TSTP Solution File: RNG128-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : RNG128-1 : TPTP v8.1.0. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 : Mon Jul 18 20:36:01 EDT 2022
% Result : Unsatisfiable 0.20s 0.40s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 65
% Syntax : Number of clauses : 257 ( 131 unt; 0 nHn; 135 RR)
% Number of literals : 438 ( 437 equ; 183 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 384 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(sos,axiom,
add(A,add(B,C)) = add(add(A,B),C) ).
cnf(sos_001,axiom,
add(A,B) = add(B,A) ).
cnf(sos_002,axiom,
mult(A,B) = mult(B,A) ).
cnf(sos_003,axiom,
mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) ).
cnf(sos_004,axiom,
add(zero,A) = A ).
cnf(sos_005,axiom,
mult(A,unit) = A ).
cnf(sos_006,axiom,
add(unit,add(A,mult(A,A))) = A ).
cnf(goals,negated_conjecture,
add(x0,x1) != mult(x0,x1) ).
cnf(refute_0_0,plain,
mult(B,add(B,C)) = add(mult(B,B),mult(B,C)),
inference(subst,[],[sos_003:[bind(A,$fot(B))]]) ).
cnf(refute_0_1,plain,
mult(X_9,add(X_10,unit)) = add(mult(X_9,X_10),mult(X_9,unit)),
inference(subst,[],[sos_003:[bind(A,$fot(X_9)),bind(B,$fot(X_10)),bind(C,$fot(unit))]]) ).
cnf(refute_0_2,plain,
mult(X_9,unit) = X_9,
inference(subst,[],[sos_005:[bind(A,$fot(X_9))]]) ).
cnf(refute_0_3,plain,
( mult(X_9,add(X_10,unit)) != add(mult(X_9,X_10),mult(X_9,unit))
| mult(X_9,unit) != X_9
| mult(X_9,add(X_10,unit)) = add(mult(X_9,X_10),X_9) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_9,add(X_10,unit)),add(mult(X_9,X_10),mult(X_9,unit))) ),[1,1],$fot(X_9)]]) ).
cnf(refute_0_4,plain,
( mult(X_9,add(X_10,unit)) != add(mult(X_9,X_10),mult(X_9,unit))
| mult(X_9,add(X_10,unit)) = add(mult(X_9,X_10),X_9) ),
inference(resolve,[$cnf( $equal(mult(X_9,unit),X_9) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
mult(X_9,add(X_10,unit)) = add(mult(X_9,X_10),X_9),
inference(resolve,[$cnf( $equal(mult(X_9,add(X_10,unit)),add(mult(X_9,X_10),mult(X_9,unit))) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_7,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_8,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( add(A,B) != add(B,A)
| add(B,A) = add(A,B) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(add(A,B))),bind(Y,$fot(add(B,A)))]]) ).
cnf(refute_0_10,plain,
add(B,A) = add(A,B),
inference(resolve,[$cnf( $equal(add(A,B),add(B,A)) )],[sos_001,refute_0_9]) ).
cnf(refute_0_11,plain,
add(mult(X_9,X_10),X_9) = add(X_9,mult(X_9,X_10)),
inference(subst,[],[refute_0_10:[bind(A,$fot(X_9)),bind(B,$fot(mult(X_9,X_10)))]]) ).
cnf(refute_0_12,plain,
( add(mult(X_9,X_10),X_9) != add(X_9,mult(X_9,X_10))
| mult(X_9,add(X_10,unit)) != add(mult(X_9,X_10),X_9)
| mult(X_9,add(X_10,unit)) = add(X_9,mult(X_9,X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_9,add(X_10,unit)),add(mult(X_9,X_10),X_9)) ),[1],$fot(add(X_9,mult(X_9,X_10)))]]) ).
cnf(refute_0_13,plain,
( mult(X_9,add(X_10,unit)) != add(mult(X_9,X_10),X_9)
| mult(X_9,add(X_10,unit)) = add(X_9,mult(X_9,X_10)) ),
inference(resolve,[$cnf( $equal(add(mult(X_9,X_10),X_9),add(X_9,mult(X_9,X_10))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
mult(X_9,add(X_10,unit)) = add(X_9,mult(X_9,X_10)),
inference(resolve,[$cnf( $equal(mult(X_9,add(X_10,unit)),add(mult(X_9,X_10),X_9)) )],[refute_0_5,refute_0_13]) ).
cnf(refute_0_15,plain,
mult(A,add(A,unit)) = add(A,mult(A,A)),
inference(subst,[],[refute_0_14:[bind(X_10,$fot(A)),bind(X_9,$fot(A))]]) ).
cnf(refute_0_16,plain,
( mult(A,add(A,unit)) != add(A,mult(A,A))
| add(A,mult(A,A)) = mult(A,add(A,unit)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(mult(A,add(A,unit)))),bind(Y,$fot(add(A,mult(A,A))))]]) ).
cnf(refute_0_17,plain,
add(A,mult(A,A)) = mult(A,add(A,unit)),
inference(resolve,[$cnf( $equal(mult(A,add(A,unit)),add(A,mult(A,A))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( add(A,mult(A,A)) != mult(A,add(A,unit))
| add(unit,add(A,mult(A,A))) != A
| add(unit,mult(A,add(A,unit))) = A ),
introduced(tautology,[equality,[$cnf( $equal(add(unit,add(A,mult(A,A))),A) ),[0,1],$fot(mult(A,add(A,unit)))]]) ).
cnf(refute_0_19,plain,
( add(unit,add(A,mult(A,A))) != A
| add(unit,mult(A,add(A,unit))) = A ),
inference(resolve,[$cnf( $equal(add(A,mult(A,A)),mult(A,add(A,unit))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
add(unit,mult(A,add(A,unit))) = A,
inference(resolve,[$cnf( $equal(add(unit,add(A,mult(A,A))),A) )],[sos_006,refute_0_19]) ).
cnf(refute_0_21,plain,
add(zero,A) = add(A,zero),
inference(subst,[],[sos_001:[bind(A,$fot(zero)),bind(B,$fot(A))]]) ).
cnf(refute_0_22,plain,
( add(zero,A) != A
| add(zero,A) != add(A,zero)
| add(A,zero) = A ),
introduced(tautology,[equality,[$cnf( $equal(add(zero,A),A) ),[0],$fot(add(A,zero))]]) ).
cnf(refute_0_23,plain,
( add(zero,A) != A
| add(A,zero) = A ),
inference(resolve,[$cnf( $equal(add(zero,A),add(A,zero)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
add(A,zero) = A,
inference(resolve,[$cnf( $equal(add(zero,A),A) )],[sos_004,refute_0_23]) ).
cnf(refute_0_25,plain,
add(unit,add(zero,mult(zero,zero))) = zero,
inference(subst,[],[sos_006:[bind(A,$fot(zero))]]) ).
cnf(refute_0_26,plain,
mult(X_13,add(zero,unit)) = add(X_13,mult(X_13,zero)),
inference(subst,[],[refute_0_14:[bind(X_10,$fot(zero)),bind(X_9,$fot(X_13))]]) ).
cnf(refute_0_27,plain,
add(zero,unit) = unit,
inference(subst,[],[sos_004:[bind(A,$fot(unit))]]) ).
cnf(refute_0_28,plain,
( add(zero,unit) != unit
| mult(X_13,add(zero,unit)) != add(X_13,mult(X_13,zero))
| mult(X_13,unit) = add(X_13,mult(X_13,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_13,add(zero,unit)),add(X_13,mult(X_13,zero))) ),[0,1],$fot(unit)]]) ).
cnf(refute_0_29,plain,
( mult(X_13,add(zero,unit)) != add(X_13,mult(X_13,zero))
| mult(X_13,unit) = add(X_13,mult(X_13,zero)) ),
inference(resolve,[$cnf( $equal(add(zero,unit),unit) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
mult(X_13,unit) = add(X_13,mult(X_13,zero)),
inference(resolve,[$cnf( $equal(mult(X_13,add(zero,unit)),add(X_13,mult(X_13,zero))) )],[refute_0_26,refute_0_29]) ).
