TSTP Solution File: GRP039-7 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP039-7 : TPTP v8.1.0. Bugfixed v1.0.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 10:32:37 EDT 2022
% Result : Unsatisfiable 66.84s 67.00s
% Output : CNFRefutation 66.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 46
% Syntax : Number of clauses : 162 ( 72 unt; 16 nHn; 121 RR)
% Number of literals : 299 ( 204 equ; 115 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 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 : 118 ( 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(inverse_inverse,axiom,
inverse(inverse(X)) = X ).
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( $equal(multiply(X,Y),multiply(X,Y)) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ subgroup_member(X_48)
| ~ subgroup_member(inverse(b))
| subgroup_member(multiply(X_48,inverse(b))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_48)),bind(Y,$fot(inverse(b)))]]) ).
cnf(refute_0_7,plain,
( ~ subgroup_member(X_48)
| subgroup_member(multiply(X_48,inverse(b))) ),
inference(resolve,[$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_48,$fot(a))]]) ).
cnf(refute_0_9,plain,
( ~ subgroup_member(X_48)
| ~ subgroup_member(b)
| subgroup_member(multiply(X_48,b)) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_48)),bind(Y,$fot(b))]]) ).
cnf(refute_0_10,plain,
( ~ subgroup_member(X_48)
| subgroup_member(multiply(X_48,b)) ),
inference(resolve,[$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_48,$fot(inverse(c)))]]) ).
cnf(refute_0_12,plain,
( subgroup_member(a)
| subgroup_member(d)
| subgroup_member(element_in_O2(d,a)) ),
inference(subst,[],[an_element_in_O2:[bind(X,$fot(d)),bind(Y,$fot(a))]]) ).
cnf(refute_0_13,plain,
multiply(multiply(inverse(X_8),X_8),X_9) = multiply(inverse(X_8),multiply(X_8,X_9)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_8))),bind(Y,$fot(X_8)),bind(Z,$fot(X_9))]]) ).
cnf(refute_0_14,plain,
multiply(inverse(X_8),X_8) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_8))]]) ).
cnf(refute_0_15,plain,
( multiply(multiply(inverse(X_8),X_8),X_9) != multiply(inverse(X_8),multiply(X_8,X_9))
| multiply(inverse(X_8),X_8) != identity
| multiply(identity,X_9) = multiply(inverse(X_8),multiply(X_8,X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_8),X_8),X_9),multiply(inverse(X_8),multiply(X_8,X_9))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_16,plain,
( multiply(multiply(inverse(X_8),X_8),X_9) != multiply(inverse(X_8),multiply(X_8,X_9))
| multiply(identity,X_9) = multiply(inverse(X_8),multiply(X_8,X_9)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_8),X_8),identity) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
multiply(identity,X_9) = multiply(inverse(X_8),multiply(X_8,X_9)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_8),X_8),X_9),multiply(inverse(X_8),multiply(X_8,X_9))) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
multiply(identity,X_9) = X_9,
inference(subst,[],[left_identity:[bind(X,$fot(X_9))]]) ).
cnf(refute_0_19,plain,
( multiply(identity,X_9) != X_9
| multiply(identity,X_9) != multiply(inverse(X_8),multiply(X_8,X_9))
| X_9 = multiply(inverse(X_8),multiply(X_8,X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_9),multiply(inverse(X_8),multiply(X_8,X_9))) ),[0],$fot(X_9)]]) ).
cnf(refute_0_20,plain,
( multiply(identity,X_9) != multiply(inverse(X_8),multiply(X_8,X_9))
| X_9 = multiply(inverse(X_8),multiply(X_8,X_9)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_9),X_9) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
X_9 = multiply(inverse(X_8),multiply(X_8,X_9)),
inference(resolve,[$cnf( $equal(multiply(identity,X_9),multiply(inverse(X_8),multiply(X_8,X_9))) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
multiply(X_28,inverse(multiply(X_8,X_28))) = multiply(inverse(X_8),multiply(X_8,multiply(X_28,inverse(multiply(X_8,X_28))))),
inference(subst,[],[refute_0_21:[bind(X_9,$fot(multiply(X_28,inverse(multiply(X_8,X_28)))))]]) ).
cnf(refute_0_23,plain,
multiply(multiply(X_7,X_8),inverse(multiply(X_7,X_8))) = identity,
inference(subst,[],[right_inverse:[bind(X,$fot(multiply(X_7,X_8)))]]) ).
cnf(refute_0_24,plain,
multiply(multiply(X_7,X_8),inverse(multiply(X_7,X_8))) = multiply(X_7,multiply(X_8,inverse(multiply(X_7,X_8)))),
inference(subst,[],[associativity:[bind(X,$fot(X_7)),bind(Y,$fot(X_8)),bind(Z,$fot(inverse(multiply(X_7,X_8))))]]) ).
