TSTP Solution File: GRP704-12 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP704-12 : TPTP v8.1.0. Released v8.1.0.
% 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 10:50:22 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 57
% Syntax : Number of clauses : 192 ( 100 unt; 0 nHn; 116 RR)
% Number of literals : 325 ( 324 equ; 135 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 197 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(f01,axiom,
mult(A,ld(A,B)) = B ).
cnf(f03,axiom,
mult(rd(A,B),B) = A ).
cnf(f04,axiom,
rd(mult(A,B),B) = A ).
cnf(f05,axiom,
mult(A,unit) = A ).
cnf(f06,axiom,
mult(unit,A) = A ).
cnf(f08,axiom,
mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ).
cnf(f09,axiom,
mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) ).
cnf(f11,axiom,
op_d = ld(A,mult(op_c,A)) ).
cnf(f12,axiom,
op_e = mult(mult(rd(op_c,mult(A,B)),B),A) ).
cnf(f13,axiom,
op_f = mult(A,mult(B,ld(mult(A,B),op_c))) ).
cnf(goal,negated_conjecture,
mult(x4,mult(op_f,x5)) != mult(mult(x4,op_f),x5) ).
cnf(refute_0_0,plain,
mult(X_3,ld(X_3,mult(op_c,X_3))) = mult(op_c,X_3),
inference(subst,[],[f01:[bind(A,$fot(X_3)),bind(B,$fot(mult(op_c,X_3)))]]) ).
cnf(refute_0_1,plain,
op_d = ld(X_3,mult(op_c,X_3)),
inference(subst,[],[f11:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( op_d != ld(X_3,mult(op_c,X_3))
| ld(X_3,mult(op_c,X_3)) = op_d ),
inference(subst,[],[refute_0_4:[bind(X,$fot(op_d)),bind(Y,$fot(ld(X_3,mult(op_c,X_3))))]]) ).
cnf(refute_0_6,plain,
ld(X_3,mult(op_c,X_3)) = op_d,
inference(resolve,[$cnf( $equal(op_d,ld(X_3,mult(op_c,X_3))) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( ld(X_3,mult(op_c,X_3)) != op_d
| mult(X_3,ld(X_3,mult(op_c,X_3))) != mult(op_c,X_3)
| mult(X_3,op_d) = mult(op_c,X_3) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_3,ld(X_3,mult(op_c,X_3))),mult(op_c,X_3)) ),[0,1],$fot(op_d)]]) ).
cnf(refute_0_8,plain,
( mult(X_3,ld(X_3,mult(op_c,X_3))) != mult(op_c,X_3)
| mult(X_3,op_d) = mult(op_c,X_3) ),
inference(resolve,[$cnf( $equal(ld(X_3,mult(op_c,X_3)),op_d) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
mult(X_3,op_d) = mult(op_c,X_3),
inference(resolve,[$cnf( $equal(mult(X_3,ld(X_3,mult(op_c,X_3))),mult(op_c,X_3)) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
mult(unit,ld(unit,op_c)) = op_c,
inference(subst,[],[f01:[bind(A,$fot(unit)),bind(B,$fot(op_c))]]) ).
cnf(refute_0_11,plain,
op_d = ld(unit,mult(op_c,unit)),
inference(subst,[],[f11:[bind(A,$fot(unit))]]) ).
cnf(refute_0_12,plain,
mult(op_c,unit) = op_c,
inference(subst,[],[f05:[bind(A,$fot(op_c))]]) ).
cnf(refute_0_13,plain,
( mult(op_c,unit) != op_c
| op_d != ld(unit,mult(op_c,unit))
| op_d = ld(unit,op_c) ),
introduced(tautology,[equality,[$cnf( $equal(op_d,ld(unit,mult(op_c,unit))) ),[1,1],$fot(op_c)]]) ).
cnf(refute_0_14,plain,
( op_d != ld(unit,mult(op_c,unit))
| op_d = ld(unit,op_c) ),
inference(resolve,[$cnf( $equal(mult(op_c,unit),op_c) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
op_d = ld(unit,op_c),
inference(resolve,[$cnf( $equal(op_d,ld(unit,mult(op_c,unit))) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
( op_d != ld(unit,op_c)
| ld(unit,op_c) = op_d ),
inference(subst,[],[refute_0_4:[bind(X,$fot(op_d)),bind(Y,$fot(ld(unit,op_c)))]]) ).
cnf(refute_0_17,plain,
ld(unit,op_c) = op_d,
inference(resolve,[$cnf( $equal(op_d,ld(unit,op_c)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( ld(unit,op_c) != op_d
| mult(unit,ld(unit,op_c)) != op_c
| mult(unit,op_d) = op_c ),
introduced(tautology,[equality,[$cnf( $equal(mult(unit,ld(unit,op_c)),op_c) ),[0,1],$fot(op_d)]]) ).
cnf(refute_0_19,plain,
( mult(unit,ld(unit,op_c)) != op_c
| mult(unit,op_d) = op_c ),
inference(resolve,[$cnf( $equal(ld(unit,op_c),op_d) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
mult(unit,op_d) = op_c,
inference(resolve,[$cnf( $equal(mult(unit,ld(unit,op_c)),op_c) )],[refute_0_10,refute_0_19]) ).
cnf(refute_0_21,plain,
mult(unit,op_d) = op_d,
inference(subst,[],[f06:[bind(A,$fot(op_d))]]) ).
cnf(refute_0_22,plain,
( mult(unit,op_d) != op_c
| mult(unit,op_d) != op_d
| op_d = op_c ),
introduced(tautology,[equality,[$cnf( $equal(mult(unit,op_d),op_c) ),[0],$fot(op_d)]]) ).
cnf(refute_0_23,plain,
( mult(unit,op_d) != op_c
| op_d = op_c ),
inference(resolve,[$cnf( $equal(mult(unit,op_d),op_d) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
op_d = op_c,
inference(resolve,[$cnf( $equal(mult(unit,op_d),op_c) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
mult(X_3,op_d) = mult(X_3,op_d),
introduced(tautology,[refl,[$fot(mult(X_3,op_d))]]) ).
cnf(refute_0_26,plain,
( mult(X_3,op_d) != mult(X_3,op_d)
| op_d != op_c
| mult(X_3,op_d) = mult(X_3,op_c) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_3,op_d),mult(X_3,op_d)) ),[1,1],$fot(op_c)]]) ).
