_65,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_39,c_0_39]) ).
cnf(c_0_66,negated_conjecture,
( multiply(inverse(sk_c1),sk_c9) = sk_c8
| multiply(sk_c9,sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_39,c_0_62]) ).
cnf(c_0_67,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c9,sk_c6) = sk_c8 ),
prove_this_16 ).
cnf(c_0_68,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c8
| sk_c8 = sk_c9
| multiply(X1,multiply(sk_c9,sk_c3)) != sk_c8
| inverse(multiply(X1,identity)) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| inverse(X2) != sk_c8 ),
inference(spm,[status(thm)],[c_0_63,c_0_52]) ).
cnf(c_0_69,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_39,c_0_38]) ).
cnf(c_0_70,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_53,c_0_64]) ).
cnf(c_0_71,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_37]),c_0_65]) ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c8
| multiply(sk_c8,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_73,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c8
| sk_c8 = sk_c9
| multiply(X1,sk_c8) != sk_c9
| inverse(identity) != sk_c9
| inverse(X1) != sk_c8 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_69]),c_0_70]) ).
cnf(c_0_74,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_69,c_0_71]) ).
cnf(c_0_75,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c8
| identity = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_72]),c_0_37]) ).
cnf(c_0_76,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c8
| sk_c8 = sk_c9
| multiply(X1,sk_c8) != sk_c9
| inverse(X1) != sk_c8 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_74]),c_0_75]) ).
cnf(c_0_77,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_71]),c_0_71]) ).
cnf(c_0_78,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c4) = sk_c9 ),
prove_this_33 ).
cnf(c_0_79,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c8
| sk_c8 = sk_c9 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_62]),c_0_67]) ).
cnf(c_0_80,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c9) = sk_c2 ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_81,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c5) = sk_c9 ),
prove_this_36 ).
cnf(c_0_82,negated_conjecture,
( multiply(inverse(sk_c9),sk_c8) = sk_c6
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_39,c_0_79]) ).
cnf(c_0_83,negated_conjecture,
( inverse(sk_c9) = sk_c2
| inverse(sk_c9) = sk_c4 ),
inference(spm,[status(thm)],[c_0_77,c_0_80]) ).
cnf(c_0_84,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c9) = sk_c5 ),
inference(spm,[status(thm)],[c_0_77,c_0_81]) ).
cnf(c_0_85,negated_conjecture,
( multiply(inverse(sk_c2),sk_c3) = sk_c9
| multiply(sk_c9,sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_39,c_0_51]) ).
cnf(c_0_86,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c6
| inverse(sk_c9) = sk_c4
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_87,negated_conjecture,
( inverse(sk_c9) = sk_c5
| inverse(sk_c9) = sk_c2 ),
inference(spm,[status(thm)],[c_0_77,c_0_84]) ).
cnf(c_0_88,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_85,c_0_52]) ).
cnf(c_0_89,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c5,sk_c9) = sk_c6 ),
prove_this_29 ).
cnf(c_0_90,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c6
| inverse(sk_c9) = sk_c2
| sk_c8 = sk_c9
| sk_c5 = sk_c4 ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_91,negated_conjecture,
( multiply(inverse(sk_c9),sk_c8) = sk_c3
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_39,c_0_70]) ).
cnf(c_0_92,negated_conjecture,
( multiply(inverse(sk_c9),sk_c8) = sk_c6
| multiply(sk_c9,sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_39,c_0_88]) ).
cnf(c_0_93,negated_conjecture,
( multiply(inverse(sk_c5),sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(spm,[status(thm)],[c_0_39,c_0_89]) ).
cnf(c_0_94,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| inverse(sk_c5) = sk_c9 ),
prove_this_30 ).
cnf(c_0_95,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c6
| sk_c5 = sk_c4
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_82,c_0_90]) ).
cnf(c_0_96,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c9
| sk_c8 = sk_c9
| sk_c6 = sk_c3 ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_97,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c9,sk_c6) = sk_c9 ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_98,negated_conjecture,
( multiply(inverse(sk_c2),sk_c6) = sk_c8
| sk_c8 = sk_c9
| sk_c5 = sk_c4 ),
inference(spm,[status(thm)],[c_0_39,c_0_95]) ).
