TSTP Solution File: GRP704+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP704+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n014.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 10:50:23 EDT 2022
% Result : Theorem 0.20s 0.48s
% Output : CNFRefutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 109
% Syntax : Number of formulae : 443 ( 255 unt; 0 def)
% Number of atoms : 719 ( 716 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 555 ( 279 ~; 262 |; 10 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 500 ( 0 sgn 105 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f01,axiom,
! [B,A] : mult(A,ld(A,B)) = B ).
fof(f02,axiom,
! [B,A] : ld(A,mult(A,B)) = B ).
fof(f03,axiom,
! [B,A] : mult(rd(A,B),B) = A ).
fof(f04,axiom,
! [B,A] : rd(mult(A,B),B) = A ).
fof(f05,axiom,
! [A] : mult(A,unit) = A ).
fof(f06,axiom,
! [A] : mult(unit,A) = A ).
fof(f08,axiom,
! [B,A] : mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ).
fof(f09,axiom,
! [B,A] : mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) ).
fof(f10,axiom,
! [B,A] : mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ).
fof(f11,axiom,
! [A] : op_d = ld(A,mult(op_c,A)) ).
fof(f12,axiom,
! [B,A] : op_e = mult(mult(rd(op_c,mult(A,B)),B),A) ).
fof(f13,axiom,
! [B,A] : op_f = mult(A,mult(B,ld(mult(A,B),op_c))) ).
fof(goals,conjecture,
! [X4,X5] :
( mult(op_f,mult(X4,X5)) = mult(mult(op_f,X4),X5)
& mult(X4,mult(X5,op_f)) = mult(mult(X4,X5),op_f)
& mult(X4,mult(op_f,X5)) = mult(mult(X4,op_f),X5) ) ).
fof(subgoal_0,plain,
! [X4,X5] : mult(op_f,mult(X4,X5)) = mult(mult(op_f,X4),X5),
inference(strip,[],[goals]) ).
fof(subgoal_1,plain,
! [X4,X5] :
( mult(op_f,mult(X4,X5)) = mult(mult(op_f,X4),X5)
=> mult(X4,mult(X5,op_f)) = mult(mult(X4,X5),op_f) ),
inference(strip,[],[goals]) ).
fof(subgoal_2,plain,
! [X4,X5] :
( ( mult(op_f,mult(X4,X5)) = mult(mult(op_f,X4),X5)
& mult(X4,mult(X5,op_f)) = mult(mult(X4,X5),op_f) )
=> mult(X4,mult(op_f,X5)) = mult(mult(X4,op_f),X5) ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X4,X5] : mult(op_f,mult(X4,X5)) = mult(mult(op_f,X4),X5),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X4,X5] : mult(op_f,mult(X4,X5)) != mult(mult(op_f,X4),X5),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
mult(op_f,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)) != mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A] : mult(unit,A) = A,
inference(canonicalize,[],[f06]) ).
fof(normalize_0_3,plain,
! [A] : mult(unit,A) = A,
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] : op_f = mult(A,mult(B,ld(mult(A,B),op_c))),
inference(canonicalize,[],[f13]) ).
fof(normalize_0_5,plain,
! [A,B] : op_f = mult(A,mult(B,ld(mult(A,B),op_c))),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] : mult(A,ld(A,B)) = B,
inference(canonicalize,[],[f01]) ).
fof(normalize_0_7,plain,
! [A,B] : mult(A,ld(A,B)) = B,
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B] : mult(op_c,mult(A,B)) = mult(mult(op_c,A),B),
inference(canonicalize,[],[f08]) ).
fof(normalize_0_9,plain,
! [A,B] : mult(op_c,mult(A,B)) = mult(mult(op_c,A),B),
inference(specialize,[],[normalize_0_8]) ).
cnf(refute_0_0,plain,
mult(op_f,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)) != mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
mult(unit,A) = A,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
mult(unit,mult(X_17,ld(mult(unit,X_17),op_c))) = mult(X_17,ld(mult(unit,X_17),op_c)),
inference(subst,[],[refute_0_1:[bind(A,$fot(mult(X_17,ld(mult(unit,X_17),op_c))))]]) ).
cnf(refute_0_3,plain,
op_f = mult(A,mult(B,ld(mult(A,B),op_c))),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
op_f = mult(unit,mult(X_17,ld(mult(unit,X_17),op_c))),
inference(subst,[],[refute_0_3:[bind(A,$fot(unit)),bind(B,$fot(X_17))]]) ).
cnf(refute_0_5,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_6,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_7,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( op_f != mult(unit,mult(X_17,ld(mult(unit,X_17),op_c)))
| mult(unit,mult(X_17,ld(mult(unit,X_17),op_c))) = op_f ),
inference(subst,[],[refute_0_7:[bind(X,$fot(op_f)),bind(Y,$fot(mult(unit,mult(X_17,ld(mult(unit,X_17),op_c)))))]]) ).
cnf(refute_0_9,plain,
mult(unit,mult(X_17,ld(mult(unit,X_17),op_c))) = op_f,
inference(resolve,[$cnf( $equal(op_f,mult(unit,mult(X_17,ld(mult(unit,X_17),op_c)))) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( mult(unit,mult(X_17,ld(mult(unit,X_17),op_c))) != mult(X_17,ld(mult(unit,X_17),op_c))
| mult(unit,mult(X_17,ld(mult(unit,X_17),op_c))) != op_f
| op_f = mult(X_17,ld(mult(unit,X_17),op_c)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(unit,mult(X_17,ld(mult(unit,X_17),op_c))),mult(X_17,ld(mult(unit,X_17),op_c))) ),[0],$fot(op_f)]]) ).
cnf(refute_0_11,plain,
( mult(unit,mult(X_17,ld(mult(unit,X_17),op_c))) != mult(X_17,ld(mult(unit,X_17),op_c))
| op_f = mult(X_17,ld(mult(unit,X_17),op_c)) ),
inference(resolve,[$cnf( $equal(mult(unit,mult(X_17,ld(mult(unit,X_17),op_c))),op_f) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
op_f = mult(X_17,ld(mult(unit,X_17),op_c)),
inference(resolve,[$cnf( $equal(mult(unit,mult(X_17,ld(mult(unit,X_17),op_c))),mult(X_17,ld(mult(unit,X_17),op_c))) )],[refute_0_2,refute_0_11]) ).
cnf(refute_0_13,plain,
mult(A,ld(A,B)) = B,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_14,plain,
mult(X_17,ld(X_17,op_c)) = op_c,
inference(subst,[],[refute_0_13:[bind(A,$fot(X_17)),bind(B,$fot(op_c))]]) ).
cnf(refute_0_15,plain,
mult(unit,X_17) = X_17,
inference(subst,[],[refute_0_1:[bind(A,$fot(X_17))]]) ).
cnf(refute_0_16,plain,
ld(mult(unit,X_17),op_c) = ld(mult(unit,X_17),op_c),
introduced(tautology,[refl,[$fot(ld(mult(unit,X_17),op_c))]]) ).
cnf(refute_0_17,plain,
( ld(mult(unit,X_17),op_c) != ld(mult(unit,X_17),op_c)
| mult(unit,X_17) != X_17
| ld(mult(unit,X_17),op_c) = ld(X_17,op_c) ),
introduced(tautology,[equality,[$cnf( $equal(ld(mult(unit,X_17),op_c),ld(mult(unit,X_17),op_c)) ),[1,0],$fot(X_17)]]) ).
cnf(refute_0_18,plain,
( mult(unit,X_17) != X_17
| ld(mult(unit,X_17),op_c) = ld(X_17,op_c) ),
inference(resolve,[$cnf( $equal(ld(mult(unit,X_17),op_c),ld(mult(unit,X_17),op_c)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
ld(mult(unit,X_17),op_c) = ld(X_17,op_c),
inference(resolve,[$cnf( $equal(mult(unit,X_17),X_17) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
mult(X_17,ld(mult(unit,X_17),op_c)) = mult(X_17,ld(mult(unit,X_17),op_c)),
introduced(tautology,[refl,[$fot(mult(X_17,ld(mult(unit,X_17),op_c)))]]) ).
cnf(refute_0_21,plain,
( ld(mult(unit,X_17),op_c) != ld(X_17,op_c)
| mult(X_17,ld(mult(unit,X_17),op_c)) != mult(X_17,ld(mult(unit,X_17),op_c))
| mult(X_17,ld(mult(unit,X_17),op_c)) = mult(X_17,ld(X_17,op_c)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_17,ld(mult(unit,X_17),op_c)),mult(X_17,ld(mult(unit,X_17),op_c))) ),[1,1],$fot(ld(X_17,op_c))]]) ).
cnf(refute_0_22,plain,
( ld(mult(unit,X_17),op_c) != ld(X_17,op_c)
| mult(X_17,ld(mult(unit,X_17),op_c)) = mult(X_17,ld(X_17,op_c)) ),
inference(resolve,[$cnf( $equal(mult(X_17,ld(mult(unit,X_17),op_c)),mult(X_17,ld(mult(unit,X_17),op_c))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
mult(X_17,ld(mult(unit,X_17),op_c)) = mult(X_17,ld(X_17,op_c)),
inference(resolve,[$cnf( $equal(ld(mult(unit,X_17),op_c),ld(X_17,op_c)) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_25,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_7,refute_0_24]) ).
cnf(refute_0_26,plain,
( mult(X_17,ld(X_17,op_c)) != op_c
| mult(X_17,ld(mult(unit,X_17),op_c)) != mult(X_17,ld(X_17,op_c))
| mult(X_17,ld(mult(unit,X_17),op_c)) = op_c ),
inference(subst,[],[refute_0_25:[bind(X,$fot(mult(X_17,ld(mult(unit,X_17),op_c)))),bind(Y,$fot(mult(X_17,ld(X_17,op_c)))),bind(Z,$fot(op_c))]]) ).
cnf(refute_0_27,plain,
( mult(X_17,ld(X_17,op_c)) != op_c
| mult(X_17,ld(mult(unit,X_17),op_c)) = op_c ),
inference(resolve,[$cnf( $equal(mult(X_17,ld(mult(unit,X_17),op_c)),mult(X_17,ld(X_17,op_c))) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
mult(X_17,ld(mult(unit,X_17),op_c)) = op_c,
inference(resolve,[$cnf( $equal(mult(X_17,ld(X_17,op_c)),op_c) )],[refute_0_14,refute_0_27]) ).
cnf(refute_0_29,plain,
( mult(X_17,ld(mult(unit,X_17),op_c)) != op_c
| op_f != mult(X_17,ld(mult(unit,X_17),op_c))
| op_f = op_c ),
introduced(tautology,[equality,[$cnf( $equal(op_f,mult(X_17,ld(mult(unit,X_17),op_c))) ),[1],$fot(op_c)]]) ).
cnf(refute_0_30,plain,
( op_f != mult(X_17,ld(mult(unit,X_17),op_c))
| op_f = op_c ),
inference(resolve,[$cnf( $equal(mult(X_17,ld(mult(unit,X_17),op_c)),op_c) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
op_f = op_c,
inference(resolve,[$cnf( $equal(op_f,mult(X_17,ld(mult(unit,X_17),op_c))) )],[refute_0_12,refute_0_30]) ).
cnf(refute_0_32,plain,
mult(op_f,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)) = mult(op_f,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),
introduced(tautology,[refl,[$fot(mult(op_f,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)))]]) ).
