TSTP Solution File: GRP699-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP699-1 : TPTP v8.1.0. Released v4.0.0.
% 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 10:50:02 EDT 2022
% Result : Unsatisfiable 4.27s 4.45s
% Output : CNFRefutation 4.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 50
% Syntax : Number of clauses : 171 ( 96 unt; 0 nHn; 77 RR)
% Number of literals : 282 ( 281 equ; 113 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 335 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c01,axiom,
mult(A,ld(A,B)) = B ).
cnf(c02,axiom,
ld(A,mult(A,B)) = B ).
cnf(c03,axiom,
mult(rd(A,B),B) = A ).
cnf(c04,axiom,
rd(mult(A,B),B) = A ).
cnf(c05,axiom,
mult(A,unit) = A ).
cnf(c06,axiom,
mult(unit,A) = A ).
cnf(c07,axiom,
mult(mult(mult(A,B),A),mult(A,C)) = mult(A,mult(mult(mult(B,A),A),C)) ).
cnf(c08,axiom,
mult(mult(A,B),mult(B,mult(C,B))) = mult(mult(A,mult(B,mult(B,C))),B) ).
cnf(goals,negated_conjecture,
mult(mult(a,b),c) != mult(mult(a,c),ld(c,mult(b,c))) ).
cnf(refute_0_0,plain,
mult(mult(A,B),mult(B,mult(ld(B,ld(B,X_243)),B))) = mult(mult(A,mult(B,mult(B,ld(B,ld(B,X_243))))),B),
inference(subst,[],[c08:[bind(C,$fot(ld(B,ld(B,X_243))))]]) ).
cnf(refute_0_1,plain,
mult(mult(X_18,X_19),mult(X_19,mult(ld(X_19,B),X_19))) = mult(mult(X_18,mult(X_19,mult(X_19,ld(X_19,B)))),X_19),
inference(subst,[],[c08:[bind(A,$fot(X_18)),bind(B,$fot(X_19)),bind(C,$fot(ld(X_19,B)))]]) ).
cnf(refute_0_2,plain,
mult(X_19,ld(X_19,B)) = B,
inference(subst,[],[c01:[bind(A,$fot(X_19))]]) ).
cnf(refute_0_3,plain,
( mult(X_19,ld(X_19,B)) != B
| mult(mult(X_18,X_19),mult(X_19,mult(ld(X_19,B),X_19))) != mult(mult(X_18,mult(X_19,mult(X_19,ld(X_19,B)))),X_19)
| mult(mult(X_18,X_19),mult(X_19,mult(ld(X_19,B),X_19))) = mult(mult(X_18,mult(X_19,B)),X_19) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(X_18,X_19),mult(X_19,mult(ld(X_19,B),X_19))),mult(mult(X_18,mult(X_19,mult(X_19,ld(X_19,B)))),X_19)) ),[1,0,1,1],$fot(B)]]) ).
cnf(refute_0_4,plain,
( mult(mult(X_18,X_19),mult(X_19,mult(ld(X_19,B),X_19))) != mult(mult(X_18,mult(X_19,mult(X_19,ld(X_19,B)))),X_19)
| mult(mult(X_18,X_19),mult(X_19,mult(ld(X_19,B),X_19))) = mult(mult(X_18,mult(X_19,B)),X_19) ),
inference(resolve,[$cnf( $equal(mult(X_19,ld(X_19,B)),B) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
mult(mult(X_18,X_19),mult(X_19,mult(ld(X_19,B),X_19))) = mult(mult(X_18,mult(X_19,B)),X_19),
inference(resolve,[$cnf( $equal(mult(mult(X_18,X_19),mult(X_19,mult(ld(X_19,B),X_19))),mult(mult(X_18,mult(X_19,mult(X_19,ld(X_19,B)))),X_19)) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
mult(mult(ld(X_102,unit),X_102),mult(X_102,mult(ld(X_102,X_100),X_102))) = mult(mult(ld(X_102,unit),mult(X_102,X_100)),X_102),
inference(subst,[],[refute_0_5:[bind(B,$fot(X_100)),bind(X_18,$fot(ld(X_102,unit))),bind(X_19,$fot(X_102))]]) ).
cnf(refute_0_7,plain,
rd(mult(mult(B,rd(unit,B)),B),B) = mult(B,rd(unit,B)),
inference(subst,[],[c04:[bind(A,$fot(mult(B,rd(unit,B))))]]) ).
cnf(refute_0_8,plain,
rd(mult(mult(mult(B,X_30),B),B),B) = mult(mult(B,X_30),B),
inference(subst,[],[c04:[bind(A,$fot(mult(mult(B,X_30),B)))]]) ).
cnf(refute_0_9,plain,
mult(mult(mult(X_26,X_27),X_26),mult(X_26,unit)) = mult(X_26,mult(mult(mult(X_27,X_26),X_26),unit)),
inference(subst,[],[c07:[bind(A,$fot(X_26)),bind(B,$fot(X_27)),bind(C,$fot(unit))]]) ).
cnf(refute_0_10,plain,
mult(X_26,unit) = X_26,
inference(subst,[],[c05:[bind(A,$fot(X_26))]]) ).
cnf(refute_0_11,plain,
( mult(X_26,unit) != X_26
| mult(mult(mult(X_26,X_27),X_26),mult(X_26,unit)) != mult(X_26,mult(mult(mult(X_27,X_26),X_26),unit))
| mult(mult(mult(X_26,X_27),X_26),X_26) = mult(X_26,mult(mult(mult(X_27,X_26),X_26),unit)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(mult(X_26,X_27),X_26),mult(X_26,unit)),mult(X_26,mult(mult(mult(X_27,X_26),X_26),unit))) ),[0,1],$fot(X_26)]]) ).
cnf(refute_0_12,plain,
( mult(mult(mult(X_26,X_27),X_26),mult(X_26,unit)) != mult(X_26,mult(mult(mult(X_27,X_26),X_26),unit))
| mult(mult(mult(X_26,X_27),X_26),X_26) = mult(X_26,mult(mult(mult(X_27,X_26),X_26),unit)) ),
inference(resolve,[$cnf( $equal(mult(X_26,unit),X_26) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
mult(mult(mult(X_26,X_27),X_26),X_26) = mult(X_26,mult(mult(mult(X_27,X_26),X_26),unit)),
inference(resolve,[$cnf( $equal(mult(mult(mult(X_26,X_27),X_26),mult(X_26,unit)),mult(X_26,mult(mult(mult(X_27,X_26),X_26),unit))) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
mult(mult(mult(X_27,X_26),X_26),unit) = mult(mult(X_27,X_26),X_26),
inference(subst,[],[c05:[bind(A,$fot(mult(mult(X_27,X_26),X_26)))]]) ).
cnf(refute_0_15,plain,
mult(X_26,mult(mult(mult(X_27,X_26),X_26),unit)) = mult(X_26,mult(mult(mult(X_27,X_26),X_26),unit)),
introduced(tautology,[refl,[$fot(mult(X_26,mult(mult(mult(X_27,X_26),X_26),unit)))]]) ).
cnf(refute_0_16,plain,
( mult(X_26,mult(mult(mult(X_27,X_26),X_26),unit)) != mult(X_26,mult(mult(mult(X_27,X_26),X_26),unit))
| mult(mult(mult(X_27,X_26),X_26),unit) != mult(mult(X_27,X_26),X_26)
| mult(X_26,mult(mult(mult(X_27,X_26),X_26),unit)) = mult(X_26,mult(mult(X_27,X_26),X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_26,mult(mult(mult(X_27,X_26),X_26),unit)),mult(X_26,mult(mult(mult(X_27,X_26),X_26),unit))) ),[1,1],$fot(mult(mult(X_27,X_26),X_26))]]) ).
