TSTP Solution File: GRP357-1 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : GRP357-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n014.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 : Sat May 4 07:50:51 EDT 2024
% Result : Unsatisfiable 4.72s 1.12s
% Output : CNFRefutation 4.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 65
% Number of leaves : 32
% Syntax : Number of clauses : 250 ( 27 unt; 215 nHn; 219 RR)
% Number of literals : 617 ( 616 equ; 86 neg)
% Maximal clause size : 11 ( 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 : 73 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',left_identity) ).
cnf(prove_this_13,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',prove_this_13) ).
cnf(prove_this_25,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',prove_this_25) ).
cnf(prove_this_18,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',prove_this_18) ).
cnf(prove_this_15,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',prove_this_15) ).
cnf(prove_this_9,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',prove_this_9) ).
cnf(prove_this_19,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',prove_this_19) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',prove_this_1) ).
cnf(prove_this_31,negated_conjecture,
( multiply(sk_c7,sk_c6) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(X1,X2) != sk_c8
| inverse(X1) != X2
| multiply(X2,sk_c7) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(X3,sk_c8) != sk_c7
| inverse(X3) != sk_c8
| multiply(sk_c8,X4) != sk_c7
| multiply(X5,sk_c8) != X4
| inverse(X5) != sk_c8 ),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',prove_this_31) ).
cnf(prove_this_12,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',prove_this_12) ).
cnf(prove_this_24,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',prove_this_24) ).
cnf(prove_this_21,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',prove_this_21) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',prove_this_6) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',prove_this_3) ).
cnf(prove_this_16,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',prove_this_16) ).
cnf(prove_this_28,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',prove_this_28) ).
cnf(prove_this_22,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',prove_this_22) ).
cnf(prove_this_7,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',prove_this_7) ).
cnf(prove_this_4,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',prove_this_4) ).
cnf(prove_this_30,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',prove_this_30) ).
cnf(prove_this_27,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',prove_this_27) ).
cnf(prove_this_23,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',prove_this_23) ).
cnf(prove_this_20,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',prove_this_20) ).
cnf(prove_this_17,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',prove_this_17) ).
cnf(prove_this_14,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',prove_this_14) ).
cnf(prove_this_26,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',prove_this_26) ).
cnf(prove_this_29,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',prove_this_29) ).
cnf(prove_this_10,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',prove_this_10) ).
cnf(prove_this_11,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',prove_this_11) ).
cnf(prove_this_8,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p',prove_this_8) ).
cnf(c_0_32,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_33,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_34,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_35,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_36,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_35,c_0_33]) ).
cnf(c_0_37,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_35,c_0_35]) ).
cnf(c_0_38,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
prove_this_13 ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
prove_this_25 ).
cnf(c_0_41,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_38]) ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| inverse(sk_c4) = sk_c8 ),
prove_this_18 ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| inverse(sk_c3) = sk_c8 ),
prove_this_15 ).
cnf(c_0_44,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c3) = sk_c8 ),
prove_this_9 ).
cnf(c_0_45,negated_conjecture,
( multiply(inverse(sk_c1),sk_c8) = sk_c2
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_35,c_0_39]) ).
cnf(c_0_46,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c8,sk_c7) = sk_c6 ),
prove_this_19 ).
cnf(c_0_47,negated_conjecture,
( multiply(sk_c2,multiply(sk_c7,X1)) = multiply(sk_c8,X1)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_32,c_0_40]) ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
prove_this_1 ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| inverse(sk_c8) = sk_c4 ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| inverse(sk_c8) = sk_c3 ),
inference(spm,[status(thm)],[c_0_41,c_0_43]) ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c7,sk_c6) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(X1,X2) != sk_c8
| inverse(X1) != X2
| multiply(X2,sk_c7) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(X3,sk_c8) != sk_c7
| inverse(X3) != sk_c8
| multiply(sk_c8,X4) != sk_c7
| multiply(X5,sk_c8) != X4
| inverse(X5) != sk_c8 ),
inference(fof_simplification,[status(thm)],[prove_this_31]) ).
cnf(c_0_52,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c4) = sk_c8 ),
prove_this_12 ).
cnf(c_0_53,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c8) = sk_c3 ),
inference(spm,[status(thm)],[c_0_41,c_0_44]) ).
cnf(c_0_54,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c2 ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c2,sk_c8) = multiply(sk_c8,sk_c6)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| sk_c4 = sk_c3 ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_57,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c4) = sk_c8 ),
prove_this_24 ).
cnf(c_0_58,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c3) = sk_c8 ),
prove_this_21 ).
cnf(c_0_59,negated_conjecture,
( multiply(sk_c7,sk_c6) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(X1,X2) != sk_c8
| inverse(X1) != X2
| multiply(X2,sk_c7) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(X3,sk_c8) != sk_c7
| inverse(X3) != sk_c8
| multiply(sk_c8,X4) != sk_c7
| multiply(X5,sk_c8) != X4
| inverse(X5) != sk_c8 ),
c_0_51 ).