cnf(refute_0_27,plain,
( op_d != op_c
| mult(X_3,op_d) = mult(X_3,op_c) ),
inference(resolve,[$cnf( $equal(mult(X_3,op_d),mult(X_3,op_d)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
mult(X_3,op_d) = mult(X_3,op_c),
inference(resolve,[$cnf( $equal(op_d,op_c) )],[refute_0_24,refute_0_27]) ).
cnf(refute_0_29,plain,
( mult(X_3,op_d) != mult(X_3,op_c)
| mult(X_3,op_d) != mult(op_c,X_3)
| mult(X_3,op_c) = mult(op_c,X_3) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_3,op_d),mult(op_c,X_3)) ),[0],$fot(mult(X_3,op_c))]]) ).
cnf(refute_0_30,plain,
( mult(X_3,op_d) != mult(op_c,X_3)
| mult(X_3,op_c) = mult(op_c,X_3) ),
inference(resolve,[$cnf( $equal(mult(X_3,op_d),mult(X_3,op_c)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
mult(X_3,op_c) = mult(op_c,X_3),
inference(resolve,[$cnf( $equal(mult(X_3,op_d),mult(op_c,X_3)) )],[refute_0_9,refute_0_30]) ).
cnf(refute_0_32,plain,
mult(mult(A,B),op_c) = mult(op_c,mult(A,B)),
inference(subst,[],[refute_0_31:[bind(X_3,$fot(mult(A,B)))]]) ).
cnf(refute_0_33,plain,
( mult(A,mult(B,op_c)) != mult(mult(A,B),op_c)
| mult(mult(A,B),op_c) != mult(op_c,mult(A,B))
| mult(A,mult(B,op_c)) = mult(op_c,mult(A,B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(A,mult(B,op_c)),mult(op_c,mult(A,B))) ),[0],$fot(mult(mult(A,B),op_c))]]) ).
cnf(refute_0_34,plain,
( mult(A,mult(B,op_c)) != mult(mult(A,B),op_c)
| mult(A,mult(B,op_c)) = mult(op_c,mult(A,B)) ),
inference(resolve,[$cnf( $equal(mult(mult(A,B),op_c),mult(op_c,mult(A,B))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
mult(A,mult(B,op_c)) = mult(op_c,mult(A,B)),
inference(resolve,[$cnf( $equal(mult(A,mult(B,op_c)),mult(mult(A,B),op_c)) )],[f09,refute_0_34]) ).
cnf(refute_0_36,plain,
mult(X_29,mult(X_30,op_c)) = mult(op_c,mult(X_29,X_30)),
inference(subst,[],[refute_0_35:[bind(A,$fot(X_29)),bind(B,$fot(X_30))]]) ).
cnf(refute_0_37,plain,
mult(X_30,op_c) = mult(op_c,X_30),
inference(subst,[],[refute_0_31:[bind(X_3,$fot(X_30))]]) ).
cnf(refute_0_38,plain,
( mult(X_29,mult(X_30,op_c)) != mult(op_c,mult(X_29,X_30))
| mult(X_30,op_c) != mult(op_c,X_30)
| mult(X_29,mult(op_c,X_30)) = mult(op_c,mult(X_29,X_30)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_29,mult(X_30,op_c)),mult(op_c,mult(X_29,X_30))) ),[0,1],$fot(mult(op_c,X_30))]]) ).
cnf(refute_0_39,plain,
( mult(X_29,mult(X_30,op_c)) != mult(op_c,mult(X_29,X_30))
| mult(X_29,mult(op_c,X_30)) = mult(op_c,mult(X_29,X_30)) ),
inference(resolve,[$cnf( $equal(mult(X_30,op_c),mult(op_c,X_30)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
mult(X_29,mult(op_c,X_30)) = mult(op_c,mult(X_29,X_30)),
inference(resolve,[$cnf( $equal(mult(X_29,mult(X_30,op_c)),mult(op_c,mult(X_29,X_30))) )],[refute_0_36,refute_0_39]) ).
cnf(refute_0_41,plain,
mult(x4,mult(op_c,x5)) = mult(op_c,mult(x4,x5)),
inference(subst,[],[refute_0_40:[bind(X_29,$fot(x4)),bind(X_30,$fot(x5))]]) ).
cnf(refute_0_42,plain,
mult(mult(X_38,ld(mult(op_c,X_38),op_c)),op_c) = mult(op_c,mult(X_38,ld(mult(op_c,X_38),op_c))),
inference(subst,[],[refute_0_31:[bind(X_3,$fot(mult(X_38,ld(mult(op_c,X_38),op_c))))]]) ).
cnf(refute_0_43,plain,
op_f = mult(op_c,mult(X_38,ld(mult(op_c,X_38),op_c))),
inference(subst,[],[f13:[bind(A,$fot(op_c)),bind(B,$fot(X_38))]]) ).
cnf(refute_0_44,plain,
( op_f != mult(op_c,mult(X_38,ld(mult(op_c,X_38),op_c)))
| mult(op_c,mult(X_38,ld(mult(op_c,X_38),op_c))) = op_f ),
inference(subst,[],[refute_0_4:[bind(X,$fot(op_f)),bind(Y,$fot(mult(op_c,mult(X_38,ld(mult(op_c,X_38),op_c)))))]]) ).
cnf(refute_0_45,plain,
mult(op_c,mult(X_38,ld(mult(op_c,X_38),op_c))) = op_f,
inference(resolve,[$cnf( $equal(op_f,mult(op_c,mult(X_38,ld(mult(op_c,X_38),op_c)))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( mult(mult(X_38,ld(mult(op_c,X_38),op_c)),op_c) != mult(op_c,mult(X_38,ld(mult(op_c,X_38),op_c)))
| mult(op_c,mult(X_38,ld(mult(op_c,X_38),op_c))) != op_f
| mult(mult(X_38,ld(mult(op_c,X_38),op_c)),op_c) = op_f ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(mult(X_38,ld(mult(op_c,X_38),op_c)),op_c),op_f) ),[0],$fot(mult(op_c,mult(X_38,ld(mult(op_c,X_38),op_c))))]]) ).
cnf(refute_0_47,plain,
( mult(mult(X_38,ld(mult(op_c,X_38),op_c)),op_c) != mult(op_c,mult(X_38,ld(mult(op_c,X_38),op_c)))
| mult(mult(X_38,ld(mult(op_c,X_38),op_c)),op_c) = op_f ),
inference(resolve,[$cnf( $equal(mult(op_c,mult(X_38,ld(mult(op_c,X_38),op_c))),op_f) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
mult(mult(X_38,ld(mult(op_c,X_38),op_c)),op_c) = op_f,
inference(resolve,[$cnf( $equal(mult(mult(X_38,ld(mult(op_c,X_38),op_c)),op_c),mult(op_c,mult(X_38,ld(mult(op_c,X_38),op_c)))) )],[refute_0_42,refute_0_47]) ).