cnf(refute_0_31,plain,
mult(X_13,unit) = X_13,
inference(subst,[],[sos_005:[bind(A,$fot(X_13))]]) ).
cnf(refute_0_32,plain,
( mult(X_13,unit) != X_13
| mult(X_13,unit) != add(X_13,mult(X_13,zero))
| X_13 = add(X_13,mult(X_13,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_13,unit),add(X_13,mult(X_13,zero))) ),[0],$fot(X_13)]]) ).
cnf(refute_0_33,plain,
( mult(X_13,unit) != add(X_13,mult(X_13,zero))
| X_13 = add(X_13,mult(X_13,zero)) ),
inference(resolve,[$cnf( $equal(mult(X_13,unit),X_13) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
X_13 = add(X_13,mult(X_13,zero)),
inference(resolve,[$cnf( $equal(mult(X_13,unit),add(X_13,mult(X_13,zero))) )],[refute_0_30,refute_0_33]) ).
cnf(refute_0_35,plain,
zero = add(zero,mult(zero,zero)),
inference(subst,[],[refute_0_34:[bind(X_13,$fot(zero))]]) ).
cnf(refute_0_36,plain,
( zero != add(zero,mult(zero,zero))
| add(zero,mult(zero,zero)) = zero ),
inference(subst,[],[refute_0_8:[bind(X,$fot(zero)),bind(Y,$fot(add(zero,mult(zero,zero))))]]) ).
cnf(refute_0_37,plain,
add(zero,mult(zero,zero)) = zero,
inference(resolve,[$cnf( $equal(zero,add(zero,mult(zero,zero))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( add(unit,add(zero,mult(zero,zero))) != zero
| add(zero,mult(zero,zero)) != zero
| add(unit,zero) = zero ),
introduced(tautology,[equality,[$cnf( $equal(add(unit,add(zero,mult(zero,zero))),zero) ),[0,1],$fot(zero)]]) ).
cnf(refute_0_39,plain,
( add(unit,add(zero,mult(zero,zero))) != zero
| add(unit,zero) = zero ),
inference(resolve,[$cnf( $equal(add(zero,mult(zero,zero)),zero) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
add(unit,zero) = zero,
inference(resolve,[$cnf( $equal(add(unit,add(zero,mult(zero,zero))),zero) )],[refute_0_25,refute_0_39]) ).
cnf(refute_0_41,plain,
add(unit,zero) = unit,
inference(subst,[],[refute_0_24:[bind(A,$fot(unit))]]) ).
cnf(refute_0_42,plain,
( add(unit,zero) != unit
| add(unit,zero) != zero
| unit = zero ),
introduced(tautology,[equality,[$cnf( $equal(add(unit,zero),zero) ),[0],$fot(unit)]]) ).
cnf(refute_0_43,plain,
( add(unit,zero) != zero
| unit = zero ),
inference(resolve,[$cnf( $equal(add(unit,zero),unit) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
unit = zero,
inference(resolve,[$cnf( $equal(add(unit,zero),zero) )],[refute_0_40,refute_0_43]) ).
cnf(refute_0_45,plain,
( unit != zero
| zero = unit ),
inference(subst,[],[refute_0_8:[bind(X,$fot(unit)),bind(Y,$fot(zero))]]) ).
cnf(refute_0_46,plain,
zero = unit,
inference(resolve,[$cnf( $equal(unit,zero) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
add(A,zero) = add(A,zero),
introduced(tautology,[refl,[$fot(add(A,zero))]]) ).
cnf(refute_0_48,plain,
( add(A,zero) != add(A,zero)
| zero != unit
| add(A,zero) = add(A,unit) ),
introduced(tautology,[equality,[$cnf( $equal(add(A,zero),add(A,zero)) ),[1,1],$fot(unit)]]) ).
cnf(refute_0_49,plain,
( zero != unit
| add(A,zero) = add(A,unit) ),
inference(resolve,[$cnf( $equal(add(A,zero),add(A,zero)) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
add(A,zero) = add(A,unit),
inference(resolve,[$cnf( $equal(zero,unit) )],[refute_0_46,refute_0_49]) ).
cnf(refute_0_51,plain,
( add(A,zero) != A
| add(A,zero) != add(A,unit)
| add(A,unit) = A ),
introduced(tautology,[equality,[$cnf( $equal(add(A,zero),A) ),[0],$fot(add(A,unit))]]) ).
cnf(refute_0_52,plain,
( add(A,zero) != A
| add(A,unit) = A ),
inference(resolve,[$cnf( $equal(add(A,zero),add(A,unit)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
add(A,unit) = A,
inference(resolve,[$cnf( $equal(add(A,zero),A) )],[refute_0_24,refute_0_52]) ).
cnf(refute_0_54,plain,
mult(A,add(A,unit)) = mult(A,add(A,unit)),
introduced(tautology,[refl,[$fot(mult(A,add(A,unit)))]]) ).
cnf(refute_0_55,plain,
( add(A,unit) != A
| mult(A,add(A,unit)) != mult(A,add(A,unit))
| mult(A,add(A,unit)) = mult(A,A) ),
introduced(tautology,[equality,[$cnf( $equal(mult(A,add(A,unit)),mult(A,add(A,unit))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_56,plain,
( add(A,unit) != A
| mult(A,add(A,unit)) = mult(A,A) ),
inference(resolve,[$cnf( $equal(mult(A,add(A,unit)),mult(A,add(A,unit))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
mult(A,add(A,unit)) = mult(A,A),
inference(resolve,[$cnf( $equal(add(A,unit),A) )],[refute_0_53,refute_0_56]) ).
cnf(refute_0_58,plain,
add(zero,A) = add(zero,A),
introduced(tautology,[refl,[$fot(add(zero,A))]]) ).
cnf(refute_0_59,plain,
( add(zero,A) != add(zero,A)
| zero != unit
| add(zero,A) = add(unit,A) ),
introduced(tautology,[equality,[$cnf( $equal(add(zero,A),add(zero,A)) ),[1,0],$fot(unit)]]) ).
cnf(refute_0_60,plain,
( zero != unit
| add(zero,A) = add(unit,A) ),
inference(resolve,[$cnf( $equal(add(zero,A),add(zero,A)) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
add(zero,A) = add(unit,A),
inference(resolve,[$cnf( $equal(zero,unit) )],[refute_0_46,refute_0_60]) ).
cnf(refute_0_62,plain,
( add(zero,A) != A
| add(zero,A) != add(unit,A)
| add(unit,A) = A ),
introduced(tautology,[equality,[$cnf( $equal(add(zero,A),A) ),[0],$fot(add(unit,A))]]) ).
cnf(refute_0_63,plain,
( add(zero,A) != A
| add(unit,A) = A ),
inference(resolve,[$cnf( $equal(add(zero,A),add(unit,A)) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
add(unit,A) = A,
inference(resolve,[$cnf( $equal(add(zero,A),A) )],[sos_004,refute_0_63]) ).
cnf(refute_0_65,plain,
add(unit,mult(A,add(A,unit))) = mult(A,add(A,unit)),
inference(subst,[],[refute_0_64:[bind(A,$fot(mult(A,add(A,unit))))]]) ).
cnf(refute_0_66,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_67,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_8,refute_0_66]) ).
cnf(refute_0_68,plain,
( add(unit,mult(A,add(A,unit))) != mult(A,add(A,unit))
| mult(A,add(A,unit)) != mult(A,A)
| add(unit,mult(A,add(A,unit))) = mult(A,A) ),
inference(subst,[],[refute_0_67:[bind(X,$fot(add(unit,mult(A,add(A,unit))))),bind(Y,$fot(mult(A,add(A,unit)))),bind(Z,$fot(mult(A,A)))]]) ).