cnf(refute_0_17,plain,
( mult(mult(mult(X_27,X_26),X_26),unit) != mult(mult(X_27,X_26),X_26)
| mult(X_26,mult(mult(mult(X_27,X_26),X_26),unit)) = mult(X_26,mult(mult(X_27,X_26),X_26)) ),
inference(resolve,[$cnf( $equal(mult(X_26,mult(mult(mult(X_27,X_26),X_26),unit)),mult(X_26,mult(mult(mult(X_27,X_26),X_26),unit))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
mult(X_26,mult(mult(mult(X_27,X_26),X_26),unit)) = mult(X_26,mult(mult(X_27,X_26),X_26)),
inference(resolve,[$cnf( $equal(mult(mult(mult(X_27,X_26),X_26),unit),mult(mult(X_27,X_26),X_26)) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
( mult(X_26,mult(mult(mult(X_27,X_26),X_26),unit)) != mult(X_26,mult(mult(X_27,X_26),X_26))
| mult(mult(mult(X_26,X_27),X_26),X_26) != mult(X_26,mult(mult(mult(X_27,X_26),X_26),unit))
| mult(mult(mult(X_26,X_27),X_26),X_26) = mult(X_26,mult(mult(X_27,X_26),X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(mult(X_26,X_27),X_26),X_26),mult(X_26,mult(mult(mult(X_27,X_26),X_26),unit))) ),[1],$fot(mult(X_26,mult(mult(X_27,X_26),X_26)))]]) ).
cnf(refute_0_20,plain,
( mult(mult(mult(X_26,X_27),X_26),X_26) != mult(X_26,mult(mult(mult(X_27,X_26),X_26),unit))
| mult(mult(mult(X_26,X_27),X_26),X_26) = mult(X_26,mult(mult(X_27,X_26),X_26)) ),
inference(resolve,[$cnf( $equal(mult(X_26,mult(mult(mult(X_27,X_26),X_26),unit)),mult(X_26,mult(mult(X_27,X_26),X_26))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
mult(mult(mult(X_26,X_27),X_26),X_26) = mult(X_26,mult(mult(X_27,X_26),X_26)),
inference(resolve,[$cnf( $equal(mult(mult(mult(X_26,X_27),X_26),X_26),mult(X_26,mult(mult(mult(X_27,X_26),X_26),unit))) )],[refute_0_13,refute_0_20]) ).
cnf(refute_0_22,plain,
mult(mult(mult(B,X_30),B),B) = mult(B,mult(mult(X_30,B),B)),
inference(subst,[],[refute_0_21:[bind(X_26,$fot(B)),bind(X_27,$fot(X_30))]]) ).
cnf(refute_0_23,plain,
( mult(mult(mult(B,X_30),B),B) != mult(B,mult(mult(X_30,B),B))
| rd(mult(mult(mult(B,X_30),B),B),B) != mult(mult(B,X_30),B)
| rd(mult(B,mult(mult(X_30,B),B)),B) = mult(mult(B,X_30),B) ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(mult(mult(B,X_30),B),B),B),mult(mult(B,X_30),B)) ),[0,0],$fot(mult(B,mult(mult(X_30,B),B)))]]) ).
cnf(refute_0_24,plain,
( rd(mult(mult(mult(B,X_30),B),B),B) != mult(mult(B,X_30),B)
| rd(mult(B,mult(mult(X_30,B),B)),B) = mult(mult(B,X_30),B) ),
inference(resolve,[$cnf( $equal(mult(mult(mult(B,X_30),B),B),mult(B,mult(mult(X_30,B),B))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
rd(mult(B,mult(mult(X_30,B),B)),B) = mult(mult(B,X_30),B),
inference(resolve,[$cnf( $equal(rd(mult(mult(mult(B,X_30),B),B),B),mult(mult(B,X_30),B)) )],[refute_0_8,refute_0_24]) ).
cnf(refute_0_26,plain,
rd(mult(X_45,mult(mult(rd(A,X_45),X_45),X_45)),X_45) = mult(mult(X_45,rd(A,X_45)),X_45),
inference(subst,[],[refute_0_25:[bind(B,$fot(X_45)),bind(X_30,$fot(rd(A,X_45)))]]) ).
cnf(refute_0_27,plain,
mult(rd(A,X_45),X_45) = A,
inference(subst,[],[c03:[bind(B,$fot(X_45))]]) ).
cnf(refute_0_28,plain,
( mult(rd(A,X_45),X_45) != A
| rd(mult(X_45,mult(mult(rd(A,X_45),X_45),X_45)),X_45) != mult(mult(X_45,rd(A,X_45)),X_45)
| rd(mult(X_45,mult(A,X_45)),X_45) = mult(mult(X_45,rd(A,X_45)),X_45) ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(X_45,mult(mult(rd(A,X_45),X_45),X_45)),X_45),mult(mult(X_45,rd(A,X_45)),X_45)) ),[0,0,1,0],$fot(A)]]) ).
cnf(refute_0_29,plain,
( rd(mult(X_45,mult(mult(rd(A,X_45),X_45),X_45)),X_45) != mult(mult(X_45,rd(A,X_45)),X_45)
| rd(mult(X_45,mult(A,X_45)),X_45) = mult(mult(X_45,rd(A,X_45)),X_45) ),
inference(resolve,[$cnf( $equal(mult(rd(A,X_45),X_45),A) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
rd(mult(X_45,mult(A,X_45)),X_45) = mult(mult(X_45,rd(A,X_45)),X_45),
inference(resolve,[$cnf( $equal(rd(mult(X_45,mult(mult(rd(A,X_45),X_45),X_45)),X_45),mult(mult(X_45,rd(A,X_45)),X_45)) )],[refute_0_26,refute_0_29]) ).
cnf(refute_0_31,plain,
rd(mult(X_74,mult(unit,X_74)),X_74) = mult(mult(X_74,rd(unit,X_74)),X_74),
inference(subst,[],[refute_0_30:[bind(A,$fot(unit)),bind(X_45,$fot(X_74))]]) ).
cnf(refute_0_32,plain,
mult(unit,X_74) = X_74,
inference(subst,[],[c06:[bind(A,$fot(X_74))]]) ).
cnf(refute_0_33,plain,
( mult(unit,X_74) != X_74
| rd(mult(X_74,mult(unit,X_74)),X_74) != mult(mult(X_74,rd(unit,X_74)),X_74)
| rd(mult(X_74,X_74),X_74) = mult(mult(X_74,rd(unit,X_74)),X_74) ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(X_74,mult(unit,X_74)),X_74),mult(mult(X_74,rd(unit,X_74)),X_74)) ),[0,0,1],$fot(X_74)]]) ).
cnf(refute_0_34,plain,
( rd(mult(X_74,mult(unit,X_74)),X_74) != mult(mult(X_74,rd(unit,X_74)),X_74)
| rd(mult(X_74,X_74),X_74) = mult(mult(X_74,rd(unit,X_74)),X_74) ),
inference(resolve,[$cnf( $equal(mult(unit,X_74),X_74) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
rd(mult(X_74,X_74),X_74) = mult(mult(X_74,rd(unit,X_74)),X_74),
inference(resolve,[$cnf( $equal(rd(mult(X_74,mult(unit,X_74)),X_74),mult(mult(X_74,rd(unit,X_74)),X_74)) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
rd(mult(X_74,X_74),X_74) = X_74,
inference(subst,[],[c04:[bind(A,$fot(X_74)),bind(B,$fot(X_74))]]) ).
cnf(refute_0_37,plain,
( rd(mult(X_74,X_74),X_74) != X_74
| rd(mult(X_74,X_74),X_74) != mult(mult(X_74,rd(unit,X_74)),X_74)
| X_74 = mult(mult(X_74,rd(unit,X_74)),X_74) ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(X_74,X_74),X_74),mult(mult(X_74,rd(unit,X_74)),X_74)) ),[0],$fot(X_74)]]) ).
