TSTP Solution File: GRP324-1 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : GRP324-1 : TPTP v8.2.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n032.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 : Mon May 20 20:47:29 EDT 2024
% Result : Unsatisfiable 2.07s 0.66s
% Output : CNFRefutation 2.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 36
% Syntax : Number of clauses : 245 ( 20 unt; 204 nHn; 219 RR)
% Number of literals : 593 ( 592 equ; 114 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 : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 72 ( 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_7,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_13,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_23,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_24,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_37,negated_conjecture,
( multiply(sk_c7,sk_c8) != sk_c6
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c7
| multiply(sk_c8,X2) != sk_c7
| multiply(X3,sk_c8) != X2
| inverse(X3) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(X4,sk_c8) != sk_c7
| inverse(X4) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(X5,sk_c7) != sk_c6
| inverse(X5) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
cnf(prove_this_4,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_22,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_19,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_25,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_31,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_20,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_21,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_28,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
cnf(prove_this_34,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
cnf(prove_this_36,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
cnf(prove_this_35,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
cnf(prove_this_2,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_12,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_18,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_33,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
cnf(prove_this_8,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_17,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_15,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_9,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_16,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_27,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_11,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_14,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
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_c1,sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
prove_this_7 ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c5,sk_c7) = sk_c6 ),
prove_this_5 ).
cnf(c_0_42,negated_conjecture,
( multiply(inverse(sk_c1),sk_c8) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
prove_this_13 ).
cnf(c_0_44,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c5,sk_c7) = sk_c6 ),
prove_this_23 ).
cnf(c_0_45,negated_conjecture,
( multiply(inverse(sk_c5),sk_c6) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_39,c_0_41]) ).
cnf(c_0_46,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c5) = sk_c7 ),
prove_this_6 ).
cnf(c_0_47,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
prove_this_1 ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,negated_conjecture,
( multiply(inverse(sk_c5),sk_c6) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(spm,[status(thm)],[c_0_39,c_0_44]) ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c5) = sk_c7 ),
prove_this_24 ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c7,sk_c8) != sk_c6
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c7
| multiply(sk_c8,X2) != sk_c7
| multiply(X3,sk_c8) != X2
| inverse(X3) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(X4,sk_c8) != sk_c7
| inverse(X4) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(X5,sk_c7) != sk_c6
| inverse(X5) != sk_c7 ),
inference(fof_simplification,[status(thm)],[prove_this_37]) ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_53,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c6 ),
prove_this_4 ).
cnf(c_0_54,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_39,c_0_39]) ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c5,multiply(sk_c7,X1)) = multiply(sk_c6,X1)
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(spm,[status(thm)],[c_0_36,c_0_44]) ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c7,sk_c8) != sk_c6
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c7
| multiply(sk_c8,X2) != sk_c7
| multiply(X3,sk_c8) != X2
| inverse(X3) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(X4,sk_c8) != sk_c7
| inverse(X4) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(X5,sk_c7) != sk_c6
| inverse(X5) != sk_c7 ),
c_0_51 ).
cnf(c_0_59,negated_conjecture,
( multiply(sk_c7,multiply(sk_c6,X1)) = multiply(sk_c7,X1)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_36,c_0_52]) ).
cnf(c_0_60,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c6,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_37,c_0_53]) ).
cnf(c_0_61,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_37]),c_0_54]) ).
cnf(c_0_62,negated_conjecture,
( multiply(inverse(sk_c8),sk_c6) = sk_c7
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_39,c_0_55]) ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c8) = sk_c6 ),
prove_this_22 ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c5,sk_c7) = multiply(sk_c6,sk_c6)
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(X2,sk_c7) != sk_c6
| multiply(X3,sk_c8) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| inverse(sk_c8) != sk_c6
| inverse(X2) != sk_c7
| inverse(X3) != sk_c8
| inverse(X1) != sk_c8
| inverse(X4) != sk_c7 ),
inference(er,[status(thm)],[c_0_58]) ).
cnf(c_0_66,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
prove_this_19 ).
cnf(c_0_67,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]) ).
cnf(c_0_68,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c6,sk_c6) = sk_c7
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_69,negated_conjecture,
( multiply(sk_c6,sk_c6) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(spm,[status(thm)],[c_0_44,c_0_64]) ).
cnf(c_0_70,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c8,sk_c7) = sk_c6 ),
prove_this_25 ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(X2,sk_c7) != sk_c6
| multiply(X3,sk_c8) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| inverse(X2) != sk_c7
| inverse(X3) != sk_c8
| inverse(X1) != sk_c8
| inverse(X4) != sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_63]),c_0_66]) ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c7
| sk_c6 != sk_c7 ),
inference(ef,[status(thm)],[c_0_67]) ).