cnf(refute_0_69,plain,
( mult(A,add(A,unit)) != mult(A,A)
| add(unit,mult(A,add(A,unit))) = mult(A,A) ),
inference(resolve,[$cnf( $equal(add(unit,mult(A,add(A,unit))),mult(A,add(A,unit))) )],[refute_0_65,refute_0_68]) ).
cnf(refute_0_70,plain,
add(unit,mult(A,add(A,unit))) = mult(A,A),
inference(resolve,[$cnf( $equal(mult(A,add(A,unit)),mult(A,A)) )],[refute_0_57,refute_0_69]) ).
cnf(refute_0_71,plain,
( add(unit,mult(A,add(A,unit))) != A
| add(unit,mult(A,add(A,unit))) != mult(A,A)
| mult(A,A) = A ),
introduced(tautology,[equality,[$cnf( $equal(add(unit,mult(A,add(A,unit))),A) ),[0],$fot(mult(A,A))]]) ).
cnf(refute_0_72,plain,
( add(unit,mult(A,add(A,unit))) != A
| mult(A,A) = A ),
inference(resolve,[$cnf( $equal(add(unit,mult(A,add(A,unit))),mult(A,A)) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
mult(A,A) = A,
inference(resolve,[$cnf( $equal(add(unit,mult(A,add(A,unit))),A) )],[refute_0_20,refute_0_72]) ).
cnf(refute_0_74,plain,
mult(B,B) = B,
inference(subst,[],[refute_0_73:[bind(A,$fot(B))]]) ).
cnf(refute_0_75,plain,
( mult(B,B) != B
| mult(B,add(B,C)) != add(mult(B,B),mult(B,C))
| mult(B,add(B,C)) = add(B,mult(B,C)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(B,add(B,C)),add(mult(B,B),mult(B,C))) ),[1,0],$fot(B)]]) ).
cnf(refute_0_76,plain,
( mult(B,add(B,C)) != add(mult(B,B),mult(B,C))
| mult(B,add(B,C)) = add(B,mult(B,C)) ),
inference(resolve,[$cnf( $equal(mult(B,B),B) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
mult(B,add(B,C)) = add(B,mult(B,C)),
inference(resolve,[$cnf( $equal(mult(B,add(B,C)),add(mult(B,B),mult(B,C))) )],[refute_0_0,refute_0_76]) ).
cnf(refute_0_78,plain,
add(X_10,unit) = X_10,
inference(subst,[],[refute_0_53:[bind(A,$fot(X_10))]]) ).
cnf(refute_0_79,plain,
mult(X_9,add(X_10,unit)) = mult(X_9,add(X_10,unit)),
introduced(tautology,[refl,[$fot(mult(X_9,add(X_10,unit)))]]) ).
cnf(refute_0_80,plain,
( add(X_10,unit) != X_10
| mult(X_9,add(X_10,unit)) != mult(X_9,add(X_10,unit))
| mult(X_9,add(X_10,unit)) = mult(X_9,X_10) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_9,add(X_10,unit)),mult(X_9,add(X_10,unit))) ),[1,1],$fot(X_10)]]) ).
cnf(refute_0_81,plain,
( add(X_10,unit) != X_10
| mult(X_9,add(X_10,unit)) = mult(X_9,X_10) ),
inference(resolve,[$cnf( $equal(mult(X_9,add(X_10,unit)),mult(X_9,add(X_10,unit))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
mult(X_9,add(X_10,unit)) = mult(X_9,X_10),
inference(resolve,[$cnf( $equal(add(X_10,unit),X_10) )],[refute_0_78,refute_0_81]) ).
cnf(refute_0_83,plain,
( mult(X_9,add(X_10,unit)) != add(X_9,mult(X_9,X_10))
| mult(X_9,add(X_10,unit)) != mult(X_9,X_10)
| mult(X_9,X_10) = add(X_9,mult(X_9,X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_9,add(X_10,unit)),add(X_9,mult(X_9,X_10))) ),[0],$fot(mult(X_9,X_10))]]) ).
cnf(refute_0_84,plain,
( mult(X_9,add(X_10,unit)) != add(X_9,mult(X_9,X_10))
| mult(X_9,X_10) = add(X_9,mult(X_9,X_10)) ),
inference(resolve,[$cnf( $equal(mult(X_9,add(X_10,unit)),mult(X_9,X_10)) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
mult(X_9,X_10) = add(X_9,mult(X_9,X_10)),
inference(resolve,[$cnf( $equal(mult(X_9,add(X_10,unit)),add(X_9,mult(X_9,X_10))) )],[refute_0_14,refute_0_84]) ).
cnf(refute_0_86,plain,
( mult(X_9,X_10) != add(X_9,mult(X_9,X_10))
| add(X_9,mult(X_9,X_10)) = mult(X_9,X_10) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(mult(X_9,X_10))),bind(Y,$fot(add(X_9,mult(X_9,X_10))))]]) ).
cnf(refute_0_87,plain,
add(X_9,mult(X_9,X_10)) = mult(X_9,X_10),
inference(resolve,[$cnf( $equal(mult(X_9,X_10),add(X_9,mult(X_9,X_10))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
add(B,mult(B,C)) = mult(B,C),
inference(subst,[],[refute_0_87:[bind(X_10,$fot(C)),bind(X_9,$fot(B))]]) ).
cnf(refute_0_89,plain,
( add(B,mult(B,C)) != mult(B,C)
| mult(B,add(B,C)) != add(B,mult(B,C))
| mult(B,add(B,C)) = mult(B,C) ),
introduced(tautology,[equality,[$cnf( $equal(mult(B,add(B,C)),add(B,mult(B,C))) ),[1],$fot(mult(B,C))]]) ).
cnf(refute_0_90,plain,
( mult(B,add(B,C)) != add(B,mult(B,C))
| mult(B,add(B,C)) = mult(B,C) ),
inference(resolve,[$cnf( $equal(add(B,mult(B,C)),mult(B,C)) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
mult(B,add(B,C)) = mult(B,C),
inference(resolve,[$cnf( $equal(mult(B,add(B,C)),add(B,mult(B,C))) )],[refute_0_77,refute_0_90]) ).
cnf(refute_0_92,plain,
add(X_24,add(X_24,X_25)) = add(add(X_24,X_24),X_25),
inference(subst,[],[sos:[bind(A,$fot(X_24)),bind(B,$fot(X_24)),bind(C,$fot(X_25))]]) ).
cnf(refute_0_93,plain,
X_14 = add(X_14,mult(X_14,zero)),
inference(subst,[],[refute_0_34:[bind(X_13,$fot(X_14))]]) ).
cnf(refute_0_94,plain,
mult(zero,X_14) = mult(X_14,zero),
inference(subst,[],[sos_002:[bind(A,$fot(zero)),bind(B,$fot(X_14))]]) ).
cnf(refute_0_95,plain,
( mult(zero,X_14) != mult(X_14,zero)
| mult(X_14,zero) = mult(zero,X_14) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(mult(zero,X_14))),bind(Y,$fot(mult(X_14,zero)))]]) ).
cnf(refute_0_96,plain,
mult(X_14,zero) = mult(zero,X_14),
inference(resolve,[$cnf( $equal(mult(zero,X_14),mult(X_14,zero)) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
( X_14 != add(X_14,mult(X_14,zero))
| mult(X_14,zero) != mult(zero,X_14)
| X_14 = add(X_14,mult(zero,X_14)) ),
introduced(tautology,[equality,[$cnf( $equal(X_14,add(X_14,mult(X_14,zero))) ),[1,1],$fot(mult(zero,X_14))]]) ).
cnf(refute_0_98,plain,
( X_14 != add(X_14,mult(X_14,zero))
| X_14 = add(X_14,mult(zero,X_14)) ),
inference(resolve,[$cnf( $equal(mult(X_14,zero),mult(zero,X_14)) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
X_14 = add(X_14,mult(zero,X_14)),
inference(resolve,[$cnf( $equal(X_14,add(X_14,mult(X_14,zero))) )],[refute_0_93,refute_0_98]) ).