cnf(refute_0_49,plain,
mult(mult(op_c,X_26),ld(mult(op_c,X_26),B)) = B,
inference(subst,[],[f01:[bind(A,$fot(mult(op_c,X_26)))]]) ).
cnf(refute_0_50,plain,
mult(op_c,mult(X_26,ld(mult(op_c,X_26),B))) = mult(mult(op_c,X_26),ld(mult(op_c,X_26),B)),
inference(subst,[],[f08:[bind(A,$fot(X_26)),bind(B,$fot(ld(mult(op_c,X_26),B)))]]) ).
cnf(refute_0_51,plain,
( mult(op_c,mult(X_26,ld(mult(op_c,X_26),B))) != mult(mult(op_c,X_26),ld(mult(op_c,X_26),B))
| mult(mult(op_c,X_26),ld(mult(op_c,X_26),B)) = mult(op_c,mult(X_26,ld(mult(op_c,X_26),B))) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(mult(op_c,mult(X_26,ld(mult(op_c,X_26),B))))),bind(Y,$fot(mult(mult(op_c,X_26),ld(mult(op_c,X_26),B))))]]) ).
cnf(refute_0_52,plain,
mult(mult(op_c,X_26),ld(mult(op_c,X_26),B)) = mult(op_c,mult(X_26,ld(mult(op_c,X_26),B))),
inference(resolve,[$cnf( $equal(mult(op_c,mult(X_26,ld(mult(op_c,X_26),B))),mult(mult(op_c,X_26),ld(mult(op_c,X_26),B))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
( mult(mult(op_c,X_26),ld(mult(op_c,X_26),B)) != B
| mult(mult(op_c,X_26),ld(mult(op_c,X_26),B)) != mult(op_c,mult(X_26,ld(mult(op_c,X_26),B)))
| mult(op_c,mult(X_26,ld(mult(op_c,X_26),B))) = B ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(op_c,X_26),ld(mult(op_c,X_26),B)),B) ),[0],$fot(mult(op_c,mult(X_26,ld(mult(op_c,X_26),B))))]]) ).
cnf(refute_0_54,plain,
( mult(mult(op_c,X_26),ld(mult(op_c,X_26),B)) != B
| mult(op_c,mult(X_26,ld(mult(op_c,X_26),B))) = B ),
inference(resolve,[$cnf( $equal(mult(mult(op_c,X_26),ld(mult(op_c,X_26),B)),mult(op_c,mult(X_26,ld(mult(op_c,X_26),B)))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
mult(op_c,mult(X_26,ld(mult(op_c,X_26),B))) = B,
inference(resolve,[$cnf( $equal(mult(mult(op_c,X_26),ld(mult(op_c,X_26),B)),B) )],[refute_0_49,refute_0_54]) ).
cnf(refute_0_56,plain,
mult(op_c,mult(X_38,ld(mult(op_c,X_38),op_c))) = op_c,
inference(subst,[],[refute_0_55:[bind(B,$fot(op_c)),bind(X_26,$fot(X_38))]]) ).
cnf(refute_0_57,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_58,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_57]) ).
cnf(refute_0_59,plain,
( mult(mult(X_38,ld(mult(op_c,X_38),op_c)),op_c) != mult(op_c,mult(X_38,ld(mult(op_c,X_38),op_c)))
| mult(op_c,mult(X_38,ld(mult(op_c,X_38),op_c))) != op_c
| mult(mult(X_38,ld(mult(op_c,X_38),op_c)),op_c) = op_c ),
inference(subst,[],[refute_0_58:[bind(X,$fot(mult(mult(X_38,ld(mult(op_c,X_38),op_c)),op_c))),bind(Y,$fot(mult(op_c,mult(X_38,ld(mult(op_c,X_38),op_c))))),bind(Z,$fot(op_c))]]) ).
cnf(refute_0_60,plain,
( mult(op_c,mult(X_38,ld(mult(op_c,X_38),op_c))) != op_c
| mult(mult(X_38,ld(mult(op_c,X_38),op_c)),op_c) = op_c ),
inference(resolve,[$cnf( $equal(mult(mult(X_38,ld(mult(op_c,X_38),op_c)),op_c),mult(op_c,mult(X_38,ld(mult(op_c,X_38),op_c)))) )],[refute_0_42,refute_0_59]) ).
cnf(refute_0_61,plain,
mult(mult(X_38,ld(mult(op_c,X_38),op_c)),op_c) = op_c,
inference(resolve,[$cnf( $equal(mult(op_c,mult(X_38,ld(mult(op_c,X_38),op_c))),op_c) )],[refute_0_56,refute_0_60]) ).
cnf(refute_0_62,plain,
( mult(mult(X_38,ld(mult(op_c,X_38),op_c)),op_c) != op_c
| mult(mult(X_38,ld(mult(op_c,X_38),op_c)),op_c) != op_f
| op_c = op_f ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(X_38,ld(mult(op_c,X_38),op_c)),op_c),op_f) ),[0],$fot(op_c)]]) ).
cnf(refute_0_63,plain,
( mult(mult(X_38,ld(mult(op_c,X_38),op_c)),op_c) != op_f
| op_c = op_f ),
inference(resolve,[$cnf( $equal(mult(mult(X_38,ld(mult(op_c,X_38),op_c)),op_c),op_c) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
op_c = op_f,
inference(resolve,[$cnf( $equal(mult(mult(X_38,ld(mult(op_c,X_38),op_c)),op_c),op_f) )],[refute_0_48,refute_0_63]) ).
cnf(refute_0_65,plain,
( op_c != op_f
| op_f = op_c ),
inference(subst,[],[refute_0_4:[bind(X,$fot(op_c)),bind(Y,$fot(op_f))]]) ).
cnf(refute_0_66,plain,
op_f = op_c,
inference(resolve,[$cnf( $equal(op_c,op_f) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
mult(op_f,x5) = mult(op_f,x5),
introduced(tautology,[refl,[$fot(mult(op_f,x5))]]) ).