cnf(refute_0_38,plain,
( rd(mult(X_74,X_74),X_74) != mult(mult(X_74,rd(unit,X_74)),X_74)
| X_74 = mult(mult(X_74,rd(unit,X_74)),X_74) ),
inference(resolve,[$cnf( $equal(rd(mult(X_74,X_74),X_74),X_74) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
X_74 = mult(mult(X_74,rd(unit,X_74)),X_74),
inference(resolve,[$cnf( $equal(rd(mult(X_74,X_74),X_74),mult(mult(X_74,rd(unit,X_74)),X_74)) )],[refute_0_35,refute_0_38]) ).
cnf(refute_0_40,plain,
B = mult(mult(B,rd(unit,B)),B),
inference(subst,[],[refute_0_39:[bind(X_74,$fot(B))]]) ).
cnf(refute_0_41,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_42,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_43,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
( B != mult(mult(B,rd(unit,B)),B)
| mult(mult(B,rd(unit,B)),B) = B ),
inference(subst,[],[refute_0_43:[bind(X,$fot(B)),bind(Y,$fot(mult(mult(B,rd(unit,B)),B)))]]) ).
cnf(refute_0_45,plain,
mult(mult(B,rd(unit,B)),B) = B,
inference(resolve,[$cnf( $equal(B,mult(mult(B,rd(unit,B)),B)) )],[refute_0_40,refute_0_44]) ).
cnf(refute_0_46,plain,
( mult(mult(B,rd(unit,B)),B) != B
| rd(mult(mult(B,rd(unit,B)),B),B) != mult(B,rd(unit,B))
| rd(B,B) = mult(B,rd(unit,B)) ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(mult(B,rd(unit,B)),B),B),mult(B,rd(unit,B))) ),[0,0],$fot(B)]]) ).
cnf(refute_0_47,plain,
( rd(mult(mult(B,rd(unit,B)),B),B) != mult(B,rd(unit,B))
| rd(B,B) = mult(B,rd(unit,B)) ),
inference(resolve,[$cnf( $equal(mult(mult(B,rd(unit,B)),B),B) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
rd(B,B) = mult(B,rd(unit,B)),
inference(resolve,[$cnf( $equal(rd(mult(mult(B,rd(unit,B)),B),B),mult(B,rd(unit,B))) )],[refute_0_7,refute_0_47]) ).
cnf(refute_0_49,plain,
rd(mult(unit,X_14),X_14) = unit,
inference(subst,[],[c04:[bind(A,$fot(unit)),bind(B,$fot(X_14))]]) ).
cnf(refute_0_50,plain,
mult(unit,X_14) = X_14,
inference(subst,[],[c06:[bind(A,$fot(X_14))]]) ).
cnf(refute_0_51,plain,
( mult(unit,X_14) != X_14
| rd(mult(unit,X_14),X_14) != unit
| rd(X_14,X_14) = unit ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(unit,X_14),X_14),unit) ),[0,0],$fot(X_14)]]) ).
cnf(refute_0_52,plain,
( rd(mult(unit,X_14),X_14) != unit
| rd(X_14,X_14) = unit ),
inference(resolve,[$cnf( $equal(mult(unit,X_14),X_14) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
rd(X_14,X_14) = unit,
inference(resolve,[$cnf( $equal(rd(mult(unit,X_14),X_14),unit) )],[refute_0_49,refute_0_52]) ).
cnf(refute_0_54,plain,
rd(B,B) = unit,
inference(subst,[],[refute_0_53:[bind(X_14,$fot(B))]]) ).
cnf(refute_0_55,plain,
( rd(B,B) != mult(B,rd(unit,B))
| rd(B,B) != unit
| unit = mult(B,rd(unit,B)) ),
introduced(tautology,[equality,[$cnf( $equal(rd(B,B),mult(B,rd(unit,B))) ),[0],$fot(unit)]]) ).
cnf(refute_0_56,plain,
( rd(B,B) != mult(B,rd(unit,B))
| unit = mult(B,rd(unit,B)) ),
inference(resolve,[$cnf( $equal(rd(B,B),unit) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
unit = mult(B,rd(unit,B)),
inference(resolve,[$cnf( $equal(rd(B,B),mult(B,rd(unit,B))) )],[refute_0_48,refute_0_56]) ).
cnf(refute_0_58,plain,
unit = mult(ld(X_13,unit),rd(unit,ld(X_13,unit))),
inference(subst,[],[refute_0_57:[bind(B,$fot(ld(X_13,unit)))]]) ).
cnf(refute_0_59,plain,
rd(mult(X_13,ld(X_13,B)),ld(X_13,B)) = X_13,
inference(subst,[],[c04:[bind(A,$fot(X_13)),bind(B,$fot(ld(X_13,B)))]]) ).
cnf(refute_0_60,plain,
mult(X_13,ld(X_13,B)) = B,
inference(subst,[],[c01:[bind(A,$fot(X_13))]]) ).
cnf(refute_0_61,plain,
( mult(X_13,ld(X_13,B)) != B
| rd(mult(X_13,ld(X_13,B)),ld(X_13,B)) != X_13
| rd(B,ld(X_13,B)) = X_13 ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(X_13,ld(X_13,B)),ld(X_13,B)),X_13) ),[0,0],$fot(B)]]) ).
cnf(refute_0_62,plain,
( rd(mult(X_13,ld(X_13,B)),ld(X_13,B)) != X_13
| rd(B,ld(X_13,B)) = X_13 ),
inference(resolve,[$cnf( $equal(mult(X_13,ld(X_13,B)),B) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
rd(B,ld(X_13,B)) = X_13,
inference(resolve,[$cnf( $equal(rd(mult(X_13,ld(X_13,B)),ld(X_13,B)),X_13) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
rd(unit,ld(X_13,unit)) = X_13,
inference(subst,[],[refute_0_63:[bind(B,$fot(unit))]]) ).
cnf(refute_0_65,plain,
( rd(unit,ld(X_13,unit)) != X_13
| unit != mult(ld(X_13,unit),rd(unit,ld(X_13,unit)))
| unit = mult(ld(X_13,unit),X_13) ),
introduced(tautology,[equality,[$cnf( $equal(unit,mult(ld(X_13,unit),rd(unit,ld(X_13,unit)))) ),[1,1],$fot(X_13)]]) ).
cnf(refute_0_66,plain,
( unit != mult(ld(X_13,unit),rd(unit,ld(X_13,unit)))
| unit = mult(ld(X_13,unit),X_13) ),
inference(resolve,[$cnf( $equal(rd(unit,ld(X_13,unit)),X_13) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
unit = mult(ld(X_13,unit),X_13),
inference(resolve,[$cnf( $equal(unit,mult(ld(X_13,unit),rd(unit,ld(X_13,unit)))) )],[refute_0_58,refute_0_66]) ).
cnf(refute_0_68,plain,
unit = mult(ld(X_102,unit),X_102),
inference(subst,[],[refute_0_67:[bind(X_13,$fot(X_102))]]) ).
cnf(refute_0_69,plain,
( unit != mult(ld(X_102,unit),X_102)
| mult(ld(X_102,unit),X_102) = unit ),
inference(subst,[],[refute_0_43:[bind(X,$fot(unit)),bind(Y,$fot(mult(ld(X_102,unit),X_102)))]]) ).
cnf(refute_0_70,plain,
mult(ld(X_102,unit),X_102) = unit,
inference(resolve,[$cnf( $equal(unit,mult(ld(X_102,unit),X_102)) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
( mult(ld(X_102,unit),X_102) != unit
| mult(mult(ld(X_102,unit),X_102),mult(X_102,mult(ld(X_102,X_100),X_102))) != mult(mult(ld(X_102,unit),mult(X_102,X_100)),X_102)
| mult(unit,mult(X_102,mult(ld(X_102,X_100),X_102))) = mult(mult(ld(X_102,unit),mult(X_102,X_100)),X_102) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(ld(X_102,unit),X_102),mult(X_102,mult(ld(X_102,X_100),X_102))),mult(mult(ld(X_102,unit),mult(X_102,X_100)),X_102)) ),[0,0],$fot(unit)]]) ).