cnf(refute_0_25,plain,
( multiply(multiply(X_7,X_8),inverse(multiply(X_7,X_8))) != multiply(X_7,multiply(X_8,inverse(multiply(X_7,X_8))))
| multiply(multiply(X_7,X_8),inverse(multiply(X_7,X_8))) != identity
| multiply(X_7,multiply(X_8,inverse(multiply(X_7,X_8)))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_7,X_8),inverse(multiply(X_7,X_8))),identity) ),[0],$fot(multiply(X_7,multiply(X_8,inverse(multiply(X_7,X_8)))))]]) ).
cnf(refute_0_26,plain,
( multiply(multiply(X_7,X_8),inverse(multiply(X_7,X_8))) != identity
| multiply(X_7,multiply(X_8,inverse(multiply(X_7,X_8)))) = identity ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_7,X_8),inverse(multiply(X_7,X_8))),multiply(X_7,multiply(X_8,inverse(multiply(X_7,X_8))))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
multiply(X_7,multiply(X_8,inverse(multiply(X_7,X_8)))) = identity,
inference(resolve,[$cnf( $equal(multiply(multiply(X_7,X_8),inverse(multiply(X_7,X_8))),identity) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
multiply(X_8,multiply(X_28,inverse(multiply(X_8,X_28)))) = identity,
inference(subst,[],[refute_0_27:[bind(X_7,$fot(X_8)),bind(X_8,$fot(X_28))]]) ).
cnf(refute_0_29,plain,
( multiply(X_28,inverse(multiply(X_8,X_28))) != multiply(inverse(X_8),multiply(X_8,multiply(X_28,inverse(multiply(X_8,X_28)))))
| multiply(X_8,multiply(X_28,inverse(multiply(X_8,X_28)))) != identity
| multiply(X_28,inverse(multiply(X_8,X_28))) = multiply(inverse(X_8),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_28,inverse(multiply(X_8,X_28))),multiply(inverse(X_8),multiply(X_8,multiply(X_28,inverse(multiply(X_8,X_28)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_30,plain,
( multiply(X_28,inverse(multiply(X_8,X_28))) != multiply(inverse(X_8),multiply(X_8,multiply(X_28,inverse(multiply(X_8,X_28)))))
| multiply(X_28,inverse(multiply(X_8,X_28))) = multiply(inverse(X_8),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_8,multiply(X_28,inverse(multiply(X_8,X_28)))),identity) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
multiply(X_28,inverse(multiply(X_8,X_28))) = multiply(inverse(X_8),identity),
inference(resolve,[$cnf( $equal(multiply(X_28,inverse(multiply(X_8,X_28))),multiply(inverse(X_8),multiply(X_8,multiply(X_28,inverse(multiply(X_8,X_28)))))) )],[refute_0_22,refute_0_30]) ).
cnf(refute_0_32,plain,
multiply(inverse(X_8),identity) = inverse(X_8),
inference(subst,[],[right_identity:[bind(X,$fot(inverse(X_8)))]]) ).
cnf(refute_0_33,plain,
( multiply(X_28,inverse(multiply(X_8,X_28))) != multiply(inverse(X_8),identity)
| multiply(inverse(X_8),identity) != inverse(X_8)
| multiply(X_28,inverse(multiply(X_8,X_28))) = inverse(X_8) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_28,inverse(multiply(X_8,X_28))),inverse(X_8)) ),[0],$fot(multiply(inverse(X_8),identity))]]) ).
cnf(refute_0_34,plain,
( multiply(X_28,inverse(multiply(X_8,X_28))) != multiply(inverse(X_8),identity)
| multiply(X_28,inverse(multiply(X_8,X_28))) = inverse(X_8) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_8),identity),inverse(X_8)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
multiply(X_28,inverse(multiply(X_8,X_28))) = inverse(X_8),
inference(resolve,[$cnf( $equal(multiply(X_28,inverse(multiply(X_8,X_28))),multiply(inverse(X_8),identity)) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
multiply(element_in_O2(d,a),inverse(multiply(c,element_in_O2(d,a)))) = inverse(c),
inference(subst,[],[refute_0_35:[bind(X_28,$fot(element_in_O2(d,a))),bind(X_8,$fot(c))]]) ).
cnf(refute_0_37,plain,
inverse(multiply(X_35,X_8)) = multiply(inverse(X_8),multiply(X_8,inverse(multiply(X_35,X_8)))),
inference(subst,[],[refute_0_21:[bind(X_9,$fot(inverse(multiply(X_35,X_8))))]]) ).