cnf(refute_0_68,plain,
( mult(op_f,x5) != mult(op_f,x5)
| op_f != op_c
| mult(op_f,x5) = mult(op_c,x5) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_f,x5),mult(op_f,x5)) ),[1,0],$fot(op_c)]]) ).
cnf(refute_0_69,plain,
( op_f != op_c
| mult(op_f,x5) = mult(op_c,x5) ),
inference(resolve,[$cnf( $equal(mult(op_f,x5),mult(op_f,x5)) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
mult(op_f,x5) = mult(op_c,x5),
inference(resolve,[$cnf( $equal(op_f,op_c) )],[refute_0_66,refute_0_69]) ).
cnf(refute_0_71,plain,
mult(x4,mult(op_f,x5)) = mult(x4,mult(op_f,x5)),
introduced(tautology,[refl,[$fot(mult(x4,mult(op_f,x5)))]]) ).
cnf(refute_0_72,plain,
( mult(op_f,x5) != mult(op_c,x5)
| mult(x4,mult(op_f,x5)) != mult(x4,mult(op_f,x5))
| mult(x4,mult(op_f,x5)) = mult(x4,mult(op_c,x5)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(x4,mult(op_f,x5)),mult(x4,mult(op_f,x5))) ),[1,1],$fot(mult(op_c,x5))]]) ).
cnf(refute_0_73,plain,
( mult(op_f,x5) != mult(op_c,x5)
| mult(x4,mult(op_f,x5)) = mult(x4,mult(op_c,x5)) ),
inference(resolve,[$cnf( $equal(mult(x4,mult(op_f,x5)),mult(x4,mult(op_f,x5))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
mult(x4,mult(op_f,x5)) = mult(x4,mult(op_c,x5)),
inference(resolve,[$cnf( $equal(mult(op_f,x5),mult(op_c,x5)) )],[refute_0_70,refute_0_73]) ).
cnf(refute_0_75,plain,
( mult(x4,mult(op_c,x5)) != mult(op_c,mult(x4,x5))
| mult(x4,mult(op_f,x5)) != mult(x4,mult(op_c,x5))
| mult(x4,mult(op_f,x5)) = mult(op_c,mult(x4,x5)) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(mult(x4,mult(op_f,x5)))),bind(Y,$fot(mult(x4,mult(op_c,x5)))),bind(Z,$fot(mult(op_c,mult(x4,x5))))]]) ).
cnf(refute_0_76,plain,
( mult(x4,mult(op_c,x5)) != mult(op_c,mult(x4,x5))
| mult(x4,mult(op_f,x5)) = mult(op_c,mult(x4,x5)) ),
inference(resolve,[$cnf( $equal(mult(x4,mult(op_f,x5)),mult(x4,mult(op_c,x5))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
mult(x4,mult(op_f,x5)) = mult(op_c,mult(x4,x5)),
inference(resolve,[$cnf( $equal(mult(x4,mult(op_c,x5)),mult(op_c,mult(x4,x5))) )],[refute_0_41,refute_0_76]) ).
cnf(refute_0_78,plain,
( mult(op_c,mult(x4,x5)) != mult(mult(x4,op_f),x5)
| mult(x4,mult(op_f,x5)) != mult(op_c,mult(x4,x5))
| mult(x4,mult(op_f,x5)) = mult(mult(x4,op_f),x5) ),
introduced(tautology,[equality,[$cnf( $equal(mult(x4,mult(op_f,x5)),mult(op_c,mult(x4,x5))) ),[1],$fot(mult(mult(x4,op_f),x5))]]) ).
cnf(refute_0_79,plain,
( mult(op_c,mult(x4,x5)) != mult(mult(x4,op_f),x5)
| mult(x4,mult(op_f,x5)) = mult(mult(x4,op_f),x5) ),
inference(resolve,[$cnf( $equal(mult(x4,mult(op_f,x5)),mult(op_c,mult(x4,x5))) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
( mult(op_c,mult(A,B)) != mult(mult(op_c,A),B)
| mult(mult(op_c,A),B) = mult(op_c,mult(A,B)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(mult(op_c,mult(A,B)))),bind(Y,$fot(mult(mult(op_c,A),B)))]]) ).
cnf(refute_0_81,plain,
mult(mult(op_c,A),B) = mult(op_c,mult(A,B)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(A,B)),mult(mult(op_c,A),B)) )],[f08,refute_0_80]) ).
cnf(refute_0_82,plain,
mult(mult(op_c,x4),x5) = mult(op_c,mult(x4,x5)),
inference(subst,[],[refute_0_81:[bind(A,$fot(x4)),bind(B,$fot(x5))]]) ).
cnf(refute_0_83,plain,
mult(A,mult(mult(rd(op_c,mult(op_c,X_32)),X_32),op_c)) = mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32))),
inference(subst,[],[refute_0_35:[bind(B,$fot(mult(rd(op_c,mult(op_c,X_32)),X_32)))]]) ).
cnf(refute_0_84,plain,
op_e = mult(mult(rd(op_c,mult(op_c,X_32)),X_32),op_c),
inference(subst,[],[f12:[bind(A,$fot(op_c)),bind(B,$fot(X_32))]]) ).
cnf(refute_0_85,plain,
( op_e != mult(mult(rd(op_c,mult(op_c,X_32)),X_32),op_c)
| mult(mult(rd(op_c,mult(op_c,X_32)),X_32),op_c) = op_e ),
inference(subst,[],[refute_0_4:[bind(X,$fot(op_e)),bind(Y,$fot(mult(mult(rd(op_c,mult(op_c,X_32)),X_32),op_c)))]]) ).
cnf(refute_0_86,plain,
mult(mult(rd(op_c,mult(op_c,X_32)),X_32),op_c) = op_e,
inference(resolve,[$cnf( $equal(op_e,mult(mult(rd(op_c,mult(op_c,X_32)),X_32),op_c)) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
( mult(A,mult(mult(rd(op_c,mult(op_c,X_32)),X_32),op_c)) != mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)))
| mult(mult(rd(op_c,mult(op_c,X_32)),X_32),op_c) != op_e
| mult(A,op_e) = mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(A,mult(mult(rd(op_c,mult(op_c,X_32)),X_32),op_c)),mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)))) ),[0,1],$fot(op_e)]]) ).
cnf(refute_0_88,plain,
( mult(A,mult(mult(rd(op_c,mult(op_c,X_32)),X_32),op_c)) != mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)))
| mult(A,op_e) = mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32))) ),
inference(resolve,[$cnf( $equal(mult(mult(rd(op_c,mult(op_c,X_32)),X_32),op_c),op_e) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
mult(A,op_e) = mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32))),
inference(resolve,[$cnf( $equal(mult(A,mult(mult(rd(op_c,mult(op_c,X_32)),X_32),op_c)),mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)))) )],[refute_0_83,refute_0_88]) ).