cnf(c_0_73,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_74,negated_conjecture,
( multiply(inverse(sk_c2),sk_c3) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_39,c_0_70]) ).
cnf(c_0_75,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
prove_this_31 ).
cnf(c_0_76,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| multiply(X3,sk_c8) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| inverse(X2) != sk_c7
| inverse(X3) != sk_c8
| inverse(X1) != sk_c8
| inverse(X4) != sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
cnf(c_0_77,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c7 ),
prove_this_20 ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c4) = sk_c8 ),
prove_this_21 ).
cnf(c_0_79,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_80,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c8,sk_c7) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| multiply(X2,sk_c8) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X1) != sk_c7
| inverse(X2) != sk_c8
| inverse(X3) != sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]) ).
cnf(c_0_81,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| identity = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_79]),c_0_37]) ).
cnf(c_0_82,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_37,c_0_54]) ).
cnf(c_0_83,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| identity = sk_c3
| multiply(X1,sk_c7) != sk_c6
| multiply(X2,sk_c8) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X1) != sk_c7
| inverse(X2) != sk_c8
| inverse(X3) != sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_73]) ).
cnf(c_0_84,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_61]),c_0_61]) ).
cnf(c_0_85,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| identity = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_57]),c_0_37]) ).
cnf(c_0_86,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_38,c_0_82]) ).
cnf(c_0_87,negated_conjecture,
( identity = sk_c8
| sk_c6 != sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_72]),c_0_37]) ).
cnf(c_0_88,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| identity = sk_c3
| multiply(X1,sk_c8) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| inverse(X2) != sk_c7 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_37]),c_0_84])]),c_0_85]) ).
cnf(c_0_89,negated_conjecture,
( inverse(sk_c8) = sk_c8
| sk_c6 != sk_c7 ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_90,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| identity = sk_c3
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_77]),c_0_78]) ).
cnf(c_0_91,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| sk_c6 = sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_89]),c_0_73]) ).
cnf(c_0_92,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c8) = sk_c6 ),
prove_this_28 ).
cnf(c_0_93,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| identity = sk_c3 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_44]),c_0_91]),c_0_50]) ).
cnf(c_0_94,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c8) = sk_c6 ),
prove_this_34 ).
cnf(c_0_95,negated_conjecture,
( multiply(sk_c6,multiply(sk_c8,X1)) = X1
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(spm,[status(thm)],[c_0_39,c_0_92]) ).
cnf(c_0_96,negated_conjecture,
( multiply(inverse(sk_c8),sk_c7) = sk_c3
| identity = sk_c3 ),
inference(spm,[status(thm)],[c_0_39,c_0_93]) ).
cnf(c_0_97,negated_conjecture,
( multiply(sk_c2,sk_c8) = identity
| inverse(sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_82,c_0_94]) ).
cnf(c_0_98,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c6,sk_c7) = sk_c3
| identity = sk_c3 ),
inference(spm,[status(thm)],[c_0_95,c_0_93]) ).
cnf(c_0_99,negated_conjecture,
( multiply(sk_c2,sk_c8) = identity
| multiply(sk_c6,sk_c7) = sk_c3
| identity = sk_c3 ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_100,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c3
| identity = sk_c3 ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_101,negated_conjecture,
( multiply(sk_c8,multiply(sk_c3,X1)) = multiply(sk_c7,X1)
| identity = sk_c3 ),
inference(spm,[status(thm)],[c_0_36,c_0_93]) ).
cnf(c_0_102,negated_conjecture,
( multiply(inverse(sk_c8),sk_c6) = sk_c7
| identity = sk_c3 ),
inference(spm,[status(thm)],[c_0_39,c_0_81]) ).
cnf(c_0_103,negated_conjecture,
( multiply(sk_c6,multiply(sk_c7,X1)) = multiply(sk_c3,X1)
| identity = sk_c3 ),
inference(spm,[status(thm)],[c_0_36,c_0_100]) ).
cnf(c_0_104,negated_conjecture,
( multiply(sk_c7,inverse(sk_c3)) = sk_c8
| identity = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_82]),c_0_61]) ).
cnf(c_0_105,negated_conjecture,
( multiply(inverse(sk_c8),multiply(sk_c6,X1)) = multiply(sk_c7,X1)
| identity = sk_c3 ),
inference(spm,[status(thm)],[c_0_36,c_0_102]) ).