cnf(refute_0_33,plain,
( mult(op_f,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)) != mult(op_f,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5))
| op_f != op_c
| mult(op_f,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)) = mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_f,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),mult(op_f,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5))) ),[1,0],$fot(op_c)]]) ).
cnf(refute_0_34,plain,
( op_f != op_c
| mult(op_f,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)) = mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)) ),
inference(resolve,[$cnf( $equal(mult(op_f,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),mult(op_f,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
mult(op_f,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)) = mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),
inference(resolve,[$cnf( $equal(op_f,op_c) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
( mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)) != mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5)
| mult(op_f,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)) != mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5))
| mult(op_f,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)) = mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_f,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5))) ),[1],$fot(mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5))]]) ).
cnf(refute_0_37,plain,
( mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)) != mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5)
| mult(op_f,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)) = mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5) ),
inference(resolve,[$cnf( $equal(mult(op_f,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
mult(op_c,mult(A,B)) = mult(mult(op_c,A),B),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_39,plain,
( mult(op_c,mult(A,B)) != mult(mult(op_c,A),B)
| mult(mult(op_c,A),B) = mult(op_c,mult(A,B)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(mult(op_c,mult(A,B)))),bind(Y,$fot(mult(mult(op_c,A),B)))]]) ).
cnf(refute_0_40,plain,
mult(mult(op_c,A),B) = mult(op_c,mult(A,B)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(A,B)),mult(mult(op_c,A),B)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
mult(mult(op_c,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5) = mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),
inference(subst,[],[refute_0_40:[bind(A,$fot(skolemFOFtoCNF_X4)),bind(B,$fot(skolemFOFtoCNF_X5))]]) ).
cnf(refute_0_42,plain,
mult(op_f,skolemFOFtoCNF_X4) = mult(op_f,skolemFOFtoCNF_X4),
introduced(tautology,[refl,[$fot(mult(op_f,skolemFOFtoCNF_X4))]]) ).
cnf(refute_0_43,plain,
( mult(op_f,skolemFOFtoCNF_X4) != mult(op_f,skolemFOFtoCNF_X4)
| op_f != op_c
| mult(op_f,skolemFOFtoCNF_X4) = mult(op_c,skolemFOFtoCNF_X4) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_f,skolemFOFtoCNF_X4),mult(op_f,skolemFOFtoCNF_X4)) ),[1,0],$fot(op_c)]]) ).
cnf(refute_0_44,plain,
( op_f != op_c
| mult(op_f,skolemFOFtoCNF_X4) = mult(op_c,skolemFOFtoCNF_X4) ),
inference(resolve,[$cnf( $equal(mult(op_f,skolemFOFtoCNF_X4),mult(op_f,skolemFOFtoCNF_X4)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
mult(op_f,skolemFOFtoCNF_X4) = mult(op_c,skolemFOFtoCNF_X4),
inference(resolve,[$cnf( $equal(op_f,op_c) )],[refute_0_31,refute_0_44]) ).
cnf(refute_0_46,plain,
mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5) = mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5),
introduced(tautology,[refl,[$fot(mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5))]]) ).
cnf(refute_0_47,plain,
( mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5) != mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5)
| mult(op_f,skolemFOFtoCNF_X4) != mult(op_c,skolemFOFtoCNF_X4)
| mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5) = mult(mult(op_c,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5),mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5)) ),[1,0],$fot(mult(op_c,skolemFOFtoCNF_X4))]]) ).
cnf(refute_0_48,plain,
( mult(op_f,skolemFOFtoCNF_X4) != mult(op_c,skolemFOFtoCNF_X4)
| mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5) = mult(mult(op_c,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5) ),
inference(resolve,[$cnf( $equal(mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5),mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5) = mult(mult(op_c,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5),
inference(resolve,[$cnf( $equal(mult(op_f,skolemFOFtoCNF_X4),mult(op_c,skolemFOFtoCNF_X4)) )],[refute_0_45,refute_0_48]) ).
cnf(refute_0_50,plain,
( mult(mult(op_c,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5) != mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5))
| mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5) != mult(mult(op_c,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5)
| mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5) = mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5))),bind(Y,$fot(mult(mult(op_c,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5))),bind(Z,$fot(mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5))))]]) ).
cnf(refute_0_51,plain,
( mult(mult(op_c,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5) != mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5))
| mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5) = mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)) ),
inference(resolve,[$cnf( $equal(mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5),mult(mult(op_c,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5) = mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),
inference(resolve,[$cnf( $equal(mult(mult(op_c,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5),mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5))) )],[refute_0_41,refute_0_51]) ).
cnf(refute_0_53,plain,
( mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5) != mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5))
| mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)) != mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5))
| mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)) = mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5)) ),[1],$fot(mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)))]]) ).
cnf(refute_0_54,plain,
( mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)) != mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5))
| mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)) = mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5) ),
inference(resolve,[$cnf( $equal(mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5),mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)) != mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5))
| mult(op_f,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)) = mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5) ),
inference(resolve,[$cnf( $equal(mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5)) )],[refute_0_54,refute_0_37]) ).
cnf(refute_0_56,plain,
mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)) != mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),
inference(resolve,[$cnf( $equal(mult(op_f,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),mult(mult(op_f,skolemFOFtoCNF_X4),skolemFOFtoCNF_X5)) )],[refute_0_55,refute_0_0]) ).
cnf(refute_0_57,plain,
mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)) = mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),
introduced(tautology,[refl,[$fot(mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)))]]) ).
cnf(refute_0_58,plain,
$false,
inference(resolve,[$cnf( $equal(mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),mult(op_c,mult(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5))) )],[refute_0_57,refute_0_56]) ).
fof(negate_1_0,plain,
~ ! [X4,X5] :
( mult(op_f,mult(X4,X5)) = mult(mult(op_f,X4),X5)
=> mult(X4,mult(X5,op_f)) = mult(mult(X4,X5),op_f) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [X4,X5] :
( mult(X4,mult(X5,op_f)) != mult(mult(X4,X5),op_f)
& mult(op_f,mult(X4,X5)) = mult(mult(op_f,X4),X5) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( mult(skolemFOFtoCNF_X4_1,mult(skolemFOFtoCNF_X5_1,op_f)) != mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f)
& mult(op_f,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1)) = mult(mult(op_f,skolemFOFtoCNF_X4_1),skolemFOFtoCNF_X5_1) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
mult(skolemFOFtoCNF_X4_1,mult(skolemFOFtoCNF_X5_1,op_f)) != mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A,B] : mult(A,mult(B,op_c)) = mult(mult(A,B),op_c),
inference(canonicalize,[],[f09]) ).
fof(normalize_1_4,plain,
! [A,B] : mult(A,mult(B,op_c)) = mult(mult(A,B),op_c),
inference(specialize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [A,B] : mult(A,ld(A,B)) = B,
inference(canonicalize,[],[f01]) ).
fof(normalize_1_6,plain,
! [A,B] : mult(A,ld(A,B)) = B,
inference(specialize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [A] : op_d = ld(A,mult(op_c,A)),
inference(canonicalize,[],[f11]) ).
fof(normalize_1_8,plain,
! [A] : op_d = ld(A,mult(op_c,A)),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [A,B] : ld(A,mult(A,B)) = B,
inference(canonicalize,[],[f02]) ).
fof(normalize_1_10,plain,
! [A,B] : ld(A,mult(A,B)) = B,
inference(specialize,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [A] : mult(unit,A) = A,
inference(canonicalize,[],[f06]) ).
fof(normalize_1_12,plain,
! [A] : mult(unit,A) = A,
inference(specialize,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
! [A] : mult(A,unit) = A,
inference(canonicalize,[],[f05]) ).
fof(normalize_1_14,plain,
! [A] : mult(A,unit) = A,
inference(specialize,[],[normalize_1_13]) ).
fof(normalize_1_15,plain,
! [A,B] : op_e = mult(mult(rd(op_c,mult(A,B)),B),A),
inference(canonicalize,[],[f12]) ).
fof(normalize_1_16,plain,
! [A,B] : op_e = mult(mult(rd(op_c,mult(A,B)),B),A),
inference(specialize,[],[normalize_1_15]) ).
fof(normalize_1_17,plain,
! [A,B] : mult(rd(A,B),B) = A,
inference(canonicalize,[],[f03]) ).
fof(normalize_1_18,plain,
! [A,B] : mult(rd(A,B),B) = A,
inference(specialize,[],[normalize_1_17]) ).
fof(normalize_1_19,plain,
! [A,B] : rd(mult(A,B),B) = A,
inference(canonicalize,[],[f04]) ).
fof(normalize_1_20,plain,
! [A,B] : rd(mult(A,B),B) = A,
inference(specialize,[],[normalize_1_19]) ).
fof(normalize_1_21,plain,
! [A,B] : mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
inference(canonicalize,[],[f10]) ).
fof(normalize_1_22,plain,
! [A,B] : mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
inference(specialize,[],[normalize_1_21]) ).
fof(normalize_1_23,plain,
! [A,B] : op_f = mult(A,mult(B,ld(mult(A,B),op_c))),
inference(canonicalize,[],[f13]) ).
fof(normalize_1_24,plain,
! [A,B] : op_f = mult(A,mult(B,ld(mult(A,B),op_c))),
inference(specialize,[],[normalize_1_23]) ).
fof(normalize_1_25,plain,
! [A,B] : mult(op_c,mult(A,B)) = mult(mult(op_c,A),B),
inference(canonicalize,[],[f08]) ).
fof(normalize_1_26,plain,
! [A,B] : mult(op_c,mult(A,B)) = mult(mult(op_c,A),B),
inference(specialize,[],[normalize_1_25]) ).
cnf(refute_1_0,plain,
mult(skolemFOFtoCNF_X4_1,mult(skolemFOFtoCNF_X5_1,op_f)) != mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
mult(A,mult(B,op_c)) = mult(mult(A,B),op_c),
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_2,plain,
mult(A,mult(ld(A,X_29),op_c)) = mult(mult(A,ld(A,X_29)),op_c),
inference(subst,[],[refute_1_1:[bind(B,$fot(ld(A,X_29)))]]) ).
cnf(refute_1_3,plain,
mult(A,ld(A,B)) = B,
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_4,plain,
mult(A,ld(A,X_29)) = X_29,
inference(subst,[],[refute_1_3:[bind(B,$fot(X_29))]]) ).
cnf(refute_1_5,plain,
( mult(A,ld(A,X_29)) != X_29
| mult(A,mult(ld(A,X_29),op_c)) != mult(mult(A,ld(A,X_29)),op_c)
| mult(A,mult(ld(A,X_29),op_c)) = mult(X_29,op_c) ),
introduced(tautology,[equality,[$cnf( $equal(mult(A,mult(ld(A,X_29),op_c)),mult(mult(A,ld(A,X_29)),op_c)) ),[1,0],$fot(X_29)]]) ).
cnf(refute_1_6,plain,
( mult(A,mult(ld(A,X_29),op_c)) != mult(mult(A,ld(A,X_29)),op_c)
| mult(A,mult(ld(A,X_29),op_c)) = mult(X_29,op_c) ),
inference(resolve,[$cnf( $equal(mult(A,ld(A,X_29)),X_29) )],[refute_1_4,refute_1_5]) ).
cnf(refute_1_7,plain,
mult(A,mult(ld(A,X_29),op_c)) = mult(X_29,op_c),
inference(resolve,[$cnf( $equal(mult(A,mult(ld(A,X_29),op_c)),mult(mult(A,ld(A,X_29)),op_c)) )],[refute_1_2,refute_1_6]) ).