cnf(refute_0_90,plain,
mult(mult(rd(op_c,mult(unit,X_32)),X_32),unit) = mult(rd(op_c,mult(unit,X_32)),X_32),
inference(subst,[],[f05:[bind(A,$fot(mult(rd(op_c,mult(unit,X_32)),X_32)))]]) ).
cnf(refute_0_91,plain,
op_e = mult(mult(rd(op_c,mult(unit,X_32)),X_32),unit),
inference(subst,[],[f12:[bind(A,$fot(unit)),bind(B,$fot(X_32))]]) ).
cnf(refute_0_92,plain,
( op_e != mult(mult(rd(op_c,mult(unit,X_32)),X_32),unit)
| mult(mult(rd(op_c,mult(unit,X_32)),X_32),unit) = op_e ),
inference(subst,[],[refute_0_4:[bind(X,$fot(op_e)),bind(Y,$fot(mult(mult(rd(op_c,mult(unit,X_32)),X_32),unit)))]]) ).
cnf(refute_0_93,plain,
mult(mult(rd(op_c,mult(unit,X_32)),X_32),unit) = op_e,
inference(resolve,[$cnf( $equal(op_e,mult(mult(rd(op_c,mult(unit,X_32)),X_32),unit)) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
( mult(mult(rd(op_c,mult(unit,X_32)),X_32),unit) != mult(rd(op_c,mult(unit,X_32)),X_32)
| mult(mult(rd(op_c,mult(unit,X_32)),X_32),unit) != op_e
| op_e = mult(rd(op_c,mult(unit,X_32)),X_32) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(rd(op_c,mult(unit,X_32)),X_32),unit),mult(rd(op_c,mult(unit,X_32)),X_32)) ),[0],$fot(op_e)]]) ).
cnf(refute_0_95,plain,
( mult(mult(rd(op_c,mult(unit,X_32)),X_32),unit) != mult(rd(op_c,mult(unit,X_32)),X_32)
| op_e = mult(rd(op_c,mult(unit,X_32)),X_32) ),
inference(resolve,[$cnf( $equal(mult(mult(rd(op_c,mult(unit,X_32)),X_32),unit),op_e) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
op_e = mult(rd(op_c,mult(unit,X_32)),X_32),
inference(resolve,[$cnf( $equal(mult(mult(rd(op_c,mult(unit,X_32)),X_32),unit),mult(rd(op_c,mult(unit,X_32)),X_32)) )],[refute_0_90,refute_0_95]) ).
cnf(refute_0_97,plain,
mult(rd(op_c,X_32),X_32) = op_c,
inference(subst,[],[f03:[bind(A,$fot(op_c)),bind(B,$fot(X_32))]]) ).
cnf(refute_0_98,plain,
mult(unit,X_32) = X_32,
inference(subst,[],[f06:[bind(A,$fot(X_32))]]) ).
cnf(refute_0_99,plain,
rd(op_c,mult(unit,X_32)) = rd(op_c,mult(unit,X_32)),
introduced(tautology,[refl,[$fot(rd(op_c,mult(unit,X_32)))]]) ).
cnf(refute_0_100,plain,
( mult(unit,X_32) != X_32
| rd(op_c,mult(unit,X_32)) != rd(op_c,mult(unit,X_32))
| rd(op_c,mult(unit,X_32)) = rd(op_c,X_32) ),
introduced(tautology,[equality,[$cnf( $equal(rd(op_c,mult(unit,X_32)),rd(op_c,mult(unit,X_32))) ),[1,1],$fot(X_32)]]) ).
cnf(refute_0_101,plain,
( mult(unit,X_32) != X_32
| rd(op_c,mult(unit,X_32)) = rd(op_c,X_32) ),
inference(resolve,[$cnf( $equal(rd(op_c,mult(unit,X_32)),rd(op_c,mult(unit,X_32))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
rd(op_c,mult(unit,X_32)) = rd(op_c,X_32),
inference(resolve,[$cnf( $equal(mult(unit,X_32),X_32) )],[refute_0_98,refute_0_101]) ).
cnf(refute_0_103,plain,
mult(rd(op_c,mult(unit,X_32)),X_32) = mult(rd(op_c,mult(unit,X_32)),X_32),
introduced(tautology,[refl,[$fot(mult(rd(op_c,mult(unit,X_32)),X_32))]]) ).
cnf(refute_0_104,plain,
( mult(rd(op_c,mult(unit,X_32)),X_32) != mult(rd(op_c,mult(unit,X_32)),X_32)
| rd(op_c,mult(unit,X_32)) != rd(op_c,X_32)
| mult(rd(op_c,mult(unit,X_32)),X_32) = mult(rd(op_c,X_32),X_32) ),
introduced(tautology,[equality,[$cnf( $equal(mult(rd(op_c,mult(unit,X_32)),X_32),mult(rd(op_c,mult(unit,X_32)),X_32)) ),[1,0],$fot(rd(op_c,X_32))]]) ).
cnf(refute_0_105,plain,
( rd(op_c,mult(unit,X_32)) != rd(op_c,X_32)
| mult(rd(op_c,mult(unit,X_32)),X_32) = mult(rd(op_c,X_32),X_32) ),
inference(resolve,[$cnf( $equal(mult(rd(op_c,mult(unit,X_32)),X_32),mult(rd(op_c,mult(unit,X_32)),X_32)) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
mult(rd(op_c,mult(unit,X_32)),X_32) = mult(rd(op_c,X_32),X_32),
inference(resolve,[$cnf( $equal(rd(op_c,mult(unit,X_32)),rd(op_c,X_32)) )],[refute_0_102,refute_0_105]) ).
cnf(refute_0_107,plain,
( mult(rd(op_c,X_32),X_32) != op_c
| mult(rd(op_c,mult(unit,X_32)),X_32) != mult(rd(op_c,X_32),X_32)
| mult(rd(op_c,mult(unit,X_32)),X_32) = op_c ),
inference(subst,[],[refute_0_58:[bind(X,$fot(mult(rd(op_c,mult(unit,X_32)),X_32))),bind(Y,$fot(mult(rd(op_c,X_32),X_32))),bind(Z,$fot(op_c))]]) ).