cnf(c_0_99,negated_conjecture,
( sk_c6 = sk_c3
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_70,c_0_96]) ).
cnf(c_0_100,negated_conjecture,
( multiply(inverse(sk_c2),sk_c3) = sk_c9
| multiply(sk_c9,sk_c6) = sk_c9 ),
inference(spm,[status(thm)],[c_0_39,c_0_97]) ).
cnf(c_0_101,negated_conjecture,
( multiply(inverse(sk_c2),sk_c3) = sk_c8
| sk_c5 = sk_c4
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_102,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c5,sk_c9) = sk_c6 ),
prove_this_35 ).
cnf(c_0_103,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c9
| sk_c5 = sk_c4
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_104,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c8 ),
prove_this_32 ).
cnf(c_0_105,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c9,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_37,c_0_102]) ).
cnf(c_0_106,negated_conjecture,
( sk_c5 = sk_c4
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_79,c_0_103]) ).
cnf(c_0_107,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c9,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_37,c_0_104]) ).
cnf(c_0_108,negated_conjecture,
( multiply(sk_c9,sk_c2) = identity
| multiply(sk_c4,sk_c9) = sk_c6
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_109,negated_conjecture,
( multiply(sk_c9,sk_c2) = identity
| sk_c8 = sk_c9
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_110,negated_conjecture,
( inverse(sk_c9) = sk_c2
| sk_c6 = sk_c8
| sk_c8 = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_109]),c_0_71]) ).
cnf(c_0_111,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| sk_c6 = sk_c8
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_91,c_0_110]) ).
cnf(c_0_112,negated_conjecture,
( multiply(inverse(sk_c2),sk_c3) = sk_c8
| sk_c8 = sk_c9
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_39,c_0_111]) ).
cnf(c_0_113,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c5,sk_c9) = sk_c6 ),
prove_this_5 ).
cnf(c_0_114,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c9
| sk_c6 = sk_c8
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_100,c_0_112]) ).
cnf(c_0_115,negated_conjecture,
( multiply(inverse(sk_c5),sk_c6) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_39,c_0_113]) ).
cnf(c_0_116,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c5) = sk_c9 ),
prove_this_6 ).
cnf(c_0_117,negated_conjecture,
( sk_c6 = sk_c8
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_79,c_0_114]) ).
cnf(c_0_118,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c9,sk_c6) = sk_c9 ),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_119,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c8
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_79,c_0_117]) ).
cnf(c_0_120,negated_conjecture,
( multiply(inverse(sk_c8),sk_c7) = sk_c9
| multiply(sk_c9,sk_c6) = sk_c9 ),
inference(spm,[status(thm)],[c_0_39,c_0_118]) ).
cnf(c_0_121,negated_conjecture,
( sk_c8 = sk_c9
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_49,c_0_119]) ).
cnf(c_0_122,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c9
| sk_c8 = sk_c9
| identity = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_37]) ).
cnf(c_0_123,negated_conjecture,
( identity = sk_c9
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_75,c_0_122]) ).
cnf(c_0_124,negated_conjecture,
( multiply(X1,sk_c9) = X1
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_71,c_0_123]) ).
cnf(c_0_125,negated_conjecture,
( inverse(sk_c9) = identity
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_37,c_0_124]) ).
cnf(c_0_126,negated_conjecture,
( sk_c8 = sk_c9
| identity = sk_c4
| identity = sk_c2 ),
inference(spm,[status(thm)],[c_0_83,c_0_125]) ).
cnf(c_0_127,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| inverse(sk_c9) = sk_c5 ),
inference(spm,[status(thm)],[c_0_77,c_0_94]) ).
cnf(c_0_128,negated_conjecture,
( inverse(sk_c9) = sk_c9
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_74,c_0_123]) ).
cnf(c_0_129,negated_conjecture,
( sk_c8 = sk_c9
| identity = sk_c2
| identity = sk_c5 ),
inference(spm,[status(thm)],[c_0_87,c_0_125]) ).
