TSTP Solution File: GRP039-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP039-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 : 600s
% DateTime : Sat Jul 16 10:32:36 EDT 2022
% Result : Unsatisfiable 37.40s 37.68s
% Output : CNFRefutation 37.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 64
% Syntax : Number of clauses : 219 ( 97 unt; 18 nHn; 154 RR)
% Number of literals : 404 ( 303 equ; 161 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 177 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X ).
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity ).
cnf(associativity,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ).
cnf(closure_of_inverse,axiom,
( ~ subgroup_member(X)
| subgroup_member(inverse(X)) ) ).
cnf(closure_of_multiply,axiom,
( ~ subgroup_member(X)
| ~ subgroup_member(Y)
| multiply(X,Y) != Z
| subgroup_member(Z) ) ).
cnf(right_identity,axiom,
multiply(X,identity) = X ).
cnf(right_inverse,axiom,
multiply(X,inverse(X)) = identity ).
cnf(an_element_in_O2,axiom,
( subgroup_member(X)
| subgroup_member(Y)
| subgroup_member(element_in_O2(X,Y)) ) ).
cnf(property_of_O2,axiom,
( subgroup_member(X)
| subgroup_member(Y)
| multiply(X,element_in_O2(X,Y)) = Y ) ).
cnf(b_in_O2,negated_conjecture,
subgroup_member(b) ).
cnf(b_times_a_inverse_is_c,negated_conjecture,
multiply(b,inverse(a)) = c ).
cnf(a_times_c_is_d,negated_conjecture,
multiply(a,c) = d ).
cnf(prove_d_in_O2,negated_conjecture,
~ subgroup_member(d) ).
cnf(refute_0_0,plain,
( ~ subgroup_member(inverse(c))
| subgroup_member(inverse(inverse(c))) ),
inference(subst,[],[closure_of_inverse:[bind(X,$fot(inverse(c)))]]) ).
cnf(refute_0_1,plain,
( ~ subgroup_member(b)
| subgroup_member(inverse(b)) ),
inference(subst,[],[closure_of_inverse:[bind(X,$fot(b))]]) ).
cnf(refute_0_2,plain,
subgroup_member(inverse(b)),
inference(resolve,[$cnf( subgroup_member(b) )],[b_in_O2,refute_0_1]) ).
cnf(refute_0_3,plain,
( multiply(X,Y) != multiply(X,Y)
| ~ subgroup_member(X)
| ~ subgroup_member(Y)
| subgroup_member(multiply(X,Y)) ),
inference(subst,[],[closure_of_multiply:[bind(Z,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_4,plain,
multiply(X,Y) = multiply(X,Y),
introduced(tautology,[refl,[$fot(multiply(X,Y))]]) ).
cnf(refute_0_5,plain,
( ~ subgroup_member(X)
| ~ subgroup_member(Y)
| subgroup_member(multiply(X,Y)) ),
inference(resolve,[$cnf( $equal(multiply(X,Y),multiply(X,Y)) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ subgroup_member(X_52)
| ~ subgroup_member(inverse(b))
| subgroup_member(multiply(X_52,inverse(b))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_52)),bind(Y,$fot(inverse(b)))]]) ).
cnf(refute_0_7,plain,
( ~ subgroup_member(X_52)
| subgroup_member(multiply(X_52,inverse(b))) ),
inference(resolve,[$cnf( subgroup_member(inverse(b)) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ subgroup_member(a)
| subgroup_member(multiply(a,inverse(b))) ),
inference(subst,[],[refute_0_7:[bind(X_52,$fot(a))]]) ).
cnf(refute_0_9,plain,
( ~ subgroup_member(X_52)
| ~ subgroup_member(b)
| subgroup_member(multiply(X_52,b)) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_52)),bind(Y,$fot(b))]]) ).
cnf(refute_0_10,plain,
( ~ subgroup_member(X_52)
| subgroup_member(multiply(X_52,b)) ),
inference(resolve,[$cnf( subgroup_member(b) )],[b_in_O2,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ subgroup_member(inverse(c))
| subgroup_member(multiply(inverse(c),b)) ),
inference(subst,[],[refute_0_10:[bind(X_52,$fot(inverse(c)))]]) ).
cnf(refute_0_12,plain,
( subgroup_member(a)
| subgroup_member(d)
| subgroup_member(element_in_O2(d,a)) ),
inference(subst,[],[an_element_in_O2:[bind(X,$fot(d)),bind(Y,$fot(a))]]) ).
cnf(refute_0_13,plain,
multiply(multiply(inverse(X_7),X_7),X_8) = multiply(inverse(X_7),multiply(X_7,X_8)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_7))),bind(Y,$fot(X_7)),bind(Z,$fot(X_8))]]) ).
cnf(refute_0_14,plain,
multiply(inverse(X_7),X_7) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_7))]]) ).
cnf(refute_0_15,plain,
( multiply(multiply(inverse(X_7),X_7),X_8) != multiply(inverse(X_7),multiply(X_7,X_8))
| multiply(inverse(X_7),X_7) != identity
| multiply(identity,X_8) = multiply(inverse(X_7),multiply(X_7,X_8)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_7),X_7),X_8),multiply(inverse(X_7),multiply(X_7,X_8))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_16,plain,
( multiply(multiply(inverse(X_7),X_7),X_8) != multiply(inverse(X_7),multiply(X_7,X_8))
| multiply(identity,X_8) = multiply(inverse(X_7),multiply(X_7,X_8)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_7),X_7),identity) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
multiply(identity,X_8) = multiply(inverse(X_7),multiply(X_7,X_8)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_7),X_7),X_8),multiply(inverse(X_7),multiply(X_7,X_8))) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
multiply(identity,X_8) = X_8,
inference(subst,[],[left_identity:[bind(X,$fot(X_8))]]) ).
cnf(refute_0_19,plain,
( multiply(identity,X_8) != X_8
| multiply(identity,X_8) != multiply(inverse(X_7),multiply(X_7,X_8))
| X_8 = multiply(inverse(X_7),multiply(X_7,X_8)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_8),multiply(inverse(X_7),multiply(X_7,X_8))) ),[0],$fot(X_8)]]) ).
cnf(refute_0_20,plain,
( multiply(identity,X_8) != multiply(inverse(X_7),multiply(X_7,X_8))
| X_8 = multiply(inverse(X_7),multiply(X_7,X_8)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_8),X_8) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
X_8 = multiply(inverse(X_7),multiply(X_7,X_8)),
inference(resolve,[$cnf( $equal(multiply(identity,X_8),multiply(inverse(X_7),multiply(X_7,X_8))) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
multiply(X_7,inverse(multiply(X_19,X_7))) = multiply(inverse(X_19),multiply(X_19,multiply(X_7,inverse(multiply(X_19,X_7))))),
inference(subst,[],[refute_0_21:[bind(X_7,$fot(X_19)),bind(X_8,$fot(multiply(X_7,inverse(multiply(X_19,X_7)))))]]) ).
cnf(refute_0_23,plain,
multiply(multiply(X_6,X_7),inverse(multiply(X_6,X_7))) = identity,
inference(subst,[],[right_inverse:[bind(X,$fot(multiply(X_6,X_7)))]]) ).
cnf(refute_0_24,plain,
multiply(multiply(X_6,X_7),inverse(multiply(X_6,X_7))) = multiply(X_6,multiply(X_7,inverse(multiply(X_6,X_7)))),
inference(subst,[],[associativity:[bind(X,$fot(X_6)),bind(Y,$fot(X_7)),bind(Z,$fot(inverse(multiply(X_6,X_7))))]]) ).