cnf(c_0_106,negated_conjecture,
( multiply(sk_c6,sk_c8) = identity
| identity = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_82]) ).
cnf(c_0_107,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c5) = sk_c7 ),
prove_this_36 ).
cnf(c_0_108,negated_conjecture,
( inverse(sk_c8) = multiply(sk_c7,sk_c8)
| identity = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_61]) ).
cnf(c_0_109,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_84,c_0_107]) ).
cnf(c_0_110,negated_conjecture,
( multiply(sk_c7,multiply(sk_c8,sk_c8)) = identity
| identity = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_108]),c_0_36]) ).
cnf(c_0_111,negated_conjecture,
( inverse(sk_c6) = sk_c8
| identity = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_106]),c_0_61]) ).
cnf(c_0_112,negated_conjecture,
( inverse(sk_c7) = sk_c5
| inverse(sk_c8) = sk_c2 ),
inference(spm,[status(thm)],[c_0_84,c_0_109]) ).
cnf(c_0_113,negated_conjecture,
( inverse(sk_c7) = multiply(sk_c8,sk_c8)
| identity = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_110]),c_0_61]) ).
cnf(c_0_114,negated_conjecture,
( inverse(sk_c8) = sk_c6
| identity = sk_c3 ),
inference(spm,[status(thm)],[c_0_84,c_0_111]) ).
cnf(c_0_115,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c5
| inverse(sk_c8) = sk_c2
| identity = sk_c3 ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_116,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c5,sk_c7) = sk_c6 ),
prove_this_35 ).
cnf(c_0_117,negated_conjecture,
( inverse(multiply(sk_c8,sk_c8)) = sk_c7
| identity = sk_c3 ),
inference(spm,[status(thm)],[c_0_84,c_0_113]) ).
cnf(c_0_118,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c5
| identity = sk_c3
| sk_c2 = sk_c6 ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_119,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c8) = sk_c2 ),
inference(spm,[status(thm)],[c_0_84,c_0_116]) ).
cnf(c_0_120,negated_conjecture,
( inverse(sk_c5) = sk_c7
| sk_c2 = sk_c6
| identity = sk_c3 ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_121,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| identity = sk_c3
| sk_c2 = sk_c6 ),
inference(spm,[status(thm)],[c_0_119,c_0_114]) ).
cnf(c_0_122,negated_conjecture,
( multiply(sk_c5,sk_c7) = identity
| identity = sk_c3
| sk_c2 = sk_c6 ),
inference(spm,[status(thm)],[c_0_82,c_0_120]) ).
cnf(c_0_123,negated_conjecture,
( multiply(sk_c5,multiply(sk_c7,X1)) = multiply(sk_c6,X1)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_36,c_0_41]) ).
cnf(c_0_124,negated_conjecture,
( sk_c2 = sk_c6
| identity = sk_c3
| identity = sk_c6 ),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_125,negated_conjecture,
( multiply(sk_c5,sk_c7) = multiply(sk_c6,sk_c6)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_123,c_0_52]) ).
cnf(c_0_126,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_66,c_0_79]) ).
cnf(c_0_127,negated_conjecture,
( multiply(X1,sk_c3) = X1
| identity = sk_c6
| sk_c2 = sk_c6 ),
inference(spm,[status(thm)],[c_0_61,c_0_124]) ).
cnf(c_0_128,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c4,sk_c8) = sk_c7 ),
prove_this_2 ).
cnf(c_0_129,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c6,sk_c6) = sk_c7
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_62,c_0_53]) ).
cnf(c_0_130,negated_conjecture,
( multiply(sk_c6,sk_c6) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_41,c_0_125]) ).
cnf(c_0_131,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c4) = sk_c8 ),
prove_this_3 ).
cnf(c_0_132,negated_conjecture,
( multiply(sk_c8,multiply(sk_c7,X1)) = multiply(sk_c6,X1)
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_36,c_0_126]) ).
cnf(c_0_133,negated_conjecture,
( sk_c2 = sk_c6
| identity = sk_c6
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_85,c_0_127]) ).
cnf(c_0_134,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c5) = sk_c7 ),
prove_this_12 ).
cnf(c_0_135,negated_conjecture,
( multiply(sk_c4,multiply(sk_c8,X1)) = multiply(sk_c7,X1)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_36,c_0_128]) ).
cnf(c_0_136,negated_conjecture,
( multiply(sk_c8,sk_c8) = identity
| sk_c6 != sk_c7 ),
inference(spm,[status(thm)],[c_0_37,c_0_89]) ).