cnf(c_0_130,negated_conjecture,
( multiply(sk_c2,X1) = X1
| identity = sk_c4
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_38,c_0_126]) ).
cnf(c_0_131,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| sk_c8 = sk_c9
| sk_c5 = sk_c9 ),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_132,negated_conjecture,
( identity = sk_c2
| sk_c8 = sk_c9
| sk_c5 = sk_c9 ),
inference(spm,[status(thm)],[c_0_123,c_0_129]) ).
cnf(c_0_133,negated_conjecture,
( sk_c5 = sk_c9
| sk_c8 = sk_c9
| identity = sk_c4
| sk_c3 = sk_c9 ),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_134,negated_conjecture,
( identity = sk_c4
| sk_c8 = sk_c9
| sk_c2 = sk_c9 ),
inference(spm,[status(thm)],[c_0_123,c_0_126]) ).
cnf(c_0_135,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c9) = sk_c2 ),
inference(spm,[status(thm)],[c_0_77,c_0_104]) ).
cnf(c_0_136,negated_conjecture,
( inverse(sk_c9) = sk_c2
| sk_c5 != sk_c2 ),
inference(ef,[status(thm)],[c_0_87]) ).
cnf(c_0_137,negated_conjecture,
( sk_c8 = sk_c9
| sk_c3 = sk_c8 ),
inference(spm,[status(thm)],[c_0_99,c_0_117]) ).
cnf(c_0_138,negated_conjecture,
( sk_c3 = sk_c9
| sk_c5 = sk_c9
| sk_c8 = sk_c9
| sk_c2 = sk_c4 ),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_139,negated_conjecture,
( multiply(sk_c4,X1) = X1
| sk_c2 = sk_c9
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_38,c_0_134]) ).
cnf(c_0_140,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| sk_c8 = sk_c9
| sk_c2 = sk_c9 ),
inference(spm,[status(thm)],[c_0_135,c_0_128]) ).
cnf(c_0_141,negated_conjecture,
( sk_c8 = sk_c9
| identity = sk_c2
| sk_c5 != sk_c2 ),
inference(spm,[status(thm)],[c_0_136,c_0_125]) ).
cnf(c_0_142,negated_conjecture,
( sk_c2 = sk_c4
| sk_c5 = sk_c9
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_143,negated_conjecture,
( sk_c2 = sk_c9
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_144,negated_conjecture,
( identity = sk_c2
| sk_c8 = sk_c9
| sk_c2 != sk_c4 ),
inference(spm,[status(thm)],[c_0_141,c_0_106]) ).
cnf(c_0_145,negated_conjecture,
( identity = sk_c2
| sk_c8 = sk_c9 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_143]),c_0_144]) ).
cnf(c_0_146,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| inverse(sk_c4) = sk_c9 ),
prove_this_27 ).
cnf(c_0_147,negated_conjecture,
( multiply(sk_c2,X1) = X1
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_38,c_0_145]) ).
cnf(c_0_148,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| inverse(sk_c9) = sk_c4 ),
inference(spm,[status(thm)],[c_0_77,c_0_146]) ).
cnf(c_0_149,negated_conjecture,
( sk_c5 = sk_c9
| sk_c8 = sk_c9
| sk_c3 = sk_c9 ),
inference(spm,[status(thm)],[c_0_131,c_0_147]) ).
cnf(c_0_150,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| sk_c2 = sk_c4
| sk_c5 != sk_c2 ),
inference(spm,[status(thm)],[c_0_136,c_0_148]) ).
cnf(c_0_151,negated_conjecture,
( sk_c5 = sk_c9
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_137,c_0_149]) ).
cnf(c_0_152,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c4,sk_c9) = sk_c8 ),
prove_this_26 ).
cnf(c_0_153,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| sk_c8 = sk_c9
| sk_c2 = sk_c4 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_143]) ).
cnf(c_0_154,negated_conjecture,
( multiply(inverse(sk_c2),sk_c3) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_39,c_0_152]) ).
cnf(c_0_155,negated_conjecture,
( multiply(X1,sk_c2) = X1
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_71,c_0_145]) ).