cnf(refute_0_100,plain,
mult(A,unit) = mult(unit,A),
inference(subst,[],[sos_002:[bind(B,$fot(unit))]]) ).
cnf(refute_0_101,plain,
( mult(A,unit) != A
| mult(A,unit) != mult(unit,A)
| mult(unit,A) = A ),
introduced(tautology,[equality,[$cnf( $equal(mult(A,unit),A) ),[0],$fot(mult(unit,A))]]) ).
cnf(refute_0_102,plain,
( mult(A,unit) != A
| mult(unit,A) = A ),
inference(resolve,[$cnf( $equal(mult(A,unit),mult(unit,A)) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
mult(unit,A) = A,
inference(resolve,[$cnf( $equal(mult(A,unit),A) )],[sos_005,refute_0_102]) ).
cnf(refute_0_104,plain,
mult(unit,X_14) = X_14,
inference(subst,[],[refute_0_103:[bind(A,$fot(X_14))]]) ).
cnf(refute_0_105,plain,
mult(zero,X_14) = mult(zero,X_14),
introduced(tautology,[refl,[$fot(mult(zero,X_14))]]) ).
cnf(refute_0_106,plain,
( mult(zero,X_14) != mult(zero,X_14)
| zero != unit
| mult(zero,X_14) = mult(unit,X_14) ),
introduced(tautology,[equality,[$cnf( $equal(mult(zero,X_14),mult(zero,X_14)) ),[1,0],$fot(unit)]]) ).
cnf(refute_0_107,plain,
( zero != unit
| mult(zero,X_14) = mult(unit,X_14) ),
inference(resolve,[$cnf( $equal(mult(zero,X_14),mult(zero,X_14)) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
mult(zero,X_14) = mult(unit,X_14),
inference(resolve,[$cnf( $equal(zero,unit) )],[refute_0_46,refute_0_107]) ).
cnf(refute_0_109,plain,
( mult(unit,X_14) != X_14
| mult(zero,X_14) != mult(unit,X_14)
| mult(zero,X_14) = X_14 ),
inference(subst,[],[refute_0_67:[bind(X,$fot(mult(zero,X_14))),bind(Y,$fot(mult(unit,X_14))),bind(Z,$fot(X_14))]]) ).
cnf(refute_0_110,plain,
( mult(unit,X_14) != X_14
| mult(zero,X_14) = X_14 ),
inference(resolve,[$cnf( $equal(mult(zero,X_14),mult(unit,X_14)) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
mult(zero,X_14) = X_14,
inference(resolve,[$cnf( $equal(mult(unit,X_14),X_14) )],[refute_0_104,refute_0_110]) ).
cnf(refute_0_112,plain,
add(X_14,mult(zero,X_14)) = add(X_14,mult(zero,X_14)),
introduced(tautology,[refl,[$fot(add(X_14,mult(zero,X_14)))]]) ).
cnf(refute_0_113,plain,
( add(X_14,mult(zero,X_14)) != add(X_14,mult(zero,X_14))
| mult(zero,X_14) != X_14
| add(X_14,mult(zero,X_14)) = add(X_14,X_14) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_14,mult(zero,X_14)),add(X_14,mult(zero,X_14))) ),[1,1],$fot(X_14)]]) ).
cnf(refute_0_114,plain,
( mult(zero,X_14) != X_14
| add(X_14,mult(zero,X_14)) = add(X_14,X_14) ),
inference(resolve,[$cnf( $equal(add(X_14,mult(zero,X_14)),add(X_14,mult(zero,X_14))) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
add(X_14,mult(zero,X_14)) = add(X_14,X_14),
inference(resolve,[$cnf( $equal(mult(zero,X_14),X_14) )],[refute_0_111,refute_0_114]) ).
cnf(refute_0_116,plain,
( X_14 != add(X_14,mult(zero,X_14))
| add(X_14,mult(zero,X_14)) != add(X_14,X_14)
| X_14 = add(X_14,X_14) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_14,add(X_14,X_14)) ),[0],$fot(add(X_14,mult(zero,X_14)))]]) ).
cnf(refute_0_117,plain,
( X_14 != add(X_14,mult(zero,X_14))
| X_14 = add(X_14,X_14) ),
inference(resolve,[$cnf( $equal(add(X_14,mult(zero,X_14)),add(X_14,X_14)) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
X_14 = add(X_14,X_14),
inference(resolve,[$cnf( $equal(X_14,add(X_14,mult(zero,X_14))) )],[refute_0_99,refute_0_117]) ).
cnf(refute_0_119,plain,
X_24 = add(X_24,X_24),
inference(subst,[],[refute_0_118:[bind(X_14,$fot(X_24))]]) ).
cnf(refute_0_120,plain,
( X_24 != add(X_24,X_24)
| add(X_24,X_24) = X_24 ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_24)),bind(Y,$fot(add(X_24,X_24)))]]) ).
cnf(refute_0_121,plain,
add(X_24,X_24) = X_24,
inference(resolve,[$cnf( $equal(X_24,add(X_24,X_24)) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
( add(X_24,X_24) != X_24
| add(X_24,add(X_24,X_25)) != add(add(X_24,X_24),X_25)
| add(X_24,add(X_24,X_25)) = add(X_24,X_25) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_24,add(X_24,X_25)),add(add(X_24,X_24),X_25)) ),[1,0],$fot(X_24)]]) ).
cnf(refute_0_123,plain,
( add(X_24,add(X_24,X_25)) != add(add(X_24,X_24),X_25)
| add(X_24,add(X_24,X_25)) = add(X_24,X_25) ),
inference(resolve,[$cnf( $equal(add(X_24,X_24),X_24) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
add(X_24,add(X_24,X_25)) = add(X_24,X_25),
inference(resolve,[$cnf( $equal(add(X_24,add(X_24,X_25)),add(add(X_24,X_24),X_25)) )],[refute_0_92,refute_0_123]) ).
cnf(refute_0_125,plain,
add(B,add(B,C)) = add(B,C),
inference(subst,[],[refute_0_124:[bind(X_24,$fot(B)),bind(X_25,$fot(C))]]) ).
cnf(refute_0_126,plain,
mult(X_13,add(X_12,unit)) = add(X_13,mult(X_13,X_12)),
inference(subst,[],[refute_0_14:[bind(X_10,$fot(X_12)),bind(X_9,$fot(X_13))]]) ).
cnf(refute_0_127,plain,
mult(X_12,X_13) = mult(X_13,X_12),
inference(subst,[],[sos_002:[bind(A,$fot(X_12)),bind(B,$fot(X_13))]]) ).
cnf(refute_0_128,plain,
( mult(X_12,X_13) != mult(X_13,X_12)
| mult(X_13,X_12) = mult(X_12,X_13) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(mult(X_12,X_13))),bind(Y,$fot(mult(X_13,X_12)))]]) ).
cnf(refute_0_129,plain,
mult(X_13,X_12) = mult(X_12,X_13),
inference(resolve,[$cnf( $equal(mult(X_12,X_13),mult(X_13,X_12)) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
( mult(X_13,X_12) != mult(X_12,X_13)
| mult(X_13,add(X_12,unit)) != add(X_13,mult(X_13,X_12))
| mult(X_13,add(X_12,unit)) = add(X_13,mult(X_12,X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_13,add(X_12,unit)),add(X_13,mult(X_13,X_12))) ),[1,1],$fot(mult(X_12,X_13))]]) ).
cnf(refute_0_131,plain,
( mult(X_13,add(X_12,unit)) != add(X_13,mult(X_13,X_12))
| mult(X_13,add(X_12,unit)) = add(X_13,mult(X_12,X_13)) ),
inference(resolve,[$cnf( $equal(mult(X_13,X_12),mult(X_12,X_13)) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
mult(X_13,add(X_12,unit)) = add(X_13,mult(X_12,X_13)),
inference(resolve,[$cnf( $equal(mult(X_13,add(X_12,unit)),add(X_13,mult(X_13,X_12))) )],[refute_0_126,refute_0_131]) ).