cnf(refute_1_8,plain,
mult(X_28,ld(X_28,mult(op_c,X_28))) = mult(op_c,X_28),
inference(subst,[],[refute_1_3:[bind(A,$fot(X_28)),bind(B,$fot(mult(op_c,X_28)))]]) ).
cnf(refute_1_9,plain,
op_d = ld(A,mult(op_c,A)),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_10,plain,
ld(A,mult(A,B)) = B,
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_11,plain,
ld(unit,mult(unit,X_21)) = X_21,
inference(subst,[],[refute_1_10:[bind(A,$fot(unit)),bind(B,$fot(X_21))]]) ).
cnf(refute_1_12,plain,
mult(unit,A) = A,
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_13,plain,
mult(unit,X_21) = X_21,
inference(subst,[],[refute_1_12:[bind(A,$fot(X_21))]]) ).
cnf(refute_1_14,plain,
( ld(unit,mult(unit,X_21)) != X_21
| mult(unit,X_21) != X_21
| ld(unit,X_21) = X_21 ),
introduced(tautology,[equality,[$cnf( $equal(ld(unit,mult(unit,X_21)),X_21) ),[0,1],$fot(X_21)]]) ).
cnf(refute_1_15,plain,
( ld(unit,mult(unit,X_21)) != X_21
| ld(unit,X_21) = X_21 ),
inference(resolve,[$cnf( $equal(mult(unit,X_21),X_21) )],[refute_1_13,refute_1_14]) ).
cnf(refute_1_16,plain,
ld(unit,X_21) = X_21,
inference(resolve,[$cnf( $equal(ld(unit,mult(unit,X_21)),X_21) )],[refute_1_11,refute_1_15]) ).
cnf(refute_1_17,plain,
ld(unit,mult(op_c,unit)) = mult(op_c,unit),
inference(subst,[],[refute_1_16:[bind(X_21,$fot(mult(op_c,unit)))]]) ).
cnf(refute_1_18,plain,
op_d = ld(unit,mult(op_c,unit)),
inference(subst,[],[refute_1_9:[bind(A,$fot(unit))]]) ).
cnf(refute_1_19,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_20,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_21,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_19,refute_1_20]) ).
cnf(refute_1_22,plain,
( op_d != ld(unit,mult(op_c,unit))
| ld(unit,mult(op_c,unit)) = op_d ),
inference(subst,[],[refute_1_21:[bind(X,$fot(op_d)),bind(Y,$fot(ld(unit,mult(op_c,unit))))]]) ).
cnf(refute_1_23,plain,
ld(unit,mult(op_c,unit)) = op_d,
inference(resolve,[$cnf( $equal(op_d,ld(unit,mult(op_c,unit))) )],[refute_1_18,refute_1_22]) ).
cnf(refute_1_24,plain,
( ld(unit,mult(op_c,unit)) != mult(op_c,unit)
| ld(unit,mult(op_c,unit)) != op_d
| op_d = mult(op_c,unit) ),
introduced(tautology,[equality,[$cnf( $equal(ld(unit,mult(op_c,unit)),mult(op_c,unit)) ),[0],$fot(op_d)]]) ).
cnf(refute_1_25,plain,
( ld(unit,mult(op_c,unit)) != mult(op_c,unit)
| op_d = mult(op_c,unit) ),
inference(resolve,[$cnf( $equal(ld(unit,mult(op_c,unit)),op_d) )],[refute_1_23,refute_1_24]) ).
cnf(refute_1_26,plain,
op_d = mult(op_c,unit),
inference(resolve,[$cnf( $equal(ld(unit,mult(op_c,unit)),mult(op_c,unit)) )],[refute_1_17,refute_1_25]) ).
cnf(refute_1_27,plain,
mult(A,unit) = A,
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_28,plain,
mult(op_c,unit) = op_c,
inference(subst,[],[refute_1_27:[bind(A,$fot(op_c))]]) ).
cnf(refute_1_29,plain,
( mult(op_c,unit) != op_c
| op_d != mult(op_c,unit)
| op_d = op_c ),
introduced(tautology,[equality,[$cnf( $equal(op_d,mult(op_c,unit)) ),[1],$fot(op_c)]]) ).
cnf(refute_1_30,plain,
( op_d != mult(op_c,unit)
| op_d = op_c ),
inference(resolve,[$cnf( $equal(mult(op_c,unit),op_c) )],[refute_1_28,refute_1_29]) ).
cnf(refute_1_31,plain,
op_d = op_c,
inference(resolve,[$cnf( $equal(op_d,mult(op_c,unit)) )],[refute_1_26,refute_1_30]) ).
cnf(refute_1_32,plain,
( op_d != ld(A,mult(op_c,A))
| op_d != op_c
| op_c = ld(A,mult(op_c,A)) ),
introduced(tautology,[equality,[$cnf( $equal(op_d,ld(A,mult(op_c,A))) ),[0],$fot(op_c)]]) ).
cnf(refute_1_33,plain,
( op_d != ld(A,mult(op_c,A))
| op_c = ld(A,mult(op_c,A)) ),
inference(resolve,[$cnf( $equal(op_d,op_c) )],[refute_1_31,refute_1_32]) ).
cnf(refute_1_34,plain,
op_c = ld(A,mult(op_c,A)),
inference(resolve,[$cnf( $equal(op_d,ld(A,mult(op_c,A))) )],[refute_1_9,refute_1_33]) ).
cnf(refute_1_35,plain,
op_c = ld(X_28,mult(op_c,X_28)),
inference(subst,[],[refute_1_34:[bind(A,$fot(X_28))]]) ).
cnf(refute_1_36,plain,
( op_c != ld(X_28,mult(op_c,X_28))
| ld(X_28,mult(op_c,X_28)) = op_c ),
inference(subst,[],[refute_1_21:[bind(X,$fot(op_c)),bind(Y,$fot(ld(X_28,mult(op_c,X_28))))]]) ).
cnf(refute_1_37,plain,
ld(X_28,mult(op_c,X_28)) = op_c,
inference(resolve,[$cnf( $equal(op_c,ld(X_28,mult(op_c,X_28))) )],[refute_1_35,refute_1_36]) ).
cnf(refute_1_38,plain,
( ld(X_28,mult(op_c,X_28)) != op_c
| mult(X_28,ld(X_28,mult(op_c,X_28))) != mult(op_c,X_28)
| mult(X_28,op_c) = mult(op_c,X_28) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_28,ld(X_28,mult(op_c,X_28))),mult(op_c,X_28)) ),[0,1],$fot(op_c)]]) ).
cnf(refute_1_39,plain,
( mult(X_28,ld(X_28,mult(op_c,X_28))) != mult(op_c,X_28)
| mult(X_28,op_c) = mult(op_c,X_28) ),
inference(resolve,[$cnf( $equal(ld(X_28,mult(op_c,X_28)),op_c) )],[refute_1_37,refute_1_38]) ).
cnf(refute_1_40,plain,
mult(X_28,op_c) = mult(op_c,X_28),
inference(resolve,[$cnf( $equal(mult(X_28,ld(X_28,mult(op_c,X_28))),mult(op_c,X_28)) )],[refute_1_8,refute_1_39]) ).
cnf(refute_1_41,plain,
mult(ld(A,X_29),op_c) = mult(op_c,ld(A,X_29)),
inference(subst,[],[refute_1_40:[bind(X_28,$fot(ld(A,X_29)))]]) ).
cnf(refute_1_42,plain,
mult(A,mult(ld(A,X_29),op_c)) = mult(A,mult(ld(A,X_29),op_c)),
introduced(tautology,[refl,[$fot(mult(A,mult(ld(A,X_29),op_c)))]]) ).
cnf(refute_1_43,plain,
( mult(A,mult(ld(A,X_29),op_c)) != mult(A,mult(ld(A,X_29),op_c))
| mult(ld(A,X_29),op_c) != mult(op_c,ld(A,X_29))
| mult(A,mult(ld(A,X_29),op_c)) = mult(A,mult(op_c,ld(A,X_29))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(A,mult(ld(A,X_29),op_c)),mult(A,mult(ld(A,X_29),op_c))) ),[1,1],$fot(mult(op_c,ld(A,X_29)))]]) ).
cnf(refute_1_44,plain,
( mult(ld(A,X_29),op_c) != mult(op_c,ld(A,X_29))
| mult(A,mult(ld(A,X_29),op_c)) = mult(A,mult(op_c,ld(A,X_29))) ),
inference(resolve,[$cnf( $equal(mult(A,mult(ld(A,X_29),op_c)),mult(A,mult(ld(A,X_29),op_c))) )],[refute_1_42,refute_1_43]) ).
cnf(refute_1_45,plain,
mult(A,mult(ld(A,X_29),op_c)) = mult(A,mult(op_c,ld(A,X_29))),
inference(resolve,[$cnf( $equal(mult(ld(A,X_29),op_c),mult(op_c,ld(A,X_29))) )],[refute_1_41,refute_1_44]) ).
cnf(refute_1_46,plain,
( mult(A,mult(ld(A,X_29),op_c)) != mult(A,mult(op_c,ld(A,X_29)))
| mult(A,mult(ld(A,X_29),op_c)) != mult(X_29,op_c)
| mult(A,mult(op_c,ld(A,X_29))) = mult(X_29,op_c) ),
introduced(tautology,[equality,[$cnf( $equal(mult(A,mult(ld(A,X_29),op_c)),mult(X_29,op_c)) ),[0],$fot(mult(A,mult(op_c,ld(A,X_29))))]]) ).
cnf(refute_1_47,plain,
( mult(A,mult(ld(A,X_29),op_c)) != mult(X_29,op_c)
| mult(A,mult(op_c,ld(A,X_29))) = mult(X_29,op_c) ),
inference(resolve,[$cnf( $equal(mult(A,mult(ld(A,X_29),op_c)),mult(A,mult(op_c,ld(A,X_29)))) )],[refute_1_45,refute_1_46]) ).
cnf(refute_1_48,plain,
mult(A,mult(op_c,ld(A,X_29))) = mult(X_29,op_c),
inference(resolve,[$cnf( $equal(mult(A,mult(ld(A,X_29),op_c)),mult(X_29,op_c)) )],[refute_1_7,refute_1_47]) ).
cnf(refute_1_49,plain,
mult(X_55,mult(op_c,ld(X_55,mult(X_55,B)))) = mult(mult(X_55,B),op_c),
inference(subst,[],[refute_1_48:[bind(A,$fot(X_55)),bind(X_29,$fot(mult(X_55,B)))]]) ).
cnf(refute_1_50,plain,
ld(X_55,mult(X_55,B)) = B,
inference(subst,[],[refute_1_10:[bind(A,$fot(X_55))]]) ).
cnf(refute_1_51,plain,
( ld(X_55,mult(X_55,B)) != B
| mult(X_55,mult(op_c,ld(X_55,mult(X_55,B)))) != mult(mult(X_55,B),op_c)
| mult(X_55,mult(op_c,B)) = mult(mult(X_55,B),op_c) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_55,mult(op_c,ld(X_55,mult(X_55,B)))),mult(mult(X_55,B),op_c)) ),[0,1,1],$fot(B)]]) ).
cnf(refute_1_52,plain,
( mult(X_55,mult(op_c,ld(X_55,mult(X_55,B)))) != mult(mult(X_55,B),op_c)
| mult(X_55,mult(op_c,B)) = mult(mult(X_55,B),op_c) ),
inference(resolve,[$cnf( $equal(ld(X_55,mult(X_55,B)),B) )],[refute_1_50,refute_1_51]) ).