cnf(refute_0_72,plain,
( mult(mult(ld(X_102,unit),X_102),mult(X_102,mult(ld(X_102,X_100),X_102))) != mult(mult(ld(X_102,unit),mult(X_102,X_100)),X_102)
| mult(unit,mult(X_102,mult(ld(X_102,X_100),X_102))) = mult(mult(ld(X_102,unit),mult(X_102,X_100)),X_102) ),
inference(resolve,[$cnf( $equal(mult(ld(X_102,unit),X_102),unit) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
mult(unit,mult(X_102,mult(ld(X_102,X_100),X_102))) = mult(mult(ld(X_102,unit),mult(X_102,X_100)),X_102),
inference(resolve,[$cnf( $equal(mult(mult(ld(X_102,unit),X_102),mult(X_102,mult(ld(X_102,X_100),X_102))),mult(mult(ld(X_102,unit),mult(X_102,X_100)),X_102)) )],[refute_0_6,refute_0_72]) ).
cnf(refute_0_74,plain,
mult(unit,mult(X_102,mult(ld(X_102,X_100),X_102))) = mult(X_102,mult(ld(X_102,X_100),X_102)),
inference(subst,[],[c06:[bind(A,$fot(mult(X_102,mult(ld(X_102,X_100),X_102))))]]) ).
cnf(refute_0_75,plain,
( mult(unit,mult(X_102,mult(ld(X_102,X_100),X_102))) != mult(X_102,mult(ld(X_102,X_100),X_102))
| mult(unit,mult(X_102,mult(ld(X_102,X_100),X_102))) != mult(mult(ld(X_102,unit),mult(X_102,X_100)),X_102)
| mult(X_102,mult(ld(X_102,X_100),X_102)) = mult(mult(ld(X_102,unit),mult(X_102,X_100)),X_102) ),
introduced(tautology,[equality,[$cnf( $equal(mult(unit,mult(X_102,mult(ld(X_102,X_100),X_102))),mult(mult(ld(X_102,unit),mult(X_102,X_100)),X_102)) ),[0],$fot(mult(X_102,mult(ld(X_102,X_100),X_102)))]]) ).
cnf(refute_0_76,plain,
( mult(unit,mult(X_102,mult(ld(X_102,X_100),X_102))) != mult(mult(ld(X_102,unit),mult(X_102,X_100)),X_102)
| mult(X_102,mult(ld(X_102,X_100),X_102)) = mult(mult(ld(X_102,unit),mult(X_102,X_100)),X_102) ),
inference(resolve,[$cnf( $equal(mult(unit,mult(X_102,mult(ld(X_102,X_100),X_102))),mult(X_102,mult(ld(X_102,X_100),X_102))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
mult(X_102,mult(ld(X_102,X_100),X_102)) = mult(mult(ld(X_102,unit),mult(X_102,X_100)),X_102),
inference(resolve,[$cnf( $equal(mult(unit,mult(X_102,mult(ld(X_102,X_100),X_102))),mult(mult(ld(X_102,unit),mult(X_102,X_100)),X_102)) )],[refute_0_73,refute_0_76]) ).
cnf(refute_0_78,plain,
mult(X_104,mult(ld(X_104,ld(X_104,B)),X_104)) = mult(mult(ld(X_104,unit),mult(X_104,ld(X_104,B))),X_104),
inference(subst,[],[refute_0_77:[bind(X_100,$fot(ld(X_104,B))),bind(X_102,$fot(X_104))]]) ).
cnf(refute_0_79,plain,
mult(X_104,ld(X_104,B)) = B,
inference(subst,[],[c01:[bind(A,$fot(X_104))]]) ).
cnf(refute_0_80,plain,
( mult(X_104,ld(X_104,B)) != B
| mult(X_104,mult(ld(X_104,ld(X_104,B)),X_104)) != mult(mult(ld(X_104,unit),mult(X_104,ld(X_104,B))),X_104)
| mult(X_104,mult(ld(X_104,ld(X_104,B)),X_104)) = mult(mult(ld(X_104,unit),B),X_104) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_104,mult(ld(X_104,ld(X_104,B)),X_104)),mult(mult(ld(X_104,unit),mult(X_104,ld(X_104,B))),X_104)) ),[1,0,1],$fot(B)]]) ).
cnf(refute_0_81,plain,
( mult(X_104,mult(ld(X_104,ld(X_104,B)),X_104)) != mult(mult(ld(X_104,unit),mult(X_104,ld(X_104,B))),X_104)
| mult(X_104,mult(ld(X_104,ld(X_104,B)),X_104)) = mult(mult(ld(X_104,unit),B),X_104) ),
inference(resolve,[$cnf( $equal(mult(X_104,ld(X_104,B)),B) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
mult(X_104,mult(ld(X_104,ld(X_104,B)),X_104)) = mult(mult(ld(X_104,unit),B),X_104),
inference(resolve,[$cnf( $equal(mult(X_104,mult(ld(X_104,ld(X_104,B)),X_104)),mult(mult(ld(X_104,unit),mult(X_104,ld(X_104,B))),X_104)) )],[refute_0_78,refute_0_81]) ).
cnf(refute_0_83,plain,
mult(B,mult(ld(B,ld(B,X_243)),B)) = mult(mult(ld(B,unit),X_243),B),
inference(subst,[],[refute_0_82:[bind(B,$fot(X_243)),bind(X_104,$fot(B))]]) ).
cnf(refute_0_84,plain,
( mult(B,mult(ld(B,ld(B,X_243)),B)) != mult(mult(ld(B,unit),X_243),B)
| mult(mult(A,B),mult(B,mult(ld(B,ld(B,X_243)),B))) != mult(mult(A,mult(B,mult(B,ld(B,ld(B,X_243))))),B)
| mult(mult(A,B),mult(mult(ld(B,unit),X_243),B)) = mult(mult(A,mult(B,mult(B,ld(B,ld(B,X_243))))),B) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(A,B),mult(B,mult(ld(B,ld(B,X_243)),B))),mult(mult(A,mult(B,mult(B,ld(B,ld(B,X_243))))),B)) ),[0,1],$fot(mult(mult(ld(B,unit),X_243),B))]]) ).
cnf(refute_0_85,plain,
( mult(mult(A,B),mult(B,mult(ld(B,ld(B,X_243)),B))) != mult(mult(A,mult(B,mult(B,ld(B,ld(B,X_243))))),B)
| mult(mult(A,B),mult(mult(ld(B,unit),X_243),B)) = mult(mult(A,mult(B,mult(B,ld(B,ld(B,X_243))))),B) ),
inference(resolve,[$cnf( $equal(mult(B,mult(ld(B,ld(B,X_243)),B)),mult(mult(ld(B,unit),X_243),B)) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
mult(mult(A,B),mult(mult(ld(B,unit),X_243),B)) = mult(mult(A,mult(B,mult(B,ld(B,ld(B,X_243))))),B),
inference(resolve,[$cnf( $equal(mult(mult(A,B),mult(B,mult(ld(B,ld(B,X_243)),B))),mult(mult(A,mult(B,mult(B,ld(B,ld(B,X_243))))),B)) )],[refute_0_0,refute_0_85]) ).
cnf(refute_0_87,plain,
mult(B,ld(B,X_243)) = X_243,
inference(subst,[],[c01:[bind(A,$fot(B)),bind(B,$fot(X_243))]]) ).
cnf(refute_0_88,plain,
mult(A,mult(B,ld(B,X_243))) = mult(A,mult(B,ld(B,X_243))),
introduced(tautology,[refl,[$fot(mult(A,mult(B,ld(B,X_243))))]]) ).