cnf(c_0_137,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_138,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c4 ),
inference(spm,[status(thm)],[c_0_84,c_0_131]) ).
cnf(c_0_139,negated_conjecture,
( multiply(sk_c6,inverse(sk_c7)) = sk_c8
| sk_c7 = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_82]),c_0_61]) ).
cnf(c_0_140,negated_conjecture,
( multiply(sk_c6,X1) = X1
| sk_c7 = sk_c8
| sk_c2 = sk_c6 ),
inference(spm,[status(thm)],[c_0_38,c_0_133]) ).
cnf(c_0_141,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c7,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_37,c_0_134]) ).
cnf(c_0_142,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c5) = sk_c7 ),
prove_this_18 ).
cnf(c_0_143,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c4 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_61]),c_0_137]) ).
cnf(c_0_144,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_53,c_0_138]) ).
cnf(c_0_145,negated_conjecture,
( inverse(sk_c7) = sk_c8
| sk_c2 = sk_c6
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_146,negated_conjecture,
( multiply(inverse(sk_c1),sk_c8) = sk_c7
| multiply(sk_c7,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_39,c_0_141]) ).
cnf(c_0_147,negated_conjecture,
( multiply(sk_c7,sk_c5) = identity
| inverse(sk_c1) = sk_c7 ),
inference(spm,[status(thm)],[c_0_37,c_0_142]) ).
cnf(c_0_148,negated_conjecture,
multiply(sk_c7,sk_c8) = sk_c6,
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_143]),c_0_144]) ).
cnf(c_0_149,negated_conjecture,
( inverse(sk_c8) = sk_c7
| sk_c7 = sk_c8
| sk_c2 = sk_c6 ),
inference(spm,[status(thm)],[c_0_84,c_0_145]) ).
cnf(c_0_150,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c4) = sk_c8 ),
prove_this_33 ).
cnf(c_0_151,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c7 ),
prove_this_8 ).
cnf(c_0_152,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_84,c_0_142]) ).
cnf(c_0_153,negated_conjecture,
( multiply(sk_c7,sk_c5) = identity
| sk_c6 = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_148]) ).
cnf(c_0_154,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c5,sk_c7) = sk_c6 ),
prove_this_17 ).
cnf(c_0_155,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| identity = sk_c3
| identity != sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_37]),c_0_84])]) ).
cnf(c_0_156,negated_conjecture,
( multiply(sk_c6,sk_c6) = sk_c7
| identity = sk_c3 ),
inference(spm,[status(thm)],[c_0_102,c_0_114]) ).
cnf(c_0_157,negated_conjecture,
( sk_c2 = sk_c6
| sk_c7 = sk_c8
| sk_c6 != sk_c7 ),
inference(spm,[status(thm)],[c_0_89,c_0_149]) ).
cnf(c_0_158,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c8) = sk_c4 ),
inference(spm,[status(thm)],[c_0_84,c_0_150]) ).
cnf(c_0_159,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c8 ),
prove_this_15 ).
cnf(c_0_160,negated_conjecture,
( multiply(inverse(sk_c4),sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_39,c_0_151]) ).
cnf(c_0_161,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c8 ),
prove_this_9 ).
cnf(c_0_162,negated_conjecture,
( inverse(sk_c7) = sk_c5
| inverse(sk_c7) = sk_c1 ),
inference(spm,[status(thm)],[c_0_84,c_0_152]) ).
cnf(c_0_163,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c8) = sk_c6 ),
prove_this_16 ).
cnf(c_0_164,negated_conjecture,
( inverse(sk_c7) = sk_c5
| sk_c6 = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_153]),c_0_61]) ).
cnf(c_0_165,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c7) = sk_c1 ),
inference(spm,[status(thm)],[c_0_84,c_0_154]) ).
cnf(c_0_166,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| sk_c3 = sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_87]),c_0_73]) ).
cnf(c_0_167,negated_conjecture,
( sk_c2 = sk_c6
| sk_c7 = sk_c8
| identity = sk_c3 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_140]),c_0_157]) ).
cnf(c_0_168,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c4) = sk_c8 ),
prove_this_27 ).
cnf(c_0_169,negated_conjecture,
( inverse(sk_c8) = sk_c4
| inverse(sk_c8) = sk_c2 ),
inference(spm,[status(thm)],[c_0_84,c_0_158]) ).
cnf(c_0_170,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c8) = sk_c4 ),
inference(spm,[status(thm)],[c_0_84,c_0_159]) ).
cnf(c_0_171,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_160,c_0_161]) ).