cnf(refute_1_53,plain,
mult(X_55,mult(op_c,B)) = mult(mult(X_55,B),op_c),
inference(resolve,[$cnf( $equal(mult(X_55,mult(op_c,ld(X_55,mult(X_55,B)))),mult(mult(X_55,B),op_c)) )],[refute_1_49,refute_1_52]) ).
cnf(refute_1_54,plain,
mult(mult(X_55,B),op_c) = mult(op_c,mult(X_55,B)),
inference(subst,[],[refute_1_40:[bind(X_28,$fot(mult(X_55,B)))]]) ).
cnf(refute_1_55,plain,
( mult(X_55,mult(op_c,B)) != mult(mult(X_55,B),op_c)
| mult(mult(X_55,B),op_c) != mult(op_c,mult(X_55,B))
| mult(X_55,mult(op_c,B)) = mult(op_c,mult(X_55,B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(X_55,mult(op_c,B)),mult(op_c,mult(X_55,B))) ),[0],$fot(mult(mult(X_55,B),op_c))]]) ).
cnf(refute_1_56,plain,
( mult(X_55,mult(op_c,B)) != mult(mult(X_55,B),op_c)
| mult(X_55,mult(op_c,B)) = mult(op_c,mult(X_55,B)) ),
inference(resolve,[$cnf( $equal(mult(mult(X_55,B),op_c),mult(op_c,mult(X_55,B))) )],[refute_1_54,refute_1_55]) ).
cnf(refute_1_57,plain,
mult(X_55,mult(op_c,B)) = mult(op_c,mult(X_55,B)),
inference(resolve,[$cnf( $equal(mult(X_55,mult(op_c,B)),mult(mult(X_55,B),op_c)) )],[refute_1_53,refute_1_56]) ).
cnf(refute_1_58,plain,
mult(skolemFOFtoCNF_X4_1,mult(op_c,skolemFOFtoCNF_X5_1)) = mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1)),
inference(subst,[],[refute_1_57:[bind(B,$fot(skolemFOFtoCNF_X5_1)),bind(X_55,$fot(skolemFOFtoCNF_X4_1))]]) ).
cnf(refute_1_59,plain,
mult(skolemFOFtoCNF_X5_1,op_c) = mult(op_c,skolemFOFtoCNF_X5_1),
inference(subst,[],[refute_1_40:[bind(X_28,$fot(skolemFOFtoCNF_X5_1))]]) ).
cnf(refute_1_60,plain,
op_e = mult(mult(rd(op_c,mult(A,B)),B),A),
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_61,plain,
op_e = mult(mult(rd(op_c,mult(mult(rd(op_c,mult(X_49,B)),B),X_49)),X_49),mult(rd(op_c,mult(X_49,B)),B)),
inference(subst,[],[refute_1_60:[bind(A,$fot(mult(rd(op_c,mult(X_49,B)),B))),bind(B,$fot(X_49))]]) ).
cnf(refute_1_62,plain,
op_e = mult(mult(rd(op_c,mult(X_49,B)),B),X_49),
inference(subst,[],[refute_1_60:[bind(A,$fot(X_49))]]) ).
cnf(refute_1_63,plain,
( op_e != mult(mult(rd(op_c,mult(X_49,B)),B),X_49)
| mult(mult(rd(op_c,mult(X_49,B)),B),X_49) = op_e ),
inference(subst,[],[refute_1_21:[bind(X,$fot(op_e)),bind(Y,$fot(mult(mult(rd(op_c,mult(X_49,B)),B),X_49)))]]) ).
cnf(refute_1_64,plain,
mult(mult(rd(op_c,mult(X_49,B)),B),X_49) = op_e,
inference(resolve,[$cnf( $equal(op_e,mult(mult(rd(op_c,mult(X_49,B)),B),X_49)) )],[refute_1_62,refute_1_63]) ).
cnf(refute_1_65,plain,
( mult(mult(rd(op_c,mult(X_49,B)),B),X_49) != op_e
| op_e != mult(mult(rd(op_c,mult(mult(rd(op_c,mult(X_49,B)),B),X_49)),X_49),mult(rd(op_c,mult(X_49,B)),B))
| op_e = mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B)) ),
introduced(tautology,[equality,[$cnf( $equal(op_e,mult(mult(rd(op_c,mult(mult(rd(op_c,mult(X_49,B)),B),X_49)),X_49),mult(rd(op_c,mult(X_49,B)),B))) ),[1,0,0,1],$fot(op_e)]]) ).
cnf(refute_1_66,plain,
( op_e != mult(mult(rd(op_c,mult(mult(rd(op_c,mult(X_49,B)),B),X_49)),X_49),mult(rd(op_c,mult(X_49,B)),B))
| op_e = mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B)) ),
inference(resolve,[$cnf( $equal(mult(mult(rd(op_c,mult(X_49,B)),B),X_49),op_e) )],[refute_1_64,refute_1_65]) ).
cnf(refute_1_67,plain,
op_e = mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B)),
inference(resolve,[$cnf( $equal(op_e,mult(mult(rd(op_c,mult(mult(rd(op_c,mult(X_49,B)),B),X_49)),X_49),mult(rd(op_c,mult(X_49,B)),B))) )],[refute_1_61,refute_1_66]) ).
cnf(refute_1_68,plain,
mult(mult(rd(op_c,mult(unit,X_49)),X_49),unit) = mult(rd(op_c,mult(unit,X_49)),X_49),
inference(subst,[],[refute_1_27:[bind(A,$fot(mult(rd(op_c,mult(unit,X_49)),X_49)))]]) ).
cnf(refute_1_69,plain,
op_e = mult(mult(rd(op_c,mult(unit,X_49)),X_49),unit),
inference(subst,[],[refute_1_60:[bind(A,$fot(unit)),bind(B,$fot(X_49))]]) ).
cnf(refute_1_70,plain,
( op_e != mult(mult(rd(op_c,mult(unit,X_49)),X_49),unit)
| mult(mult(rd(op_c,mult(unit,X_49)),X_49),unit) = op_e ),
inference(subst,[],[refute_1_21:[bind(X,$fot(op_e)),bind(Y,$fot(mult(mult(rd(op_c,mult(unit,X_49)),X_49),unit)))]]) ).
cnf(refute_1_71,plain,
mult(mult(rd(op_c,mult(unit,X_49)),X_49),unit) = op_e,
inference(resolve,[$cnf( $equal(op_e,mult(mult(rd(op_c,mult(unit,X_49)),X_49),unit)) )],[refute_1_69,refute_1_70]) ).
cnf(refute_1_72,plain,
( mult(mult(rd(op_c,mult(unit,X_49)),X_49),unit) != mult(rd(op_c,mult(unit,X_49)),X_49)
| mult(mult(rd(op_c,mult(unit,X_49)),X_49),unit) != op_e
| op_e = mult(rd(op_c,mult(unit,X_49)),X_49) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(rd(op_c,mult(unit,X_49)),X_49),unit),mult(rd(op_c,mult(unit,X_49)),X_49)) ),[0],$fot(op_e)]]) ).
cnf(refute_1_73,plain,
( mult(mult(rd(op_c,mult(unit,X_49)),X_49),unit) != mult(rd(op_c,mult(unit,X_49)),X_49)
| op_e = mult(rd(op_c,mult(unit,X_49)),X_49) ),
inference(resolve,[$cnf( $equal(mult(mult(rd(op_c,mult(unit,X_49)),X_49),unit),op_e) )],[refute_1_71,refute_1_72]) ).
cnf(refute_1_74,plain,
op_e = mult(rd(op_c,mult(unit,X_49)),X_49),
inference(resolve,[$cnf( $equal(mult(mult(rd(op_c,mult(unit,X_49)),X_49),unit),mult(rd(op_c,mult(unit,X_49)),X_49)) )],[refute_1_68,refute_1_73]) ).
cnf(refute_1_75,plain,
mult(rd(A,B),B) = A,
inference(canonicalize,[],[normalize_1_18]) ).
cnf(refute_1_76,plain,
mult(rd(op_c,X_49),X_49) = op_c,
inference(subst,[],[refute_1_75:[bind(A,$fot(op_c)),bind(B,$fot(X_49))]]) ).
cnf(refute_1_77,plain,
mult(unit,X_49) = X_49,
inference(subst,[],[refute_1_12:[bind(A,$fot(X_49))]]) ).
cnf(refute_1_78,plain,
rd(op_c,mult(unit,X_49)) = rd(op_c,mult(unit,X_49)),
introduced(tautology,[refl,[$fot(rd(op_c,mult(unit,X_49)))]]) ).
cnf(refute_1_79,plain,
( mult(unit,X_49) != X_49
| rd(op_c,mult(unit,X_49)) != rd(op_c,mult(unit,X_49))
| rd(op_c,mult(unit,X_49)) = rd(op_c,X_49) ),
introduced(tautology,[equality,[$cnf( $equal(rd(op_c,mult(unit,X_49)),rd(op_c,mult(unit,X_49))) ),[1,1],$fot(X_49)]]) ).
cnf(refute_1_80,plain,
( mult(unit,X_49) != X_49
| rd(op_c,mult(unit,X_49)) = rd(op_c,X_49) ),
inference(resolve,[$cnf( $equal(rd(op_c,mult(unit,X_49)),rd(op_c,mult(unit,X_49))) )],[refute_1_78,refute_1_79]) ).
cnf(refute_1_81,plain,
rd(op_c,mult(unit,X_49)) = rd(op_c,X_49),
inference(resolve,[$cnf( $equal(mult(unit,X_49),X_49) )],[refute_1_77,refute_1_80]) ).
cnf(refute_1_82,plain,
mult(rd(op_c,mult(unit,X_49)),X_49) = mult(rd(op_c,mult(unit,X_49)),X_49),
introduced(tautology,[refl,[$fot(mult(rd(op_c,mult(unit,X_49)),X_49))]]) ).
cnf(refute_1_83,plain,
( mult(rd(op_c,mult(unit,X_49)),X_49) != mult(rd(op_c,mult(unit,X_49)),X_49)
| rd(op_c,mult(unit,X_49)) != rd(op_c,X_49)
| mult(rd(op_c,mult(unit,X_49)),X_49) = mult(rd(op_c,X_49),X_49) ),
introduced(tautology,[equality,[$cnf( $equal(mult(rd(op_c,mult(unit,X_49)),X_49),mult(rd(op_c,mult(unit,X_49)),X_49)) ),[1,0],$fot(rd(op_c,X_49))]]) ).
cnf(refute_1_84,plain,
( rd(op_c,mult(unit,X_49)) != rd(op_c,X_49)
| mult(rd(op_c,mult(unit,X_49)),X_49) = mult(rd(op_c,X_49),X_49) ),
inference(resolve,[$cnf( $equal(mult(rd(op_c,mult(unit,X_49)),X_49),mult(rd(op_c,mult(unit,X_49)),X_49)) )],[refute_1_82,refute_1_83]) ).
cnf(refute_1_85,plain,
mult(rd(op_c,mult(unit,X_49)),X_49) = mult(rd(op_c,X_49),X_49),
inference(resolve,[$cnf( $equal(rd(op_c,mult(unit,X_49)),rd(op_c,X_49)) )],[refute_1_81,refute_1_84]) ).
cnf(refute_1_86,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_1_87,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_1_21,refute_1_86]) ).