cnf(refute_0_89,plain,
( mult(A,mult(B,ld(B,X_243))) != mult(A,mult(B,ld(B,X_243)))
| mult(B,ld(B,X_243)) != X_243
| mult(A,mult(B,ld(B,X_243))) = mult(A,X_243) ),
introduced(tautology,[equality,[$cnf( $equal(mult(A,mult(B,ld(B,X_243))),mult(A,mult(B,ld(B,X_243)))) ),[1,1],$fot(X_243)]]) ).
cnf(refute_0_90,plain,
( mult(B,ld(B,X_243)) != X_243
| mult(A,mult(B,ld(B,X_243))) = mult(A,X_243) ),
inference(resolve,[$cnf( $equal(mult(A,mult(B,ld(B,X_243))),mult(A,mult(B,ld(B,X_243)))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
mult(A,mult(B,ld(B,X_243))) = mult(A,X_243),
inference(resolve,[$cnf( $equal(mult(B,ld(B,X_243)),X_243) )],[refute_0_87,refute_0_90]) ).
cnf(refute_0_92,plain,
mult(mult(A,mult(B,ld(B,X_243))),B) = mult(mult(A,mult(B,ld(B,X_243))),B),
introduced(tautology,[refl,[$fot(mult(mult(A,mult(B,ld(B,X_243))),B))]]) ).
cnf(refute_0_93,plain,
( mult(A,mult(B,ld(B,X_243))) != mult(A,X_243)
| mult(mult(A,mult(B,ld(B,X_243))),B) != mult(mult(A,mult(B,ld(B,X_243))),B)
| mult(mult(A,mult(B,ld(B,X_243))),B) = mult(mult(A,X_243),B) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(A,mult(B,ld(B,X_243))),B),mult(mult(A,mult(B,ld(B,X_243))),B)) ),[1,0],$fot(mult(A,X_243))]]) ).
cnf(refute_0_94,plain,
( mult(A,mult(B,ld(B,X_243))) != mult(A,X_243)
| mult(mult(A,mult(B,ld(B,X_243))),B) = mult(mult(A,X_243),B) ),
inference(resolve,[$cnf( $equal(mult(mult(A,mult(B,ld(B,X_243))),B),mult(mult(A,mult(B,ld(B,X_243))),B)) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
mult(mult(A,mult(B,ld(B,X_243))),B) = mult(mult(A,X_243),B),
inference(resolve,[$cnf( $equal(mult(A,mult(B,ld(B,X_243))),mult(A,X_243)) )],[refute_0_91,refute_0_94]) ).
cnf(refute_0_96,plain,
mult(mult(A,B),mult(B,mult(ld(B,ld(B,X_243)),B))) = mult(mult(A,mult(B,ld(B,X_243))),B),
inference(subst,[],[refute_0_5:[bind(B,$fot(ld(B,X_243))),bind(X_18,$fot(A)),bind(X_19,$fot(B))]]) ).
cnf(refute_0_97,plain,
( mult(mult(A,B),mult(B,mult(C,B))) != mult(mult(A,mult(B,mult(B,C))),B)
| mult(mult(A,mult(B,mult(B,C))),B) = mult(mult(A,B),mult(B,mult(C,B))) ),
inference(subst,[],[refute_0_43:[bind(X,$fot(mult(mult(A,B),mult(B,mult(C,B))))),bind(Y,$fot(mult(mult(A,mult(B,mult(B,C))),B)))]]) ).
cnf(refute_0_98,plain,
mult(mult(A,mult(B,mult(B,C))),B) = mult(mult(A,B),mult(B,mult(C,B))),
inference(resolve,[$cnf( $equal(mult(mult(A,B),mult(B,mult(C,B))),mult(mult(A,mult(B,mult(B,C))),B)) )],[c08,refute_0_97]) ).
cnf(refute_0_99,plain,
mult(mult(A,mult(B,mult(B,ld(B,ld(B,X_243))))),B) = mult(mult(A,B),mult(B,mult(ld(B,ld(B,X_243)),B))),
inference(subst,[],[refute_0_98:[bind(C,$fot(ld(B,ld(B,X_243))))]]) ).
cnf(refute_0_100,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_101,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_43,refute_0_100]) ).
cnf(refute_0_102,plain,
( mult(mult(A,B),mult(B,mult(ld(B,ld(B,X_243)),B))) != mult(mult(A,mult(B,ld(B,X_243))),B)
| mult(mult(A,mult(B,mult(B,ld(B,ld(B,X_243))))),B) != mult(mult(A,B),mult(B,mult(ld(B,ld(B,X_243)),B)))
| mult(mult(A,mult(B,mult(B,ld(B,ld(B,X_243))))),B) = mult(mult(A,mult(B,ld(B,X_243))),B) ),
inference(subst,[],[refute_0_101:[bind(X,$fot(mult(mult(A,mult(B,mult(B,ld(B,ld(B,X_243))))),B))),bind(Y,$fot(mult(mult(A,B),mult(B,mult(ld(B,ld(B,X_243)),B))))),bind(Z,$fot(mult(mult(A,mult(B,ld(B,X_243))),B)))]]) ).
cnf(refute_0_103,plain,
( mult(mult(A,B),mult(B,mult(ld(B,ld(B,X_243)),B))) != mult(mult(A,mult(B,ld(B,X_243))),B)
| mult(mult(A,mult(B,mult(B,ld(B,ld(B,X_243))))),B) = mult(mult(A,mult(B,ld(B,X_243))),B) ),
inference(resolve,[$cnf( $equal(mult(mult(A,mult(B,mult(B,ld(B,ld(B,X_243))))),B),mult(mult(A,B),mult(B,mult(ld(B,ld(B,X_243)),B)))) )],[refute_0_99,refute_0_102]) ).
cnf(refute_0_104,plain,
mult(mult(A,mult(B,mult(B,ld(B,ld(B,X_243))))),B) = mult(mult(A,mult(B,ld(B,X_243))),B),
inference(resolve,[$cnf( $equal(mult(mult(A,B),mult(B,mult(ld(B,ld(B,X_243)),B))),mult(mult(A,mult(B,ld(B,X_243))),B)) )],[refute_0_96,refute_0_103]) ).
cnf(refute_0_105,plain,
( mult(mult(A,mult(B,ld(B,X_243))),B) != mult(mult(A,X_243),B)
| mult(mult(A,mult(B,mult(B,ld(B,ld(B,X_243))))),B) != mult(mult(A,mult(B,ld(B,X_243))),B)
| mult(mult(A,mult(B,mult(B,ld(B,ld(B,X_243))))),B) = mult(mult(A,X_243),B) ),
inference(subst,[],[refute_0_101:[bind(X,$fot(mult(mult(A,mult(B,mult(B,ld(B,ld(B,X_243))))),B))),bind(Y,$fot(mult(mult(A,mult(B,ld(B,X_243))),B))),bind(Z,$fot(mult(mult(A,X_243),B)))]]) ).
cnf(refute_0_106,plain,
( mult(mult(A,mult(B,ld(B,X_243))),B) != mult(mult(A,X_243),B)
| mult(mult(A,mult(B,mult(B,ld(B,ld(B,X_243))))),B) = mult(mult(A,X_243),B) ),
inference(resolve,[$cnf( $equal(mult(mult(A,mult(B,mult(B,ld(B,ld(B,X_243))))),B),mult(mult(A,mult(B,ld(B,X_243))),B)) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
mult(mult(A,mult(B,mult(B,ld(B,ld(B,X_243))))),B) = mult(mult(A,X_243),B),
inference(resolve,[$cnf( $equal(mult(mult(A,mult(B,ld(B,X_243))),B),mult(mult(A,X_243),B)) )],[refute_0_95,refute_0_106]) ).