cnf(c_0_60,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c8) = sk_c4 ),
inference(spm,[status(thm)],[c_0_41,c_0_52]) ).
cnf(c_0_61,negated_conjecture,
( inverse(sk_c8) = sk_c6
| sk_c3 != sk_c6 ),
inference(ef,[status(thm)],[c_0_53]) ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c4) = sk_c8 ),
prove_this_6 ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c3) = sk_c8 ),
prove_this_3 ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c2
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
prove_this_16 ).
cnf(c_0_66,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
prove_this_28 ).
cnf(c_0_67,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c8,sk_c5) = sk_c7 ),
prove_this_22 ).
cnf(c_0_68,negated_conjecture,
( multiply(inverse(sk_c1),sk_c8) = sk_c2
| sk_c4 = sk_c3 ),
inference(spm,[status(thm)],[c_0_35,c_0_56]) ).
cnf(c_0_69,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c8) = sk_c4 ),
inference(spm,[status(thm)],[c_0_41,c_0_57]) ).
cnf(c_0_70,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c8) = sk_c3 ),
inference(spm,[status(thm)],[c_0_41,c_0_58]) ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(inverse(X2),sk_c7) != sk_c8
| multiply(sk_c7,sk_c6) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(X2,inverse(X2)) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c6
| inverse(X1) != sk_c8
| inverse(X3) != sk_c8 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_59])]) ).
cnf(c_0_72,negated_conjecture,
( inverse(sk_c8) = sk_c6
| sk_c4 = sk_c3 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_53]),c_0_61]) ).
cnf(c_0_73,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c8) = sk_c4 ),
inference(spm,[status(thm)],[c_0_41,c_0_62]) ).
cnf(c_0_74,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c8) = sk_c3 ),
inference(spm,[status(thm)],[c_0_41,c_0_63]) ).
cnf(c_0_75,negated_conjecture,
( multiply(inverse(sk_c8),sk_c2) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_35,c_0_64]) ).
cnf(c_0_76,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
prove_this_7 ).
cnf(c_0_77,negated_conjecture,
( multiply(sk_c1,multiply(sk_c2,X1)) = multiply(sk_c8,X1)
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_32,c_0_65]) ).
cnf(c_0_78,negated_conjecture,
( multiply(inverse(sk_c2),sk_c8) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_35,c_0_66]) ).
cnf(c_0_79,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c2) = sk_c1 ),
inference(spm,[status(thm)],[c_0_41,c_0_67]) ).
cnf(c_0_80,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_35,c_0_34]) ).
cnf(c_0_81,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c2
| inverse(sk_c8) = sk_c4
| sk_c4 = sk_c3 ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_82,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c2
| inverse(sk_c8) = sk_c3
| sk_c4 = sk_c3 ),
inference(spm,[status(thm)],[c_0_68,c_0_70]) ).
cnf(c_0_83,negated_conjecture,
( multiply(inverse(sk_c1),sk_c8) = sk_c2
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_35,c_0_65]) ).
cnf(c_0_84,negated_conjecture,
( sk_c4 = sk_c3
| multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(inverse(X2),sk_c7) != sk_c8
| multiply(sk_c7,sk_c6) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(X2,inverse(X2)) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| inverse(X1) != sk_c8
| inverse(X3) != sk_c8 ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_85,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c4 = sk_c3 ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_86,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c6,sk_c2) = sk_c6 ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_87,negated_conjecture,
( multiply(sk_c1,sk_c8) = multiply(sk_c8,sk_c7)
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_77,c_0_66]) ).
cnf(c_0_88,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_89,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_35,c_0_80]) ).
cnf(c_0_90,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c2
| sk_c4 = sk_c3 ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_91,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c2 ),
inference(spm,[status(thm)],[c_0_83,c_0_67]) ).
cnf(c_0_92,negated_conjecture,
( sk_c4 = sk_c3
| multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(inverse(X2),sk_c7) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(X2,inverse(X2)) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| inverse(X1) != sk_c8
| inverse(X3) != sk_c8 ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_93,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| identity = sk_c2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_86]),c_0_33]) ).
cnf(c_0_94,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c7 ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_95,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_33,c_0_89]) ).
cnf(c_0_96,negated_conjecture,
( sk_c4 = sk_c3
| identity = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_90]),c_0_33]) ).
cnf(c_0_97,negated_conjecture,
( multiply(sk_c1,sk_c2) = multiply(sk_c8,sk_c8)
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_77,c_0_91]) ).