cnf(refute_0_25,plain,
( multiply(multiply(X_6,X_7),inverse(multiply(X_6,X_7))) != multiply(X_6,multiply(X_7,inverse(multiply(X_6,X_7))))
| multiply(multiply(X_6,X_7),inverse(multiply(X_6,X_7))) != identity
| multiply(X_6,multiply(X_7,inverse(multiply(X_6,X_7)))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_6,X_7),inverse(multiply(X_6,X_7))),identity) ),[0],$fot(multiply(X_6,multiply(X_7,inverse(multiply(X_6,X_7)))))]]) ).
cnf(refute_0_26,plain,
( multiply(multiply(X_6,X_7),inverse(multiply(X_6,X_7))) != identity
| multiply(X_6,multiply(X_7,inverse(multiply(X_6,X_7)))) = identity ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_6,X_7),inverse(multiply(X_6,X_7))),multiply(X_6,multiply(X_7,inverse(multiply(X_6,X_7))))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
multiply(X_6,multiply(X_7,inverse(multiply(X_6,X_7)))) = identity,
inference(resolve,[$cnf( $equal(multiply(multiply(X_6,X_7),inverse(multiply(X_6,X_7))),identity) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
multiply(X_19,multiply(X_7,inverse(multiply(X_19,X_7)))) = identity,
inference(subst,[],[refute_0_27:[bind(X_6,$fot(X_19))]]) ).
cnf(refute_0_29,plain,
( multiply(X_19,multiply(X_7,inverse(multiply(X_19,X_7)))) != identity
| multiply(X_7,inverse(multiply(X_19,X_7))) != multiply(inverse(X_19),multiply(X_19,multiply(X_7,inverse(multiply(X_19,X_7)))))
| multiply(X_7,inverse(multiply(X_19,X_7))) = multiply(inverse(X_19),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_7,inverse(multiply(X_19,X_7))),multiply(inverse(X_19),multiply(X_19,multiply(X_7,inverse(multiply(X_19,X_7)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_30,plain,
( multiply(X_7,inverse(multiply(X_19,X_7))) != multiply(inverse(X_19),multiply(X_19,multiply(X_7,inverse(multiply(X_19,X_7)))))
| multiply(X_7,inverse(multiply(X_19,X_7))) = multiply(inverse(X_19),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_19,multiply(X_7,inverse(multiply(X_19,X_7)))),identity) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
multiply(X_7,inverse(multiply(X_19,X_7))) = multiply(inverse(X_19),identity),
inference(resolve,[$cnf( $equal(multiply(X_7,inverse(multiply(X_19,X_7))),multiply(inverse(X_19),multiply(X_19,multiply(X_7,inverse(multiply(X_19,X_7)))))) )],[refute_0_22,refute_0_30]) ).
cnf(refute_0_32,plain,
multiply(inverse(X_19),identity) = inverse(X_19),
inference(subst,[],[right_identity:[bind(X,$fot(inverse(X_19)))]]) ).
cnf(refute_0_33,plain,
( multiply(X_7,inverse(multiply(X_19,X_7))) != multiply(inverse(X_19),identity)
| multiply(inverse(X_19),identity) != inverse(X_19)
| multiply(X_7,inverse(multiply(X_19,X_7))) = inverse(X_19) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_7,inverse(multiply(X_19,X_7))),inverse(X_19)) ),[0],$fot(multiply(inverse(X_19),identity))]]) ).
cnf(refute_0_34,plain,
( multiply(X_7,inverse(multiply(X_19,X_7))) != multiply(inverse(X_19),identity)
| multiply(X_7,inverse(multiply(X_19,X_7))) = inverse(X_19) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_19),identity),inverse(X_19)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
multiply(X_7,inverse(multiply(X_19,X_7))) = inverse(X_19),
inference(resolve,[$cnf( $equal(multiply(X_7,inverse(multiply(X_19,X_7))),multiply(inverse(X_19),identity)) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
multiply(element_in_O2(d,a),inverse(multiply(c,element_in_O2(d,a)))) = inverse(c),
inference(subst,[],[refute_0_35:[bind(X_19,$fot(c)),bind(X_7,$fot(element_in_O2(d,a)))]]) ).
cnf(refute_0_37,plain,
multiply(c,X_8) = multiply(inverse(a),multiply(a,multiply(c,X_8))),
inference(subst,[],[refute_0_21:[bind(X_7,$fot(a)),bind(X_8,$fot(multiply(c,X_8)))]]) ).
cnf(refute_0_38,plain,
multiply(multiply(a,c),X_8) = multiply(a,multiply(c,X_8)),
inference(subst,[],[associativity:[bind(X,$fot(a)),bind(Y,$fot(c)),bind(Z,$fot(X_8))]]) ).
cnf(refute_0_39,plain,
( multiply(multiply(a,c),X_8) != multiply(a,multiply(c,X_8))
| multiply(a,c) != d
| multiply(d,X_8) = multiply(a,multiply(c,X_8)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(a,c),X_8),multiply(a,multiply(c,X_8))) ),[0,0],$fot(d)]]) ).
cnf(refute_0_40,plain,
( multiply(multiply(a,c),X_8) != multiply(a,multiply(c,X_8))
| multiply(d,X_8) = multiply(a,multiply(c,X_8)) ),
inference(resolve,[$cnf( $equal(multiply(a,c),d) )],[a_times_c_is_d,refute_0_39]) ).
cnf(refute_0_41,plain,
multiply(d,X_8) = multiply(a,multiply(c,X_8)),
inference(resolve,[$cnf( $equal(multiply(multiply(a,c),X_8),multiply(a,multiply(c,X_8))) )],[refute_0_38,refute_0_40]) ).
cnf(refute_0_42,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_43,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_44,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
( multiply(d,X_8) != multiply(a,multiply(c,X_8))
| multiply(a,multiply(c,X_8)) = multiply(d,X_8) ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(multiply(d,X_8))),bind(Y0,$fot(multiply(a,multiply(c,X_8))))]]) ).
cnf(refute_0_46,plain,
multiply(a,multiply(c,X_8)) = multiply(d,X_8),
inference(resolve,[$cnf( $equal(multiply(d,X_8),multiply(a,multiply(c,X_8))) )],[refute_0_41,refute_0_45]) ).
cnf(refute_0_47,plain,
( multiply(a,multiply(c,X_8)) != multiply(d,X_8)
| multiply(c,X_8) != multiply(inverse(a),multiply(a,multiply(c,X_8)))
| multiply(c,X_8) = multiply(inverse(a),multiply(d,X_8)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,X_8),multiply(inverse(a),multiply(a,multiply(c,X_8)))) ),[1,1],$fot(multiply(d,X_8))]]) ).
cnf(refute_0_48,plain,
( multiply(c,X_8) != multiply(inverse(a),multiply(a,multiply(c,X_8)))
| multiply(c,X_8) = multiply(inverse(a),multiply(d,X_8)) ),
inference(resolve,[$cnf( $equal(multiply(a,multiply(c,X_8)),multiply(d,X_8)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
multiply(c,X_8) = multiply(inverse(a),multiply(d,X_8)),
inference(resolve,[$cnf( $equal(multiply(c,X_8),multiply(inverse(a),multiply(a,multiply(c,X_8)))) )],[refute_0_37,refute_0_48]) ).
cnf(refute_0_50,plain,
multiply(c,element_in_O2(d,X_126)) = multiply(inverse(a),multiply(d,element_in_O2(d,X_126))),
inference(subst,[],[refute_0_49:[bind(X_8,$fot(element_in_O2(d,X_126)))]]) ).