cnf(refute_0_108,plain,
( mult(mult(A,B),mult(mult(ld(B,unit),X_243),B)) != mult(mult(A,mult(B,mult(B,ld(B,ld(B,X_243))))),B)
| mult(mult(A,mult(B,mult(B,ld(B,ld(B,X_243))))),B) != mult(mult(A,X_243),B)
| mult(mult(A,B),mult(mult(ld(B,unit),X_243),B)) = mult(mult(A,X_243),B) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(mult(A,B),mult(mult(ld(B,unit),X_243),B)),mult(mult(A,X_243),B)) ),[0],$fot(mult(mult(A,mult(B,mult(B,ld(B,ld(B,X_243))))),B))]]) ).
cnf(refute_0_109,plain,
( mult(mult(A,B),mult(mult(ld(B,unit),X_243),B)) != mult(mult(A,mult(B,mult(B,ld(B,ld(B,X_243))))),B)
| mult(mult(A,B),mult(mult(ld(B,unit),X_243),B)) = mult(mult(A,X_243),B) ),
inference(resolve,[$cnf( $equal(mult(mult(A,mult(B,mult(B,ld(B,ld(B,X_243))))),B),mult(mult(A,X_243),B)) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
mult(mult(A,B),mult(mult(ld(B,unit),X_243),B)) = mult(mult(A,X_243),B),
inference(resolve,[$cnf( $equal(mult(mult(A,B),mult(mult(ld(B,unit),X_243),B)),mult(mult(A,mult(B,mult(B,ld(B,ld(B,X_243))))),B)) )],[refute_0_86,refute_0_109]) ).
cnf(refute_0_111,plain,
mult(mult(X_104,ld(X_104,B)),X_104) = mult(mult(X_104,ld(X_104,B)),X_104),
introduced(tautology,[refl,[$fot(mult(mult(X_104,ld(X_104,B)),X_104))]]) ).
cnf(refute_0_112,plain,
( mult(X_104,ld(X_104,B)) != B
| mult(mult(X_104,ld(X_104,B)),X_104) != mult(mult(X_104,ld(X_104,B)),X_104)
| mult(mult(X_104,ld(X_104,B)),X_104) = mult(B,X_104) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(X_104,ld(X_104,B)),X_104),mult(mult(X_104,ld(X_104,B)),X_104)) ),[1,0],$fot(B)]]) ).
cnf(refute_0_113,plain,
( mult(X_104,ld(X_104,B)) != B
| mult(mult(X_104,ld(X_104,B)),X_104) = mult(B,X_104) ),
inference(resolve,[$cnf( $equal(mult(mult(X_104,ld(X_104,B)),X_104),mult(mult(X_104,ld(X_104,B)),X_104)) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
mult(mult(X_104,ld(X_104,B)),X_104) = mult(B,X_104),
inference(resolve,[$cnf( $equal(mult(X_104,ld(X_104,B)),B) )],[refute_0_79,refute_0_113]) ).
cnf(refute_0_115,plain,
ld(X_104,mult(mult(X_104,ld(X_104,B)),X_104)) = ld(X_104,mult(mult(X_104,ld(X_104,B)),X_104)),
introduced(tautology,[refl,[$fot(ld(X_104,mult(mult(X_104,ld(X_104,B)),X_104)))]]) ).
cnf(refute_0_116,plain,
( ld(X_104,mult(mult(X_104,ld(X_104,B)),X_104)) != ld(X_104,mult(mult(X_104,ld(X_104,B)),X_104))
| mult(mult(X_104,ld(X_104,B)),X_104) != mult(B,X_104)
| ld(X_104,mult(mult(X_104,ld(X_104,B)),X_104)) = ld(X_104,mult(B,X_104)) ),
introduced(tautology,[equality,[$cnf( $equal(ld(X_104,mult(mult(X_104,ld(X_104,B)),X_104)),ld(X_104,mult(mult(X_104,ld(X_104,B)),X_104))) ),[1,1],$fot(mult(B,X_104))]]) ).
cnf(refute_0_117,plain,
( mult(mult(X_104,ld(X_104,B)),X_104) != mult(B,X_104)
| ld(X_104,mult(mult(X_104,ld(X_104,B)),X_104)) = ld(X_104,mult(B,X_104)) ),
inference(resolve,[$cnf( $equal(ld(X_104,mult(mult(X_104,ld(X_104,B)),X_104)),ld(X_104,mult(mult(X_104,ld(X_104,B)),X_104))) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
ld(X_104,mult(mult(X_104,ld(X_104,B)),X_104)) = ld(X_104,mult(B,X_104)),
inference(resolve,[$cnf( $equal(mult(mult(X_104,ld(X_104,B)),X_104),mult(B,X_104)) )],[refute_0_114,refute_0_117]) ).
cnf(refute_0_119,plain,
ld(mult(X_101,X_102),mult(mult(X_101,X_102),mult(X_102,mult(ld(X_102,X_100),X_102)))) = mult(X_102,mult(ld(X_102,X_100),X_102)),
inference(subst,[],[c02:[bind(A,$fot(mult(X_101,X_102))),bind(B,$fot(mult(X_102,mult(ld(X_102,X_100),X_102))))]]) ).
cnf(refute_0_120,plain,
mult(mult(X_101,X_102),mult(X_102,mult(ld(X_102,X_100),X_102))) = mult(mult(X_101,mult(X_102,X_100)),X_102),
inference(subst,[],[refute_0_5:[bind(B,$fot(X_100)),bind(X_18,$fot(X_101)),bind(X_19,$fot(X_102))]]) ).
cnf(refute_0_121,plain,
( ld(mult(X_101,X_102),mult(mult(X_101,X_102),mult(X_102,mult(ld(X_102,X_100),X_102)))) != mult(X_102,mult(ld(X_102,X_100),X_102))
| mult(mult(X_101,X_102),mult(X_102,mult(ld(X_102,X_100),X_102))) != mult(mult(X_101,mult(X_102,X_100)),X_102)
| ld(mult(X_101,X_102),mult(mult(X_101,mult(X_102,X_100)),X_102)) = mult(X_102,mult(ld(X_102,X_100),X_102)) ),
introduced(tautology,[equality,[$cnf( $equal(ld(mult(X_101,X_102),mult(mult(X_101,X_102),mult(X_102,mult(ld(X_102,X_100),X_102)))),mult(X_102,mult(ld(X_102,X_100),X_102))) ),[0,1],$fot(mult(mult(X_101,mult(X_102,X_100)),X_102))]]) ).
cnf(refute_0_122,plain,
( ld(mult(X_101,X_102),mult(mult(X_101,X_102),mult(X_102,mult(ld(X_102,X_100),X_102)))) != mult(X_102,mult(ld(X_102,X_100),X_102))
| ld(mult(X_101,X_102),mult(mult(X_101,mult(X_102,X_100)),X_102)) = mult(X_102,mult(ld(X_102,X_100),X_102)) ),
inference(resolve,[$cnf( $equal(mult(mult(X_101,X_102),mult(X_102,mult(ld(X_102,X_100),X_102))),mult(mult(X_101,mult(X_102,X_100)),X_102)) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
ld(mult(X_101,X_102),mult(mult(X_101,mult(X_102,X_100)),X_102)) = mult(X_102,mult(ld(X_102,X_100),X_102)),
inference(resolve,[$cnf( $equal(ld(mult(X_101,X_102),mult(mult(X_101,X_102),mult(X_102,mult(ld(X_102,X_100),X_102)))),mult(X_102,mult(ld(X_102,X_100),X_102))) )],[refute_0_119,refute_0_122]) ).
cnf(refute_0_124,plain,
ld(mult(unit,X_262),mult(mult(unit,mult(X_262,X_260)),X_262)) = mult(X_262,mult(ld(X_262,X_260),X_262)),
inference(subst,[],[refute_0_123:[bind(X_100,$fot(X_260)),bind(X_101,$fot(unit)),bind(X_102,$fot(X_262))]]) ).