cnf(c_0_98,negated_conjecture,
( identity = sk_c2
| sk_c4 = sk_c3
| multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(inverse(X2),sk_c7) != sk_c8
| multiply(X2,inverse(X2)) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| inverse(X1) != sk_c8
| inverse(X3) != sk_c8 ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_99,negated_conjecture,
( multiply(inverse(sk_c8),sk_c7) = sk_c5
| multiply(sk_c8,sk_c7) = sk_c7 ),
inference(spm,[status(thm)],[c_0_35,c_0_94]) ).
cnf(c_0_100,negated_conjecture,
( inverse(sk_c8) = sk_c8
| sk_c4 = sk_c3 ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_101,negated_conjecture,
( multiply(sk_c7,multiply(sk_c6,X1)) = multiply(sk_c8,X1)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_32,c_0_48]) ).
cnf(c_0_102,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c6,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_33,c_0_76]) ).
cnf(c_0_103,negated_conjecture,
( multiply(sk_c1,multiply(sk_c2,X1)) = multiply(sk_c8,X1)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_32,c_0_39]) ).
cnf(c_0_104,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_65,c_0_97]) ).
cnf(c_0_105,negated_conjecture,
( sk_c4 = sk_c3
| identity = sk_c2
| multiply(inverse(X1),sk_c7) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(X1,inverse(X1)) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| inverse(X2) != sk_c8
| identity != sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_95]),c_0_34]) ).
cnf(c_0_106,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c5
| sk_c4 = sk_c3 ),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_107,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_38]) ).
cnf(c_0_108,negated_conjecture,
( multiply(sk_c1,sk_c2) = multiply(sk_c8,sk_c8)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_103,c_0_54]) ).
cnf(c_0_109,negated_conjecture,
( multiply(inverse(sk_c8),sk_c7) = sk_c5
| multiply(sk_c8,sk_c8) = sk_c8 ),
inference(spm,[status(thm)],[c_0_35,c_0_104]) ).
cnf(c_0_110,negated_conjecture,
( sk_c2 = sk_c8
| sk_c4 = sk_c3
| multiply(inverse(X1),sk_c7) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(X1,inverse(X1)) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| inverse(X2) != sk_c8 ),
inference(spm,[status(thm)],[c_0_105,c_0_96]) ).
cnf(c_0_111,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c7
| sk_c4 = sk_c3
| sk_c5 = sk_c6
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_112,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_39,c_0_108]) ).
cnf(c_0_113,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c5
| sk_c4 = sk_c3 ),
inference(spm,[status(thm)],[c_0_109,c_0_100]) ).
cnf(c_0_114,negated_conjecture,
( sk_c6 = sk_c7
| sk_c5 = sk_c6
| sk_c4 = sk_c3
| sk_c2 = sk_c8
| multiply(inverse(X1),sk_c7) != sk_c8
| multiply(X1,inverse(X1)) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| inverse(X2) != sk_c8 ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_115,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c8
| sk_c4 = sk_c3
| sk_c5 = sk_c6 ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_116,negated_conjecture,
( multiply(sk_c2,multiply(sk_c7,X1)) = multiply(sk_c8,X1)
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_32,c_0_66]) ).
cnf(c_0_117,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
prove_this_4 ).
cnf(c_0_118,negated_conjecture,
( sk_c2 = sk_c8
| sk_c4 = sk_c3
| sk_c5 = sk_c6
| sk_c6 = sk_c7
| multiply(inverse(X1),sk_c7) != sk_c8
| multiply(X1,inverse(X1)) != sk_c8
| identity != sk_c7 ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_41])]),c_0_33]) ).
cnf(c_0_119,negated_conjecture,
( sk_c6 = sk_c7
| sk_c5 = sk_c6
| sk_c4 = sk_c3
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_115,c_0_111]) ).
cnf(c_0_120,negated_conjecture,
( multiply(sk_c2,sk_c8) = multiply(sk_c8,sk_c6)
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_121,negated_conjecture,
( sk_c6 = sk_c7
| sk_c5 = sk_c6
| sk_c4 = sk_c3
| sk_c2 = sk_c8
| multiply(inverse(X1),sk_c7) != sk_c8
| multiply(X1,inverse(X1)) != sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_96]),c_0_119]) ).
cnf(c_0_122,negated_conjecture,
( inverse(sk_c6) = sk_c8
| sk_c4 = sk_c3 ),
inference(spm,[status(thm)],[c_0_41,c_0_72]) ).
cnf(c_0_123,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c2
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_91,c_0_120]) ).
cnf(c_0_124,negated_conjecture,
( sk_c2 = sk_c8
| sk_c4 = sk_c3
| sk_c5 = sk_c6
| sk_c6 = sk_c7 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_95]),c_0_34]),c_0_34]),c_0_96]),c_0_119]) ).
cnf(c_0_125,negated_conjecture,
( multiply(sk_c8,sk_c6) = identity
| sk_c4 = sk_c3 ),
inference(spm,[status(thm)],[c_0_33,c_0_122]) ).