cnf(refute_0_51,plain,
( multiply(d,element_in_O2(d,X_126)) = X_126
| subgroup_member(X_126)
| subgroup_member(d) ),
inference(subst,[],[property_of_O2:[bind(X,$fot(d)),bind(Y,$fot(X_126))]]) ).
cnf(refute_0_52,plain,
( multiply(c,element_in_O2(d,X_126)) != multiply(inverse(a),multiply(d,element_in_O2(d,X_126)))
| multiply(d,element_in_O2(d,X_126)) != X_126
| multiply(c,element_in_O2(d,X_126)) = multiply(inverse(a),X_126) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,element_in_O2(d,X_126)),multiply(inverse(a),multiply(d,element_in_O2(d,X_126)))) ),[1,1],$fot(X_126)]]) ).
cnf(refute_0_53,plain,
( multiply(c,element_in_O2(d,X_126)) != multiply(inverse(a),multiply(d,element_in_O2(d,X_126)))
| multiply(c,element_in_O2(d,X_126)) = multiply(inverse(a),X_126)
| subgroup_member(X_126)
| subgroup_member(d) ),
inference(resolve,[$cnf( $equal(multiply(d,element_in_O2(d,X_126)),X_126) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
( multiply(c,element_in_O2(d,X_126)) = multiply(inverse(a),X_126)
| subgroup_member(X_126)
| subgroup_member(d) ),
inference(resolve,[$cnf( $equal(multiply(c,element_in_O2(d,X_126)),multiply(inverse(a),multiply(d,element_in_O2(d,X_126)))) )],[refute_0_50,refute_0_53]) ).
cnf(refute_0_55,plain,
( multiply(c,element_in_O2(d,X_126)) = multiply(inverse(a),X_126)
| subgroup_member(X_126) ),
inference(resolve,[$cnf( subgroup_member(d) )],[refute_0_54,prove_d_in_O2]) ).
cnf(refute_0_56,plain,
( multiply(c,element_in_O2(d,inverse(inverse(a)))) = multiply(inverse(a),inverse(inverse(a)))
| subgroup_member(inverse(inverse(a))) ),
inference(subst,[],[refute_0_55:[bind(X_126,$fot(inverse(inverse(a))))]]) ).
cnf(refute_0_57,plain,
multiply(inverse(a),inverse(inverse(a))) = identity,
inference(subst,[],[right_inverse:[bind(X,$fot(inverse(a)))]]) ).
cnf(refute_0_58,plain,
( multiply(c,element_in_O2(d,inverse(inverse(a)))) != multiply(inverse(a),inverse(inverse(a)))
| multiply(inverse(a),inverse(inverse(a))) != identity
| multiply(c,element_in_O2(d,inverse(inverse(a)))) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(c,element_in_O2(d,inverse(inverse(a)))),identity) ),[0],$fot(multiply(inverse(a),inverse(inverse(a))))]]) ).
cnf(refute_0_59,plain,
( multiply(c,element_in_O2(d,inverse(inverse(a)))) != multiply(inverse(a),inverse(inverse(a)))
| multiply(c,element_in_O2(d,inverse(inverse(a)))) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),inverse(inverse(a))),identity) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
( multiply(c,element_in_O2(d,inverse(inverse(a)))) = identity
| subgroup_member(inverse(inverse(a))) ),
inference(resolve,[$cnf( $equal(multiply(c,element_in_O2(d,inverse(inverse(a)))),multiply(inverse(a),inverse(inverse(a)))) )],[refute_0_56,refute_0_59]) ).
cnf(refute_0_61,plain,
multiply(multiply(X_6,inverse(X_6)),X_8) = multiply(X_6,multiply(inverse(X_6),X_8)),
inference(subst,[],[associativity:[bind(X,$fot(X_6)),bind(Y,$fot(inverse(X_6))),bind(Z,$fot(X_8))]]) ).
cnf(refute_0_62,plain,
multiply(X_6,inverse(X_6)) = identity,
inference(subst,[],[right_inverse:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_63,plain,
( multiply(X_6,inverse(X_6)) != identity
| multiply(multiply(X_6,inverse(X_6)),X_8) != multiply(X_6,multiply(inverse(X_6),X_8))
| multiply(identity,X_8) = multiply(X_6,multiply(inverse(X_6),X_8)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_6,inverse(X_6)),X_8),multiply(X_6,multiply(inverse(X_6),X_8))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_64,plain,
( multiply(multiply(X_6,inverse(X_6)),X_8) != multiply(X_6,multiply(inverse(X_6),X_8))
| multiply(identity,X_8) = multiply(X_6,multiply(inverse(X_6),X_8)) ),
inference(resolve,[$cnf( $equal(multiply(X_6,inverse(X_6)),identity) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
multiply(identity,X_8) = multiply(X_6,multiply(inverse(X_6),X_8)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_6,inverse(X_6)),X_8),multiply(X_6,multiply(inverse(X_6),X_8))) )],[refute_0_61,refute_0_64]) ).
cnf(refute_0_66,plain,
( multiply(identity,X_8) != X_8
| multiply(identity,X_8) != multiply(X_6,multiply(inverse(X_6),X_8))
| X_8 = multiply(X_6,multiply(inverse(X_6),X_8)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_8),multiply(X_6,multiply(inverse(X_6),X_8))) ),[0],$fot(X_8)]]) ).
cnf(refute_0_67,plain,
( multiply(identity,X_8) != multiply(X_6,multiply(inverse(X_6),X_8))
| X_8 = multiply(X_6,multiply(inverse(X_6),X_8)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_8),X_8) )],[refute_0_18,refute_0_66]) ).
cnf(refute_0_68,plain,
X_8 = multiply(X_6,multiply(inverse(X_6),X_8)),
inference(resolve,[$cnf( $equal(multiply(identity,X_8),multiply(X_6,multiply(inverse(X_6),X_8))) )],[refute_0_65,refute_0_67]) ).
cnf(refute_0_69,plain,
inverse(inverse(X_9)) = multiply(X_9,multiply(inverse(X_9),inverse(inverse(X_9)))),
inference(subst,[],[refute_0_68:[bind(X_6,$fot(X_9)),bind(X_8,$fot(inverse(inverse(X_9))))]]) ).
cnf(refute_0_70,plain,
multiply(inverse(X_9),inverse(inverse(X_9))) = identity,
inference(subst,[],[right_inverse:[bind(X,$fot(inverse(X_9)))]]) ).
cnf(refute_0_71,plain,
( multiply(inverse(X_9),inverse(inverse(X_9))) != identity
| inverse(inverse(X_9)) != multiply(X_9,multiply(inverse(X_9),inverse(inverse(X_9))))
| inverse(inverse(X_9)) = multiply(X_9,identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_9)),multiply(X_9,multiply(inverse(X_9),inverse(inverse(X_9))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_72,plain,
( inverse(inverse(X_9)) != multiply(X_9,multiply(inverse(X_9),inverse(inverse(X_9))))
| inverse(inverse(X_9)) = multiply(X_9,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_9),inverse(inverse(X_9))),identity) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
inverse(inverse(X_9)) = multiply(X_9,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(X_9)),multiply(X_9,multiply(inverse(X_9),inverse(inverse(X_9))))) )],[refute_0_69,refute_0_72]) ).
cnf(refute_0_74,plain,
multiply(X_9,identity) = X_9,
inference(subst,[],[right_identity:[bind(X,$fot(X_9))]]) ).
cnf(refute_0_75,plain,
( multiply(X_9,identity) != X_9
| inverse(inverse(X_9)) != multiply(X_9,identity)
| inverse(inverse(X_9)) = X_9 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_9)),multiply(X_9,identity)) ),[1],$fot(X_9)]]) ).