cnf(refute_0_38,plain,
multiply(X_8,inverse(multiply(X_35,X_8))) = inverse(X_35),
inference(subst,[],[refute_0_35:[bind(X_28,$fot(X_8)),bind(X_8,$fot(X_35))]]) ).
cnf(refute_0_39,plain,
( multiply(X_8,inverse(multiply(X_35,X_8))) != inverse(X_35)
| inverse(multiply(X_35,X_8)) != multiply(inverse(X_8),multiply(X_8,inverse(multiply(X_35,X_8))))
| inverse(multiply(X_35,X_8)) = multiply(inverse(X_8),inverse(X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_35,X_8)),multiply(inverse(X_8),multiply(X_8,inverse(multiply(X_35,X_8))))) ),[1,1],$fot(inverse(X_35))]]) ).
cnf(refute_0_40,plain,
( inverse(multiply(X_35,X_8)) != multiply(inverse(X_8),multiply(X_8,inverse(multiply(X_35,X_8))))
| inverse(multiply(X_35,X_8)) = multiply(inverse(X_8),inverse(X_35)) ),
inference(resolve,[$cnf( $equal(multiply(X_8,inverse(multiply(X_35,X_8))),inverse(X_35)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
inverse(multiply(X_35,X_8)) = multiply(inverse(X_8),inverse(X_35)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_35,X_8)),multiply(inverse(X_8),multiply(X_8,inverse(multiply(X_35,X_8))))) )],[refute_0_37,refute_0_40]) ).
cnf(refute_0_42,plain,
inverse(multiply(inverse(X),X_42)) = multiply(inverse(X_42),inverse(inverse(X))),
inference(subst,[],[refute_0_41:[bind(X_35,$fot(inverse(X))),bind(X_8,$fot(X_42))]]) ).
cnf(refute_0_43,plain,
( inverse(multiply(inverse(X),X_42)) != multiply(inverse(X_42),inverse(inverse(X)))
| inverse(inverse(X)) != X
| inverse(multiply(inverse(X),X_42)) = multiply(inverse(X_42),X) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X),X_42)),multiply(inverse(X_42),inverse(inverse(X)))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_44,plain,
( inverse(multiply(inverse(X),X_42)) != multiply(inverse(X_42),inverse(inverse(X)))
| inverse(multiply(inverse(X),X_42)) = multiply(inverse(X_42),X) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[inverse_inverse,refute_0_43]) ).
cnf(refute_0_45,plain,
inverse(multiply(inverse(X),X_42)) = multiply(inverse(X_42),X),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),X_42)),multiply(inverse(X_42),inverse(inverse(X)))) )],[refute_0_42,refute_0_44]) ).
cnf(refute_0_46,plain,
inverse(multiply(inverse(a),multiply(d,Z))) = multiply(inverse(multiply(d,Z)),a),
inference(subst,[],[refute_0_45:[bind(X,$fot(a)),bind(X_42,$fot(multiply(d,Z)))]]) ).
cnf(refute_0_47,plain,
multiply(multiply(inverse(a),d),Z) = multiply(inverse(a),multiply(d,Z)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(a))),bind(Y,$fot(d))]]) ).
cnf(refute_0_48,plain,
c = multiply(inverse(a),multiply(a,c)),
inference(subst,[],[refute_0_21:[bind(X_8,$fot(a)),bind(X_9,$fot(c))]]) ).
cnf(refute_0_49,plain,
( multiply(a,c) != d
| c != multiply(inverse(a),multiply(a,c))
| c = multiply(inverse(a),d) ),
introduced(tautology,[equality,[$cnf( $equal(c,multiply(inverse(a),multiply(a,c))) ),[1,1],$fot(d)]]) ).
cnf(refute_0_50,plain,
( c != multiply(inverse(a),multiply(a,c))
| c = multiply(inverse(a),d) ),
inference(resolve,[$cnf( $equal(multiply(a,c),d) )],[a_times_c_is_d,refute_0_49]) ).
cnf(refute_0_51,plain,
c = multiply(inverse(a),d),
inference(resolve,[$cnf( $equal(c,multiply(inverse(a),multiply(a,c))) )],[refute_0_48,refute_0_50]) ).
cnf(refute_0_52,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_53,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_54,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( c != multiply(inverse(a),d)
| multiply(inverse(a),d) = c ),
inference(subst,[],[refute_0_54:[bind(X0,$fot(c)),bind(Y0,$fot(multiply(inverse(a),d)))]]) ).
cnf(refute_0_56,plain,
multiply(inverse(a),d) = c,
inference(resolve,[$cnf( $equal(c,multiply(inverse(a),d)) )],[refute_0_51,refute_0_55]) ).