cnf(c_0_126,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c2
| sk_c6 = sk_c7
| sk_c4 = sk_c3
| sk_c2 = sk_c8 ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_127,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| sk_c2 = sk_c8
| sk_c6 = sk_c7
| sk_c4 = sk_c3
| identity = sk_c2 ),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_128,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c8 ),
prove_this_30 ).
cnf(c_0_129,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
prove_this_27 ).
cnf(c_0_130,negated_conjecture,
( identity = sk_c2
| sk_c6 = sk_c7
| sk_c2 = sk_c8
| sk_c4 = sk_c3
| identity = sk_c7 ),
inference(spm,[status(thm)],[c_0_125,c_0_127]) ).
cnf(c_0_131,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c4 ),
inference(spm,[status(thm)],[c_0_41,c_0_128]) ).
cnf(c_0_132,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c3 ),
inference(spm,[status(thm)],[c_0_41,c_0_129]) ).
cnf(c_0_133,negated_conjecture,
( identity = sk_c7
| sk_c6 = sk_c7
| sk_c2 = sk_c8
| sk_c4 = sk_c3 ),
inference(spm,[status(thm)],[c_0_96,c_0_130]) ).
cnf(c_0_134,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c4,sk_c8) = sk_c5 ),
prove_this_23 ).
cnf(c_0_135,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| sk_c4 = sk_c3 ),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_136,negated_conjecture,
( multiply(X1,sk_c7) = X1
| sk_c4 = sk_c3
| sk_c2 = sk_c8
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_38,c_0_133]) ).
cnf(c_0_137,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c3,sk_c8) = sk_c7 ),
prove_this_20 ).
cnf(c_0_138,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c2,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_33,c_0_134]) ).
cnf(c_0_139,negated_conjecture,
( sk_c6 = sk_c7
| sk_c4 = sk_c3
| sk_c2 = sk_c8 ),
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
cnf(c_0_140,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c2,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_33,c_0_137]) ).
cnf(c_0_141,negated_conjecture,
( multiply(sk_c2,sk_c1) = identity
| multiply(sk_c3,sk_c8) = sk_c5
| sk_c2 = sk_c8
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_142,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c5 ),
prove_this_17 ).
cnf(c_0_143,negated_conjecture,
( multiply(sk_c2,sk_c1) = identity
| sk_c6 = sk_c7
| sk_c2 = sk_c8
| sk_c5 = sk_c7 ),
inference(spm,[status(thm)],[c_0_140,c_0_141]) ).
cnf(c_0_144,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
prove_this_14 ).
cnf(c_0_145,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c5
| sk_c2 = sk_c8
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_142,c_0_139]) ).
cnf(c_0_146,negated_conjecture,
( inverse(sk_c2) = sk_c1
| sk_c5 = sk_c7
| sk_c2 = sk_c8
| sk_c6 = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_143]),c_0_38]) ).
cnf(c_0_147,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| sk_c6 = sk_c7
| sk_c2 = sk_c8
| sk_c5 = sk_c7 ),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_148,negated_conjecture,
( multiply(sk_c1,sk_c2) = identity
| sk_c6 = sk_c7
| sk_c2 = sk_c8
| sk_c5 = sk_c7 ),
inference(spm,[status(thm)],[c_0_33,c_0_146]) ).
cnf(c_0_149,negated_conjecture,
( sk_c5 = sk_c7
| sk_c2 = sk_c8
| sk_c6 = sk_c7
| identity = sk_c8 ),
inference(spm,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_150,negated_conjecture,
( multiply(inverse(sk_c2),sk_c8) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_35,c_0_40]) ).
cnf(c_0_151,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c1 ),
inference(spm,[status(thm)],[c_0_41,c_0_46]) ).
cnf(c_0_152,negated_conjecture,
( multiply(sk_c8,X1) = X1
| sk_c6 = sk_c7
| sk_c2 = sk_c8
| sk_c5 = sk_c7 ),
inference(spm,[status(thm)],[c_0_34,c_0_149]) ).
cnf(c_0_153,negated_conjecture,
( multiply(sk_c1,sk_c8) = multiply(sk_c8,sk_c7)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_103,c_0_40]) ).
cnf(c_0_154,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_150,c_0_151]) ).
cnf(c_0_155,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
prove_this_26 ).
cnf(c_0_156,negated_conjecture,
( sk_c5 = sk_c7
| sk_c2 = sk_c8
| identity = sk_c2
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_93,c_0_152]) ).
cnf(c_0_157,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c7 ),
inference(spm,[status(thm)],[c_0_153,c_0_154]) ).
cnf(c_0_158,negated_conjecture,
( multiply(inverse(sk_c3),sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_35,c_0_155]) ).
cnf(c_0_159,negated_conjecture,
( sk_c6 = sk_c7
| sk_c2 = sk_c8
| sk_c5 = sk_c7 ),
inference(spm,[status(thm)],[c_0_149,c_0_156]) ).