cnf(refute_0_76,plain,
( inverse(inverse(X_9)) != multiply(X_9,identity)
| inverse(inverse(X_9)) = X_9 ),
inference(resolve,[$cnf( $equal(multiply(X_9,identity),X_9) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
inverse(inverse(X_9)) = X_9,
inference(resolve,[$cnf( $equal(inverse(inverse(X_9)),multiply(X_9,identity)) )],[refute_0_73,refute_0_76]) ).
cnf(refute_0_78,plain,
inverse(inverse(a)) = a,
inference(subst,[],[refute_0_77:[bind(X_9,$fot(a))]]) ).
cnf(refute_0_79,plain,
element_in_O2(d,inverse(inverse(a))) = element_in_O2(d,inverse(inverse(a))),
introduced(tautology,[refl,[$fot(element_in_O2(d,inverse(inverse(a))))]]) ).
cnf(refute_0_80,plain,
( element_in_O2(d,inverse(inverse(a))) != element_in_O2(d,inverse(inverse(a)))
| inverse(inverse(a)) != a
| element_in_O2(d,inverse(inverse(a))) = element_in_O2(d,a) ),
introduced(tautology,[equality,[$cnf( $equal(element_in_O2(d,inverse(inverse(a))),element_in_O2(d,inverse(inverse(a)))) ),[1,1],$fot(a)]]) ).
cnf(refute_0_81,plain,
( inverse(inverse(a)) != a
| element_in_O2(d,inverse(inverse(a))) = element_in_O2(d,a) ),
inference(resolve,[$cnf( $equal(element_in_O2(d,inverse(inverse(a))),element_in_O2(d,inverse(inverse(a)))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
element_in_O2(d,inverse(inverse(a))) = element_in_O2(d,a),
inference(resolve,[$cnf( $equal(inverse(inverse(a)),a) )],[refute_0_78,refute_0_81]) ).
cnf(refute_0_83,plain,
multiply(c,element_in_O2(d,inverse(inverse(a)))) = multiply(c,element_in_O2(d,inverse(inverse(a)))),
introduced(tautology,[refl,[$fot(multiply(c,element_in_O2(d,inverse(inverse(a)))))]]) ).
cnf(refute_0_84,plain,
( multiply(c,element_in_O2(d,inverse(inverse(a)))) != multiply(c,element_in_O2(d,inverse(inverse(a))))
| element_in_O2(d,inverse(inverse(a))) != element_in_O2(d,a)
| multiply(c,element_in_O2(d,inverse(inverse(a)))) = multiply(c,element_in_O2(d,a)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,element_in_O2(d,inverse(inverse(a)))),multiply(c,element_in_O2(d,inverse(inverse(a))))) ),[1,1],$fot(element_in_O2(d,a))]]) ).
cnf(refute_0_85,plain,
( element_in_O2(d,inverse(inverse(a))) != element_in_O2(d,a)
| multiply(c,element_in_O2(d,inverse(inverse(a)))) = multiply(c,element_in_O2(d,a)) ),
inference(resolve,[$cnf( $equal(multiply(c,element_in_O2(d,inverse(inverse(a)))),multiply(c,element_in_O2(d,inverse(inverse(a))))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
multiply(c,element_in_O2(d,inverse(inverse(a)))) = multiply(c,element_in_O2(d,a)),
inference(resolve,[$cnf( $equal(element_in_O2(d,inverse(inverse(a))),element_in_O2(d,a)) )],[refute_0_82,refute_0_85]) ).
cnf(refute_0_87,plain,
( multiply(c,element_in_O2(d,inverse(inverse(a)))) != multiply(c,element_in_O2(d,a))
| multiply(c,element_in_O2(d,inverse(inverse(a)))) != identity
| multiply(c,element_in_O2(d,a)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,element_in_O2(d,inverse(inverse(a)))),identity) ),[0],$fot(multiply(c,element_in_O2(d,a)))]]) ).
cnf(refute_0_88,plain,
( multiply(c,element_in_O2(d,inverse(inverse(a)))) != identity
| multiply(c,element_in_O2(d,a)) = identity ),
inference(resolve,[$cnf( $equal(multiply(c,element_in_O2(d,inverse(inverse(a)))),multiply(c,element_in_O2(d,a))) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
( multiply(c,element_in_O2(d,a)) = identity
| subgroup_member(inverse(inverse(a))) ),
inference(resolve,[$cnf( $equal(multiply(c,element_in_O2(d,inverse(inverse(a)))),identity) )],[refute_0_60,refute_0_88]) ).
cnf(refute_0_90,plain,
( inverse(inverse(a)) != a
| ~ subgroup_member(inverse(inverse(a)))
| subgroup_member(a) ),
introduced(tautology,[equality,[$cnf( subgroup_member(inverse(inverse(a))) ),[0],$fot(a)]]) ).
cnf(refute_0_91,plain,
( ~ subgroup_member(inverse(inverse(a)))
| subgroup_member(a) ),
inference(resolve,[$cnf( $equal(inverse(inverse(a)),a) )],[refute_0_78,refute_0_90]) ).
cnf(refute_0_92,plain,
( multiply(c,element_in_O2(d,a)) = identity
| subgroup_member(a) ),
inference(resolve,[$cnf( subgroup_member(inverse(inverse(a))) )],[refute_0_89,refute_0_91]) ).
cnf(refute_0_93,plain,
( multiply(c,element_in_O2(d,a)) != identity
| multiply(element_in_O2(d,a),inverse(multiply(c,element_in_O2(d,a)))) != inverse(c)
| multiply(element_in_O2(d,a),inverse(identity)) = inverse(c) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(element_in_O2(d,a),inverse(multiply(c,element_in_O2(d,a)))),inverse(c)) ),[0,1,0],$fot(identity)]]) ).
cnf(refute_0_94,plain,
( multiply(element_in_O2(d,a),inverse(multiply(c,element_in_O2(d,a)))) != inverse(c)
| multiply(element_in_O2(d,a),inverse(identity)) = inverse(c)
| subgroup_member(a) ),
inference(resolve,[$cnf( $equal(multiply(c,element_in_O2(d,a)),identity) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
( multiply(element_in_O2(d,a),inverse(identity)) = inverse(c)
| subgroup_member(a) ),
inference(resolve,[$cnf( $equal(multiply(element_in_O2(d,a),inverse(multiply(c,element_in_O2(d,a)))),inverse(c)) )],[refute_0_36,refute_0_94]) ).
cnf(refute_0_96,plain,
multiply(element_in_O2(d,a),identity) = element_in_O2(d,a),
inference(subst,[],[right_identity:[bind(X,$fot(element_in_O2(d,a)))]]) ).
cnf(refute_0_97,plain,
multiply(identity,inverse(identity)) = identity,
inference(subst,[],[right_inverse:[bind(X,$fot(identity))]]) ).
cnf(refute_0_98,plain,
multiply(identity,inverse(identity)) = inverse(identity),
inference(subst,[],[left_identity:[bind(X,$fot(inverse(identity)))]]) ).
cnf(refute_0_99,plain,
( multiply(identity,inverse(identity)) != identity
| multiply(identity,inverse(identity)) != inverse(identity)
| inverse(identity) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,inverse(identity)),identity) ),[0],$fot(inverse(identity))]]) ).
cnf(refute_0_100,plain,
( multiply(identity,inverse(identity)) != identity
| inverse(identity) = identity ),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(identity)),inverse(identity)) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
inverse(identity) = identity,
inference(resolve,[$cnf( $equal(multiply(identity,inverse(identity)),identity) )],[refute_0_97,refute_0_100]) ).