cnf(refute_1_88,plain,
( mult(rd(op_c,X_49),X_49) != op_c
| mult(rd(op_c,mult(unit,X_49)),X_49) != mult(rd(op_c,X_49),X_49)
| mult(rd(op_c,mult(unit,X_49)),X_49) = op_c ),
inference(subst,[],[refute_1_87:[bind(X,$fot(mult(rd(op_c,mult(unit,X_49)),X_49))),bind(Y,$fot(mult(rd(op_c,X_49),X_49))),bind(Z,$fot(op_c))]]) ).
cnf(refute_1_89,plain,
( mult(rd(op_c,X_49),X_49) != op_c
| mult(rd(op_c,mult(unit,X_49)),X_49) = op_c ),
inference(resolve,[$cnf( $equal(mult(rd(op_c,mult(unit,X_49)),X_49),mult(rd(op_c,X_49),X_49)) )],[refute_1_85,refute_1_88]) ).
cnf(refute_1_90,plain,
mult(rd(op_c,mult(unit,X_49)),X_49) = op_c,
inference(resolve,[$cnf( $equal(mult(rd(op_c,X_49),X_49),op_c) )],[refute_1_76,refute_1_89]) ).
cnf(refute_1_91,plain,
( mult(rd(op_c,mult(unit,X_49)),X_49) != op_c
| op_e != mult(rd(op_c,mult(unit,X_49)),X_49)
| op_e = op_c ),
introduced(tautology,[equality,[$cnf( $equal(op_e,mult(rd(op_c,mult(unit,X_49)),X_49)) ),[1],$fot(op_c)]]) ).
cnf(refute_1_92,plain,
( op_e != mult(rd(op_c,mult(unit,X_49)),X_49)
| op_e = op_c ),
inference(resolve,[$cnf( $equal(mult(rd(op_c,mult(unit,X_49)),X_49),op_c) )],[refute_1_90,refute_1_91]) ).
cnf(refute_1_93,plain,
op_e = op_c,
inference(resolve,[$cnf( $equal(op_e,mult(rd(op_c,mult(unit,X_49)),X_49)) )],[refute_1_74,refute_1_92]) ).
cnf(refute_1_94,plain,
( op_e != mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B))
| op_e != op_c
| op_c = mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B)) ),
introduced(tautology,[equality,[$cnf( $equal(op_e,mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B))) ),[0],$fot(op_c)]]) ).
cnf(refute_1_95,plain,
( op_e != mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B))
| op_c = mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B)) ),
inference(resolve,[$cnf( $equal(op_e,op_c) )],[refute_1_93,refute_1_94]) ).
cnf(refute_1_96,plain,
rd(mult(A,B),B) = A,
inference(canonicalize,[],[normalize_1_20]) ).
cnf(refute_1_97,plain,
rd(mult(mult(rd(op_c,mult(B,X_49)),X_49),B),B) = mult(rd(op_c,mult(B,X_49)),X_49),
inference(subst,[],[refute_1_96:[bind(A,$fot(mult(rd(op_c,mult(B,X_49)),X_49)))]]) ).
cnf(refute_1_98,plain,
op_e = mult(mult(rd(op_c,mult(B,X_49)),X_49),B),
inference(subst,[],[refute_1_60:[bind(A,$fot(B)),bind(B,$fot(X_49))]]) ).
cnf(refute_1_99,plain,
( op_e != mult(mult(rd(op_c,mult(B,X_49)),X_49),B)
| mult(mult(rd(op_c,mult(B,X_49)),X_49),B) = op_e ),
inference(subst,[],[refute_1_21:[bind(X,$fot(op_e)),bind(Y,$fot(mult(mult(rd(op_c,mult(B,X_49)),X_49),B)))]]) ).
cnf(refute_1_100,plain,
mult(mult(rd(op_c,mult(B,X_49)),X_49),B) = op_e,
inference(resolve,[$cnf( $equal(op_e,mult(mult(rd(op_c,mult(B,X_49)),X_49),B)) )],[refute_1_98,refute_1_99]) ).
cnf(refute_1_101,plain,
( mult(mult(rd(op_c,mult(B,X_49)),X_49),B) != op_e
| rd(mult(mult(rd(op_c,mult(B,X_49)),X_49),B),B) != mult(rd(op_c,mult(B,X_49)),X_49)
| rd(op_e,B) = mult(rd(op_c,mult(B,X_49)),X_49) ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(mult(rd(op_c,mult(B,X_49)),X_49),B),B),mult(rd(op_c,mult(B,X_49)),X_49)) ),[0,0],$fot(op_e)]]) ).
cnf(refute_1_102,plain,
( rd(mult(mult(rd(op_c,mult(B,X_49)),X_49),B),B) != mult(rd(op_c,mult(B,X_49)),X_49)
| rd(op_e,B) = mult(rd(op_c,mult(B,X_49)),X_49) ),
inference(resolve,[$cnf( $equal(mult(mult(rd(op_c,mult(B,X_49)),X_49),B),op_e) )],[refute_1_100,refute_1_101]) ).
cnf(refute_1_103,plain,
rd(op_e,B) = mult(rd(op_c,mult(B,X_49)),X_49),
inference(resolve,[$cnf( $equal(rd(mult(mult(rd(op_c,mult(B,X_49)),X_49),B),B),mult(rd(op_c,mult(B,X_49)),X_49)) )],[refute_1_97,refute_1_102]) ).
cnf(refute_1_104,plain,
rd(op_e,B) = rd(op_e,B),
introduced(tautology,[refl,[$fot(rd(op_e,B))]]) ).
cnf(refute_1_105,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_1_106,plain,
( op_e != op_c
| rd(op_e,B) = rd(op_c,B) ),
inference(resolve,[$cnf( $equal(rd(op_e,B),rd(op_e,B)) )],[refute_1_104,refute_1_105]) ).
cnf(refute_1_107,plain,
rd(op_e,B) = rd(op_c,B),
inference(resolve,[$cnf( $equal(op_e,op_c) )],[refute_1_93,refute_1_106]) ).
cnf(refute_1_108,plain,
( rd(op_e,B) != mult(rd(op_c,mult(B,X_49)),X_49)
| rd(op_e,B) != rd(op_c,B)
| rd(op_c,B) = mult(rd(op_c,mult(B,X_49)),X_49) ),
introduced(tautology,[equality,[$cnf( $equal(rd(op_e,B),mult(rd(op_c,mult(B,X_49)),X_49)) ),[0],$fot(rd(op_c,B))]]) ).
cnf(refute_1_109,plain,
( rd(op_e,B) != mult(rd(op_c,mult(B,X_49)),X_49)
| rd(op_c,B) = mult(rd(op_c,mult(B,X_49)),X_49) ),
inference(resolve,[$cnf( $equal(rd(op_e,B),rd(op_c,B)) )],[refute_1_107,refute_1_108]) ).
cnf(refute_1_110,plain,
rd(op_c,B) = mult(rd(op_c,mult(B,X_49)),X_49),
inference(resolve,[$cnf( $equal(rd(op_e,B),mult(rd(op_c,mult(B,X_49)),X_49)) )],[refute_1_103,refute_1_109]) ).
cnf(refute_1_111,plain,
( rd(op_c,B) != mult(rd(op_c,mult(B,X_49)),X_49)
| mult(rd(op_c,mult(B,X_49)),X_49) = rd(op_c,B) ),
inference(subst,[],[refute_1_21:[bind(X,$fot(rd(op_c,B))),bind(Y,$fot(mult(rd(op_c,mult(B,X_49)),X_49)))]]) ).
cnf(refute_1_112,plain,
mult(rd(op_c,mult(B,X_49)),X_49) = rd(op_c,B),
inference(resolve,[$cnf( $equal(rd(op_c,B),mult(rd(op_c,mult(B,X_49)),X_49)) )],[refute_1_110,refute_1_111]) ).
cnf(refute_1_113,plain,
mult(rd(op_c,mult(X_49,B)),B) = rd(op_c,X_49),
inference(subst,[],[refute_1_112:[bind(B,$fot(X_49)),bind(X_49,$fot(B))]]) ).
cnf(refute_1_114,plain,
mult(X_49,mult(rd(op_c,mult(X_49,B)),B)) = mult(X_49,mult(rd(op_c,mult(X_49,B)),B)),
introduced(tautology,[refl,[$fot(mult(X_49,mult(rd(op_c,mult(X_49,B)),B)))]]) ).
cnf(refute_1_115,plain,
( mult(X_49,mult(rd(op_c,mult(X_49,B)),B)) != mult(X_49,mult(rd(op_c,mult(X_49,B)),B))
| mult(rd(op_c,mult(X_49,B)),B) != rd(op_c,X_49)
| mult(X_49,mult(rd(op_c,mult(X_49,B)),B)) = mult(X_49,rd(op_c,X_49)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_49,mult(rd(op_c,mult(X_49,B)),B)),mult(X_49,mult(rd(op_c,mult(X_49,B)),B))) ),[1,1],$fot(rd(op_c,X_49))]]) ).
cnf(refute_1_116,plain,
( mult(rd(op_c,mult(X_49,B)),B) != rd(op_c,X_49)
| mult(X_49,mult(rd(op_c,mult(X_49,B)),B)) = mult(X_49,rd(op_c,X_49)) ),
inference(resolve,[$cnf( $equal(mult(X_49,mult(rd(op_c,mult(X_49,B)),B)),mult(X_49,mult(rd(op_c,mult(X_49,B)),B))) )],[refute_1_114,refute_1_115]) ).
cnf(refute_1_117,plain,
mult(X_49,mult(rd(op_c,mult(X_49,B)),B)) = mult(X_49,rd(op_c,X_49)),
inference(resolve,[$cnf( $equal(mult(rd(op_c,mult(X_49,B)),B),rd(op_c,X_49)) )],[refute_1_113,refute_1_116]) ).
cnf(refute_1_118,plain,
rd(mult(unit,X_40),X_40) = unit,
inference(subst,[],[refute_1_96:[bind(A,$fot(unit)),bind(B,$fot(X_40))]]) ).
cnf(refute_1_119,plain,
mult(unit,X_40) = X_40,
inference(subst,[],[refute_1_12:[bind(A,$fot(X_40))]]) ).
cnf(refute_1_120,plain,
( mult(unit,X_40) != X_40
| rd(mult(unit,X_40),X_40) != unit
| rd(X_40,X_40) = unit ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(unit,X_40),X_40),unit) ),[0,0],$fot(X_40)]]) ).
cnf(refute_1_121,plain,
( rd(mult(unit,X_40),X_40) != unit
| rd(X_40,X_40) = unit ),
inference(resolve,[$cnf( $equal(mult(unit,X_40),X_40) )],[refute_1_119,refute_1_120]) ).
cnf(refute_1_122,plain,
rd(X_40,X_40) = unit,
inference(resolve,[$cnf( $equal(rd(mult(unit,X_40),X_40),unit) )],[refute_1_118,refute_1_121]) ).
cnf(refute_1_123,plain,
rd(op_c,op_c) = unit,
inference(subst,[],[refute_1_122:[bind(X_40,$fot(op_c))]]) ).
cnf(refute_1_124,plain,
rd(op_c,op_e) = rd(op_c,op_e),
introduced(tautology,[refl,[$fot(rd(op_c,op_e))]]) ).
cnf(refute_1_125,plain,
( op_e != op_c
| rd(op_c,op_e) != rd(op_c,op_e)
| rd(op_c,op_e) = rd(op_c,op_c) ),
introduced(tautology,[equality,[$cnf( $equal(rd(op_c,op_e),rd(op_c,op_e)) ),[1,1],$fot(op_c)]]) ).