cnf(c_0_156,negated_conjecture,
( sk_c2 = sk_c4
| sk_c8 = sk_c9
| sk_c3 = sk_c9 ),
inference(spm,[status(thm)],[c_0_147,c_0_153]) ).
cnf(c_0_157,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_154,c_0_104]) ).
cnf(c_0_158,negated_conjecture,
( inverse(sk_c2) = identity
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_37,c_0_155]) ).
cnf(c_0_159,negated_conjecture,
( sk_c2 = sk_c4
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_137,c_0_156]) ).
cnf(c_0_160,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c9 ),
prove_this_18 ).
cnf(c_0_161,negated_conjecture,
( multiply(inverse(sk_c4),sk_c8) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_39,c_0_157]) ).
cnf(c_0_162,negated_conjecture,
( inverse(sk_c4) = identity
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_158,c_0_159]) ).
cnf(c_0_163,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c9 ),
prove_this_15 ).
cnf(c_0_164,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c9) = sk_c5 ),
inference(spm,[status(thm)],[c_0_77,c_0_160]) ).
cnf(c_0_165,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c9
| sk_c8 = sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_38])]) ).
cnf(c_0_166,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c8) = sk_c1 ),
inference(spm,[status(thm)],[c_0_77,c_0_163]) ).
cnf(c_0_167,negated_conjecture,
( inverse(sk_c9) = sk_c5
| inverse(sk_c8) = sk_c1 ),
inference(spm,[status(thm)],[c_0_77,c_0_164]) ).
cnf(c_0_168,negated_conjecture,
sk_c8 = sk_c9,
inference(spm,[status(thm)],[c_0_70,c_0_165]) ).
cnf(c_0_169,negated_conjecture,
( inverse(sk_c8) = sk_c1
| inverse(sk_c9) = sk_c4 ),
inference(spm,[status(thm)],[c_0_77,c_0_166]) ).
cnf(c_0_170,negated_conjecture,
( inverse(sk_c9) = sk_c1
| inverse(sk_c9) = sk_c5 ),
inference(rw,[status(thm)],[c_0_167,c_0_168]) ).
cnf(c_0_171,negated_conjecture,
( multiply(inverse(sk_c9),sk_c8) = sk_c6
| identity = sk_c9 ),
inference(spm,[status(thm)],[c_0_39,c_0_75]) ).
cnf(c_0_172,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c9) = sk_c6 ),
prove_this_17 ).
cnf(c_0_173,negated_conjecture,
( inverse(sk_c9) = sk_c4
| inverse(sk_c9) = sk_c1 ),
inference(rw,[status(thm)],[c_0_169,c_0_168]) ).
cnf(c_0_174,negated_conjecture,
( inverse(sk_c9) = sk_c2
| sk_c5 = sk_c4 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_87]),c_0_136]) ).
cnf(c_0_175,negated_conjecture,
( inverse(sk_c9) = sk_c1
| sk_c5 = sk_c4
| sk_c5 = sk_c2 ),
inference(spm,[status(thm)],[c_0_83,c_0_170]) ).
cnf(c_0_176,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c8 ),
prove_this_20 ).
cnf(c_0_177,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c8 ),
prove_this_8 ).
cnf(c_0_178,negated_conjecture,
( identity = sk_c9
| identity = sk_c6 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_171,c_0_168]),c_0_37]) ).
cnf(c_0_179,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c8 ),
prove_this_14 ).
cnf(c_0_180,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c6
| inverse(sk_c8) = sk_c1 ),
inference(spm,[status(thm)],[c_0_77,c_0_172]) ).
cnf(c_0_181,negated_conjecture,
( inverse(sk_c9) = sk_c4
| sk_c1 != sk_c4 ),
inference(ef,[status(thm)],[c_0_173]) ).
cnf(c_0_182,negated_conjecture,
( sk_c5 = sk_c2
| sk_c5 = sk_c4
| sk_c2 = sk_c1 ),
inference(spm,[status(thm)],[c_0_174,c_0_175]) ).
cnf(c_0_183,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
prove_this_7 ).
cnf(c_0_184,negated_conjecture,
( multiply(inverse(sk_c4),sk_c8) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_39,c_0_176]) ).