cnf(refute_0_102,plain,
multiply(element_in_O2(d,a),inverse(identity)) = multiply(element_in_O2(d,a),inverse(identity)),
introduced(tautology,[refl,[$fot(multiply(element_in_O2(d,a),inverse(identity)))]]) ).
cnf(refute_0_103,plain,
( multiply(element_in_O2(d,a),inverse(identity)) != multiply(element_in_O2(d,a),inverse(identity))
| inverse(identity) != identity
| multiply(element_in_O2(d,a),inverse(identity)) = multiply(element_in_O2(d,a),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(element_in_O2(d,a),inverse(identity)),multiply(element_in_O2(d,a),inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_104,plain,
( inverse(identity) != identity
| multiply(element_in_O2(d,a),inverse(identity)) = multiply(element_in_O2(d,a),identity) ),
inference(resolve,[$cnf( $equal(multiply(element_in_O2(d,a),inverse(identity)),multiply(element_in_O2(d,a),inverse(identity))) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
multiply(element_in_O2(d,a),inverse(identity)) = multiply(element_in_O2(d,a),identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_101,refute_0_104]) ).
cnf(refute_0_106,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_107,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_44,refute_0_106]) ).
cnf(refute_0_108,plain,
( multiply(element_in_O2(d,a),identity) != element_in_O2(d,a)
| multiply(element_in_O2(d,a),inverse(identity)) != multiply(element_in_O2(d,a),identity)
| multiply(element_in_O2(d,a),inverse(identity)) = element_in_O2(d,a) ),
inference(subst,[],[refute_0_107:[bind(X0,$fot(multiply(element_in_O2(d,a),inverse(identity)))),bind(Y0,$fot(multiply(element_in_O2(d,a),identity))),bind(Z0,$fot(element_in_O2(d,a)))]]) ).
cnf(refute_0_109,plain,
( multiply(element_in_O2(d,a),identity) != element_in_O2(d,a)
| multiply(element_in_O2(d,a),inverse(identity)) = element_in_O2(d,a) ),
inference(resolve,[$cnf( $equal(multiply(element_in_O2(d,a),inverse(identity)),multiply(element_in_O2(d,a),identity)) )],[refute_0_105,refute_0_108]) ).
cnf(refute_0_110,plain,
multiply(element_in_O2(d,a),inverse(identity)) = element_in_O2(d,a),
inference(resolve,[$cnf( $equal(multiply(element_in_O2(d,a),identity),element_in_O2(d,a)) )],[refute_0_96,refute_0_109]) ).
cnf(refute_0_111,plain,
( multiply(element_in_O2(d,a),inverse(identity)) != element_in_O2(d,a)
| multiply(element_in_O2(d,a),inverse(identity)) != inverse(c)
| element_in_O2(d,a) = inverse(c) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(element_in_O2(d,a),inverse(identity)),inverse(c)) ),[0],$fot(element_in_O2(d,a))]]) ).
cnf(refute_0_112,plain,
( multiply(element_in_O2(d,a),inverse(identity)) != inverse(c)
| element_in_O2(d,a) = inverse(c) ),
inference(resolve,[$cnf( $equal(multiply(element_in_O2(d,a),inverse(identity)),element_in_O2(d,a)) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
( element_in_O2(d,a) = inverse(c)
| subgroup_member(a) ),
inference(resolve,[$cnf( $equal(multiply(element_in_O2(d,a),inverse(identity)),inverse(c)) )],[refute_0_95,refute_0_112]) ).
cnf(refute_0_114,plain,
( element_in_O2(d,a) != inverse(c)
| ~ subgroup_member(element_in_O2(d,a))
| subgroup_member(inverse(c)) ),
introduced(tautology,[equality,[$cnf( subgroup_member(element_in_O2(d,a)) ),[0],$fot(inverse(c))]]) ).
cnf(refute_0_115,plain,
( ~ subgroup_member(element_in_O2(d,a))
| subgroup_member(a)
| subgroup_member(inverse(c)) ),
inference(resolve,[$cnf( $equal(element_in_O2(d,a),inverse(c)) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
( subgroup_member(a)
| subgroup_member(d)
| subgroup_member(inverse(c)) ),
inference(resolve,[$cnf( subgroup_member(element_in_O2(d,a)) )],[refute_0_12,refute_0_115]) ).
cnf(refute_0_117,plain,
( subgroup_member(a)
| subgroup_member(inverse(c)) ),
inference(resolve,[$cnf( subgroup_member(d) )],[refute_0_116,prove_d_in_O2]) ).
cnf(refute_0_118,plain,
( subgroup_member(multiply(inverse(c),b))
| subgroup_member(a) ),
inference(resolve,[$cnf( subgroup_member(inverse(c)) )],[refute_0_117,refute_0_11]) ).
cnf(refute_0_119,plain,
a = multiply(inverse(c),multiply(c,a)),
inference(subst,[],[refute_0_21:[bind(X_7,$fot(c)),bind(X_8,$fot(a))]]) ).
cnf(refute_0_120,plain,
multiply(multiply(b,inverse(a)),X_8) = multiply(b,multiply(inverse(a),X_8)),
inference(subst,[],[associativity:[bind(X,$fot(b)),bind(Y,$fot(inverse(a))),bind(Z,$fot(X_8))]]) ).
cnf(refute_0_121,plain,
( multiply(multiply(b,inverse(a)),X_8) != multiply(b,multiply(inverse(a),X_8))
| multiply(b,inverse(a)) != c
| multiply(c,X_8) = multiply(b,multiply(inverse(a),X_8)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(b,inverse(a)),X_8),multiply(b,multiply(inverse(a),X_8))) ),[0,0],$fot(c)]]) ).
cnf(refute_0_122,plain,
( multiply(multiply(b,inverse(a)),X_8) != multiply(b,multiply(inverse(a),X_8))
| multiply(c,X_8) = multiply(b,multiply(inverse(a),X_8)) ),
inference(resolve,[$cnf( $equal(multiply(b,inverse(a)),c) )],[b_times_a_inverse_is_c,refute_0_121]) ).
cnf(refute_0_123,plain,
multiply(c,X_8) = multiply(b,multiply(inverse(a),X_8)),
inference(resolve,[$cnf( $equal(multiply(multiply(b,inverse(a)),X_8),multiply(b,multiply(inverse(a),X_8))) )],[refute_0_120,refute_0_122]) ).
cnf(refute_0_124,plain,
multiply(c,multiply(X_7,inverse(multiply(inverse(a),X_7)))) = multiply(b,multiply(inverse(a),multiply(X_7,inverse(multiply(inverse(a),X_7))))),
inference(subst,[],[refute_0_123:[bind(X_8,$fot(multiply(X_7,inverse(multiply(inverse(a),X_7)))))]]) ).
cnf(refute_0_125,plain,
multiply(inverse(a),multiply(X_7,inverse(multiply(inverse(a),X_7)))) = identity,
inference(subst,[],[refute_0_27:[bind(X_6,$fot(inverse(a)))]]) ).
cnf(refute_0_126,plain,
( multiply(c,multiply(X_7,inverse(multiply(inverse(a),X_7)))) != multiply(b,multiply(inverse(a),multiply(X_7,inverse(multiply(inverse(a),X_7)))))
| multiply(inverse(a),multiply(X_7,inverse(multiply(inverse(a),X_7)))) != identity
| multiply(c,multiply(X_7,inverse(multiply(inverse(a),X_7)))) = multiply(b,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,multiply(X_7,inverse(multiply(inverse(a),X_7)))),multiply(b,multiply(inverse(a),multiply(X_7,inverse(multiply(inverse(a),X_7)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_127,plain,
( multiply(c,multiply(X_7,inverse(multiply(inverse(a),X_7)))) != multiply(b,multiply(inverse(a),multiply(X_7,inverse(multiply(inverse(a),X_7)))))
| multiply(c,multiply(X_7,inverse(multiply(inverse(a),X_7)))) = multiply(b,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),multiply(X_7,inverse(multiply(inverse(a),X_7)))),identity) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
multiply(c,multiply(X_7,inverse(multiply(inverse(a),X_7)))) = multiply(b,identity),
inference(resolve,[$cnf( $equal(multiply(c,multiply(X_7,inverse(multiply(inverse(a),X_7)))),multiply(b,multiply(inverse(a),multiply(X_7,inverse(multiply(inverse(a),X_7)))))) )],[refute_0_124,refute_0_127]) ).