cnf(refute_0_57,plain,
( multiply(multiply(inverse(a),d),Z) != multiply(inverse(a),multiply(d,Z))
| multiply(inverse(a),d) != c
| multiply(c,Z) = multiply(inverse(a),multiply(d,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(a),d),Z),multiply(inverse(a),multiply(d,Z))) ),[0,0],$fot(c)]]) ).
cnf(refute_0_58,plain,
( multiply(multiply(inverse(a),d),Z) != multiply(inverse(a),multiply(d,Z))
| multiply(c,Z) = multiply(inverse(a),multiply(d,Z)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),d),c) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
multiply(c,Z) = multiply(inverse(a),multiply(d,Z)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(a),d),Z),multiply(inverse(a),multiply(d,Z))) )],[refute_0_47,refute_0_58]) ).
cnf(refute_0_60,plain,
( multiply(c,Z) != multiply(inverse(a),multiply(d,Z))
| multiply(inverse(a),multiply(d,Z)) = multiply(c,Z) ),
inference(subst,[],[refute_0_54:[bind(X0,$fot(multiply(c,Z))),bind(Y0,$fot(multiply(inverse(a),multiply(d,Z))))]]) ).
cnf(refute_0_61,plain,
multiply(inverse(a),multiply(d,Z)) = multiply(c,Z),
inference(resolve,[$cnf( $equal(multiply(c,Z),multiply(inverse(a),multiply(d,Z))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
( multiply(inverse(a),multiply(d,Z)) != multiply(c,Z)
| inverse(multiply(inverse(a),multiply(d,Z))) != multiply(inverse(multiply(d,Z)),a)
| inverse(multiply(c,Z)) = multiply(inverse(multiply(d,Z)),a) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(a),multiply(d,Z))),multiply(inverse(multiply(d,Z)),a)) ),[0,0],$fot(multiply(c,Z))]]) ).
cnf(refute_0_63,plain,
( inverse(multiply(inverse(a),multiply(d,Z))) != multiply(inverse(multiply(d,Z)),a)
| inverse(multiply(c,Z)) = multiply(inverse(multiply(d,Z)),a) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),multiply(d,Z)),multiply(c,Z)) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
inverse(multiply(c,Z)) = multiply(inverse(multiply(d,Z)),a),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(a),multiply(d,Z))),multiply(inverse(multiply(d,Z)),a)) )],[refute_0_46,refute_0_63]) ).
cnf(refute_0_65,plain,
inverse(multiply(c,element_in_O2(d,X_108))) = multiply(inverse(multiply(d,element_in_O2(d,X_108))),a),
inference(subst,[],[refute_0_64:[bind(Z,$fot(element_in_O2(d,X_108)))]]) ).
cnf(refute_0_66,plain,
( multiply(d,element_in_O2(d,X_108)) = X_108
| subgroup_member(X_108)
| subgroup_member(d) ),
inference(subst,[],[property_of_O2:[bind(X,$fot(d)),bind(Y,$fot(X_108))]]) ).
cnf(refute_0_67,plain,
( multiply(d,element_in_O2(d,X_108)) != X_108
| inverse(multiply(c,element_in_O2(d,X_108))) != multiply(inverse(multiply(d,element_in_O2(d,X_108))),a)
| inverse(multiply(c,element_in_O2(d,X_108))) = multiply(inverse(X_108),a) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(c,element_in_O2(d,X_108))),multiply(inverse(multiply(d,element_in_O2(d,X_108))),a)) ),[1,0,0],$fot(X_108)]]) ).
cnf(refute_0_68,plain,
( inverse(multiply(c,element_in_O2(d,X_108))) != multiply(inverse(multiply(d,element_in_O2(d,X_108))),a)
| inverse(multiply(c,element_in_O2(d,X_108))) = multiply(inverse(X_108),a)
| subgroup_member(X_108)
| subgroup_member(d) ),
inference(resolve,[$cnf( $equal(multiply(d,element_in_O2(d,X_108)),X_108) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
( inverse(multiply(c,element_in_O2(d,X_108))) = multiply(inverse(X_108),a)
| subgroup_member(X_108)
| subgroup_member(d) ),
inference(resolve,[$cnf( $equal(inverse(multiply(c,element_in_O2(d,X_108))),multiply(inverse(multiply(d,element_in_O2(d,X_108))),a)) )],[refute_0_65,refute_0_68]) ).
cnf(refute_0_70,plain,
( inverse(multiply(c,element_in_O2(d,X_108))) = multiply(inverse(X_108),a)
| subgroup_member(X_108) ),
inference(resolve,[$cnf( subgroup_member(d) )],[refute_0_69,prove_d_in_O2]) ).