cnf(c_0_172,negated_conjecture,
( inverse(sk_c7) = sk_c1
| sk_c5 != sk_c1 ),
inference(ef,[status(thm)],[c_0_162]) ).
cnf(c_0_173,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c7) = sk_c1 ),
inference(spm,[status(thm)],[c_0_84,c_0_163]) ).
cnf(c_0_174,negated_conjecture,
( multiply(sk_c5,sk_c7) = identity
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_37,c_0_164]) ).
cnf(c_0_175,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| sk_c6 = sk_c7
| sk_c5 = sk_c1 ),
inference(spm,[status(thm)],[c_0_165,c_0_164]) ).
cnf(c_0_176,negated_conjecture,
( multiply(sk_c8,multiply(sk_c3,X1)) = multiply(sk_c7,X1)
| sk_c3 = sk_c8 ),
inference(spm,[status(thm)],[c_0_36,c_0_166]) ).
cnf(c_0_177,negated_conjecture,
( multiply(sk_c3,X1) = X1
| sk_c7 = sk_c8
| sk_c2 = sk_c6 ),
inference(spm,[status(thm)],[c_0_38,c_0_167]) ).
cnf(c_0_178,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c8) = sk_c4 ),
inference(spm,[status(thm)],[c_0_84,c_0_168]) ).
cnf(c_0_179,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c8) = sk_c2 ),
inference(spm,[status(thm)],[c_0_84,c_0_94]) ).
cnf(c_0_180,negated_conjecture,
( inverse(sk_c8) = sk_c2
| sk_c4 != sk_c2 ),
inference(ef,[status(thm)],[c_0_169]) ).
cnf(c_0_181,negated_conjecture,
( multiply(inverse(sk_c7),sk_c6) = sk_c8
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_39,c_0_144]) ).
cnf(c_0_182,negated_conjecture,
( inverse(sk_c8) = sk_c4
| inverse(sk_c7) = sk_c1 ),
inference(spm,[status(thm)],[c_0_84,c_0_170]) ).
cnf(c_0_183,negated_conjecture,
( multiply(inverse(sk_c1),sk_c8) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_39,c_0_171]) ).
cnf(c_0_184,negated_conjecture,
( inverse(sk_c1) = sk_c7
| sk_c5 != sk_c1 ),
inference(spm,[status(thm)],[c_0_84,c_0_172]) ).
cnf(c_0_185,negated_conjecture,
( inverse(sk_c8) = sk_c6
| sk_c6 = sk_c7
| sk_c5 = sk_c1 ),
inference(spm,[status(thm)],[c_0_173,c_0_164]) ).
cnf(c_0_186,negated_conjecture,
( sk_c5 = sk_c1
| sk_c6 = sk_c7
| identity = sk_c6 ),
inference(spm,[status(thm)],[c_0_174,c_0_175]) ).
cnf(c_0_187,negated_conjecture,
( multiply(sk_c7,inverse(sk_c3)) = sk_c8
| sk_c3 = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_82]),c_0_61]) ).
cnf(c_0_188,negated_conjecture,
( inverse(sk_c3) = identity
| sk_c2 = sk_c6
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_82,c_0_177]) ).
cnf(c_0_189,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_92,c_0_178]) ).
cnf(c_0_190,negated_conjecture,
( inverse(sk_c8) = sk_c2
| sk_c4 = sk_c6 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_169]),c_0_180]) ).
cnf(c_0_191,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c6 ),
prove_this_10 ).
cnf(c_0_192,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c4 ),
inference(spm,[status(thm)],[c_0_84,c_0_161]) ).
cnf(c_0_193,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c8
| inverse(sk_c8) = sk_c6
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_181,c_0_173]) ).
cnf(c_0_194,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c8
| inverse(sk_c8) = sk_c4
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_181,c_0_182]) ).
cnf(c_0_195,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c5,sk_c7) = sk_c6 ),
prove_this_11 ).
cnf(c_0_196,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c7
| sk_c5 != sk_c1 ),
inference(spm,[status(thm)],[c_0_183,c_0_184]) ).
cnf(c_0_197,negated_conjecture,
( inverse(sk_c6) = sk_c8
| sk_c5 = sk_c1
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_84,c_0_185]) ).
cnf(c_0_198,negated_conjecture,
( inverse(sk_c6) = sk_c6
| sk_c6 = sk_c7
| sk_c5 = sk_c1 ),
inference(spm,[status(thm)],[c_0_86,c_0_186]) ).