cnf(refute_0_125,plain,
mult(unit,mult(X_262,X_260)) = mult(X_262,X_260),
inference(subst,[],[c06:[bind(A,$fot(mult(X_262,X_260)))]]) ).
cnf(refute_0_126,plain,
( ld(mult(unit,X_262),mult(mult(unit,mult(X_262,X_260)),X_262)) != mult(X_262,mult(ld(X_262,X_260),X_262))
| mult(unit,mult(X_262,X_260)) != mult(X_262,X_260)
| ld(mult(unit,X_262),mult(mult(X_262,X_260),X_262)) = mult(X_262,mult(ld(X_262,X_260),X_262)) ),
introduced(tautology,[equality,[$cnf( $equal(ld(mult(unit,X_262),mult(mult(unit,mult(X_262,X_260)),X_262)),mult(X_262,mult(ld(X_262,X_260),X_262))) ),[0,1,0],$fot(mult(X_262,X_260))]]) ).
cnf(refute_0_127,plain,
( ld(mult(unit,X_262),mult(mult(unit,mult(X_262,X_260)),X_262)) != mult(X_262,mult(ld(X_262,X_260),X_262))
| ld(mult(unit,X_262),mult(mult(X_262,X_260),X_262)) = mult(X_262,mult(ld(X_262,X_260),X_262)) ),
inference(resolve,[$cnf( $equal(mult(unit,mult(X_262,X_260)),mult(X_262,X_260)) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
ld(mult(unit,X_262),mult(mult(X_262,X_260),X_262)) = mult(X_262,mult(ld(X_262,X_260),X_262)),
inference(resolve,[$cnf( $equal(ld(mult(unit,X_262),mult(mult(unit,mult(X_262,X_260)),X_262)),mult(X_262,mult(ld(X_262,X_260),X_262))) )],[refute_0_124,refute_0_127]) ).
cnf(refute_0_129,plain,
mult(unit,X_262) = X_262,
inference(subst,[],[c06:[bind(A,$fot(X_262))]]) ).
cnf(refute_0_130,plain,
ld(mult(unit,X_262),mult(mult(X_262,X_260),X_262)) = ld(mult(unit,X_262),mult(mult(X_262,X_260),X_262)),
introduced(tautology,[refl,[$fot(ld(mult(unit,X_262),mult(mult(X_262,X_260),X_262)))]]) ).
cnf(refute_0_131,plain,
( ld(mult(unit,X_262),mult(mult(X_262,X_260),X_262)) != ld(mult(unit,X_262),mult(mult(X_262,X_260),X_262))
| mult(unit,X_262) != X_262
| ld(mult(unit,X_262),mult(mult(X_262,X_260),X_262)) = ld(X_262,mult(mult(X_262,X_260),X_262)) ),
introduced(tautology,[equality,[$cnf( $equal(ld(mult(unit,X_262),mult(mult(X_262,X_260),X_262)),ld(mult(unit,X_262),mult(mult(X_262,X_260),X_262))) ),[1,0],$fot(X_262)]]) ).
cnf(refute_0_132,plain,
( mult(unit,X_262) != X_262
| ld(mult(unit,X_262),mult(mult(X_262,X_260),X_262)) = ld(X_262,mult(mult(X_262,X_260),X_262)) ),
inference(resolve,[$cnf( $equal(ld(mult(unit,X_262),mult(mult(X_262,X_260),X_262)),ld(mult(unit,X_262),mult(mult(X_262,X_260),X_262))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
ld(mult(unit,X_262),mult(mult(X_262,X_260),X_262)) = ld(X_262,mult(mult(X_262,X_260),X_262)),
inference(resolve,[$cnf( $equal(mult(unit,X_262),X_262) )],[refute_0_129,refute_0_132]) ).
cnf(refute_0_134,plain,
( ld(mult(unit,X_262),mult(mult(X_262,X_260),X_262)) != ld(X_262,mult(mult(X_262,X_260),X_262))
| ld(mult(unit,X_262),mult(mult(X_262,X_260),X_262)) != mult(X_262,mult(ld(X_262,X_260),X_262))
| ld(X_262,mult(mult(X_262,X_260),X_262)) = mult(X_262,mult(ld(X_262,X_260),X_262)) ),
introduced(tautology,[equality,[$cnf( $equal(ld(mult(unit,X_262),mult(mult(X_262,X_260),X_262)),mult(X_262,mult(ld(X_262,X_260),X_262))) ),[0],$fot(ld(X_262,mult(mult(X_262,X_260),X_262)))]]) ).
cnf(refute_0_135,plain,
( ld(mult(unit,X_262),mult(mult(X_262,X_260),X_262)) != mult(X_262,mult(ld(X_262,X_260),X_262))
| ld(X_262,mult(mult(X_262,X_260),X_262)) = mult(X_262,mult(ld(X_262,X_260),X_262)) ),
inference(resolve,[$cnf( $equal(ld(mult(unit,X_262),mult(mult(X_262,X_260),X_262)),ld(X_262,mult(mult(X_262,X_260),X_262))) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
ld(X_262,mult(mult(X_262,X_260),X_262)) = mult(X_262,mult(ld(X_262,X_260),X_262)),
inference(resolve,[$cnf( $equal(ld(mult(unit,X_262),mult(mult(X_262,X_260),X_262)),mult(X_262,mult(ld(X_262,X_260),X_262))) )],[refute_0_128,refute_0_135]) ).
cnf(refute_0_137,plain,
( ld(X_262,mult(mult(X_262,X_260),X_262)) != mult(X_262,mult(ld(X_262,X_260),X_262))
| mult(X_262,mult(ld(X_262,X_260),X_262)) = ld(X_262,mult(mult(X_262,X_260),X_262)) ),
inference(subst,[],[refute_0_43:[bind(X,$fot(ld(X_262,mult(mult(X_262,X_260),X_262)))),bind(Y,$fot(mult(X_262,mult(ld(X_262,X_260),X_262))))]]) ).
cnf(refute_0_138,plain,
mult(X_262,mult(ld(X_262,X_260),X_262)) = ld(X_262,mult(mult(X_262,X_260),X_262)),
inference(resolve,[$cnf( $equal(ld(X_262,mult(mult(X_262,X_260),X_262)),mult(X_262,mult(ld(X_262,X_260),X_262))) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
mult(X_104,mult(ld(X_104,ld(X_104,B)),X_104)) = ld(X_104,mult(mult(X_104,ld(X_104,B)),X_104)),
inference(subst,[],[refute_0_138:[bind(X_260,$fot(ld(X_104,B))),bind(X_262,$fot(X_104))]]) ).
cnf(refute_0_140,plain,
( ld(X_104,mult(mult(X_104,ld(X_104,B)),X_104)) != ld(X_104,mult(B,X_104))
| mult(X_104,mult(ld(X_104,ld(X_104,B)),X_104)) != ld(X_104,mult(mult(X_104,ld(X_104,B)),X_104))
| mult(X_104,mult(ld(X_104,ld(X_104,B)),X_104)) = ld(X_104,mult(B,X_104)) ),
inference(subst,[],[refute_0_101:[bind(X,$fot(mult(X_104,mult(ld(X_104,ld(X_104,B)),X_104)))),bind(Y,$fot(ld(X_104,mult(mult(X_104,ld(X_104,B)),X_104)))),bind(Z,$fot(ld(X_104,mult(B,X_104))))]]) ).