cnf(refute_0_71,plain,
( inverse(multiply(c,element_in_O2(d,a))) = multiply(inverse(a),a)
| subgroup_member(a) ),
inference(subst,[],[refute_0_70:[bind(X_108,$fot(a))]]) ).
cnf(refute_0_72,plain,
multiply(inverse(a),a) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(a))]]) ).
cnf(refute_0_73,plain,
( multiply(inverse(a),a) != identity
| inverse(multiply(c,element_in_O2(d,a))) != multiply(inverse(a),a)
| inverse(multiply(c,element_in_O2(d,a))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(c,element_in_O2(d,a))),multiply(inverse(a),a)) ),[1],$fot(identity)]]) ).
cnf(refute_0_74,plain,
( inverse(multiply(c,element_in_O2(d,a))) != multiply(inverse(a),a)
| inverse(multiply(c,element_in_O2(d,a))) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),a),identity) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
( inverse(multiply(c,element_in_O2(d,a))) = identity
| subgroup_member(a) ),
inference(resolve,[$cnf( $equal(inverse(multiply(c,element_in_O2(d,a))),multiply(inverse(a),a)) )],[refute_0_71,refute_0_74]) ).
cnf(refute_0_76,plain,
( multiply(element_in_O2(d,a),inverse(multiply(c,element_in_O2(d,a)))) != inverse(c)
| inverse(multiply(c,element_in_O2(d,a))) != identity
| multiply(element_in_O2(d,a),identity) = inverse(c) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(element_in_O2(d,a),inverse(multiply(c,element_in_O2(d,a)))),inverse(c)) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_77,plain,
( multiply(element_in_O2(d,a),inverse(multiply(c,element_in_O2(d,a)))) != inverse(c)
| multiply(element_in_O2(d,a),identity) = inverse(c)
| subgroup_member(a) ),
inference(resolve,[$cnf( $equal(inverse(multiply(c,element_in_O2(d,a))),identity) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
( multiply(element_in_O2(d,a),identity) = inverse(c)
| subgroup_member(a) ),
inference(resolve,[$cnf( $equal(multiply(element_in_O2(d,a),inverse(multiply(c,element_in_O2(d,a)))),inverse(c)) )],[refute_0_36,refute_0_77]) ).
cnf(refute_0_79,plain,
multiply(element_in_O2(d,a),identity) = element_in_O2(d,a),
inference(subst,[],[right_identity:[bind(X,$fot(element_in_O2(d,a)))]]) ).
cnf(refute_0_80,plain,
( multiply(element_in_O2(d,a),identity) != element_in_O2(d,a)
| multiply(element_in_O2(d,a),identity) != inverse(c)
| element_in_O2(d,a) = inverse(c) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(element_in_O2(d,a),identity),inverse(c)) ),[0],$fot(element_in_O2(d,a))]]) ).
cnf(refute_0_81,plain,
( multiply(element_in_O2(d,a),identity) != inverse(c)
| element_in_O2(d,a) = inverse(c) ),
inference(resolve,[$cnf( $equal(multiply(element_in_O2(d,a),identity),element_in_O2(d,a)) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
( element_in_O2(d,a) = inverse(c)
| subgroup_member(a) ),
inference(resolve,[$cnf( $equal(multiply(element_in_O2(d,a),identity),inverse(c)) )],[refute_0_78,refute_0_81]) ).
cnf(refute_0_83,plain,
( element_in_O2(d,a) != inverse(c)
| ~ subgroup_member(element_in_O2(d,a))
| subgroup_member(inverse(c)) ),
introduced(tautology,[equality,[$cnf( subgroup_member(element_in_O2(d,a)) ),[0],$fot(inverse(c))]]) ).
cnf(refute_0_84,plain,
( ~ subgroup_member(element_in_O2(d,a))
| subgroup_member(a)
| subgroup_member(inverse(c)) ),
inference(resolve,[$cnf( $equal(element_in_O2(d,a),inverse(c)) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
( subgroup_member(a)
| subgroup_member(d)
| subgroup_member(inverse(c)) ),
inference(resolve,[$cnf( subgroup_member(element_in_O2(d,a)) )],[refute_0_12,refute_0_84]) ).
cnf(refute_0_86,plain,
( subgroup_member(a)
| subgroup_member(inverse(c)) ),
inference(resolve,[$cnf( subgroup_member(d) )],[refute_0_85,prove_d_in_O2]) ).
cnf(refute_0_87,plain,
( subgroup_member(multiply(inverse(c),b))
| subgroup_member(a) ),
inference(resolve,[$cnf( subgroup_member(inverse(c)) )],[refute_0_86,refute_0_11]) ).