cnf(refute_0_133,plain,
add(X_12,unit) = X_12,
inference(subst,[],[refute_0_53:[bind(A,$fot(X_12))]]) ).
cnf(refute_0_134,plain,
mult(X_13,add(X_12,unit)) = mult(X_13,add(X_12,unit)),
introduced(tautology,[refl,[$fot(mult(X_13,add(X_12,unit)))]]) ).
cnf(refute_0_135,plain,
( add(X_12,unit) != X_12
| mult(X_13,add(X_12,unit)) != mult(X_13,add(X_12,unit))
| mult(X_13,add(X_12,unit)) = mult(X_13,X_12) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_13,add(X_12,unit)),mult(X_13,add(X_12,unit))) ),[1,1],$fot(X_12)]]) ).
cnf(refute_0_136,plain,
( add(X_12,unit) != X_12
| mult(X_13,add(X_12,unit)) = mult(X_13,X_12) ),
inference(resolve,[$cnf( $equal(mult(X_13,add(X_12,unit)),mult(X_13,add(X_12,unit))) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
mult(X_13,add(X_12,unit)) = mult(X_13,X_12),
inference(resolve,[$cnf( $equal(add(X_12,unit),X_12) )],[refute_0_133,refute_0_136]) ).
cnf(refute_0_138,plain,
( mult(X_13,add(X_12,unit)) != add(X_13,mult(X_12,X_13))
| mult(X_13,add(X_12,unit)) != mult(X_13,X_12)
| mult(X_13,X_12) = add(X_13,mult(X_12,X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_13,add(X_12,unit)),add(X_13,mult(X_12,X_13))) ),[0],$fot(mult(X_13,X_12))]]) ).
cnf(refute_0_139,plain,
( mult(X_13,add(X_12,unit)) != add(X_13,mult(X_12,X_13))
| mult(X_13,X_12) = add(X_13,mult(X_12,X_13)) ),
inference(resolve,[$cnf( $equal(mult(X_13,add(X_12,unit)),mult(X_13,X_12)) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
mult(X_13,X_12) = add(X_13,mult(X_12,X_13)),
inference(resolve,[$cnf( $equal(mult(X_13,add(X_12,unit)),add(X_13,mult(X_12,X_13))) )],[refute_0_132,refute_0_139]) ).
cnf(refute_0_141,plain,
mult(C,add(B,C)) = add(mult(C,B),mult(C,C)),
inference(subst,[],[sos_003:[bind(A,$fot(C))]]) ).
cnf(refute_0_142,plain,
mult(C,C) = C,
inference(subst,[],[refute_0_73:[bind(A,$fot(C))]]) ).
cnf(refute_0_143,plain,
( mult(C,C) != C
| mult(C,add(B,C)) != add(mult(C,B),mult(C,C))
| mult(C,add(B,C)) = add(mult(C,B),C) ),
introduced(tautology,[equality,[$cnf( $equal(mult(C,add(B,C)),add(mult(C,B),mult(C,C))) ),[1,1],$fot(C)]]) ).
cnf(refute_0_144,plain,
( mult(C,add(B,C)) != add(mult(C,B),mult(C,C))
| mult(C,add(B,C)) = add(mult(C,B),C) ),
inference(resolve,[$cnf( $equal(mult(C,C),C) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
mult(C,add(B,C)) = add(mult(C,B),C),
inference(resolve,[$cnf( $equal(mult(C,add(B,C)),add(mult(C,B),mult(C,C))) )],[refute_0_141,refute_0_144]) ).
cnf(refute_0_146,plain,
add(C,mult(C,B)) = mult(C,B),
inference(subst,[],[refute_0_87:[bind(X_10,$fot(B)),bind(X_9,$fot(C))]]) ).
cnf(refute_0_147,plain,
add(mult(C,B),C) = add(C,mult(C,B)),
inference(subst,[],[refute_0_10:[bind(A,$fot(C)),bind(B,$fot(mult(C,B)))]]) ).
cnf(refute_0_148,plain,
( add(C,mult(C,B)) != mult(C,B)
| add(mult(C,B),C) != add(C,mult(C,B))
| add(mult(C,B),C) = mult(C,B) ),
inference(subst,[],[refute_0_67:[bind(X,$fot(add(mult(C,B),C))),bind(Y,$fot(add(C,mult(C,B)))),bind(Z,$fot(mult(C,B)))]]) ).
cnf(refute_0_149,plain,
( add(C,mult(C,B)) != mult(C,B)
| add(mult(C,B),C) = mult(C,B) ),
inference(resolve,[$cnf( $equal(add(mult(C,B),C),add(C,mult(C,B))) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
add(mult(C,B),C) = mult(C,B),
inference(resolve,[$cnf( $equal(add(C,mult(C,B)),mult(C,B)) )],[refute_0_146,refute_0_149]) ).
cnf(refute_0_151,plain,
( add(mult(C,B),C) != mult(C,B)
| mult(C,add(B,C)) != add(mult(C,B),C)
| mult(C,add(B,C)) = mult(C,B) ),
introduced(tautology,[equality,[$cnf( $equal(mult(C,add(B,C)),add(mult(C,B),C)) ),[1],$fot(mult(C,B))]]) ).
cnf(refute_0_152,plain,
( mult(C,add(B,C)) != add(mult(C,B),C)
| mult(C,add(B,C)) = mult(C,B) ),
inference(resolve,[$cnf( $equal(add(mult(C,B),C),mult(C,B)) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
mult(C,add(B,C)) = mult(C,B),
inference(resolve,[$cnf( $equal(mult(C,add(B,C)),add(mult(C,B),C)) )],[refute_0_145,refute_0_152]) ).
cnf(refute_0_154,plain,
mult(add(X_26,B),add(B,add(X_26,B))) = mult(add(X_26,B),B),
inference(subst,[],[refute_0_153:[bind(C,$fot(add(X_26,B)))]]) ).
cnf(refute_0_155,plain,
add(X_23,add(X_25,X_25)) = add(add(X_23,X_25),X_25),
inference(subst,[],[sos:[bind(A,$fot(X_23)),bind(B,$fot(X_25)),bind(C,$fot(X_25))]]) ).
cnf(refute_0_156,plain,
X_25 = add(X_25,X_25),
inference(subst,[],[refute_0_118:[bind(X_14,$fot(X_25))]]) ).
cnf(refute_0_157,plain,
( X_25 != add(X_25,X_25)
| add(X_25,X_25) = X_25 ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_25)),bind(Y,$fot(add(X_25,X_25)))]]) ).
cnf(refute_0_158,plain,
add(X_25,X_25) = X_25,
inference(resolve,[$cnf( $equal(X_25,add(X_25,X_25)) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
( add(X_23,add(X_25,X_25)) != add(add(X_23,X_25),X_25)
| add(X_25,X_25) != X_25
| add(X_23,X_25) = add(add(X_23,X_25),X_25) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_23,add(X_25,X_25)),add(add(X_23,X_25),X_25)) ),[0,1],$fot(X_25)]]) ).
cnf(refute_0_160,plain,
( add(X_23,add(X_25,X_25)) != add(add(X_23,X_25),X_25)
| add(X_23,X_25) = add(add(X_23,X_25),X_25) ),
inference(resolve,[$cnf( $equal(add(X_25,X_25),X_25) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
add(X_23,X_25) = add(add(X_23,X_25),X_25),
inference(resolve,[$cnf( $equal(add(X_23,add(X_25,X_25)),add(add(X_23,X_25),X_25)) )],[refute_0_155,refute_0_160]) ).
cnf(refute_0_162,plain,
add(add(X_23,X_25),X_25) = add(X_25,add(X_23,X_25)),
inference(subst,[],[refute_0_10:[bind(A,$fot(X_25)),bind(B,$fot(add(X_23,X_25)))]]) ).