cnf(c_0_185,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| inverse(sk_c4) = sk_c9 ),
prove_this_21 ).
cnf(c_0_186,negated_conjecture,
( multiply(inverse(sk_c1),sk_c9) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_39,c_0_177]) ).
cnf(c_0_187,negated_conjecture,
( identity = sk_c9
| sk_c6 != sk_c9 ),
inference(ef,[status(thm)],[c_0_178]) ).
cnf(c_0_188,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c9,sk_c8) = sk_c7 ),
prove_this_1 ).
cnf(c_0_189,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c8) = sk_c1 ),
inference(spm,[status(thm)],[c_0_77,c_0_179]) ).
cnf(c_0_190,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c6
| inverse(sk_c9) = sk_c2 ),
inference(spm,[status(thm)],[c_0_77,c_0_102]) ).
cnf(c_0_191,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c6
| inverse(sk_c9) = sk_c1 ),
inference(rw,[status(thm)],[c_0_180,c_0_168]) ).
cnf(c_0_192,negated_conjecture,
( inverse(sk_c9) = sk_c4
| sk_c2 = sk_c1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_173]),c_0_181]) ).
cnf(c_0_193,negated_conjecture,
( sk_c2 = sk_c1
| sk_c5 = sk_c4
| sk_c2 != sk_c4 ),
inference(ef,[status(thm)],[c_0_182]) ).
cnf(c_0_194,negated_conjecture,
( multiply(inverse(sk_c1),sk_c9) = sk_c8
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_39,c_0_183]) ).
cnf(c_0_195,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c9,sk_c8) = sk_c7 ),
prove_this_13 ).
cnf(c_0_196,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c8
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_45,c_0_72]) ).
cnf(c_0_197,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c9,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_184,c_0_185]) ).
cnf(c_0_198,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c8,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_186,c_0_179]) ).
cnf(c_0_199,negated_conjecture,
( inverse(sk_c9) = sk_c9
| sk_c6 != sk_c9 ),
inference(spm,[status(thm)],[c_0_74,c_0_187]) ).
cnf(c_0_200,negated_conjecture,
multiply(sk_c9,sk_c9) = sk_c7,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_188,c_0_168]),c_0_168])]) ).
cnf(c_0_201,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c9
| inverse(sk_c9) = sk_c1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_189,c_0_168]),c_0_168]) ).
cnf(c_0_202,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c9
| inverse(sk_c9) = sk_c2 ),
inference(rw,[status(thm)],[c_0_135,c_0_168]) ).
cnf(c_0_203,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c6
| sk_c2 = sk_c1 ),
inference(spm,[status(thm)],[c_0_190,c_0_191]) ).
cnf(c_0_204,negated_conjecture,
( sk_c2 = sk_c1
| sk_c5 = sk_c4 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_192]),c_0_193]) ).
cnf(c_0_205,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c7
| multiply(sk_c8,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_194,c_0_195]) ).
cnf(c_0_206,negated_conjecture,
( multiply(inverse(sk_c9),sk_c8) = sk_c6
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_39,c_0_196]) ).
cnf(c_0_207,negated_conjecture,
( multiply(inverse(sk_c9),sk_c8) = sk_c3
| multiply(sk_c9,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_39,c_0_197]) ).
cnf(c_0_208,negated_conjecture,
( multiply(inverse(sk_c4),sk_c8) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_39,c_0_198]) ).
cnf(c_0_209,negated_conjecture,
( identity = sk_c7
| sk_c6 != sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_199]),c_0_200]) ).
cnf(c_0_210,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c9
| sk_c2 = sk_c1 ),
inference(spm,[status(thm)],[c_0_201,c_0_202]) ).
cnf(c_0_211,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c6
| sk_c2 = sk_c1 ),
inference(spm,[status(thm)],[c_0_203,c_0_204]) ).
cnf(c_0_212,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c9 ),
prove_this_9 ).
cnf(c_0_213,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c7
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_188,c_0_205]) ).
cnf(c_0_214,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c9
| sk_c7 = sk_c8
| sk_c6 = sk_c3 ),
inference(spm,[status(thm)],[c_0_206,c_0_207]) ).