cnf(refute_1_126,plain,
( op_e != op_c
| rd(op_c,op_e) = rd(op_c,op_c) ),
inference(resolve,[$cnf( $equal(rd(op_c,op_e),rd(op_c,op_e)) )],[refute_1_124,refute_1_125]) ).
cnf(refute_1_127,plain,
rd(op_c,op_e) = rd(op_c,op_c),
inference(resolve,[$cnf( $equal(op_e,op_c) )],[refute_1_93,refute_1_126]) ).
cnf(refute_1_128,plain,
( rd(op_c,op_c) != unit
| rd(op_c,op_e) != rd(op_c,op_c)
| rd(op_c,op_e) = unit ),
inference(subst,[],[refute_1_87:[bind(X,$fot(rd(op_c,op_e))),bind(Y,$fot(rd(op_c,op_c))),bind(Z,$fot(unit))]]) ).
cnf(refute_1_129,plain,
( rd(op_c,op_c) != unit
| rd(op_c,op_e) = unit ),
inference(resolve,[$cnf( $equal(rd(op_c,op_e),rd(op_c,op_c)) )],[refute_1_127,refute_1_128]) ).
cnf(refute_1_130,plain,
rd(op_c,op_e) = unit,
inference(resolve,[$cnf( $equal(rd(op_c,op_c),unit) )],[refute_1_123,refute_1_129]) ).
cnf(refute_1_131,plain,
mult(rd(op_c,op_e),X_49) = mult(rd(op_c,op_e),X_49),
introduced(tautology,[refl,[$fot(mult(rd(op_c,op_e),X_49))]]) ).
cnf(refute_1_132,plain,
( mult(rd(op_c,op_e),X_49) != mult(rd(op_c,op_e),X_49)
| rd(op_c,op_e) != unit
| mult(rd(op_c,op_e),X_49) = mult(unit,X_49) ),
introduced(tautology,[equality,[$cnf( $equal(mult(rd(op_c,op_e),X_49),mult(rd(op_c,op_e),X_49)) ),[1,0],$fot(unit)]]) ).
cnf(refute_1_133,plain,
( rd(op_c,op_e) != unit
| mult(rd(op_c,op_e),X_49) = mult(unit,X_49) ),
inference(resolve,[$cnf( $equal(mult(rd(op_c,op_e),X_49),mult(rd(op_c,op_e),X_49)) )],[refute_1_131,refute_1_132]) ).
cnf(refute_1_134,plain,
mult(rd(op_c,op_e),X_49) = mult(unit,X_49),
inference(resolve,[$cnf( $equal(rd(op_c,op_e),unit) )],[refute_1_130,refute_1_133]) ).
cnf(refute_1_135,plain,
( mult(rd(op_c,op_e),X_49) != mult(unit,X_49)
| mult(unit,X_49) != X_49
| mult(rd(op_c,op_e),X_49) = X_49 ),
inference(subst,[],[refute_1_87:[bind(X,$fot(mult(rd(op_c,op_e),X_49))),bind(Y,$fot(mult(unit,X_49))),bind(Z,$fot(X_49))]]) ).
cnf(refute_1_136,plain,
( mult(unit,X_49) != X_49
| mult(rd(op_c,op_e),X_49) = X_49 ),
inference(resolve,[$cnf( $equal(mult(rd(op_c,op_e),X_49),mult(unit,X_49)) )],[refute_1_134,refute_1_135]) ).
cnf(refute_1_137,plain,
mult(rd(op_c,op_e),X_49) = X_49,
inference(resolve,[$cnf( $equal(mult(unit,X_49),X_49) )],[refute_1_77,refute_1_136]) ).
cnf(refute_1_138,plain,
mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B)) = mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B)),
introduced(tautology,[refl,[$fot(mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B)))]]) ).
cnf(refute_1_139,plain,
( mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B)) != mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B))
| mult(rd(op_c,op_e),X_49) != X_49
| mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B)) = mult(X_49,mult(rd(op_c,mult(X_49,B)),B)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B)),mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B))) ),[1,0],$fot(X_49)]]) ).
cnf(refute_1_140,plain,
( mult(rd(op_c,op_e),X_49) != X_49
| mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B)) = mult(X_49,mult(rd(op_c,mult(X_49,B)),B)) ),
inference(resolve,[$cnf( $equal(mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B)),mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B))) )],[refute_1_138,refute_1_139]) ).
cnf(refute_1_141,plain,
mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B)) = mult(X_49,mult(rd(op_c,mult(X_49,B)),B)),
inference(resolve,[$cnf( $equal(mult(rd(op_c,op_e),X_49),X_49) )],[refute_1_137,refute_1_140]) ).
cnf(refute_1_142,plain,
( mult(X_49,mult(rd(op_c,mult(X_49,B)),B)) != mult(X_49,rd(op_c,X_49))
| mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B)) != mult(X_49,mult(rd(op_c,mult(X_49,B)),B))
| mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B)) = mult(X_49,rd(op_c,X_49)) ),
inference(subst,[],[refute_1_87:[bind(X,$fot(mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B)))),bind(Y,$fot(mult(X_49,mult(rd(op_c,mult(X_49,B)),B)))),bind(Z,$fot(mult(X_49,rd(op_c,X_49))))]]) ).
cnf(refute_1_143,plain,
( mult(X_49,mult(rd(op_c,mult(X_49,B)),B)) != mult(X_49,rd(op_c,X_49))
| mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B)) = mult(X_49,rd(op_c,X_49)) ),
inference(resolve,[$cnf( $equal(mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B)),mult(X_49,mult(rd(op_c,mult(X_49,B)),B))) )],[refute_1_141,refute_1_142]) ).
cnf(refute_1_144,plain,
mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B)) = mult(X_49,rd(op_c,X_49)),
inference(resolve,[$cnf( $equal(mult(X_49,mult(rd(op_c,mult(X_49,B)),B)),mult(X_49,rd(op_c,X_49))) )],[refute_1_117,refute_1_143]) ).
cnf(refute_1_145,plain,
( mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B)) != mult(X_49,rd(op_c,X_49))
| op_c != mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B))
| op_c = mult(X_49,rd(op_c,X_49)) ),
introduced(tautology,[equality,[$cnf( $equal(op_c,mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B))) ),[1],$fot(mult(X_49,rd(op_c,X_49)))]]) ).
cnf(refute_1_146,plain,
( op_c != mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B))
| op_c = mult(X_49,rd(op_c,X_49)) ),
inference(resolve,[$cnf( $equal(mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B)),mult(X_49,rd(op_c,X_49))) )],[refute_1_144,refute_1_145]) ).
cnf(refute_1_147,plain,
( op_e != mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B))
| op_c = mult(X_49,rd(op_c,X_49)) ),
inference(resolve,[$cnf( $equal(op_c,mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B))) )],[refute_1_95,refute_1_146]) ).
cnf(refute_1_148,plain,
op_c = mult(X_49,rd(op_c,X_49)),
inference(resolve,[$cnf( $equal(op_e,mult(mult(rd(op_c,op_e),X_49),mult(rd(op_c,mult(X_49,B)),B))) )],[refute_1_67,refute_1_147]) ).
cnf(refute_1_149,plain,
op_c = mult(ld(X_39,op_c),rd(op_c,ld(X_39,op_c))),
inference(subst,[],[refute_1_148:[bind(X_49,$fot(ld(X_39,op_c)))]]) ).
cnf(refute_1_150,plain,
rd(mult(X_39,ld(X_39,B)),ld(X_39,B)) = X_39,
inference(subst,[],[refute_1_96:[bind(A,$fot(X_39)),bind(B,$fot(ld(X_39,B)))]]) ).
cnf(refute_1_151,plain,
mult(X_39,ld(X_39,B)) = B,
inference(subst,[],[refute_1_3:[bind(A,$fot(X_39))]]) ).
cnf(refute_1_152,plain,
( mult(X_39,ld(X_39,B)) != B
| rd(mult(X_39,ld(X_39,B)),ld(X_39,B)) != X_39
| rd(B,ld(X_39,B)) = X_39 ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(X_39,ld(X_39,B)),ld(X_39,B)),X_39) ),[0,0],$fot(B)]]) ).
cnf(refute_1_153,plain,
( rd(mult(X_39,ld(X_39,B)),ld(X_39,B)) != X_39
| rd(B,ld(X_39,B)) = X_39 ),
inference(resolve,[$cnf( $equal(mult(X_39,ld(X_39,B)),B) )],[refute_1_151,refute_1_152]) ).
cnf(refute_1_154,plain,
rd(B,ld(X_39,B)) = X_39,
inference(resolve,[$cnf( $equal(rd(mult(X_39,ld(X_39,B)),ld(X_39,B)),X_39) )],[refute_1_150,refute_1_153]) ).
cnf(refute_1_155,plain,
rd(op_c,ld(X_39,op_c)) = X_39,
inference(subst,[],[refute_1_154:[bind(B,$fot(op_c))]]) ).
cnf(refute_1_156,plain,
( op_c != mult(ld(X_39,op_c),rd(op_c,ld(X_39,op_c)))
| rd(op_c,ld(X_39,op_c)) != X_39
| op_c = mult(ld(X_39,op_c),X_39) ),
introduced(tautology,[equality,[$cnf( $equal(op_c,mult(ld(X_39,op_c),rd(op_c,ld(X_39,op_c)))) ),[1,1],$fot(X_39)]]) ).
cnf(refute_1_157,plain,
( op_c != mult(ld(X_39,op_c),rd(op_c,ld(X_39,op_c)))
| op_c = mult(ld(X_39,op_c),X_39) ),
inference(resolve,[$cnf( $equal(rd(op_c,ld(X_39,op_c)),X_39) )],[refute_1_155,refute_1_156]) ).
cnf(refute_1_158,plain,
op_c = mult(ld(X_39,op_c),X_39),
inference(resolve,[$cnf( $equal(op_c,mult(ld(X_39,op_c),rd(op_c,ld(X_39,op_c)))) )],[refute_1_149,refute_1_157]) ).
cnf(refute_1_159,plain,
op_c = mult(ld(mult(op_c,op_c),op_c),mult(op_c,op_c)),
inference(subst,[],[refute_1_158:[bind(X_39,$fot(mult(op_c,op_c)))]]) ).
cnf(refute_1_160,plain,
mult(mult(X_45,op_c),op_c) = mult(op_c,mult(X_45,op_c)),
inference(subst,[],[refute_1_40:[bind(X_28,$fot(mult(X_45,op_c)))]]) ).
cnf(refute_1_161,plain,
mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
inference(canonicalize,[],[normalize_1_22]) ).
cnf(refute_1_162,plain,
mult(X_45,mult(op_c,op_c)) = mult(mult(X_45,op_c),op_c),
inference(subst,[],[refute_1_161:[bind(A,$fot(X_45)),bind(B,$fot(op_c))]]) ).
cnf(refute_1_163,plain,
( mult(X_45,mult(op_c,op_c)) != mult(mult(X_45,op_c),op_c)
| mult(mult(X_45,op_c),op_c) = mult(X_45,mult(op_c,op_c)) ),
inference(subst,[],[refute_1_21:[bind(X,$fot(mult(X_45,mult(op_c,op_c)))),bind(Y,$fot(mult(mult(X_45,op_c),op_c)))]]) ).
cnf(refute_1_164,plain,
mult(mult(X_45,op_c),op_c) = mult(X_45,mult(op_c,op_c)),
inference(resolve,[$cnf( $equal(mult(X_45,mult(op_c,op_c)),mult(mult(X_45,op_c),op_c)) )],[refute_1_162,refute_1_163]) ).