cnf(refute_0_163,plain,
( add(X_23,X_25) != add(add(X_23,X_25),X_25)
| add(add(X_23,X_25),X_25) != add(X_25,add(X_23,X_25))
| add(X_23,X_25) = add(X_25,add(X_23,X_25)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_23,X_25),add(X_25,add(X_23,X_25))) ),[0],$fot(add(add(X_23,X_25),X_25))]]) ).
cnf(refute_0_164,plain,
( add(X_23,X_25) != add(add(X_23,X_25),X_25)
| add(X_23,X_25) = add(X_25,add(X_23,X_25)) ),
inference(resolve,[$cnf( $equal(add(add(X_23,X_25),X_25),add(X_25,add(X_23,X_25))) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
add(X_23,X_25) = add(X_25,add(X_23,X_25)),
inference(resolve,[$cnf( $equal(add(X_23,X_25),add(add(X_23,X_25),X_25)) )],[refute_0_161,refute_0_164]) ).
cnf(refute_0_166,plain,
add(X_26,B) = add(B,add(X_26,B)),
inference(subst,[],[refute_0_165:[bind(X_23,$fot(X_26)),bind(X_25,$fot(B))]]) ).
cnf(refute_0_167,plain,
( add(X_26,B) != add(B,add(X_26,B))
| add(B,add(X_26,B)) = add(X_26,B) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(add(X_26,B))),bind(Y,$fot(add(B,add(X_26,B))))]]) ).
cnf(refute_0_168,plain,
add(B,add(X_26,B)) = add(X_26,B),
inference(resolve,[$cnf( $equal(add(X_26,B),add(B,add(X_26,B))) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
( add(B,add(X_26,B)) != add(X_26,B)
| mult(add(X_26,B),add(B,add(X_26,B))) != mult(add(X_26,B),B)
| mult(add(X_26,B),add(X_26,B)) = mult(add(X_26,B),B) ),
introduced(tautology,[equality,[$cnf( $equal(mult(add(X_26,B),add(B,add(X_26,B))),mult(add(X_26,B),B)) ),[0,1],$fot(add(X_26,B))]]) ).
cnf(refute_0_170,plain,
( mult(add(X_26,B),add(B,add(X_26,B))) != mult(add(X_26,B),B)
| mult(add(X_26,B),add(X_26,B)) = mult(add(X_26,B),B) ),
inference(resolve,[$cnf( $equal(add(B,add(X_26,B)),add(X_26,B)) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
mult(add(X_26,B),add(X_26,B)) = mult(add(X_26,B),B),
inference(resolve,[$cnf( $equal(mult(add(X_26,B),add(B,add(X_26,B))),mult(add(X_26,B),B)) )],[refute_0_154,refute_0_170]) ).
cnf(refute_0_172,plain,
mult(add(X_26,B),add(X_26,B)) = add(X_26,B),
inference(subst,[],[refute_0_73:[bind(A,$fot(add(X_26,B)))]]) ).
cnf(refute_0_173,plain,
( mult(add(X_26,B),add(X_26,B)) != add(X_26,B)
| mult(add(X_26,B),add(X_26,B)) != mult(add(X_26,B),B)
| add(X_26,B) = mult(add(X_26,B),B) ),
introduced(tautology,[equality,[$cnf( $equal(mult(add(X_26,B),add(X_26,B)),mult(add(X_26,B),B)) ),[0],$fot(add(X_26,B))]]) ).
cnf(refute_0_174,plain,
( mult(add(X_26,B),add(X_26,B)) != mult(add(X_26,B),B)
| add(X_26,B) = mult(add(X_26,B),B) ),
inference(resolve,[$cnf( $equal(mult(add(X_26,B),add(X_26,B)),add(X_26,B)) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
mult(B,add(X_26,B)) = mult(B,X_26),
inference(subst,[],[refute_0_153:[bind(B,$fot(X_26)),bind(C,$fot(B))]]) ).
cnf(refute_0_176,plain,
mult(add(X_12,unit),B) = mult(B,add(X_12,unit)),
inference(subst,[],[sos_002:[bind(A,$fot(add(X_12,unit)))]]) ).
cnf(refute_0_177,plain,
mult(B,add(X_12,unit)) = add(B,mult(B,X_12)),
inference(subst,[],[refute_0_14:[bind(X_10,$fot(X_12)),bind(X_9,$fot(B))]]) ).
cnf(refute_0_178,plain,
( mult(B,add(X_12,unit)) != add(B,mult(B,X_12))
| mult(add(X_12,unit),B) != mult(B,add(X_12,unit))
| mult(add(X_12,unit),B) = add(B,mult(B,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(add(X_12,unit),B),mult(B,add(X_12,unit))) ),[1],$fot(add(B,mult(B,X_12)))]]) ).
cnf(refute_0_179,plain,
( mult(add(X_12,unit),B) != mult(B,add(X_12,unit))
| mult(add(X_12,unit),B) = add(B,mult(B,X_12)) ),
inference(resolve,[$cnf( $equal(mult(B,add(X_12,unit)),add(B,mult(B,X_12))) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
mult(add(X_12,unit),B) = add(B,mult(B,X_12)),
inference(resolve,[$cnf( $equal(mult(add(X_12,unit),B),mult(B,add(X_12,unit))) )],[refute_0_176,refute_0_179]) ).
cnf(refute_0_181,plain,
mult(add(X_12,unit),B) = mult(add(X_12,unit),B),
introduced(tautology,[refl,[$fot(mult(add(X_12,unit),B))]]) ).
cnf(refute_0_182,plain,
( add(X_12,unit) != X_12
| mult(add(X_12,unit),B) != mult(add(X_12,unit),B)
| mult(add(X_12,unit),B) = mult(X_12,B) ),
introduced(tautology,[equality,[$cnf( $equal(mult(add(X_12,unit),B),mult(add(X_12,unit),B)) ),[1,0],$fot(X_12)]]) ).
cnf(refute_0_183,plain,
( add(X_12,unit) != X_12
| mult(add(X_12,unit),B) = mult(X_12,B) ),
inference(resolve,[$cnf( $equal(mult(add(X_12,unit),B),mult(add(X_12,unit),B)) )],[refute_0_181,refute_0_182]) ).
cnf(refute_0_184,plain,
mult(add(X_12,unit),B) = mult(X_12,B),
inference(resolve,[$cnf( $equal(add(X_12,unit),X_12) )],[refute_0_133,refute_0_183]) ).
cnf(refute_0_185,plain,
( mult(add(X_12,unit),B) != add(B,mult(B,X_12))
| mult(add(X_12,unit),B) != mult(X_12,B)
| mult(X_12,B) = add(B,mult(B,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(add(X_12,unit),B),add(B,mult(B,X_12))) ),[0],$fot(mult(X_12,B))]]) ).
cnf(refute_0_186,plain,
( mult(add(X_12,unit),B) != add(B,mult(B,X_12))
| mult(X_12,B) = add(B,mult(B,X_12)) ),
inference(resolve,[$cnf( $equal(mult(add(X_12,unit),B),mult(X_12,B)) )],[refute_0_184,refute_0_185]) ).
cnf(refute_0_187,plain,
add(B,mult(B,X_12)) = mult(B,X_12),
inference(subst,[],[refute_0_87:[bind(X_10,$fot(X_12)),bind(X_9,$fot(B))]]) ).
cnf(refute_0_188,plain,
( add(B,mult(B,X_12)) != mult(B,X_12)
| mult(X_12,B) != add(B,mult(B,X_12))
| mult(X_12,B) = mult(B,X_12) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_12,B),add(B,mult(B,X_12))) ),[1],$fot(mult(B,X_12))]]) ).