cnf(refute_0_108,plain,
( mult(rd(op_c,X_32),X_32) != op_c
| mult(rd(op_c,mult(unit,X_32)),X_32) = op_c ),
inference(resolve,[$cnf( $equal(mult(rd(op_c,mult(unit,X_32)),X_32),mult(rd(op_c,X_32),X_32)) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
mult(rd(op_c,mult(unit,X_32)),X_32) = op_c,
inference(resolve,[$cnf( $equal(mult(rd(op_c,X_32),X_32),op_c) )],[refute_0_97,refute_0_108]) ).
cnf(refute_0_110,plain,
( mult(rd(op_c,mult(unit,X_32)),X_32) != op_c
| op_e != mult(rd(op_c,mult(unit,X_32)),X_32)
| op_e = op_c ),
introduced(tautology,[equality,[$cnf( $equal(op_e,mult(rd(op_c,mult(unit,X_32)),X_32)) ),[1],$fot(op_c)]]) ).
cnf(refute_0_111,plain,
( op_e != mult(rd(op_c,mult(unit,X_32)),X_32)
| op_e = op_c ),
inference(resolve,[$cnf( $equal(mult(rd(op_c,mult(unit,X_32)),X_32),op_c) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
op_e = op_c,
inference(resolve,[$cnf( $equal(op_e,mult(rd(op_c,mult(unit,X_32)),X_32)) )],[refute_0_96,refute_0_111]) ).
cnf(refute_0_113,plain,
mult(A,op_e) = mult(A,op_e),
introduced(tautology,[refl,[$fot(mult(A,op_e))]]) ).
cnf(refute_0_114,plain,
( mult(A,op_e) != mult(A,op_e)
| op_e != op_c
| mult(A,op_e) = mult(A,op_c) ),
introduced(tautology,[equality,[$cnf( $equal(mult(A,op_e),mult(A,op_e)) ),[1,1],$fot(op_c)]]) ).
cnf(refute_0_115,plain,
( op_e != op_c
| mult(A,op_e) = mult(A,op_c) ),
inference(resolve,[$cnf( $equal(mult(A,op_e),mult(A,op_e)) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
mult(A,op_e) = mult(A,op_c),
inference(resolve,[$cnf( $equal(op_e,op_c) )],[refute_0_112,refute_0_115]) ).
cnf(refute_0_117,plain,
( mult(A,op_e) != mult(A,op_c)
| mult(A,op_e) != mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)))
| mult(A,op_c) = mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(A,op_e),mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)))) ),[0],$fot(mult(A,op_c))]]) ).
cnf(refute_0_118,plain,
( mult(A,op_e) != mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)))
| mult(A,op_c) = mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32))) ),
inference(resolve,[$cnf( $equal(mult(A,op_e),mult(A,op_c)) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
rd(mult(unit,X_21),X_21) = unit,
inference(subst,[],[f04:[bind(A,$fot(unit)),bind(B,$fot(X_21))]]) ).
cnf(refute_0_120,plain,
mult(unit,X_21) = X_21,
inference(subst,[],[f06:[bind(A,$fot(X_21))]]) ).
cnf(refute_0_121,plain,
( mult(unit,X_21) != X_21
| rd(mult(unit,X_21),X_21) != unit
| rd(X_21,X_21) = unit ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(unit,X_21),X_21),unit) ),[0,0],$fot(X_21)]]) ).
cnf(refute_0_122,plain,
( rd(mult(unit,X_21),X_21) != unit
| rd(X_21,X_21) = unit ),
inference(resolve,[$cnf( $equal(mult(unit,X_21),X_21) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
rd(X_21,X_21) = unit,
inference(resolve,[$cnf( $equal(rd(mult(unit,X_21),X_21),unit) )],[refute_0_119,refute_0_122]) ).
cnf(refute_0_124,plain,
rd(op_c,op_c) = unit,
inference(subst,[],[refute_0_123:[bind(X_21,$fot(op_c))]]) ).
cnf(refute_0_125,plain,
rd(mult(mult(rd(op_c,mult(B,X_32)),X_32),B),B) = mult(rd(op_c,mult(B,X_32)),X_32),
inference(subst,[],[f04:[bind(A,$fot(mult(rd(op_c,mult(B,X_32)),X_32)))]]) ).
cnf(refute_0_126,plain,
op_e = mult(mult(rd(op_c,mult(B,X_32)),X_32),B),
inference(subst,[],[f12:[bind(A,$fot(B)),bind(B,$fot(X_32))]]) ).
cnf(refute_0_127,plain,
( op_e != mult(mult(rd(op_c,mult(B,X_32)),X_32),B)
| mult(mult(rd(op_c,mult(B,X_32)),X_32),B) = op_e ),
inference(subst,[],[refute_0_4:[bind(X,$fot(op_e)),bind(Y,$fot(mult(mult(rd(op_c,mult(B,X_32)),X_32),B)))]]) ).
cnf(refute_0_128,plain,
mult(mult(rd(op_c,mult(B,X_32)),X_32),B) = op_e,
inference(resolve,[$cnf( $equal(op_e,mult(mult(rd(op_c,mult(B,X_32)),X_32),B)) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
( mult(mult(rd(op_c,mult(B,X_32)),X_32),B) != op_e
| rd(mult(mult(rd(op_c,mult(B,X_32)),X_32),B),B) != mult(rd(op_c,mult(B,X_32)),X_32)
| rd(op_e,B) = mult(rd(op_c,mult(B,X_32)),X_32) ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(mult(rd(op_c,mult(B,X_32)),X_32),B),B),mult(rd(op_c,mult(B,X_32)),X_32)) ),[0,0],$fot(op_e)]]) ).
cnf(refute_0_130,plain,
( rd(mult(mult(rd(op_c,mult(B,X_32)),X_32),B),B) != mult(rd(op_c,mult(B,X_32)),X_32)
| rd(op_e,B) = mult(rd(op_c,mult(B,X_32)),X_32) ),
inference(resolve,[$cnf( $equal(mult(mult(rd(op_c,mult(B,X_32)),X_32),B),op_e) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
rd(op_e,B) = mult(rd(op_c,mult(B,X_32)),X_32),
inference(resolve,[$cnf( $equal(rd(mult(mult(rd(op_c,mult(B,X_32)),X_32),B),B),mult(rd(op_c,mult(B,X_32)),X_32)) )],[refute_0_125,refute_0_130]) ).