cnf(refute_0_88,plain,
a = multiply(inverse(c),multiply(c,a)),
inference(subst,[],[refute_0_21:[bind(X_8,$fot(c)),bind(X_9,$fot(a))]]) ).
cnf(refute_0_89,plain,
multiply(multiply(b,inverse(a)),X_9) = multiply(b,multiply(inverse(a),X_9)),
inference(subst,[],[associativity:[bind(X,$fot(b)),bind(Y,$fot(inverse(a))),bind(Z,$fot(X_9))]]) ).
cnf(refute_0_90,plain,
( multiply(multiply(b,inverse(a)),X_9) != multiply(b,multiply(inverse(a),X_9))
| multiply(b,inverse(a)) != c
| multiply(c,X_9) = multiply(b,multiply(inverse(a),X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(b,inverse(a)),X_9),multiply(b,multiply(inverse(a),X_9))) ),[0,0],$fot(c)]]) ).
cnf(refute_0_91,plain,
( multiply(multiply(b,inverse(a)),X_9) != multiply(b,multiply(inverse(a),X_9))
| multiply(c,X_9) = multiply(b,multiply(inverse(a),X_9)) ),
inference(resolve,[$cnf( $equal(multiply(b,inverse(a)),c) )],[b_times_a_inverse_is_c,refute_0_90]) ).
cnf(refute_0_92,plain,
multiply(c,X_9) = multiply(b,multiply(inverse(a),X_9)),
inference(resolve,[$cnf( $equal(multiply(multiply(b,inverse(a)),X_9),multiply(b,multiply(inverse(a),X_9))) )],[refute_0_89,refute_0_91]) ).
cnf(refute_0_93,plain,
multiply(c,inverse(inverse(a))) = multiply(b,multiply(inverse(a),inverse(inverse(a)))),
inference(subst,[],[refute_0_92:[bind(X_9,$fot(inverse(inverse(a))))]]) ).
cnf(refute_0_94,plain,
multiply(inverse(a),inverse(inverse(a))) = identity,
inference(subst,[],[right_inverse:[bind(X,$fot(inverse(a)))]]) ).
cnf(refute_0_95,plain,
( multiply(c,inverse(inverse(a))) != multiply(b,multiply(inverse(a),inverse(inverse(a))))
| multiply(inverse(a),inverse(inverse(a))) != identity
| multiply(c,inverse(inverse(a))) = multiply(b,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,inverse(inverse(a))),multiply(b,multiply(inverse(a),inverse(inverse(a))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_96,plain,
( multiply(c,inverse(inverse(a))) != multiply(b,multiply(inverse(a),inverse(inverse(a))))
| multiply(c,inverse(inverse(a))) = multiply(b,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),inverse(inverse(a))),identity) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
multiply(c,inverse(inverse(a))) = multiply(b,identity),
inference(resolve,[$cnf( $equal(multiply(c,inverse(inverse(a))),multiply(b,multiply(inverse(a),inverse(inverse(a))))) )],[refute_0_93,refute_0_96]) ).
cnf(refute_0_98,plain,
inverse(inverse(a)) = a,
inference(subst,[],[inverse_inverse:[bind(X,$fot(a))]]) ).
cnf(refute_0_99,plain,
multiply(c,inverse(inverse(a))) = multiply(c,inverse(inverse(a))),
introduced(tautology,[refl,[$fot(multiply(c,inverse(inverse(a))))]]) ).
cnf(refute_0_100,plain,
( multiply(c,inverse(inverse(a))) != multiply(c,inverse(inverse(a)))
| inverse(inverse(a)) != a
| multiply(c,inverse(inverse(a))) = multiply(c,a) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,inverse(inverse(a))),multiply(c,inverse(inverse(a)))) ),[1,1],$fot(a)]]) ).
cnf(refute_0_101,plain,
( inverse(inverse(a)) != a
| multiply(c,inverse(inverse(a))) = multiply(c,a) ),
inference(resolve,[$cnf( $equal(multiply(c,inverse(inverse(a))),multiply(c,inverse(inverse(a)))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
multiply(c,inverse(inverse(a))) = multiply(c,a),
inference(resolve,[$cnf( $equal(inverse(inverse(a)),a) )],[refute_0_98,refute_0_101]) ).
cnf(refute_0_103,plain,
( multiply(c,inverse(inverse(a))) != multiply(b,identity)
| multiply(c,inverse(inverse(a))) != multiply(c,a)
| multiply(c,a) = multiply(b,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,inverse(inverse(a))),multiply(b,identity)) ),[0],$fot(multiply(c,a))]]) ).