cnf(c_0_160,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c7
| sk_c6 != sk_c7 ),
inference(ef,[status(thm)],[c_0_157]) ).
cnf(c_0_161,negated_conjecture,
( multiply(inverse(inverse(sk_c3)),sk_c8) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_35,c_0_158]) ).
cnf(c_0_162,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| identity = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_54]),c_0_33]) ).
cnf(c_0_163,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c7
| sk_c2 = sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_159]),c_0_160]) ).
cnf(c_0_164,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c5 ),
prove_this_29 ).
cnf(c_0_165,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| identity = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_129]),c_0_33]) ).
cnf(c_0_166,negated_conjecture,
( sk_c2 = sk_c8
| identity = sk_c8
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_162,c_0_163]) ).
cnf(c_0_167,negated_conjecture,
( sk_c2 = sk_c8
| identity = sk_c2
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_93,c_0_163]) ).
cnf(c_0_168,negated_conjecture,
( multiply(inverse(sk_c4),sk_c5) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_35,c_0_164]) ).
cnf(c_0_169,negated_conjecture,
( multiply(inverse(sk_c2),sk_c8) = sk_c7
| identity = sk_c7 ),
inference(spm,[status(thm)],[c_0_35,c_0_165]) ).
cnf(c_0_170,negated_conjecture,
( sk_c6 = sk_c7
| sk_c2 = sk_c8 ),
inference(spm,[status(thm)],[c_0_166,c_0_167]) ).
cnf(c_0_171,negated_conjecture,
( multiply(sk_c7,sk_c6) = multiply(sk_c8,sk_c2)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_101,c_0_86]) ).
cnf(c_0_172,negated_conjecture,
( multiply(inverse(inverse(sk_c4)),sk_c8) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_35,c_0_168]) ).
cnf(c_0_173,negated_conjecture,
( sk_c6 = sk_c7
| identity = sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_33])]) ).
cnf(c_0_174,negated_conjecture,
( multiply(sk_c6,multiply(sk_c8,X1)) = X1
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_102]),c_0_34]) ).
cnf(c_0_175,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c2) = sk_c8 ),
inference(spm,[status(thm)],[c_0_48,c_0_171]) ).
cnf(c_0_176,negated_conjecture,
( multiply(inverse(sk_c8),multiply(sk_c2,X1)) = multiply(sk_c6,X1)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_32,c_0_75]) ).
cnf(c_0_177,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| identity = sk_c5 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_128]),c_0_33]) ).
cnf(c_0_178,negated_conjecture,
( inverse(sk_c7) = sk_c7
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_95,c_0_173]) ).
cnf(c_0_179,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c6,sk_c8) = sk_c2 ),
inference(spm,[status(thm)],[c_0_174,c_0_175]) ).
cnf(c_0_180,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c6,sk_c8) = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_55]),c_0_35]) ).
cnf(c_0_181,negated_conjecture,
( multiply(sk_c2,multiply(sk_c7,X1)) = multiply(sk_c8,X1)
| identity = sk_c5 ),
inference(spm,[status(thm)],[c_0_32,c_0_177]) ).
cnf(c_0_182,negated_conjecture,
( multiply(sk_c7,sk_c7) = identity
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_33,c_0_178]) ).
cnf(c_0_183,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c2 = sk_c6 ),
inference(spm,[status(thm)],[c_0_179,c_0_180]) ).
cnf(c_0_184,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c2
| sk_c6 = sk_c7
| identity = sk_c5 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_182]),c_0_38]) ).
cnf(c_0_185,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c8,sk_c5) = sk_c7 ),
prove_this_10 ).
cnf(c_0_186,negated_conjecture,
( identity = sk_c5
| sk_c6 = sk_c7
| sk_c2 = sk_c6 ),
inference(spm,[status(thm)],[c_0_183,c_0_184]) ).
cnf(c_0_187,negated_conjecture,
( multiply(sk_c7,multiply(sk_c6,X1)) = multiply(sk_c8,X1)
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_32,c_0_117]) ).
cnf(c_0_188,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c6,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_33,c_0_185]) ).
cnf(c_0_189,negated_conjecture,
( sk_c2 = sk_c6
| sk_c5 = sk_c7
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_173,c_0_186]) ).
cnf(c_0_190,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_188]),c_0_38]) ).
cnf(c_0_191,negated_conjecture,
( multiply(sk_c8,X1) = X1
| sk_c4 = sk_c3 ),
inference(spm,[status(thm)],[c_0_34,c_0_96]) ).
cnf(c_0_192,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c7
| sk_c2 = sk_c6 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_189]),c_0_160]) ).
cnf(c_0_193,negated_conjecture,
( multiply(sk_c8,sk_c8) = identity
| sk_c4 = sk_c3 ),
inference(spm,[status(thm)],[c_0_33,c_0_100]) ).