cnf(c_0_199,negated_conjecture,
( inverse(sk_c3) = sk_c3
| sk_c7 = sk_c8
| sk_c2 = sk_c6 ),
inference(spm,[status(thm)],[c_0_86,c_0_167]) ).
cnf(c_0_200,negated_conjecture,
( sk_c2 = sk_c6
| sk_c3 = sk_c8
| sk_c7 = sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_188]),c_0_61])]) ).
cnf(c_0_201,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c8) = sk_c4 ),
inference(spm,[status(thm)],[c_0_84,c_0_78]) ).
cnf(c_0_202,negated_conjecture,
( multiply(inverse(sk_c2),sk_c3) = sk_c8
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_39,c_0_189]) ).
cnf(c_0_203,negated_conjecture,
( inverse(sk_c2) = sk_c8
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_84,c_0_190]) ).
cnf(c_0_204,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c7 ),
prove_this_14 ).
cnf(c_0_205,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_191,c_0_192]) ).
cnf(c_0_206,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c8
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_193,c_0_194]) ).
cnf(c_0_207,negated_conjecture,
( multiply(inverse(sk_c5),sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_39,c_0_195]) ).
cnf(c_0_208,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c8
| sk_c6 = sk_c7
| sk_c5 != sk_c1 ),
inference(rw,[status(thm)],[c_0_196,c_0_148]) ).
cnf(c_0_209,negated_conjecture,
( sk_c6 = sk_c7
| sk_c5 = sk_c1
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_197,c_0_198]) ).
cnf(c_0_210,negated_conjecture,
( inverse(sk_c8) = sk_c8
| sk_c2 = sk_c6
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_199,c_0_200]) ).
cnf(c_0_211,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_63,c_0_201]) ).
cnf(c_0_212,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c8
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_202,c_0_203]) ).
cnf(c_0_213,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c7) = sk_c1 ),
inference(spm,[status(thm)],[c_0_84,c_0_204]) ).
cnf(c_0_214,negated_conjecture,
( multiply(inverse(sk_c1),sk_c8) = sk_c7
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_39,c_0_205]) ).
cnf(c_0_215,negated_conjecture,
( multiply(inverse(sk_c1),sk_c8) = sk_c6
| sk_c4 = sk_c6 ),
inference(spm,[status(thm)],[c_0_39,c_0_206]) ).
cnf(c_0_216,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_207,c_0_134]) ).
cnf(c_0_217,negated_conjecture,
( inverse(sk_c8) = sk_c6
| sk_c2 != sk_c6 ),
inference(ef,[status(thm)],[c_0_179]) ).
cnf(c_0_218,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c8
| sk_c6 = sk_c8
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_208,c_0_209]) ).
cnf(c_0_219,negated_conjecture,
( multiply(sk_c2,sk_c8) = identity
| sk_c4 != sk_c2 ),
inference(spm,[status(thm)],[c_0_37,c_0_180]) ).
cnf(c_0_220,negated_conjecture,
( sk_c2 = sk_c6
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_149,c_0_210]) ).
cnf(c_0_221,negated_conjecture,
( sk_c4 = sk_c6
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_211,c_0_212]) ).
cnf(c_0_222,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| sk_c6 = sk_c7
| sk_c5 = sk_c1 ),
inference(spm,[status(thm)],[c_0_213,c_0_164]) ).
cnf(c_0_223,negated_conjecture,
( sk_c4 = sk_c6
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_214,c_0_215]) ).
cnf(c_0_224,negated_conjecture,
( multiply(inverse(sk_c1),sk_c8) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_39,c_0_216]) ).
cnf(c_0_225,negated_conjecture,
( sk_c6 = sk_c8
| sk_c2 != sk_c6
| sk_c6 != sk_c7 ),
inference(spm,[status(thm)],[c_0_217,c_0_89]) ).
cnf(c_0_226,negated_conjecture,
( sk_c6 = sk_c7
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_55,c_0_218]) ).
cnf(c_0_227,negated_conjecture,
( multiply(sk_c6,sk_c8) = identity
| sk_c7 = sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_219,c_0_220]),c_0_221]) ).
cnf(c_0_228,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| sk_c5 = sk_c1
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_222,c_0_223]) ).
cnf(c_0_229,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c7
| sk_c5 != sk_c1 ),
inference(spm,[status(thm)],[c_0_224,c_0_184]) ).
cnf(c_0_230,negated_conjecture,
( sk_c7 = sk_c8
| sk_c6 = sk_c8
| sk_c6 != sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_133]),c_0_225]) ).