cnf(refute_0_132,plain,
rd(op_e,B) = rd(op_e,B),
introduced(tautology,[refl,[$fot(rd(op_e,B))]]) ).
cnf(refute_0_133,plain,
( op_e != op_c
| rd(op_e,B) != rd(op_e,B)
| rd(op_e,B) = rd(op_c,B) ),
introduced(tautology,[equality,[$cnf( $equal(rd(op_e,B),rd(op_e,B)) ),[1,0],$fot(op_c)]]) ).
cnf(refute_0_134,plain,
( op_e != op_c
| rd(op_e,B) = rd(op_c,B) ),
inference(resolve,[$cnf( $equal(rd(op_e,B),rd(op_e,B)) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
rd(op_e,B) = rd(op_c,B),
inference(resolve,[$cnf( $equal(op_e,op_c) )],[refute_0_112,refute_0_134]) ).
cnf(refute_0_136,plain,
( rd(op_e,B) != mult(rd(op_c,mult(B,X_32)),X_32)
| rd(op_e,B) != rd(op_c,B)
| rd(op_c,B) = mult(rd(op_c,mult(B,X_32)),X_32) ),
introduced(tautology,[equality,[$cnf( $equal(rd(op_e,B),mult(rd(op_c,mult(B,X_32)),X_32)) ),[0],$fot(rd(op_c,B))]]) ).
cnf(refute_0_137,plain,
( rd(op_e,B) != mult(rd(op_c,mult(B,X_32)),X_32)
| rd(op_c,B) = mult(rd(op_c,mult(B,X_32)),X_32) ),
inference(resolve,[$cnf( $equal(rd(op_e,B),rd(op_c,B)) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
rd(op_c,B) = mult(rd(op_c,mult(B,X_32)),X_32),
inference(resolve,[$cnf( $equal(rd(op_e,B),mult(rd(op_c,mult(B,X_32)),X_32)) )],[refute_0_131,refute_0_137]) ).
cnf(refute_0_139,plain,
( rd(op_c,B) != mult(rd(op_c,mult(B,X_32)),X_32)
| mult(rd(op_c,mult(B,X_32)),X_32) = rd(op_c,B) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(rd(op_c,B))),bind(Y,$fot(mult(rd(op_c,mult(B,X_32)),X_32)))]]) ).
cnf(refute_0_140,plain,
mult(rd(op_c,mult(B,X_32)),X_32) = rd(op_c,B),
inference(resolve,[$cnf( $equal(rd(op_c,B),mult(rd(op_c,mult(B,X_32)),X_32)) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
mult(rd(op_c,mult(op_c,X_32)),X_32) = rd(op_c,op_c),
inference(subst,[],[refute_0_140:[bind(B,$fot(op_c))]]) ).
cnf(refute_0_142,plain,
( mult(rd(op_c,mult(op_c,X_32)),X_32) != rd(op_c,op_c)
| rd(op_c,op_c) != unit
| mult(rd(op_c,mult(op_c,X_32)),X_32) = unit ),
inference(subst,[],[refute_0_58:[bind(X,$fot(mult(rd(op_c,mult(op_c,X_32)),X_32))),bind(Y,$fot(rd(op_c,op_c))),bind(Z,$fot(unit))]]) ).
cnf(refute_0_143,plain,
( rd(op_c,op_c) != unit
| mult(rd(op_c,mult(op_c,X_32)),X_32) = unit ),
inference(resolve,[$cnf( $equal(mult(rd(op_c,mult(op_c,X_32)),X_32),rd(op_c,op_c)) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
mult(rd(op_c,mult(op_c,X_32)),X_32) = unit,
inference(resolve,[$cnf( $equal(rd(op_c,op_c),unit) )],[refute_0_124,refute_0_143]) ).
cnf(refute_0_145,plain,
mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)) = mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)),
introduced(tautology,[refl,[$fot(mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)))]]) ).
cnf(refute_0_146,plain,
( mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)) != mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32))
| mult(rd(op_c,mult(op_c,X_32)),X_32) != unit
| mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)) = mult(A,unit) ),
introduced(tautology,[equality,[$cnf( $equal(mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)),mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32))) ),[1,1],$fot(unit)]]) ).
cnf(refute_0_147,plain,
( mult(rd(op_c,mult(op_c,X_32)),X_32) != unit
| mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)) = mult(A,unit) ),
inference(resolve,[$cnf( $equal(mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)),mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32))) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)) = mult(A,unit),
inference(resolve,[$cnf( $equal(mult(rd(op_c,mult(op_c,X_32)),X_32),unit) )],[refute_0_144,refute_0_147]) ).
cnf(refute_0_149,plain,
( mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)) != mult(A,unit)
| mult(A,unit) != A
| mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)) = A ),
inference(subst,[],[refute_0_58:[bind(X,$fot(mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)))),bind(Y,$fot(mult(A,unit))),bind(Z,$fot(A))]]) ).
cnf(refute_0_150,plain,
( mult(A,unit) != A
| mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)) = A ),
inference(resolve,[$cnf( $equal(mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)),mult(A,unit)) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)) = A,
inference(resolve,[$cnf( $equal(mult(A,unit),A) )],[f05,refute_0_150]) ).
cnf(refute_0_152,plain,
mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32))) = mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32))),
introduced(tautology,[refl,[$fot(mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32))))]]) ).
cnf(refute_0_153,plain,
( mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)) != A
| mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32))) != mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)))
| mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32))) = mult(op_c,A) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32))),mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_154,plain,
( mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)) != A
| mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32))) = mult(op_c,A) ),
inference(resolve,[$cnf( $equal(mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32))),mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32))) = mult(op_c,A),
inference(resolve,[$cnf( $equal(mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)),A) )],[refute_0_151,refute_0_154]) ).
cnf(refute_0_156,plain,
( mult(A,op_c) != mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)))
| mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32))) != mult(op_c,A)
| mult(A,op_c) = mult(op_c,A) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(A,op_c),mult(op_c,A)) ),[0],$fot(mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32))))]]) ).
cnf(refute_0_157,plain,
( mult(A,op_c) != mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)))
| mult(A,op_c) = mult(op_c,A) ),
inference(resolve,[$cnf( $equal(mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32))),mult(op_c,A)) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
( mult(A,op_e) != mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)))
| mult(A,op_c) = mult(op_c,A) ),
inference(resolve,[$cnf( $equal(mult(A,op_c),mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)))) )],[refute_0_118,refute_0_157]) ).