cnf(c_0_194,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c7
| sk_c4 = sk_c3
| sk_c5 = sk_c7 ),
inference(spm,[status(thm)],[c_0_190,c_0_191]) ).
cnf(c_0_195,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c4,sk_c8) = sk_c5 ),
prove_this_11 ).
cnf(c_0_196,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c2) = sk_c1 ),
inference(spm,[status(thm)],[c_0_41,c_0_134]) ).
cnf(c_0_197,negated_conjecture,
( sk_c2 = sk_c6
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_183,c_0_192]) ).
cnf(c_0_198,negated_conjecture,
( sk_c6 = sk_c7
| sk_c5 = sk_c6
| sk_c4 = sk_c3
| identity = sk_c7 ),
inference(spm,[status(thm)],[c_0_193,c_0_111]) ).
cnf(c_0_199,negated_conjecture,
( sk_c4 = sk_c3
| identity = sk_c6 ),
inference(spm,[status(thm)],[c_0_125,c_0_191]) ).
cnf(c_0_200,negated_conjecture,
( sk_c5 = sk_c7
| sk_c4 = sk_c3
| identity = sk_c7 ),
inference(spm,[status(thm)],[c_0_193,c_0_194]) ).
cnf(c_0_201,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c7 ),
prove_this_8 ).
cnf(c_0_202,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c1 ),
inference(spm,[status(thm)],[c_0_41,c_0_137]) ).
cnf(c_0_203,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_41,c_0_195]) ).
cnf(c_0_204,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c6) = sk_c1
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_196,c_0_197]) ).
cnf(c_0_205,negated_conjecture,
( sk_c4 = sk_c3
| sk_c5 = sk_c6
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_198,c_0_199]) ).
cnf(c_0_206,negated_conjecture,
( sk_c5 = sk_c7
| sk_c6 = sk_c7
| sk_c4 = sk_c3 ),
inference(spm,[status(thm)],[c_0_199,c_0_200]) ).
cnf(c_0_207,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_41,c_0_201]) ).
cnf(c_0_208,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c6) = sk_c1
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_202,c_0_197]) ).
cnf(c_0_209,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| sk_c6 = sk_c7
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_203,c_0_204]) ).
cnf(c_0_210,negated_conjecture,
( sk_c6 = sk_c7
| sk_c4 = sk_c3 ),
inference(spm,[status(thm)],[c_0_205,c_0_206]) ).
cnf(c_0_211,negated_conjecture,
( multiply(inverse(sk_c4),sk_c5) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(spm,[status(thm)],[c_0_35,c_0_142]) ).
cnf(c_0_212,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c2,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_33,c_0_46]) ).
cnf(c_0_213,negated_conjecture,
( multiply(sk_c8,multiply(sk_c2,X1)) = multiply(sk_c8,X1)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_32,c_0_175]) ).
cnf(c_0_214,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| sk_c6 = sk_c7
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_207,c_0_208]) ).
cnf(c_0_215,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c5
| sk_c1 = sk_c8
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_209,c_0_210]) ).
cnf(c_0_216,negated_conjecture,
( multiply(inverse(inverse(sk_c4)),sk_c8) = sk_c5
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(spm,[status(thm)],[c_0_35,c_0_211]) ).
cnf(c_0_217,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c1) = sk_c1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_212]),c_0_38]) ).
cnf(c_0_218,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c1) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_212]),c_0_38]) ).
cnf(c_0_219,negated_conjecture,
( sk_c1 = sk_c8
| sk_c6 = sk_c7
| sk_c5 = sk_c7 ),
inference(spm,[status(thm)],[c_0_214,c_0_215]) ).
cnf(c_0_220,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| identity = sk_c5 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_216,c_0_42]),c_0_33]) ).
cnf(c_0_221,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_217,c_0_218]) ).
cnf(c_0_222,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c7
| sk_c1 = sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_219]),c_0_160]) ).
cnf(c_0_223,negated_conjecture,
( multiply(inverse(sk_c1),sk_c8) = sk_c2
| identity = sk_c5 ),
inference(spm,[status(thm)],[c_0_35,c_0_220]) ).
cnf(c_0_224,negated_conjecture,
( sk_c1 = sk_c8
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_221,c_0_222]) ).
cnf(c_0_225,negated_conjecture,
( sk_c6 = sk_c7
| identity = sk_c5
| identity = sk_c2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_223,c_0_224]),c_0_33]) ).
cnf(c_0_226,negated_conjecture,
( identity = sk_c2
| sk_c5 = sk_c7
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_173,c_0_225]) ).
cnf(c_0_227,negated_conjecture,
( sk_c5 = sk_c7
| sk_c2 = sk_c7
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_173,c_0_226]) ).