cnf(c_0_231,negated_conjecture,
( sk_c6 = sk_c8
| sk_c7 != sk_c8 ),
inference(ef,[status(thm)],[c_0_226]) ).
cnf(c_0_232,negated_conjecture,
( sk_c6 = sk_c7
| sk_c5 = sk_c1
| sk_c7 = sk_c8
| identity = sk_c7 ),
inference(spm,[status(thm)],[c_0_227,c_0_228]) ).
cnf(c_0_233,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c7
| sk_c6 = sk_c7
| sk_c5 != sk_c1 ),
inference(rw,[status(thm)],[c_0_229,c_0_148]) ).
cnf(c_0_234,negated_conjecture,
sk_c6 = sk_c8,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_230,c_0_226]),c_0_231]) ).
cnf(c_0_235,negated_conjecture,
( sk_c7 = sk_c8
| sk_c6 = sk_c7
| sk_c5 = sk_c1 ),
inference(spm,[status(thm)],[c_0_186,c_0_232]) ).
cnf(c_0_236,negated_conjecture,
( sk_c7 = sk_c8
| sk_c5 != sk_c1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_233,c_0_234]),c_0_148]),c_0_234]),c_0_234])]) ).
cnf(c_0_237,negated_conjecture,
( identity = sk_c8
| sk_c7 != sk_c8 ),
inference(rw,[status(thm)],[c_0_87,c_0_234]) ).
cnf(c_0_238,negated_conjecture,
sk_c7 = sk_c8,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_235,c_0_234])]),c_0_236]) ).
cnf(c_0_239,negated_conjecture,
identity = sk_c8,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_237,c_0_238])]) ).
cnf(c_0_240,negated_conjecture,
( multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(X2,sk_c7) != sk_c6
| multiply(X3,sk_c8) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| inverse(sk_c8) != sk_c6
| inverse(X2) != sk_c7
| inverse(X3) != sk_c8
| inverse(X1) != sk_c8
| inverse(X4) != sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_148])]) ).
cnf(c_0_241,plain,
multiply(X1,sk_c8) = X1,
inference(rw,[status(thm)],[c_0_61,c_0_239]) ).
cnf(c_0_242,plain,
multiply(sk_c8,X1) = X1,
inference(rw,[status(thm)],[c_0_38,c_0_239]) ).
cnf(c_0_243,plain,
inverse(sk_c8) = sk_c8,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_239]),c_0_239]) ).
cnf(c_0_244,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(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_240,c_0_234]),c_0_234]),c_0_234]),c_0_241]),c_0_242]),c_0_238]),c_0_238]),c_0_241]),c_0_238]),c_0_241]),c_0_241]),c_0_238]),c_0_238]),c_0_241]),c_0_243]),c_0_238]),c_0_238])])])])])]),c_0_243])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP324-1 : TPTP v8.2.0. Released v2.5.0.
% 0.00/0.10 % Command : run_E %s %d THM
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Sun May 19 05:31:22 EDT 2024
% 0.10/0.29 % CPUTime :
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 2.07/0.66 # Version: 3.1.0
% 2.07/0.66 # Preprocessing class: FSMSSMSMSSSNFFN.
% 2.07/0.66 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.07/0.66 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 2.07/0.66 # Starting new_bool_3 with 300s (1) cores
% 2.07/0.66 # Starting new_bool_1 with 300s (1) cores
% 2.07/0.66 # Starting sh5l with 300s (1) cores
% 2.07/0.66 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 16436 completed with status 0
% 2.07/0.66 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 2.07/0.66 # Preprocessing class: FSMSSMSMSSSNFFN.
% 2.07/0.66 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.07/0.66 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 2.07/0.66 # No SInE strategy applied
% 2.07/0.66 # Search class: FGHPS-FFMM21-SFFFFFNN
% 2.07/0.66 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 2.07/0.66 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 2.07/0.66 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 2.07/0.66 # Starting new_bool_3 with 136s (1) cores
% 2.07/0.66 # Starting new_bool_1 with 136s (1) cores
% 2.07/0.66 # Starting sh5l with 136s (1) cores
% 2.07/0.66 # G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 16440 completed with status 0
% 2.07/0.66 # Result found by G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 2.07/0.66 # Preprocessing class: FSMSSMSMSSSNFFN.
% 2.07/0.66 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.07/0.66 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 2.07/0.66 # No SInE strategy applied
% 2.07/0.66 # Search class: FGHPS-FFMM21-SFFFFFNN
% 2.07/0.66 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 2.07/0.66 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 2.07/0.66 # Preprocessing time : 0.001 s
% 2.07/0.66 # Presaturation interreduction done
% 2.07/0.66
% 2.07/0.66 # Proof found!