cnf(refute_0_189,plain,
( mult(X_12,B) != add(B,mult(B,X_12))
| mult(X_12,B) = mult(B,X_12) ),
inference(resolve,[$cnf( $equal(add(B,mult(B,X_12)),mult(B,X_12)) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
( mult(add(X_12,unit),B) != add(B,mult(B,X_12))
| mult(X_12,B) = mult(B,X_12) ),
inference(resolve,[$cnf( $equal(mult(X_12,B),add(B,mult(B,X_12))) )],[refute_0_186,refute_0_189]) ).
cnf(refute_0_191,plain,
mult(X_12,B) = mult(B,X_12),
inference(resolve,[$cnf( $equal(mult(add(X_12,unit),B),add(B,mult(B,X_12))) )],[refute_0_180,refute_0_190]) ).
cnf(refute_0_192,plain,
( mult(X_12,B) != mult(B,X_12)
| mult(B,X_12) = mult(X_12,B) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(mult(X_12,B))),bind(Y,$fot(mult(B,X_12)))]]) ).
cnf(refute_0_193,plain,
mult(B,X_12) = mult(X_12,B),
inference(resolve,[$cnf( $equal(mult(X_12,B),mult(B,X_12)) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
mult(add(X_26,B),B) = mult(B,add(X_26,B)),
inference(subst,[],[refute_0_193:[bind(B,$fot(add(X_26,B))),bind(X_12,$fot(B))]]) ).
cnf(refute_0_195,plain,
( mult(B,add(X_26,B)) != mult(B,X_26)
| mult(add(X_26,B),B) != mult(B,add(X_26,B))
| mult(add(X_26,B),B) = mult(B,X_26) ),
inference(subst,[],[refute_0_67:[bind(X,$fot(mult(add(X_26,B),B))),bind(Y,$fot(mult(B,add(X_26,B)))),bind(Z,$fot(mult(B,X_26)))]]) ).
cnf(refute_0_196,plain,
( mult(B,add(X_26,B)) != mult(B,X_26)
| mult(add(X_26,B),B) = mult(B,X_26) ),
inference(resolve,[$cnf( $equal(mult(add(X_26,B),B),mult(B,add(X_26,B))) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
mult(add(X_26,B),B) = mult(B,X_26),
inference(resolve,[$cnf( $equal(mult(B,add(X_26,B)),mult(B,X_26)) )],[refute_0_175,refute_0_196]) ).
cnf(refute_0_198,plain,
( add(X_26,B) != mult(add(X_26,B),B)
| mult(add(X_26,B),B) != mult(B,X_26)
| add(X_26,B) = mult(B,X_26) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_26,B),mult(B,X_26)) ),[0],$fot(mult(add(X_26,B),B))]]) ).
cnf(refute_0_199,plain,
( add(X_26,B) != mult(add(X_26,B),B)
| add(X_26,B) = mult(B,X_26) ),
inference(resolve,[$cnf( $equal(mult(add(X_26,B),B),mult(B,X_26)) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
( mult(add(X_26,B),add(X_26,B)) != mult(add(X_26,B),B)
| add(X_26,B) = mult(B,X_26) ),
inference(resolve,[$cnf( $equal(add(X_26,B),mult(add(X_26,B),B)) )],[refute_0_174,refute_0_199]) ).
cnf(refute_0_201,plain,
add(X_26,B) = mult(B,X_26),
inference(resolve,[$cnf( $equal(mult(add(X_26,B),add(X_26,B)),mult(add(X_26,B),B)) )],[refute_0_171,refute_0_200]) ).
cnf(refute_0_202,plain,
( add(X_26,B) != mult(B,X_26)
| mult(B,X_26) = add(X_26,B) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(add(X_26,B))),bind(Y,$fot(mult(B,X_26)))]]) ).
cnf(refute_0_203,plain,
mult(B,X_26) = add(X_26,B),
inference(resolve,[$cnf( $equal(add(X_26,B),mult(B,X_26)) )],[refute_0_201,refute_0_202]) ).
cnf(refute_0_204,plain,
mult(X_13,X_12) = add(X_12,X_13),
inference(subst,[],[refute_0_203:[bind(B,$fot(X_13)),bind(X_26,$fot(X_12))]]) ).
cnf(refute_0_205,plain,
( mult(X_13,X_12) != add(X_12,X_13)
| mult(X_13,X_12) != add(X_13,mult(X_12,X_13))
| add(X_12,X_13) = add(X_13,mult(X_12,X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_13,X_12),add(X_13,mult(X_12,X_13))) ),[0],$fot(add(X_12,X_13))]]) ).
cnf(refute_0_206,plain,
( mult(X_13,X_12) != add(X_13,mult(X_12,X_13))
| add(X_12,X_13) = add(X_13,mult(X_12,X_13)) ),
inference(resolve,[$cnf( $equal(mult(X_13,X_12),add(X_12,X_13)) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
add(X_13,add(X_13,X_12)) = add(X_13,X_12),
inference(subst,[],[refute_0_124:[bind(X_24,$fot(X_13)),bind(X_25,$fot(X_12))]]) ).
cnf(refute_0_208,plain,
mult(X_12,X_13) = add(X_13,X_12),
inference(subst,[],[refute_0_203:[bind(B,$fot(X_12)),bind(X_26,$fot(X_13))]]) ).
cnf(refute_0_209,plain,
add(X_13,mult(X_12,X_13)) = add(X_13,mult(X_12,X_13)),
introduced(tautology,[refl,[$fot(add(X_13,mult(X_12,X_13)))]]) ).
cnf(refute_0_210,plain,
( add(X_13,mult(X_12,X_13)) != add(X_13,mult(X_12,X_13))
| mult(X_12,X_13) != add(X_13,X_12)
| add(X_13,mult(X_12,X_13)) = add(X_13,add(X_13,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_13,mult(X_12,X_13)),add(X_13,mult(X_12,X_13))) ),[1,1],$fot(add(X_13,X_12))]]) ).
cnf(refute_0_211,plain,
( mult(X_12,X_13) != add(X_13,X_12)
| add(X_13,mult(X_12,X_13)) = add(X_13,add(X_13,X_12)) ),
inference(resolve,[$cnf( $equal(add(X_13,mult(X_12,X_13)),add(X_13,mult(X_12,X_13))) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
add(X_13,mult(X_12,X_13)) = add(X_13,add(X_13,X_12)),
inference(resolve,[$cnf( $equal(mult(X_12,X_13),add(X_13,X_12)) )],[refute_0_208,refute_0_211]) ).
cnf(refute_0_213,plain,
( add(X_13,add(X_13,X_12)) != add(X_13,X_12)
| add(X_13,mult(X_12,X_13)) != add(X_13,add(X_13,X_12))
| add(X_13,mult(X_12,X_13)) = add(X_13,X_12) ),
inference(subst,[],[refute_0_67:[bind(X,$fot(add(X_13,mult(X_12,X_13)))),bind(Y,$fot(add(X_13,add(X_13,X_12)))),bind(Z,$fot(add(X_13,X_12)))]]) ).
cnf(refute_0_214,plain,
( add(X_13,add(X_13,X_12)) != add(X_13,X_12)
| add(X_13,mult(X_12,X_13)) = add(X_13,X_12) ),
inference(resolve,[$cnf( $equal(add(X_13,mult(X_12,X_13)),add(X_13,add(X_13,X_12))) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
add(X_13,mult(X_12,X_13)) = add(X_13,X_12),
inference(resolve,[$cnf( $equal(add(X_13,add(X_13,X_12)),add(X_13,X_12)) )],[refute_0_207,refute_0_214]) ).
cnf(refute_0_216,plain,
( add(X_12,X_13) != add(X_13,mult(X_12,X_13))
| add(X_13,mult(X_12,X_13)) != add(X_13,X_12)
| add(X_12,X_13) = add(X_13,X_12) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_12,X_13),add(X_13,X_12)) ),[0],$fot(add(X_13,mult(X_12,X_13)))]]) ).