cnf(refute_0_104,plain,
( multiply(c,inverse(inverse(a))) != multiply(b,identity)
| multiply(c,a) = multiply(b,identity) ),
inference(resolve,[$cnf( $equal(multiply(c,inverse(inverse(a))),multiply(c,a)) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
multiply(b,identity) = b,
inference(subst,[],[right_identity:[bind(X,$fot(b))]]) ).
cnf(refute_0_106,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_107,plain,
( multiply(c,a) != multiply(b,identity)
| multiply(c,a) = b ),
inference(resolve,[$cnf( $equal(multiply(b,identity),b) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
( multiply(c,inverse(inverse(a))) != multiply(b,identity)
| multiply(c,a) = b ),
inference(resolve,[$cnf( $equal(multiply(c,a),multiply(b,identity)) )],[refute_0_104,refute_0_107]) ).
cnf(refute_0_109,plain,
multiply(c,a) = b,
inference(resolve,[$cnf( $equal(multiply(c,inverse(inverse(a))),multiply(b,identity)) )],[refute_0_97,refute_0_108]) ).
cnf(refute_0_110,plain,
( multiply(c,a) != b
| a != multiply(inverse(c),multiply(c,a))
| a = multiply(inverse(c),b) ),
introduced(tautology,[equality,[$cnf( $equal(a,multiply(inverse(c),multiply(c,a))) ),[1,1],$fot(b)]]) ).
cnf(refute_0_111,plain,
( a != multiply(inverse(c),multiply(c,a))
| a = multiply(inverse(c),b) ),
inference(resolve,[$cnf( $equal(multiply(c,a),b) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
a = multiply(inverse(c),b),
inference(resolve,[$cnf( $equal(a,multiply(inverse(c),multiply(c,a))) )],[refute_0_88,refute_0_111]) ).
cnf(refute_0_113,plain,
( a != multiply(inverse(c),b)
| multiply(inverse(c),b) = a ),
inference(subst,[],[refute_0_54:[bind(X0,$fot(a)),bind(Y0,$fot(multiply(inverse(c),b)))]]) ).
cnf(refute_0_114,plain,
multiply(inverse(c),b) = a,
inference(resolve,[$cnf( $equal(a,multiply(inverse(c),b)) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
( multiply(inverse(c),b) != a
| ~ subgroup_member(multiply(inverse(c),b))
| subgroup_member(a) ),
introduced(tautology,[equality,[$cnf( subgroup_member(multiply(inverse(c),b)) ),[0],$fot(a)]]) ).
cnf(refute_0_116,plain,
( ~ subgroup_member(multiply(inverse(c),b))
| subgroup_member(a) ),
inference(resolve,[$cnf( $equal(multiply(inverse(c),b),a) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
subgroup_member(a),
inference(resolve,[$cnf( subgroup_member(multiply(inverse(c),b)) )],[refute_0_87,refute_0_116]) ).
cnf(refute_0_118,plain,
subgroup_member(multiply(a,inverse(b))),
inference(resolve,[$cnf( subgroup_member(a) )],[refute_0_117,refute_0_8]) ).
cnf(refute_0_119,plain,
multiply(multiply(inverse(c),b),Z) = multiply(inverse(c),multiply(b,Z)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(c))),bind(Y,$fot(b))]]) ).
cnf(refute_0_120,plain,
( multiply(multiply(inverse(c),b),Z) != multiply(inverse(c),multiply(b,Z))
| multiply(inverse(c),b) != a
| multiply(a,Z) = multiply(inverse(c),multiply(b,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(c),b),Z),multiply(inverse(c),multiply(b,Z))) ),[0,0],$fot(a)]]) ).
cnf(refute_0_121,plain,
( multiply(multiply(inverse(c),b),Z) != multiply(inverse(c),multiply(b,Z))
| multiply(a,Z) = multiply(inverse(c),multiply(b,Z)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(c),b),a) )],[refute_0_114,refute_0_120]) ).
cnf(refute_0_122,plain,
multiply(a,Z) = multiply(inverse(c),multiply(b,Z)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(c),b),Z),multiply(inverse(c),multiply(b,Z))) )],[refute_0_119,refute_0_121]) ).
cnf(refute_0_123,plain,
multiply(a,inverse(b)) = multiply(inverse(c),multiply(b,inverse(b))),
inference(subst,[],[refute_0_122:[bind(Z,$fot(inverse(b)))]]) ).
cnf(refute_0_124,plain,
multiply(b,inverse(b)) = identity,
inference(subst,[],[right_inverse:[bind(X,$fot(b))]]) ).