cnf(refute_0_129,plain,
multiply(X_13,inverse(multiply(inverse(X_6),X_13))) = multiply(X_6,multiply(inverse(X_6),multiply(X_13,inverse(multiply(inverse(X_6),X_13))))),
inference(subst,[],[refute_0_68:[bind(X_8,$fot(multiply(X_13,inverse(multiply(inverse(X_6),X_13)))))]]) ).
cnf(refute_0_130,plain,
multiply(inverse(X_6),multiply(X_13,inverse(multiply(inverse(X_6),X_13)))) = identity,
inference(subst,[],[refute_0_27:[bind(X_6,$fot(inverse(X_6))),bind(X_7,$fot(X_13))]]) ).
cnf(refute_0_131,plain,
( multiply(X_13,inverse(multiply(inverse(X_6),X_13))) != multiply(X_6,multiply(inverse(X_6),multiply(X_13,inverse(multiply(inverse(X_6),X_13)))))
| multiply(inverse(X_6),multiply(X_13,inverse(multiply(inverse(X_6),X_13)))) != identity
| multiply(X_13,inverse(multiply(inverse(X_6),X_13))) = multiply(X_6,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_13,inverse(multiply(inverse(X_6),X_13))),multiply(X_6,multiply(inverse(X_6),multiply(X_13,inverse(multiply(inverse(X_6),X_13)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_132,plain,
( multiply(X_13,inverse(multiply(inverse(X_6),X_13))) != multiply(X_6,multiply(inverse(X_6),multiply(X_13,inverse(multiply(inverse(X_6),X_13)))))
| multiply(X_13,inverse(multiply(inverse(X_6),X_13))) = multiply(X_6,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_6),multiply(X_13,inverse(multiply(inverse(X_6),X_13)))),identity) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
multiply(X_13,inverse(multiply(inverse(X_6),X_13))) = multiply(X_6,identity),
inference(resolve,[$cnf( $equal(multiply(X_13,inverse(multiply(inverse(X_6),X_13))),multiply(X_6,multiply(inverse(X_6),multiply(X_13,inverse(multiply(inverse(X_6),X_13)))))) )],[refute_0_129,refute_0_132]) ).
cnf(refute_0_134,plain,
multiply(X_6,identity) = X_6,
inference(subst,[],[right_identity:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_135,plain,
( multiply(X_13,inverse(multiply(inverse(X_6),X_13))) != multiply(X_6,identity)
| multiply(X_6,identity) != X_6
| multiply(X_13,inverse(multiply(inverse(X_6),X_13))) = X_6 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_13,inverse(multiply(inverse(X_6),X_13))),X_6) ),[0],$fot(multiply(X_6,identity))]]) ).
cnf(refute_0_136,plain,
( multiply(X_13,inverse(multiply(inverse(X_6),X_13))) != multiply(X_6,identity)
| multiply(X_13,inverse(multiply(inverse(X_6),X_13))) = X_6 ),
inference(resolve,[$cnf( $equal(multiply(X_6,identity),X_6) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
multiply(X_13,inverse(multiply(inverse(X_6),X_13))) = X_6,
inference(resolve,[$cnf( $equal(multiply(X_13,inverse(multiply(inverse(X_6),X_13))),multiply(X_6,identity)) )],[refute_0_133,refute_0_136]) ).
cnf(refute_0_138,plain,
multiply(X_7,inverse(multiply(inverse(a),X_7))) = a,
inference(subst,[],[refute_0_137:[bind(X_13,$fot(X_7)),bind(X_6,$fot(a))]]) ).
cnf(refute_0_139,plain,
multiply(c,multiply(X_7,inverse(multiply(inverse(a),X_7)))) = multiply(c,multiply(X_7,inverse(multiply(inverse(a),X_7)))),
introduced(tautology,[refl,[$fot(multiply(c,multiply(X_7,inverse(multiply(inverse(a),X_7)))))]]) ).
cnf(refute_0_140,plain,
( multiply(X_7,inverse(multiply(inverse(a),X_7))) != a
| multiply(c,multiply(X_7,inverse(multiply(inverse(a),X_7)))) != multiply(c,multiply(X_7,inverse(multiply(inverse(a),X_7))))
| multiply(c,multiply(X_7,inverse(multiply(inverse(a),X_7)))) = multiply(c,a) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,multiply(X_7,inverse(multiply(inverse(a),X_7)))),multiply(c,multiply(X_7,inverse(multiply(inverse(a),X_7))))) ),[1,1],$fot(a)]]) ).
cnf(refute_0_141,plain,
( multiply(X_7,inverse(multiply(inverse(a),X_7))) != a
| multiply(c,multiply(X_7,inverse(multiply(inverse(a),X_7)))) = multiply(c,a) ),
inference(resolve,[$cnf( $equal(multiply(c,multiply(X_7,inverse(multiply(inverse(a),X_7)))),multiply(c,multiply(X_7,inverse(multiply(inverse(a),X_7))))) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
multiply(c,multiply(X_7,inverse(multiply(inverse(a),X_7)))) = multiply(c,a),
inference(resolve,[$cnf( $equal(multiply(X_7,inverse(multiply(inverse(a),X_7))),a) )],[refute_0_138,refute_0_141]) ).
cnf(refute_0_143,plain,
( multiply(c,multiply(X_7,inverse(multiply(inverse(a),X_7)))) != multiply(b,identity)
| multiply(c,multiply(X_7,inverse(multiply(inverse(a),X_7)))) != multiply(c,a)
| multiply(c,a) = multiply(b,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,multiply(X_7,inverse(multiply(inverse(a),X_7)))),multiply(b,identity)) ),[0],$fot(multiply(c,a))]]) ).
cnf(refute_0_144,plain,
( multiply(c,multiply(X_7,inverse(multiply(inverse(a),X_7)))) != multiply(b,identity)
| multiply(c,a) = multiply(b,identity) ),
inference(resolve,[$cnf( $equal(multiply(c,multiply(X_7,inverse(multiply(inverse(a),X_7)))),multiply(c,a)) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
multiply(b,identity) = b,
inference(subst,[],[right_identity:[bind(X,$fot(b))]]) ).
cnf(refute_0_146,plain,
( multiply(b,identity) != b
| multiply(c,a) != multiply(b,identity)
| multiply(c,a) = b ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,a),multiply(b,identity)) ),[1],$fot(b)]]) ).
cnf(refute_0_147,plain,
( multiply(c,a) != multiply(b,identity)
| multiply(c,a) = b ),
inference(resolve,[$cnf( $equal(multiply(b,identity),b) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
( multiply(c,multiply(X_7,inverse(multiply(inverse(a),X_7)))) != multiply(b,identity)
| multiply(c,a) = b ),
inference(resolve,[$cnf( $equal(multiply(c,a),multiply(b,identity)) )],[refute_0_144,refute_0_147]) ).
cnf(refute_0_149,plain,
multiply(c,a) = b,
inference(resolve,[$cnf( $equal(multiply(c,multiply(X_7,inverse(multiply(inverse(a),X_7)))),multiply(b,identity)) )],[refute_0_128,refute_0_148]) ).