cnf(refute_0_141,plain,
( ld(X_104,mult(mult(X_104,ld(X_104,B)),X_104)) != ld(X_104,mult(B,X_104))
| mult(X_104,mult(ld(X_104,ld(X_104,B)),X_104)) = ld(X_104,mult(B,X_104)) ),
inference(resolve,[$cnf( $equal(mult(X_104,mult(ld(X_104,ld(X_104,B)),X_104)),ld(X_104,mult(mult(X_104,ld(X_104,B)),X_104))) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
mult(X_104,mult(ld(X_104,ld(X_104,B)),X_104)) = ld(X_104,mult(B,X_104)),
inference(resolve,[$cnf( $equal(ld(X_104,mult(mult(X_104,ld(X_104,B)),X_104)),ld(X_104,mult(B,X_104))) )],[refute_0_118,refute_0_141]) ).
cnf(refute_0_143,plain,
( mult(X_104,mult(ld(X_104,ld(X_104,B)),X_104)) != ld(X_104,mult(B,X_104))
| mult(X_104,mult(ld(X_104,ld(X_104,B)),X_104)) != mult(mult(ld(X_104,unit),B),X_104)
| ld(X_104,mult(B,X_104)) = mult(mult(ld(X_104,unit),B),X_104) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_104,mult(ld(X_104,ld(X_104,B)),X_104)),mult(mult(ld(X_104,unit),B),X_104)) ),[0],$fot(ld(X_104,mult(B,X_104)))]]) ).
cnf(refute_0_144,plain,
( mult(X_104,mult(ld(X_104,ld(X_104,B)),X_104)) != mult(mult(ld(X_104,unit),B),X_104)
| ld(X_104,mult(B,X_104)) = mult(mult(ld(X_104,unit),B),X_104) ),
inference(resolve,[$cnf( $equal(mult(X_104,mult(ld(X_104,ld(X_104,B)),X_104)),ld(X_104,mult(B,X_104))) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
ld(X_104,mult(B,X_104)) = mult(mult(ld(X_104,unit),B),X_104),
inference(resolve,[$cnf( $equal(mult(X_104,mult(ld(X_104,ld(X_104,B)),X_104)),mult(mult(ld(X_104,unit),B),X_104)) )],[refute_0_82,refute_0_144]) ).
cnf(refute_0_146,plain,
( ld(X_104,mult(B,X_104)) != mult(mult(ld(X_104,unit),B),X_104)
| mult(mult(ld(X_104,unit),B),X_104) = ld(X_104,mult(B,X_104)) ),
inference(subst,[],[refute_0_43:[bind(X,$fot(ld(X_104,mult(B,X_104)))),bind(Y,$fot(mult(mult(ld(X_104,unit),B),X_104)))]]) ).
cnf(refute_0_147,plain,
mult(mult(ld(X_104,unit),B),X_104) = ld(X_104,mult(B,X_104)),
inference(resolve,[$cnf( $equal(ld(X_104,mult(B,X_104)),mult(mult(ld(X_104,unit),B),X_104)) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
mult(mult(ld(B,unit),X_243),B) = ld(B,mult(X_243,B)),
inference(subst,[],[refute_0_147:[bind(B,$fot(X_243)),bind(X_104,$fot(B))]]) ).
cnf(refute_0_149,plain,
mult(mult(A,B),mult(mult(ld(B,unit),X_243),B)) = mult(mult(A,B),mult(mult(ld(B,unit),X_243),B)),
introduced(tautology,[refl,[$fot(mult(mult(A,B),mult(mult(ld(B,unit),X_243),B)))]]) ).
cnf(refute_0_150,plain,
( mult(mult(A,B),mult(mult(ld(B,unit),X_243),B)) != mult(mult(A,B),mult(mult(ld(B,unit),X_243),B))
| mult(mult(ld(B,unit),X_243),B) != ld(B,mult(X_243,B))
| mult(mult(A,B),mult(mult(ld(B,unit),X_243),B)) = mult(mult(A,B),ld(B,mult(X_243,B))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(A,B),mult(mult(ld(B,unit),X_243),B)),mult(mult(A,B),mult(mult(ld(B,unit),X_243),B))) ),[1,1],$fot(ld(B,mult(X_243,B)))]]) ).
cnf(refute_0_151,plain,
( mult(mult(ld(B,unit),X_243),B) != ld(B,mult(X_243,B))
| mult(mult(A,B),mult(mult(ld(B,unit),X_243),B)) = mult(mult(A,B),ld(B,mult(X_243,B))) ),
inference(resolve,[$cnf( $equal(mult(mult(A,B),mult(mult(ld(B,unit),X_243),B)),mult(mult(A,B),mult(mult(ld(B,unit),X_243),B))) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
mult(mult(A,B),mult(mult(ld(B,unit),X_243),B)) = mult(mult(A,B),ld(B,mult(X_243,B))),
inference(resolve,[$cnf( $equal(mult(mult(ld(B,unit),X_243),B),ld(B,mult(X_243,B))) )],[refute_0_148,refute_0_151]) ).
cnf(refute_0_153,plain,
( mult(mult(A,B),mult(mult(ld(B,unit),X_243),B)) != mult(mult(A,B),ld(B,mult(X_243,B)))
| mult(mult(A,B),mult(mult(ld(B,unit),X_243),B)) != mult(mult(A,X_243),B)
| mult(mult(A,B),ld(B,mult(X_243,B))) = mult(mult(A,X_243),B) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(A,B),mult(mult(ld(B,unit),X_243),B)),mult(mult(A,X_243),B)) ),[0],$fot(mult(mult(A,B),ld(B,mult(X_243,B))))]]) ).
cnf(refute_0_154,plain,
( mult(mult(A,B),mult(mult(ld(B,unit),X_243),B)) != mult(mult(A,X_243),B)
| mult(mult(A,B),ld(B,mult(X_243,B))) = mult(mult(A,X_243),B) ),
inference(resolve,[$cnf( $equal(mult(mult(A,B),mult(mult(ld(B,unit),X_243),B)),mult(mult(A,B),ld(B,mult(X_243,B)))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
mult(mult(A,B),ld(B,mult(X_243,B))) = mult(mult(A,X_243),B),
inference(resolve,[$cnf( $equal(mult(mult(A,B),mult(mult(ld(B,unit),X_243),B)),mult(mult(A,X_243),B)) )],[refute_0_110,refute_0_154]) ).
cnf(refute_0_156,plain,
mult(mult(a,c),ld(c,mult(b,c))) = mult(mult(a,b),c),
inference(subst,[],[refute_0_155:[bind(A,$fot(a)),bind(B,$fot(c)),bind(X_243,$fot(b))]]) ).
cnf(refute_0_157,plain,
( mult(mult(a,b),c) != mult(mult(a,b),c)
| mult(mult(a,c),ld(c,mult(b,c))) != mult(mult(a,b),c)
| mult(mult(a,b),c) = mult(mult(a,c),ld(c,mult(b,c))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(mult(a,b),c),mult(mult(a,c),ld(c,mult(b,c)))) ),[1],$fot(mult(mult(a,b),c))]]) ).
cnf(refute_0_158,plain,
( mult(mult(a,b),c) != mult(mult(a,b),c)
| mult(mult(a,b),c) = mult(mult(a,c),ld(c,mult(b,c))) ),
inference(resolve,[$cnf( $equal(mult(mult(a,c),ld(c,mult(b,c))),mult(mult(a,b),c)) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
mult(mult(a,b),c) != mult(mult(a,b),c),
inference(resolve,[$cnf( $equal(mult(mult(a,b),c),mult(mult(a,c),ld(c,mult(b,c)))) )],[refute_0_158,goals]) ).
cnf(refute_0_160,plain,
mult(mult(a,b),c) = mult(mult(a,b),c),
introduced(tautology,[refl,[$fot(mult(mult(a,b),c))]]) ).
cnf(refute_0_161,plain,
$false,
inference(resolve,[$cnf( $equal(mult(mult(a,b),c),mult(mult(a,b),c)) )],[refute_0_160,refute_0_159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP699-1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % 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 09:41:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4.27/4.45 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.27/4.45
% 4.27/4.45 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.27/4.47
%------------------------------------------------------------------------------