cnf(refute_1_165,plain,
( mult(mult(X_45,op_c),op_c) != mult(X_45,mult(op_c,op_c))
| mult(mult(X_45,op_c),op_c) != mult(op_c,mult(X_45,op_c))
| mult(X_45,mult(op_c,op_c)) = mult(op_c,mult(X_45,op_c)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(X_45,op_c),op_c),mult(op_c,mult(X_45,op_c))) ),[0],$fot(mult(X_45,mult(op_c,op_c)))]]) ).
cnf(refute_1_166,plain,
( mult(mult(X_45,op_c),op_c) != mult(op_c,mult(X_45,op_c))
| mult(X_45,mult(op_c,op_c)) = mult(op_c,mult(X_45,op_c)) ),
inference(resolve,[$cnf( $equal(mult(mult(X_45,op_c),op_c),mult(X_45,mult(op_c,op_c))) )],[refute_1_164,refute_1_165]) ).
cnf(refute_1_167,plain,
mult(X_45,mult(op_c,op_c)) = mult(op_c,mult(X_45,op_c)),
inference(resolve,[$cnf( $equal(mult(mult(X_45,op_c),op_c),mult(op_c,mult(X_45,op_c))) )],[refute_1_160,refute_1_166]) ).
cnf(refute_1_168,plain,
mult(ld(mult(op_c,op_c),op_c),mult(op_c,op_c)) = mult(op_c,mult(ld(mult(op_c,op_c),op_c),op_c)),
inference(subst,[],[refute_1_167:[bind(X_45,$fot(ld(mult(op_c,op_c),op_c)))]]) ).
cnf(refute_1_169,plain,
( mult(ld(mult(op_c,op_c),op_c),mult(op_c,op_c)) != mult(op_c,mult(ld(mult(op_c,op_c),op_c),op_c))
| op_c != mult(ld(mult(op_c,op_c),op_c),mult(op_c,op_c))
| op_c = mult(op_c,mult(ld(mult(op_c,op_c),op_c),op_c)) ),
introduced(tautology,[equality,[$cnf( $equal(op_c,mult(ld(mult(op_c,op_c),op_c),mult(op_c,op_c))) ),[1],$fot(mult(op_c,mult(ld(mult(op_c,op_c),op_c),op_c)))]]) ).
cnf(refute_1_170,plain,
( op_c != mult(ld(mult(op_c,op_c),op_c),mult(op_c,op_c))
| op_c = mult(op_c,mult(ld(mult(op_c,op_c),op_c),op_c)) ),
inference(resolve,[$cnf( $equal(mult(ld(mult(op_c,op_c),op_c),mult(op_c,op_c)),mult(op_c,mult(ld(mult(op_c,op_c),op_c),op_c))) )],[refute_1_168,refute_1_169]) ).
cnf(refute_1_171,plain,
op_c = mult(op_c,mult(ld(mult(op_c,op_c),op_c),op_c)),
inference(resolve,[$cnf( $equal(op_c,mult(ld(mult(op_c,op_c),op_c),mult(op_c,op_c))) )],[refute_1_159,refute_1_170]) ).
cnf(refute_1_172,plain,
op_f = mult(A,mult(B,ld(mult(A,B),op_c))),
inference(canonicalize,[],[normalize_1_24]) ).
cnf(refute_1_173,plain,
( op_f != mult(A,mult(B,ld(mult(A,B),op_c)))
| mult(A,mult(B,ld(mult(A,B),op_c))) = op_f ),
inference(subst,[],[refute_1_21:[bind(X,$fot(op_f)),bind(Y,$fot(mult(A,mult(B,ld(mult(A,B),op_c)))))]]) ).
cnf(refute_1_174,plain,
mult(A,mult(B,ld(mult(A,B),op_c))) = op_f,
inference(resolve,[$cnf( $equal(op_f,mult(A,mult(B,ld(mult(A,B),op_c)))) )],[refute_1_172,refute_1_173]) ).
cnf(refute_1_175,plain,
mult(op_c,mult(op_c,ld(mult(op_c,op_c),op_c))) = op_f,
inference(subst,[],[refute_1_174:[bind(A,$fot(op_c)),bind(B,$fot(op_c))]]) ).
cnf(refute_1_176,plain,
mult(A,mult(op_c,mult(op_c,ld(op_c,X_56)))) = mult(mult(A,op_c),mult(op_c,ld(op_c,X_56))),
inference(subst,[],[refute_1_161:[bind(B,$fot(mult(op_c,ld(op_c,X_56))))]]) ).
cnf(refute_1_177,plain,
mult(op_c,mult(op_c,ld(op_c,X_56))) = mult(X_56,op_c),
inference(subst,[],[refute_1_48:[bind(A,$fot(op_c)),bind(X_29,$fot(X_56))]]) ).
cnf(refute_1_178,plain,
( mult(A,mult(op_c,mult(op_c,ld(op_c,X_56)))) != mult(mult(A,op_c),mult(op_c,ld(op_c,X_56)))
| mult(op_c,mult(op_c,ld(op_c,X_56))) != mult(X_56,op_c)
| mult(A,mult(X_56,op_c)) = mult(mult(A,op_c),mult(op_c,ld(op_c,X_56))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(A,mult(op_c,mult(op_c,ld(op_c,X_56)))),mult(mult(A,op_c),mult(op_c,ld(op_c,X_56)))) ),[0,1],$fot(mult(X_56,op_c))]]) ).
cnf(refute_1_179,plain,
( mult(A,mult(op_c,mult(op_c,ld(op_c,X_56)))) != mult(mult(A,op_c),mult(op_c,ld(op_c,X_56)))
| mult(A,mult(X_56,op_c)) = mult(mult(A,op_c),mult(op_c,ld(op_c,X_56))) ),
inference(resolve,[$cnf( $equal(mult(op_c,mult(op_c,ld(op_c,X_56))),mult(X_56,op_c)) )],[refute_1_177,refute_1_178]) ).
cnf(refute_1_180,plain,
mult(A,mult(X_56,op_c)) = mult(mult(A,op_c),mult(op_c,ld(op_c,X_56))),
inference(resolve,[$cnf( $equal(mult(A,mult(op_c,mult(op_c,ld(op_c,X_56)))),mult(mult(A,op_c),mult(op_c,ld(op_c,X_56)))) )],[refute_1_176,refute_1_179]) ).
cnf(refute_1_181,plain,
mult(op_c,ld(op_c,X_56)) = X_56,
inference(subst,[],[refute_1_3:[bind(A,$fot(op_c)),bind(B,$fot(X_56))]]) ).
cnf(refute_1_182,plain,
mult(A,mult(op_c,ld(op_c,X_56))) = mult(A,mult(op_c,ld(op_c,X_56))),
introduced(tautology,[refl,[$fot(mult(A,mult(op_c,ld(op_c,X_56))))]]) ).
cnf(refute_1_183,plain,
( mult(A,mult(op_c,ld(op_c,X_56))) != mult(A,mult(op_c,ld(op_c,X_56)))
| mult(op_c,ld(op_c,X_56)) != X_56
| mult(A,mult(op_c,ld(op_c,X_56))) = mult(A,X_56) ),
introduced(tautology,[equality,[$cnf( $equal(mult(A,mult(op_c,ld(op_c,X_56))),mult(A,mult(op_c,ld(op_c,X_56)))) ),[1,1],$fot(X_56)]]) ).
cnf(refute_1_184,plain,
( mult(op_c,ld(op_c,X_56)) != X_56
| mult(A,mult(op_c,ld(op_c,X_56))) = mult(A,X_56) ),
inference(resolve,[$cnf( $equal(mult(A,mult(op_c,ld(op_c,X_56))),mult(A,mult(op_c,ld(op_c,X_56)))) )],[refute_1_182,refute_1_183]) ).
cnf(refute_1_185,plain,
mult(A,mult(op_c,ld(op_c,X_56))) = mult(A,X_56),
inference(resolve,[$cnf( $equal(mult(op_c,ld(op_c,X_56)),X_56) )],[refute_1_181,refute_1_184]) ).
cnf(refute_1_186,plain,
( mult(A,mult(op_c,B)) != mult(mult(A,op_c),B)
| mult(mult(A,op_c),B) = mult(A,mult(op_c,B)) ),
inference(subst,[],[refute_1_21:[bind(X,$fot(mult(A,mult(op_c,B)))),bind(Y,$fot(mult(mult(A,op_c),B)))]]) ).
cnf(refute_1_187,plain,
mult(mult(A,op_c),B) = mult(A,mult(op_c,B)),
inference(resolve,[$cnf( $equal(mult(A,mult(op_c,B)),mult(mult(A,op_c),B)) )],[refute_1_161,refute_1_186]) ).
cnf(refute_1_188,plain,
mult(mult(A,op_c),ld(op_c,X_56)) = mult(A,mult(op_c,ld(op_c,X_56))),
inference(subst,[],[refute_1_187:[bind(B,$fot(ld(op_c,X_56)))]]) ).
cnf(refute_1_189,plain,
( mult(A,mult(op_c,ld(op_c,X_56))) != mult(A,X_56)
| mult(mult(A,op_c),ld(op_c,X_56)) != mult(A,mult(op_c,ld(op_c,X_56)))
| mult(mult(A,op_c),ld(op_c,X_56)) = mult(A,X_56) ),
inference(subst,[],[refute_1_87:[bind(X,$fot(mult(mult(A,op_c),ld(op_c,X_56)))),bind(Y,$fot(mult(A,mult(op_c,ld(op_c,X_56))))),bind(Z,$fot(mult(A,X_56)))]]) ).
cnf(refute_1_190,plain,
( mult(A,mult(op_c,ld(op_c,X_56))) != mult(A,X_56)
| mult(mult(A,op_c),ld(op_c,X_56)) = mult(A,X_56) ),
inference(resolve,[$cnf( $equal(mult(mult(A,op_c),ld(op_c,X_56)),mult(A,mult(op_c,ld(op_c,X_56)))) )],[refute_1_188,refute_1_189]) ).
cnf(refute_1_191,plain,
mult(mult(A,op_c),ld(op_c,X_56)) = mult(A,X_56),
inference(resolve,[$cnf( $equal(mult(A,mult(op_c,ld(op_c,X_56))),mult(A,X_56)) )],[refute_1_185,refute_1_190]) ).
cnf(refute_1_192,plain,
mult(op_c,mult(mult(A,op_c),ld(op_c,X_56))) = mult(op_c,mult(mult(A,op_c),ld(op_c,X_56))),
introduced(tautology,[refl,[$fot(mult(op_c,mult(mult(A,op_c),ld(op_c,X_56))))]]) ).
cnf(refute_1_193,plain,
( mult(mult(A,op_c),ld(op_c,X_56)) != mult(A,X_56)
| mult(op_c,mult(mult(A,op_c),ld(op_c,X_56))) != mult(op_c,mult(mult(A,op_c),ld(op_c,X_56)))
| mult(op_c,mult(mult(A,op_c),ld(op_c,X_56))) = mult(op_c,mult(A,X_56)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_c,mult(mult(A,op_c),ld(op_c,X_56))),mult(op_c,mult(mult(A,op_c),ld(op_c,X_56)))) ),[1,1],$fot(mult(A,X_56))]]) ).