cnf(c_0_215,negated_conjecture,
( multiply(inverse(sk_c4),sk_c9) = sk_c9
| sk_c7 = sk_c9 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_208,c_0_168]),c_0_168]),c_0_168]),c_0_200]) ).
cnf(c_0_216,negated_conjecture,
( sk_c7 = sk_c9
| sk_c6 != sk_c9 ),
inference(spm,[status(thm)],[c_0_187,c_0_209]) ).
cnf(c_0_217,negated_conjecture,
( sk_c2 = sk_c1
| sk_c6 = sk_c9 ),
inference(spm,[status(thm)],[c_0_210,c_0_211]) ).
cnf(c_0_218,negated_conjecture,
( multiply(sk_c9,multiply(sk_c4,X1)) = X1
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_39,c_0_212]) ).
cnf(c_0_219,negated_conjecture,
( sk_c6 = sk_c3
| sk_c7 = sk_c8
| sk_c7 = sk_c9 ),
inference(spm,[status(thm)],[c_0_213,c_0_214]) ).
cnf(c_0_220,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| sk_c7 = sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_146]),c_0_200])]) ).
cnf(c_0_221,negated_conjecture,
( sk_c2 = sk_c1
| sk_c7 = sk_c9 ),
inference(spm,[status(thm)],[c_0_216,c_0_217]) ).
cnf(c_0_222,negated_conjecture,
( multiply(sk_c9,multiply(sk_c4,X1)) = X1
| multiply(sk_c1,sk_c9) = sk_c9 ),
inference(rw,[status(thm)],[c_0_218,c_0_168]) ).
cnf(c_0_223,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c9
| sk_c7 = sk_c9 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_198,c_0_168]),c_0_168]),c_0_168]),c_0_200]) ).
cnf(c_0_224,negated_conjecture,
( sk_c7 = sk_c9
| sk_c6 = sk_c3 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_219,c_0_168])]) ).
cnf(c_0_225,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c3
| sk_c7 = sk_c9 ),
inference(spm,[status(thm)],[c_0_220,c_0_221]) ).
cnf(c_0_226,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c9
| sk_c7 = sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_222,c_0_223]),c_0_200])]) ).
cnf(c_0_227,negated_conjecture,
( sk_c7 = sk_c9
| sk_c3 != sk_c9 ),
inference(spm,[status(thm)],[c_0_216,c_0_224]) ).
cnf(c_0_228,negated_conjecture,
multiply(inverse(sk_c9),sk_c7) = sk_c9,
inference(spm,[status(thm)],[c_0_39,c_0_200]) ).
cnf(c_0_229,negated_conjecture,
sk_c7 = sk_c9,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_226]),c_0_227]) ).
cnf(c_0_230,negated_conjecture,
identity = sk_c9,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_228,c_0_229]),c_0_37]) ).
cnf(c_0_231,plain,
multiply(X1,sk_c9) = X1,
inference(rw,[status(thm)],[c_0_71,c_0_230]) ).
cnf(c_0_232,plain,
multiply(sk_c9,X1) = X1,
inference(rw,[status(thm)],[c_0_38,c_0_230]) ).
cnf(c_0_233,plain,
inverse(sk_c9) = sk_c9,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_230]),c_0_230]) ).
cnf(c_0_234,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(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_44,c_0_168]),c_0_168]),c_0_168]),c_0_168]),c_0_168]),c_0_168]),c_0_168])]),c_0_231]),c_0_232]),c_0_231]),c_0_232]),c_0_231]),c_0_229]),c_0_231]),c_0_231])])])])])]),c_0_233])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP322-1 : TPTP v9.2.1. Released v2.5.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n006.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 18:33:01 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 2.04/1.95 % Version : CSE_E---1.7
% 2.04/1.95 % Problem : theBenchmark.p
% 2.04/1.95 % SZS status Unsatisfiable for theBenchmark.p
% 2.04/1.95 % SZS output start CNFRefutation
% See solution above
% 2.04/1.95 % Total time : 1.371s
%------------------------------------------------------------------------------