cnf(c_0_228,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c7
| sk_c2 = sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_227]),c_0_160]) ).
cnf(c_0_229,negated_conjecture,
( sk_c2 = sk_c7
| identity = sk_c2
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_93,c_0_228]) ).
cnf(c_0_230,negated_conjecture,
( sk_c2 = sk_c7
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_173,c_0_229]) ).
cnf(c_0_231,negated_conjecture,
( multiply(sk_c3,sk_c8) = identity
| inverse(sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_33,c_0_53]) ).
cnf(c_0_232,negated_conjecture,
sk_c6 = sk_c7,
inference(spm,[status(thm)],[c_0_197,c_0_230]) ).
cnf(c_0_233,negated_conjecture,
( multiply(sk_c3,sk_c8) = identity
| inverse(sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_41,c_0_231]) ).
cnf(c_0_234,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c7) = sk_c8 ),
inference(rw,[status(thm)],[c_0_207,c_0_232]) ).
cnf(c_0_235,negated_conjecture,
multiply(sk_c8,sk_c7) = sk_c7,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_157,c_0_232])]) ).
cnf(c_0_236,negated_conjecture,
( multiply(sk_c3,sk_c8) = identity
| inverse(sk_c7) = sk_c8 ),
inference(rw,[status(thm)],[c_0_233,c_0_232]) ).
cnf(c_0_237,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| identity = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_234]),c_0_235]) ).
cnf(c_0_238,negated_conjecture,
( multiply(sk_c3,sk_c8) = identity
| identity = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_236]),c_0_235]) ).
cnf(c_0_239,negated_conjecture,
identity = sk_c7,
inference(spm,[status(thm)],[c_0_237,c_0_238]) ).
cnf(c_0_240,plain,
multiply(X1,sk_c7) = X1,
inference(rw,[status(thm)],[c_0_38,c_0_239]) ).
cnf(c_0_241,negated_conjecture,
sk_c7 = sk_c8,
inference(rw,[status(thm)],[c_0_235,c_0_240]) ).
cnf(c_0_242,plain,
multiply(inverse(X1),X1) = sk_c8,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_239]),c_0_241]) ).
cnf(c_0_243,negated_conjecture,
multiply(inverse(sk_c8),sk_c7) = sk_c7,
inference(spm,[status(thm)],[c_0_35,c_0_235]) ).
cnf(c_0_244,plain,
multiply(X1,sk_c8) = X1,
inference(rw,[status(thm)],[c_0_240,c_0_241]) ).
cnf(c_0_245,plain,
multiply(sk_c8,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_239]),c_0_241]) ).
cnf(c_0_246,plain,
multiply(X1,inverse(X1)) = sk_c8,
inference(spm,[status(thm)],[c_0_242,c_0_41]) ).
cnf(c_0_247,negated_conjecture,
inverse(sk_c8) = sk_c8,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_243,c_0_240]),c_0_241]) ).
cnf(c_0_248,negated_conjecture,
inverse(X1) != sk_c8,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(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_71,c_0_232]),c_0_232]),c_0_232]),c_0_244]),c_0_245]),c_0_241]),c_0_240]),c_0_240]),c_0_241]),c_0_240]),c_0_241]),c_0_246]),c_0_244]),c_0_241]),c_0_247]),c_0_241])])])]),c_0_247])]) ).
cnf(c_0_249,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_247,c_0_248]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP357-1 : TPTP v8.1.2. Released v2.5.0.
% 0.03/0.15 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n014.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 16:00:23 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.22/0.50 Running first-order theorem proving
% 0.22/0.50 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.cVtpZxqHMA/E---3.1_8246.p
% 4.72/1.12 # Version: 3.1.0
% 4.72/1.12 # Preprocessing class: FSMSSMSMSSSNFFN.
% 4.72/1.12 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.72/1.12 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 4.72/1.12 # Starting new_bool_3 with 300s (1) cores
% 4.72/1.12 # Starting new_bool_1 with 300s (1) cores
% 4.72/1.12 # Starting sh5l with 300s (1) cores
% 4.72/1.12 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 8334 completed with status 0
% 4.72/1.12 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 4.72/1.12 # Preprocessing class: FSMSSMSMSSSNFFN.
% 4.72/1.12 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.72/1.12 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 4.72/1.12 # No SInE strategy applied
% 4.72/1.12 # Search class: FGHPS-FFMM21-SFFFFFNN
% 4.72/1.12 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 4.72/1.12 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 4.72/1.12 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 4.72/1.12 # Starting new_bool_3 with 136s (1) cores
% 4.72/1.12 # Starting new_bool_1 with 136s (1) cores
% 4.72/1.12 # Starting sh5l with 136s (1) cores
% 4.72/1.12 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 8340 completed with status 0
% 4.72/1.12 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 4.72/1.12 # Preprocessing class: FSMSSMSMSSSNFFN.