% 2.07/0.66 # SZS status Unsatisfiable
% 2.07/0.66 # SZS output start CNFRefutation
% See solution above
% 2.07/0.66 # Parsed axioms : 40
% 2.07/0.66 # Removed by relevancy pruning/SinE : 0
% 2.07/0.66 # Initial clauses : 40
% 2.07/0.66 # Removed in clause preprocessing : 0
% 2.07/0.66 # Initial clauses in saturation : 40
% 2.07/0.66 # Processed clauses : 3702
% 2.07/0.66 # ...of these trivial : 224
% 2.07/0.66 # ...subsumed : 2079
% 2.07/0.66 # ...remaining for further processing : 1399
% 2.07/0.66 # Other redundant clauses eliminated : 7
% 2.07/0.66 # Clauses deleted for lack of memory : 0
% 2.07/0.66 # Backward-subsumed : 383
% 2.07/0.66 # Backward-rewritten : 918
% 2.07/0.66 # Generated clauses : 23471
% 2.07/0.66 # ...of the previous two non-redundant : 23429
% 2.07/0.66 # ...aggressively subsumed : 0
% 2.07/0.66 # Contextual simplify-reflections : 66
% 2.07/0.66 # Paramodulations : 23452
% 2.07/0.66 # Factorizations : 15
% 2.07/0.66 # NegExts : 0
% 2.07/0.66 # Equation resolutions : 7
% 2.07/0.66 # Disequality decompositions : 0
% 2.07/0.66 # Total rewrite steps : 5547
% 2.07/0.66 # ...of those cached : 5337
% 2.07/0.66 # Propositional unsat checks : 0
% 2.07/0.66 # Propositional check models : 0
% 2.07/0.66 # Propositional check unsatisfiable : 0
% 2.07/0.66 # Propositional clauses : 0
% 2.07/0.66 # Propositional clauses after purity: 0
% 2.07/0.66 # Propositional unsat core size : 0
% 2.07/0.66 # Propositional preprocessing time : 0.000
% 2.07/0.66 # Propositional encoding time : 0.000
% 2.07/0.66 # Propositional solver time : 0.000
% 2.07/0.66 # Success case prop preproc time : 0.000
% 2.07/0.66 # Success case prop encoding time : 0.000
% 2.07/0.66 # Success case prop solver time : 0.000
% 2.07/0.66 # Current number of processed clauses : 56
% 2.07/0.66 # Positive orientable unit clauses : 14
% 2.07/0.66 # Positive unorientable unit clauses: 0
% 2.07/0.66 # Negative unit clauses : 0
% 2.07/0.66 # Non-unit-clauses : 42
% 2.07/0.66 # Current number of unprocessed clauses: 18709
% 2.07/0.66 # ...number of literals in the above : 86507
% 2.07/0.66 # Current number of archived formulas : 0
% 2.07/0.66 # Current number of archived clauses : 1341
% 2.07/0.66 # Clause-clause subsumption calls (NU) : 52386
% 2.07/0.66 # Rec. Clause-clause subsumption calls : 12287
% 2.07/0.66 # Non-unit clause-clause subsumptions : 2505
% 2.07/0.66 # Unit Clause-clause subsumption calls : 845
% 2.07/0.66 # Rewrite failures with RHS unbound : 0
% 2.07/0.66 # BW rewrite match attempts : 30
% 2.07/0.66 # BW rewrite match successes : 28
% 2.07/0.66 # Condensation attempts : 0
% 2.07/0.66 # Condensation successes : 0
% 2.07/0.66 # Termbank termtop insertions : 304235
% 2.07/0.66 # Search garbage collected termcells : 32
% 2.07/0.66
% 2.07/0.66 # -------------------------------------------------
% 2.07/0.66 # User time : 0.247 s
% 2.07/0.66 # System time : 0.007 s
% 2.07/0.66 # Total time : 0.254 s
% 2.07/0.66 # Maximum resident set size: 1676 pages
% 2.07/0.66
% 2.07/0.66 # -------------------------------------------------
% 2.07/0.66 # User time : 1.241 s
% 2.07/0.66 # System time : 0.019 s
% 2.07/0.66 # Total time : 1.260 s
% 2.07/0.66 # Maximum resident set size: 1756 pages
% 2.07/0.66 % E---3.1 exiting
% 2.07/0.66 % E exiting
%------------------------------------------------------------------------------