cnf(refute_0_150,plain,
( multiply(c,a) != b
| a != multiply(inverse(c),multiply(c,a))
| a = multiply(inverse(c),b) ),
introduced(tautology,[equality,[$cnf( $equal(a,multiply(inverse(c),multiply(c,a))) ),[1,1],$fot(b)]]) ).
cnf(refute_0_151,plain,
( a != multiply(inverse(c),multiply(c,a))
| a = multiply(inverse(c),b) ),
inference(resolve,[$cnf( $equal(multiply(c,a),b) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
a = multiply(inverse(c),b),
inference(resolve,[$cnf( $equal(a,multiply(inverse(c),multiply(c,a))) )],[refute_0_119,refute_0_151]) ).
cnf(refute_0_153,plain,
( a != multiply(inverse(c),b)
| multiply(inverse(c),b) = a ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(a)),bind(Y0,$fot(multiply(inverse(c),b)))]]) ).
cnf(refute_0_154,plain,
multiply(inverse(c),b) = a,
inference(resolve,[$cnf( $equal(a,multiply(inverse(c),b)) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
( multiply(inverse(c),b) != a
| ~ subgroup_member(multiply(inverse(c),b))
| subgroup_member(a) ),
introduced(tautology,[equality,[$cnf( subgroup_member(multiply(inverse(c),b)) ),[0],$fot(a)]]) ).
cnf(refute_0_156,plain,
( ~ subgroup_member(multiply(inverse(c),b))
| subgroup_member(a) ),
inference(resolve,[$cnf( $equal(multiply(inverse(c),b),a) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
subgroup_member(a),
inference(resolve,[$cnf( subgroup_member(multiply(inverse(c),b)) )],[refute_0_118,refute_0_156]) ).
cnf(refute_0_158,plain,
subgroup_member(multiply(a,inverse(b))),
inference(resolve,[$cnf( subgroup_member(a) )],[refute_0_157,refute_0_8]) ).
cnf(refute_0_159,plain,
multiply(a,X_8) = multiply(inverse(c),multiply(c,multiply(a,X_8))),
inference(subst,[],[refute_0_21:[bind(X_7,$fot(c)),bind(X_8,$fot(multiply(a,X_8)))]]) ).
cnf(refute_0_160,plain,
multiply(c,multiply(inverse(inverse(a)),X_8)) = multiply(b,multiply(inverse(a),multiply(inverse(inverse(a)),X_8))),
inference(subst,[],[refute_0_123:[bind(X_8,$fot(multiply(inverse(inverse(a)),X_8)))]]) ).
cnf(refute_0_161,plain,
X_8 = multiply(inverse(a),multiply(inverse(inverse(a)),X_8)),
inference(subst,[],[refute_0_68:[bind(X_6,$fot(inverse(a)))]]) ).
cnf(refute_0_162,plain,
( X_8 != multiply(inverse(a),multiply(inverse(inverse(a)),X_8))
| multiply(inverse(a),multiply(inverse(inverse(a)),X_8)) = X_8 ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(X_8)),bind(Y0,$fot(multiply(inverse(a),multiply(inverse(inverse(a)),X_8))))]]) ).
cnf(refute_0_163,plain,
multiply(inverse(a),multiply(inverse(inverse(a)),X_8)) = X_8,
inference(resolve,[$cnf( $equal(X_8,multiply(inverse(a),multiply(inverse(inverse(a)),X_8))) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
( multiply(c,multiply(inverse(inverse(a)),X_8)) != multiply(b,multiply(inverse(a),multiply(inverse(inverse(a)),X_8)))
| multiply(inverse(a),multiply(inverse(inverse(a)),X_8)) != X_8
| multiply(c,multiply(inverse(inverse(a)),X_8)) = multiply(b,X_8) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,multiply(inverse(inverse(a)),X_8)),multiply(b,multiply(inverse(a),multiply(inverse(inverse(a)),X_8)))) ),[1,1],$fot(X_8)]]) ).
cnf(refute_0_165,plain,
( multiply(c,multiply(inverse(inverse(a)),X_8)) != multiply(b,multiply(inverse(a),multiply(inverse(inverse(a)),X_8)))
| multiply(c,multiply(inverse(inverse(a)),X_8)) = multiply(b,X_8) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),multiply(inverse(inverse(a)),X_8)),X_8) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
multiply(c,multiply(inverse(inverse(a)),X_8)) = multiply(b,X_8),
inference(resolve,[$cnf( $equal(multiply(c,multiply(inverse(inverse(a)),X_8)),multiply(b,multiply(inverse(a),multiply(inverse(inverse(a)),X_8)))) )],[refute_0_160,refute_0_165]) ).
cnf(refute_0_167,plain,
multiply(inverse(inverse(a)),X_8) = multiply(inverse(inverse(a)),X_8),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(a)),X_8))]]) ).
cnf(refute_0_168,plain,
( multiply(inverse(inverse(a)),X_8) != multiply(inverse(inverse(a)),X_8)
| inverse(inverse(a)) != a
| multiply(inverse(inverse(a)),X_8) = multiply(a,X_8) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(a)),X_8),multiply(inverse(inverse(a)),X_8)) ),[1,0],$fot(a)]]) ).
cnf(refute_0_169,plain,
( inverse(inverse(a)) != a
| multiply(inverse(inverse(a)),X_8) = multiply(a,X_8) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(a)),X_8),multiply(inverse(inverse(a)),X_8)) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
multiply(inverse(inverse(a)),X_8) = multiply(a,X_8),
inference(resolve,[$cnf( $equal(inverse(inverse(a)),a) )],[refute_0_78,refute_0_169]) ).
cnf(refute_0_171,plain,
multiply(c,multiply(inverse(inverse(a)),X_8)) = multiply(c,multiply(inverse(inverse(a)),X_8)),
introduced(tautology,[refl,[$fot(multiply(c,multiply(inverse(inverse(a)),X_8)))]]) ).
cnf(refute_0_172,plain,
( multiply(c,multiply(inverse(inverse(a)),X_8)) != multiply(c,multiply(inverse(inverse(a)),X_8))
| multiply(inverse(inverse(a)),X_8) != multiply(a,X_8)
| multiply(c,multiply(inverse(inverse(a)),X_8)) = multiply(c,multiply(a,X_8)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,multiply(inverse(inverse(a)),X_8)),multiply(c,multiply(inverse(inverse(a)),X_8))) ),[1,1],$fot(multiply(a,X_8))]]) ).
cnf(refute_0_173,plain,
( multiply(inverse(inverse(a)),X_8) != multiply(a,X_8)
| multiply(c,multiply(inverse(inverse(a)),X_8)) = multiply(c,multiply(a,X_8)) ),
inference(resolve,[$cnf( $equal(multiply(c,multiply(inverse(inverse(a)),X_8)),multiply(c,multiply(inverse(inverse(a)),X_8))) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
multiply(c,multiply(inverse(inverse(a)),X_8)) = multiply(c,multiply(a,X_8)),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(a)),X_8),multiply(a,X_8)) )],[refute_0_170,refute_0_173]) ).
cnf(refute_0_175,plain,
( multiply(c,multiply(inverse(inverse(a)),X_8)) != multiply(b,X_8)
| multiply(c,multiply(inverse(inverse(a)),X_8)) != multiply(c,multiply(a,X_8))
| multiply(c,multiply(a,X_8)) = multiply(b,X_8) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,multiply(inverse(inverse(a)),X_8)),multiply(b,X_8)) ),[0],$fot(multiply(c,multiply(a,X_8)))]]) ).