% 4.72/1.12 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.72/1.12 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 4.72/1.12 # No SInE strategy applied
% 4.72/1.12 # Search class: FGHPS-FFMM21-SFFFFFNN
% 4.72/1.12 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 4.72/1.12 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 4.72/1.12 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 4.72/1.12 # Preprocessing time : 0.001 s
% 4.72/1.12 # Presaturation interreduction done
% 4.72/1.12
% 4.72/1.12 # Proof found!
% 4.72/1.12 # SZS status Unsatisfiable
% 4.72/1.12 # SZS output start CNFRefutation
% See solution above
% 4.72/1.12 # Parsed axioms : 34
% 4.72/1.12 # Removed by relevancy pruning/SinE : 0
% 4.72/1.12 # Initial clauses : 34
% 4.72/1.12 # Removed in clause preprocessing : 0
% 4.72/1.12 # Initial clauses in saturation : 34
% 4.72/1.12 # Processed clauses : 9831
% 4.72/1.12 # ...of these trivial : 358
% 4.72/1.12 # ...subsumed : 7641
% 4.72/1.12 # ...remaining for further processing : 1832
% 4.72/1.12 # Other redundant clauses eliminated : 38
% 4.72/1.12 # Clauses deleted for lack of memory : 0
% 4.72/1.12 # Backward-subsumed : 619
% 4.72/1.12 # Backward-rewritten : 1141
% 4.72/1.12 # Generated clauses : 59621
% 4.72/1.12 # ...of the previous two non-redundant : 59479
% 4.72/1.12 # ...aggressively subsumed : 0
% 4.72/1.12 # Contextual simplify-reflections : 23
% 4.72/1.12 # Paramodulations : 59531
% 4.72/1.12 # Factorizations : 54
% 4.72/1.12 # NegExts : 0
% 4.72/1.12 # Equation resolutions : 38
% 4.72/1.12 # Disequality decompositions : 0
% 4.72/1.12 # Total rewrite steps : 9662
% 4.72/1.12 # ...of those cached : 9336
% 4.72/1.12 # Propositional unsat checks : 0
% 4.72/1.12 # Propositional check models : 0
% 4.72/1.12 # Propositional check unsatisfiable : 0
% 4.72/1.12 # Propositional clauses : 0
% 4.72/1.12 # Propositional clauses after purity: 0
% 4.72/1.12 # Propositional unsat core size : 0
% 4.72/1.12 # Propositional preprocessing time : 0.000
% 4.72/1.12 # Propositional encoding time : 0.000
% 4.72/1.12 # Propositional solver time : 0.000
% 4.72/1.12 # Success case prop preproc time : 0.000
% 4.72/1.12 # Success case prop encoding time : 0.000
% 4.72/1.12 # Success case prop solver time : 0.000
% 4.72/1.12 # Current number of processed clauses : 28
% 4.72/1.12 # Positive orientable unit clauses : 20
% 4.72/1.12 # Positive unorientable unit clauses: 0
% 4.72/1.12 # Negative unit clauses : 1
% 4.72/1.12 # Non-unit-clauses : 7
% 4.72/1.12 # Current number of unprocessed clauses: 15041
% 4.72/1.12 # ...number of literals in the above : 98942
% 4.72/1.12 # Current number of archived formulas : 0
% 4.72/1.12 # Current number of archived clauses : 1798
% 4.72/1.12 # Clause-clause subsumption calls (NU) : 75532
% 4.72/1.12 # Rec. Clause-clause subsumption calls : 25353
% 4.72/1.12 # Non-unit clause-clause subsumptions : 8254
% 4.72/1.12 # Unit Clause-clause subsumption calls : 693
% 4.72/1.12 # Rewrite failures with RHS unbound : 0
% 4.72/1.12 # BW rewrite match attempts : 62
% 4.72/1.12 # BW rewrite match successes : 52
% 4.72/1.12 # Condensation attempts : 0
% 4.72/1.12 # Condensation successes : 0
% 4.72/1.12 # Termbank termtop insertions : 694099
% 4.72/1.12 # Search garbage collected termcells : 29
% 4.72/1.12
% 4.72/1.12 # -------------------------------------------------
% 4.72/1.12 # User time : 0.567 s
% 4.72/1.12 # System time : 0.027 s
% 4.72/1.12 # Total time : 0.594 s
% 4.72/1.12 # Maximum resident set size: 1684 pages
% 4.72/1.12
% 4.72/1.12 # -------------------------------------------------
% 4.72/1.12 # User time : 2.903 s
% 4.72/1.12 # System time : 0.060 s
% 4.72/1.12 # Total time : 2.962 s
% 4.72/1.12 # Maximum resident set size: 1752 pages
% 4.72/1.12 % E---3.1 exiting
% 4.72/1.12 % E exiting
%------------------------------------------------------------------------------