cnf(refute_0_125,plain,
( multiply(a,inverse(b)) != multiply(inverse(c),multiply(b,inverse(b)))
| multiply(b,inverse(b)) != identity
| multiply(a,inverse(b)) = multiply(inverse(c),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(a,inverse(b)),multiply(inverse(c),multiply(b,inverse(b)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_126,plain,
( multiply(a,inverse(b)) != multiply(inverse(c),multiply(b,inverse(b)))
| multiply(a,inverse(b)) = multiply(inverse(c),identity) ),
inference(resolve,[$cnf( $equal(multiply(b,inverse(b)),identity) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
multiply(a,inverse(b)) = multiply(inverse(c),identity),
inference(resolve,[$cnf( $equal(multiply(a,inverse(b)),multiply(inverse(c),multiply(b,inverse(b)))) )],[refute_0_123,refute_0_126]) ).
cnf(refute_0_128,plain,
multiply(inverse(c),identity) = inverse(c),
inference(subst,[],[right_identity:[bind(X,$fot(inverse(c)))]]) ).
cnf(refute_0_129,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_130,plain,
( multiply(a,inverse(b)) != multiply(inverse(c),identity)
| multiply(a,inverse(b)) = inverse(c) ),
inference(resolve,[$cnf( $equal(multiply(inverse(c),identity),inverse(c)) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
multiply(a,inverse(b)) = inverse(c),
inference(resolve,[$cnf( $equal(multiply(a,inverse(b)),multiply(inverse(c),identity)) )],[refute_0_127,refute_0_130]) ).
cnf(refute_0_132,plain,
( multiply(a,inverse(b)) != inverse(c)
| ~ subgroup_member(multiply(a,inverse(b)))
| subgroup_member(inverse(c)) ),
introduced(tautology,[equality,[$cnf( subgroup_member(multiply(a,inverse(b))) ),[0],$fot(inverse(c))]]) ).
cnf(refute_0_133,plain,
( ~ subgroup_member(multiply(a,inverse(b)))
| subgroup_member(inverse(c)) ),
inference(resolve,[$cnf( $equal(multiply(a,inverse(b)),inverse(c)) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
subgroup_member(inverse(c)),
inference(resolve,[$cnf( subgroup_member(multiply(a,inverse(b))) )],[refute_0_118,refute_0_133]) ).
cnf(refute_0_135,plain,
subgroup_member(inverse(inverse(c))),
inference(resolve,[$cnf( subgroup_member(inverse(c)) )],[refute_0_134,refute_0_0]) ).
cnf(refute_0_136,plain,
inverse(inverse(c)) = c,
inference(subst,[],[inverse_inverse:[bind(X,$fot(c))]]) ).
cnf(refute_0_137,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_138,plain,
( ~ subgroup_member(inverse(inverse(c)))
| subgroup_member(c) ),
inference(resolve,[$cnf( $equal(inverse(inverse(c)),c) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
subgroup_member(c),
inference(resolve,[$cnf( subgroup_member(inverse(inverse(c))) )],[refute_0_135,refute_0_138]) ).
cnf(refute_0_140,plain,
( ~ subgroup_member(Y)
| ~ subgroup_member(a)
| subgroup_member(multiply(a,Y)) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(a))]]) ).
cnf(refute_0_141,plain,
( ~ subgroup_member(Y)
| subgroup_member(multiply(a,Y)) ),
inference(resolve,[$cnf( subgroup_member(a) )],[refute_0_117,refute_0_140]) ).
cnf(refute_0_142,plain,
( ~ subgroup_member(c)
| subgroup_member(multiply(a,c)) ),
inference(subst,[],[refute_0_141:[bind(Y,$fot(c))]]) ).
cnf(refute_0_143,plain,
subgroup_member(multiply(a,c)),
inference(resolve,[$cnf( subgroup_member(c) )],[refute_0_139,refute_0_142]) ).
cnf(refute_0_144,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_145,plain,
( ~ subgroup_member(multiply(a,c))
| subgroup_member(d) ),
inference(resolve,[$cnf( $equal(multiply(a,c),d) )],[a_times_c_is_d,refute_0_144]) ).
cnf(refute_0_146,plain,
subgroup_member(d),
inference(resolve,[$cnf( subgroup_member(multiply(a,c)) )],[refute_0_143,refute_0_145]) ).
cnf(refute_0_147,plain,
$false,
inference(resolve,[$cnf( subgroup_member(d) )],[refute_0_146,prove_d_in_O2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP039-7 : TPTP v8.1.0. Bugfixed v1.0.1.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n024.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jun 13 10:21:48 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 66.84/67.00 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 66.84/67.00
% 66.84/67.00 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 66.84/67.01
%------------------------------------------------------------------------------