cnf(refute_0_217,plain,
( add(X_12,X_13) != add(X_13,mult(X_12,X_13))
| add(X_12,X_13) = add(X_13,X_12) ),
inference(resolve,[$cnf( $equal(add(X_13,mult(X_12,X_13)),add(X_13,X_12)) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
( mult(X_13,X_12) != add(X_13,mult(X_12,X_13))
| add(X_12,X_13) = add(X_13,X_12) ),
inference(resolve,[$cnf( $equal(add(X_12,X_13),add(X_13,mult(X_12,X_13))) )],[refute_0_206,refute_0_217]) ).
cnf(refute_0_219,plain,
add(X_12,X_13) = add(X_13,X_12),
inference(resolve,[$cnf( $equal(mult(X_13,X_12),add(X_13,mult(X_12,X_13))) )],[refute_0_140,refute_0_218]) ).
cnf(refute_0_220,plain,
( add(X_12,X_13) != add(X_13,X_12)
| add(X_13,X_12) = add(X_12,X_13) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(add(X_12,X_13))),bind(Y,$fot(add(X_13,X_12)))]]) ).
cnf(refute_0_221,plain,
add(X_13,X_12) = add(X_12,X_13),
inference(resolve,[$cnf( $equal(add(X_12,X_13),add(X_13,X_12)) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
add(add(B,C),B) = add(B,add(B,C)),
inference(subst,[],[refute_0_221:[bind(X_12,$fot(B)),bind(X_13,$fot(add(B,C)))]]) ).
cnf(refute_0_223,plain,
( add(B,add(B,C)) != add(B,C)
| add(add(B,C),B) != add(B,add(B,C))
| add(add(B,C),B) = add(B,C) ),
inference(subst,[],[refute_0_67:[bind(X,$fot(add(add(B,C),B))),bind(Y,$fot(add(B,add(B,C)))),bind(Z,$fot(add(B,C)))]]) ).
cnf(refute_0_224,plain,
( add(B,add(B,C)) != add(B,C)
| add(add(B,C),B) = add(B,C) ),
inference(resolve,[$cnf( $equal(add(add(B,C),B),add(B,add(B,C))) )],[refute_0_222,refute_0_223]) ).
cnf(refute_0_225,plain,
add(add(B,C),B) = add(B,C),
inference(resolve,[$cnf( $equal(add(B,add(B,C)),add(B,C)) )],[refute_0_125,refute_0_224]) ).
cnf(refute_0_226,plain,
mult(B,add(B,C)) = add(add(B,C),B),
inference(subst,[],[refute_0_203:[bind(X_26,$fot(add(B,C)))]]) ).
cnf(refute_0_227,plain,
( add(add(B,C),B) != add(B,C)
| mult(B,add(B,C)) != add(add(B,C),B)
| mult(B,add(B,C)) = add(B,C) ),
inference(subst,[],[refute_0_67:[bind(X,$fot(mult(B,add(B,C)))),bind(Y,$fot(add(add(B,C),B))),bind(Z,$fot(add(B,C)))]]) ).
cnf(refute_0_228,plain,
( add(add(B,C),B) != add(B,C)
| mult(B,add(B,C)) = add(B,C) ),
inference(resolve,[$cnf( $equal(mult(B,add(B,C)),add(add(B,C),B)) )],[refute_0_226,refute_0_227]) ).
cnf(refute_0_229,plain,
mult(B,add(B,C)) = add(B,C),
inference(resolve,[$cnf( $equal(add(add(B,C),B),add(B,C)) )],[refute_0_225,refute_0_228]) ).
cnf(refute_0_230,plain,
( mult(B,add(B,C)) != add(B,C)
| mult(B,add(B,C)) != mult(B,C)
| add(B,C) = mult(B,C) ),
introduced(tautology,[equality,[$cnf( $equal(mult(B,add(B,C)),mult(B,C)) ),[0],$fot(add(B,C))]]) ).
cnf(refute_0_231,plain,
( mult(B,add(B,C)) != mult(B,C)
| add(B,C) = mult(B,C) ),
inference(resolve,[$cnf( $equal(mult(B,add(B,C)),add(B,C)) )],[refute_0_229,refute_0_230]) ).
cnf(refute_0_232,plain,
mult(B,C) = add(C,B),
inference(subst,[],[refute_0_203:[bind(X_26,$fot(C))]]) ).
cnf(refute_0_233,plain,
( add(B,C) != mult(B,C)
| mult(B,C) != add(C,B)
| add(B,C) = add(C,B) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(B,C),add(C,B)) ),[0],$fot(mult(B,C))]]) ).
cnf(refute_0_234,plain,
( add(B,C) != mult(B,C)
| add(B,C) = add(C,B) ),
inference(resolve,[$cnf( $equal(mult(B,C),add(C,B)) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
( mult(B,add(B,C)) != mult(B,C)
| add(B,C) = add(C,B) ),
inference(resolve,[$cnf( $equal(add(B,C),mult(B,C)) )],[refute_0_231,refute_0_234]) ).
cnf(refute_0_236,plain,
add(B,C) = add(C,B),
inference(resolve,[$cnf( $equal(mult(B,add(B,C)),mult(B,C)) )],[refute_0_91,refute_0_235]) ).
cnf(refute_0_237,plain,
( add(B,C) != add(C,B)
| add(C,B) = add(B,C) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(add(B,C))),bind(Y,$fot(add(C,B)))]]) ).
cnf(refute_0_238,plain,
add(C,B) = add(B,C),
inference(resolve,[$cnf( $equal(add(B,C),add(C,B)) )],[refute_0_236,refute_0_237]) ).
cnf(refute_0_239,plain,
add(x1,x0) = add(x0,x1),
inference(subst,[],[refute_0_238:[bind(B,$fot(x0)),bind(C,$fot(x1))]]) ).
cnf(refute_0_240,plain,
mult(x0,x1) = add(x1,x0),
inference(subst,[],[refute_0_203:[bind(B,$fot(x0)),bind(X_26,$fot(x1))]]) ).
cnf(refute_0_241,plain,
( add(x1,x0) != add(x0,x1)
| mult(x0,x1) != add(x1,x0)
| mult(x0,x1) = add(x0,x1) ),
inference(subst,[],[refute_0_67:[bind(X,$fot(mult(x0,x1))),bind(Y,$fot(add(x1,x0))),bind(Z,$fot(add(x0,x1)))]]) ).
cnf(refute_0_242,plain,
( add(x1,x0) != add(x0,x1)
| mult(x0,x1) = add(x0,x1) ),
inference(resolve,[$cnf( $equal(mult(x0,x1),add(x1,x0)) )],[refute_0_240,refute_0_241]) ).
cnf(refute_0_243,plain,
mult(x0,x1) = add(x0,x1),
inference(resolve,[$cnf( $equal(add(x1,x0),add(x0,x1)) )],[refute_0_239,refute_0_242]) ).
cnf(refute_0_244,plain,
( add(x0,x1) != add(x0,x1)
| mult(x0,x1) != add(x0,x1)
| add(x0,x1) = mult(x0,x1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(x0,x1),mult(x0,x1)) ),[1],$fot(add(x0,x1))]]) ).
cnf(refute_0_245,plain,
( add(x0,x1) != add(x0,x1)
| add(x0,x1) = mult(x0,x1) ),
inference(resolve,[$cnf( $equal(mult(x0,x1),add(x0,x1)) )],[refute_0_243,refute_0_244]) ).
cnf(refute_0_246,plain,
add(x0,x1) != add(x0,x1),
inference(resolve,[$cnf( $equal(add(x0,x1),mult(x0,x1)) )],[refute_0_245,goals]) ).
cnf(refute_0_247,plain,
add(x0,x1) = add(x0,x1),
introduced(tautology,[refl,[$fot(add(x0,x1))]]) ).
cnf(refute_0_248,plain,
$false,
inference(resolve,[$cnf( $equal(add(x0,x1),add(x0,x1)) )],[refute_0_247,refute_0_246]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG128-1 : TPTP v8.1.0. Released v5.4.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon May 30 09:26:55 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.40
% 0.20/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.42
%------------------------------------------------------------------------------