cnf(refute_0_159,plain,
mult(A,op_c) = mult(op_c,A),
inference(resolve,[$cnf( $equal(mult(A,op_e),mult(op_c,mult(A,mult(rd(op_c,mult(op_c,X_32)),X_32)))) )],[refute_0_89,refute_0_158]) ).
cnf(refute_0_160,plain,
mult(x4,op_c) = mult(op_c,x4),
inference(subst,[],[refute_0_159:[bind(A,$fot(x4))]]) ).
cnf(refute_0_161,plain,
mult(x4,op_f) = mult(x4,op_f),
introduced(tautology,[refl,[$fot(mult(x4,op_f))]]) ).
cnf(refute_0_162,plain,
( mult(x4,op_f) != mult(x4,op_f)
| op_f != op_c
| mult(x4,op_f) = mult(x4,op_c) ),
introduced(tautology,[equality,[$cnf( $equal(mult(x4,op_f),mult(x4,op_f)) ),[1,1],$fot(op_c)]]) ).
cnf(refute_0_163,plain,
( op_f != op_c
| mult(x4,op_f) = mult(x4,op_c) ),
inference(resolve,[$cnf( $equal(mult(x4,op_f),mult(x4,op_f)) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
mult(x4,op_f) = mult(x4,op_c),
inference(resolve,[$cnf( $equal(op_f,op_c) )],[refute_0_66,refute_0_163]) ).
cnf(refute_0_165,plain,
( mult(x4,op_c) != mult(op_c,x4)
| mult(x4,op_f) != mult(x4,op_c)
| mult(x4,op_f) = mult(op_c,x4) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(mult(x4,op_f))),bind(Y,$fot(mult(x4,op_c))),bind(Z,$fot(mult(op_c,x4)))]]) ).
cnf(refute_0_166,plain,
( mult(x4,op_c) != mult(op_c,x4)
| mult(x4,op_f) = mult(op_c,x4) ),
inference(resolve,[$cnf( $equal(mult(x4,op_f),mult(x4,op_c)) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
mult(x4,op_f) = mult(op_c,x4),
inference(resolve,[$cnf( $equal(mult(x4,op_c),mult(op_c,x4)) )],[refute_0_160,refute_0_166]) ).
cnf(refute_0_168,plain,
mult(mult(x4,op_f),x5) = mult(mult(x4,op_f),x5),
introduced(tautology,[refl,[$fot(mult(mult(x4,op_f),x5))]]) ).
cnf(refute_0_169,plain,
( mult(mult(x4,op_f),x5) != mult(mult(x4,op_f),x5)
| mult(x4,op_f) != mult(op_c,x4)
| mult(mult(x4,op_f),x5) = mult(mult(op_c,x4),x5) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(x4,op_f),x5),mult(mult(x4,op_f),x5)) ),[1,0],$fot(mult(op_c,x4))]]) ).
cnf(refute_0_170,plain,
( mult(x4,op_f) != mult(op_c,x4)
| mult(mult(x4,op_f),x5) = mult(mult(op_c,x4),x5) ),
inference(resolve,[$cnf( $equal(mult(mult(x4,op_f),x5),mult(mult(x4,op_f),x5)) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
mult(mult(x4,op_f),x5) = mult(mult(op_c,x4),x5),
inference(resolve,[$cnf( $equal(mult(x4,op_f),mult(op_c,x4)) )],[refute_0_167,refute_0_170]) ).
cnf(refute_0_172,plain,
( mult(mult(op_c,x4),x5) != mult(op_c,mult(x4,x5))
| mult(mult(x4,op_f),x5) != mult(mult(op_c,x4),x5)
| mult(mult(x4,op_f),x5) = mult(op_c,mult(x4,x5)) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(mult(mult(x4,op_f),x5))),bind(Y,$fot(mult(mult(op_c,x4),x5))),bind(Z,$fot(mult(op_c,mult(x4,x5))))]]) ).
cnf(refute_0_173,plain,
( mult(mult(op_c,x4),x5) != mult(op_c,mult(x4,x5))
| mult(mult(x4,op_f),x5) = mult(op_c,mult(x4,x5)) ),
inference(resolve,[$cnf( $equal(mult(mult(x4,op_f),x5),mult(mult(op_c,x4),x5)) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
mult(mult(x4,op_f),x5) = mult(op_c,mult(x4,x5)),
inference(resolve,[$cnf( $equal(mult(mult(op_c,x4),x5),mult(op_c,mult(x4,x5))) )],[refute_0_82,refute_0_173]) ).
cnf(refute_0_175,plain,
( mult(mult(x4,op_f),x5) != mult(op_c,mult(x4,x5))
| mult(op_c,mult(x4,x5)) != mult(op_c,mult(x4,x5))
| mult(op_c,mult(x4,x5)) = mult(mult(x4,op_f),x5) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(op_c,mult(x4,x5)),mult(mult(x4,op_f),x5)) ),[1],$fot(mult(op_c,mult(x4,x5)))]]) ).
cnf(refute_0_176,plain,
( mult(op_c,mult(x4,x5)) != mult(op_c,mult(x4,x5))
| mult(op_c,mult(x4,x5)) = mult(mult(x4,op_f),x5) ),
inference(resolve,[$cnf( $equal(mult(mult(x4,op_f),x5),mult(op_c,mult(x4,x5))) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
( mult(op_c,mult(x4,x5)) != mult(op_c,mult(x4,x5))
| mult(x4,mult(op_f,x5)) = mult(mult(x4,op_f),x5) ),
inference(resolve,[$cnf( $equal(mult(op_c,mult(x4,x5)),mult(mult(x4,op_f),x5)) )],[refute_0_176,refute_0_79]) ).
cnf(refute_0_178,plain,
mult(op_c,mult(x4,x5)) != mult(op_c,mult(x4,x5)),
inference(resolve,[$cnf( $equal(mult(x4,mult(op_f,x5)),mult(mult(x4,op_f),x5)) )],[refute_0_177,goal]) ).
cnf(refute_0_179,plain,
mult(op_c,mult(x4,x5)) = mult(op_c,mult(x4,x5)),
introduced(tautology,[refl,[$fot(mult(op_c,mult(x4,x5)))]]) ).
cnf(refute_0_180,plain,
$false,
inference(resolve,[$cnf( $equal(mult(op_c,mult(x4,x5)),mult(op_c,mult(x4,x5))) )],[refute_0_179,refute_0_178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP704-12 : TPTP v8.1.0. Released v8.1.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 01:45:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.41
% 0.19/0.41 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.44
%------------------------------------------------------------------------------