cnf(refute_0_176,plain,
( multiply(c,multiply(inverse(inverse(a)),X_8)) != multiply(b,X_8)
| multiply(c,multiply(a,X_8)) = multiply(b,X_8) ),
inference(resolve,[$cnf( $equal(multiply(c,multiply(inverse(inverse(a)),X_8)),multiply(c,multiply(a,X_8))) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
multiply(c,multiply(a,X_8)) = multiply(b,X_8),
inference(resolve,[$cnf( $equal(multiply(c,multiply(inverse(inverse(a)),X_8)),multiply(b,X_8)) )],[refute_0_166,refute_0_176]) ).
cnf(refute_0_178,plain,
( multiply(a,X_8) != multiply(inverse(c),multiply(c,multiply(a,X_8)))
| multiply(c,multiply(a,X_8)) != multiply(b,X_8)
| multiply(a,X_8) = multiply(inverse(c),multiply(b,X_8)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(a,X_8),multiply(inverse(c),multiply(c,multiply(a,X_8)))) ),[1,1],$fot(multiply(b,X_8))]]) ).
cnf(refute_0_179,plain,
( multiply(a,X_8) != multiply(inverse(c),multiply(c,multiply(a,X_8)))
| multiply(a,X_8) = multiply(inverse(c),multiply(b,X_8)) ),
inference(resolve,[$cnf( $equal(multiply(c,multiply(a,X_8)),multiply(b,X_8)) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
multiply(a,X_8) = multiply(inverse(c),multiply(b,X_8)),
inference(resolve,[$cnf( $equal(multiply(a,X_8),multiply(inverse(c),multiply(c,multiply(a,X_8)))) )],[refute_0_159,refute_0_179]) ).
cnf(refute_0_181,plain,
multiply(a,inverse(b)) = multiply(inverse(c),multiply(b,inverse(b))),
inference(subst,[],[refute_0_180:[bind(X_8,$fot(inverse(b)))]]) ).
cnf(refute_0_182,plain,
multiply(b,inverse(b)) = identity,
inference(subst,[],[right_inverse:[bind(X,$fot(b))]]) ).
cnf(refute_0_183,plain,
( multiply(a,inverse(b)) != multiply(inverse(c),multiply(b,inverse(b)))
| multiply(b,inverse(b)) != identity
| multiply(a,inverse(b)) = multiply(inverse(c),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(a,inverse(b)),multiply(inverse(c),multiply(b,inverse(b)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_184,plain,
( multiply(a,inverse(b)) != multiply(inverse(c),multiply(b,inverse(b)))
| multiply(a,inverse(b)) = multiply(inverse(c),identity) ),
inference(resolve,[$cnf( $equal(multiply(b,inverse(b)),identity) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
multiply(a,inverse(b)) = multiply(inverse(c),identity),
inference(resolve,[$cnf( $equal(multiply(a,inverse(b)),multiply(inverse(c),multiply(b,inverse(b)))) )],[refute_0_181,refute_0_184]) ).
cnf(refute_0_186,plain,
multiply(inverse(c),identity) = inverse(c),
inference(subst,[],[right_identity:[bind(X,$fot(inverse(c)))]]) ).
cnf(refute_0_187,plain,
( multiply(a,inverse(b)) != multiply(inverse(c),identity)
| multiply(inverse(c),identity) != inverse(c)
| multiply(a,inverse(b)) = inverse(c) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a,inverse(b)),inverse(c)) ),[0],$fot(multiply(inverse(c),identity))]]) ).
cnf(refute_0_188,plain,
( multiply(a,inverse(b)) != multiply(inverse(c),identity)
| multiply(a,inverse(b)) = inverse(c) ),
inference(resolve,[$cnf( $equal(multiply(inverse(c),identity),inverse(c)) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
multiply(a,inverse(b)) = inverse(c),
inference(resolve,[$cnf( $equal(multiply(a,inverse(b)),multiply(inverse(c),identity)) )],[refute_0_185,refute_0_188]) ).
cnf(refute_0_190,plain,
( multiply(a,inverse(b)) != inverse(c)
| ~ subgroup_member(multiply(a,inverse(b)))
| subgroup_member(inverse(c)) ),
introduced(tautology,[equality,[$cnf( subgroup_member(multiply(a,inverse(b))) ),[0],$fot(inverse(c))]]) ).
cnf(refute_0_191,plain,
( ~ subgroup_member(multiply(a,inverse(b)))
| subgroup_member(inverse(c)) ),
inference(resolve,[$cnf( $equal(multiply(a,inverse(b)),inverse(c)) )],[refute_0_189,refute_0_190]) ).
cnf(refute_0_192,plain,
subgroup_member(inverse(c)),
inference(resolve,[$cnf( subgroup_member(multiply(a,inverse(b))) )],[refute_0_158,refute_0_191]) ).
cnf(refute_0_193,plain,
subgroup_member(inverse(inverse(c))),
inference(resolve,[$cnf( subgroup_member(inverse(c)) )],[refute_0_192,refute_0_0]) ).
cnf(refute_0_194,plain,
inverse(inverse(c)) = c,
inference(subst,[],[refute_0_77:[bind(X_9,$fot(c))]]) ).
cnf(refute_0_195,plain,
( inverse(inverse(c)) != c
| ~ subgroup_member(inverse(inverse(c)))
| subgroup_member(c) ),
introduced(tautology,[equality,[$cnf( subgroup_member(inverse(inverse(c))) ),[0],$fot(c)]]) ).
cnf(refute_0_196,plain,
( ~ subgroup_member(inverse(inverse(c)))
| subgroup_member(c) ),
inference(resolve,[$cnf( $equal(inverse(inverse(c)),c) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
subgroup_member(c),
inference(resolve,[$cnf( subgroup_member(inverse(inverse(c))) )],[refute_0_193,refute_0_196]) ).
cnf(refute_0_198,plain,
( ~ subgroup_member(Y)
| ~ subgroup_member(a)
| subgroup_member(multiply(a,Y)) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(a))]]) ).
cnf(refute_0_199,plain,
( ~ subgroup_member(Y)
| subgroup_member(multiply(a,Y)) ),
inference(resolve,[$cnf( subgroup_member(a) )],[refute_0_157,refute_0_198]) ).
cnf(refute_0_200,plain,
( ~ subgroup_member(c)
| subgroup_member(multiply(a,c)) ),
inference(subst,[],[refute_0_199:[bind(Y,$fot(c))]]) ).
cnf(refute_0_201,plain,
subgroup_member(multiply(a,c)),
inference(resolve,[$cnf( subgroup_member(c) )],[refute_0_197,refute_0_200]) ).
cnf(refute_0_202,plain,
( multiply(a,c) != d
| ~ subgroup_member(multiply(a,c))
| subgroup_member(d) ),
introduced(tautology,[equality,[$cnf( subgroup_member(multiply(a,c)) ),[0],$fot(d)]]) ).
cnf(refute_0_203,plain,
( ~ subgroup_member(multiply(a,c))
| subgroup_member(d) ),
inference(resolve,[$cnf( $equal(multiply(a,c),d) )],[a_times_c_is_d,refute_0_202]) ).
cnf(refute_0_204,plain,
subgroup_member(d),
inference(resolve,[$cnf( subgroup_member(multiply(a,c)) )],[refute_0_201,refute_0_203]) ).
cnf(refute_0_205,plain,
$false,
inference(resolve,[$cnf( subgroup_member(d) )],[refute_0_204,prove_d_in_O2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP039-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 08:59:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 37.40/37.68 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.40/37.68
% 37.40/37.68 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 37.50/37.69
%------------------------------------------------------------------------------