cnf(refute_1_194,plain,
( mult(mult(A,op_c),ld(op_c,X_56)) != mult(A,X_56)
| mult(op_c,mult(mult(A,op_c),ld(op_c,X_56))) = mult(op_c,mult(A,X_56)) ),
inference(resolve,[$cnf( $equal(mult(op_c,mult(mult(A,op_c),ld(op_c,X_56))),mult(op_c,mult(mult(A,op_c),ld(op_c,X_56)))) )],[refute_1_192,refute_1_193]) ).
cnf(refute_1_195,plain,
mult(op_c,mult(mult(A,op_c),ld(op_c,X_56))) = mult(op_c,mult(A,X_56)),
inference(resolve,[$cnf( $equal(mult(mult(A,op_c),ld(op_c,X_56)),mult(A,X_56)) )],[refute_1_191,refute_1_194]) ).
cnf(refute_1_196,plain,
mult(X_45,mult(op_c,X_46)) = mult(mult(X_45,op_c),X_46),
inference(subst,[],[refute_1_161:[bind(A,$fot(X_45)),bind(B,$fot(X_46))]]) ).
cnf(refute_1_197,plain,
mult(X_45,op_c) = mult(op_c,X_45),
inference(subst,[],[refute_1_40:[bind(X_28,$fot(X_45))]]) ).
cnf(refute_1_198,plain,
( mult(X_45,mult(op_c,X_46)) != mult(mult(X_45,op_c),X_46)
| mult(X_45,op_c) != mult(op_c,X_45)
| mult(X_45,mult(op_c,X_46)) = mult(mult(op_c,X_45),X_46) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_45,mult(op_c,X_46)),mult(mult(X_45,op_c),X_46)) ),[1,0],$fot(mult(op_c,X_45))]]) ).
cnf(refute_1_199,plain,
( mult(X_45,mult(op_c,X_46)) != mult(mult(X_45,op_c),X_46)
| mult(X_45,mult(op_c,X_46)) = mult(mult(op_c,X_45),X_46) ),
inference(resolve,[$cnf( $equal(mult(X_45,op_c),mult(op_c,X_45)) )],[refute_1_197,refute_1_198]) ).
cnf(refute_1_200,plain,
mult(X_45,mult(op_c,X_46)) = mult(mult(op_c,X_45),X_46),
inference(resolve,[$cnf( $equal(mult(X_45,mult(op_c,X_46)),mult(mult(X_45,op_c),X_46)) )],[refute_1_196,refute_1_199]) ).
cnf(refute_1_201,plain,
mult(op_c,mult(A,B)) = mult(mult(op_c,A),B),
inference(canonicalize,[],[normalize_1_26]) ).
cnf(refute_1_202,plain,
( mult(op_c,mult(A,B)) != mult(mult(op_c,A),B)
| mult(mult(op_c,A),B) = mult(op_c,mult(A,B)) ),
inference(subst,[],[refute_1_21:[bind(X,$fot(mult(op_c,mult(A,B)))),bind(Y,$fot(mult(mult(op_c,A),B)))]]) ).
cnf(refute_1_203,plain,
mult(mult(op_c,A),B) = mult(op_c,mult(A,B)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(A,B)),mult(mult(op_c,A),B)) )],[refute_1_201,refute_1_202]) ).
cnf(refute_1_204,plain,
mult(mult(op_c,X_45),X_46) = mult(op_c,mult(X_45,X_46)),
inference(subst,[],[refute_1_203:[bind(A,$fot(X_45)),bind(B,$fot(X_46))]]) ).
cnf(refute_1_205,plain,
( mult(X_45,mult(op_c,X_46)) != mult(mult(op_c,X_45),X_46)
| mult(mult(op_c,X_45),X_46) != mult(op_c,mult(X_45,X_46))
| mult(X_45,mult(op_c,X_46)) = mult(op_c,mult(X_45,X_46)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(X_45,mult(op_c,X_46)),mult(op_c,mult(X_45,X_46))) ),[0],$fot(mult(mult(op_c,X_45),X_46))]]) ).
cnf(refute_1_206,plain,
( mult(X_45,mult(op_c,X_46)) != mult(mult(op_c,X_45),X_46)
| mult(X_45,mult(op_c,X_46)) = mult(op_c,mult(X_45,X_46)) ),
inference(resolve,[$cnf( $equal(mult(mult(op_c,X_45),X_46),mult(op_c,mult(X_45,X_46))) )],[refute_1_204,refute_1_205]) ).
cnf(refute_1_207,plain,
mult(X_45,mult(op_c,X_46)) = mult(op_c,mult(X_45,X_46)),
inference(resolve,[$cnf( $equal(mult(X_45,mult(op_c,X_46)),mult(mult(op_c,X_45),X_46)) )],[refute_1_200,refute_1_206]) ).
cnf(refute_1_208,plain,
mult(mult(A,op_c),mult(op_c,ld(op_c,X_56))) = mult(op_c,mult(mult(A,op_c),ld(op_c,X_56))),
inference(subst,[],[refute_1_207:[bind(X_45,$fot(mult(A,op_c))),bind(X_46,$fot(ld(op_c,X_56)))]]) ).
cnf(refute_1_209,plain,
( mult(mult(A,op_c),mult(op_c,ld(op_c,X_56))) != mult(op_c,mult(mult(A,op_c),ld(op_c,X_56)))
| mult(op_c,mult(mult(A,op_c),ld(op_c,X_56))) != mult(op_c,mult(A,X_56))
| mult(mult(A,op_c),mult(op_c,ld(op_c,X_56))) = mult(op_c,mult(A,X_56)) ),
inference(subst,[],[refute_1_87:[bind(X,$fot(mult(mult(A,op_c),mult(op_c,ld(op_c,X_56))))),bind(Y,$fot(mult(op_c,mult(mult(A,op_c),ld(op_c,X_56))))),bind(Z,$fot(mult(op_c,mult(A,X_56))))]]) ).
cnf(refute_1_210,plain,
( mult(op_c,mult(mult(A,op_c),ld(op_c,X_56))) != mult(op_c,mult(A,X_56))
| mult(mult(A,op_c),mult(op_c,ld(op_c,X_56))) = mult(op_c,mult(A,X_56)) ),
inference(resolve,[$cnf( $equal(mult(mult(A,op_c),mult(op_c,ld(op_c,X_56))),mult(op_c,mult(mult(A,op_c),ld(op_c,X_56)))) )],[refute_1_208,refute_1_209]) ).
cnf(refute_1_211,plain,
mult(mult(A,op_c),mult(op_c,ld(op_c,X_56))) = mult(op_c,mult(A,X_56)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(mult(A,op_c),ld(op_c,X_56))),mult(op_c,mult(A,X_56))) )],[refute_1_195,refute_1_210]) ).
cnf(refute_1_212,plain,
( mult(A,mult(X_56,op_c)) != mult(mult(A,op_c),mult(op_c,ld(op_c,X_56)))
| mult(mult(A,op_c),mult(op_c,ld(op_c,X_56))) != mult(op_c,mult(A,X_56))
| mult(A,mult(X_56,op_c)) = mult(op_c,mult(A,X_56)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(A,mult(X_56,op_c)),mult(op_c,mult(A,X_56))) ),[0],$fot(mult(mult(A,op_c),mult(op_c,ld(op_c,X_56))))]]) ).
cnf(refute_1_213,plain,
( mult(A,mult(X_56,op_c)) != mult(mult(A,op_c),mult(op_c,ld(op_c,X_56)))
| mult(A,mult(X_56,op_c)) = mult(op_c,mult(A,X_56)) ),
inference(resolve,[$cnf( $equal(mult(mult(A,op_c),mult(op_c,ld(op_c,X_56))),mult(op_c,mult(A,X_56))) )],[refute_1_211,refute_1_212]) ).
cnf(refute_1_214,plain,
mult(A,mult(X_56,op_c)) = mult(op_c,mult(A,X_56)),
inference(resolve,[$cnf( $equal(mult(A,mult(X_56,op_c)),mult(mult(A,op_c),mult(op_c,ld(op_c,X_56)))) )],[refute_1_180,refute_1_213]) ).
cnf(refute_1_215,plain,
mult(op_c,mult(ld(mult(op_c,op_c),op_c),op_c)) = mult(op_c,mult(op_c,ld(mult(op_c,op_c),op_c))),
inference(subst,[],[refute_1_214:[bind(A,$fot(op_c)),bind(X_56,$fot(ld(mult(op_c,op_c),op_c)))]]) ).
cnf(refute_1_216,plain,
( mult(op_c,mult(ld(mult(op_c,op_c),op_c),op_c)) != mult(op_c,mult(op_c,ld(mult(op_c,op_c),op_c)))
| mult(op_c,mult(op_c,ld(mult(op_c,op_c),op_c))) != op_f
| mult(op_c,mult(ld(mult(op_c,op_c),op_c),op_c)) = op_f ),
inference(subst,[],[refute_1_87:[bind(X,$fot(mult(op_c,mult(ld(mult(op_c,op_c),op_c),op_c)))),bind(Y,$fot(mult(op_c,mult(op_c,ld(mult(op_c,op_c),op_c))))),bind(Z,$fot(op_f))]]) ).
cnf(refute_1_217,plain,
( mult(op_c,mult(op_c,ld(mult(op_c,op_c),op_c))) != op_f
| mult(op_c,mult(ld(mult(op_c,op_c),op_c),op_c)) = op_f ),
inference(resolve,[$cnf( $equal(mult(op_c,mult(ld(mult(op_c,op_c),op_c),op_c)),mult(op_c,mult(op_c,ld(mult(op_c,op_c),op_c)))) )],[refute_1_215,refute_1_216]) ).
cnf(refute_1_218,plain,
mult(op_c,mult(ld(mult(op_c,op_c),op_c),op_c)) = op_f,
inference(resolve,[$cnf( $equal(mult(op_c,mult(op_c,ld(mult(op_c,op_c),op_c))),op_f) )],[refute_1_175,refute_1_217]) ).
cnf(refute_1_219,plain,
( mult(op_c,mult(ld(mult(op_c,op_c),op_c),op_c)) != op_f
| op_c != mult(op_c,mult(ld(mult(op_c,op_c),op_c),op_c))
| op_c = op_f ),
introduced(tautology,[equality,[$cnf( $equal(op_c,mult(op_c,mult(ld(mult(op_c,op_c),op_c),op_c))) ),[1],$fot(op_f)]]) ).
cnf(refute_1_220,plain,
( op_c != mult(op_c,mult(ld(mult(op_c,op_c),op_c),op_c))
| op_c = op_f ),
inference(resolve,[$cnf( $equal(mult(op_c,mult(ld(mult(op_c,op_c),op_c),op_c)),op_f) )],[refute_1_218,refute_1_219]) ).
cnf(refute_1_221,plain,
op_c = op_f,
inference(resolve,[$cnf( $equal(op_c,mult(op_c,mult(ld(mult(op_c,op_c),op_c),op_c))) )],[refute_1_171,refute_1_220]) ).
cnf(refute_1_222,plain,
( op_c != op_f
| op_f = op_c ),
inference(subst,[],[refute_1_21:[bind(X,$fot(op_c)),bind(Y,$fot(op_f))]]) ).
cnf(refute_1_223,plain,
op_f = op_c,
inference(resolve,[$cnf( $equal(op_c,op_f) )],[refute_1_221,refute_1_222]) ).
cnf(refute_1_224,plain,
mult(skolemFOFtoCNF_X5_1,op_f) = mult(skolemFOFtoCNF_X5_1,op_f),
introduced(tautology,[refl,[$fot(mult(skolemFOFtoCNF_X5_1,op_f))]]) ).
cnf(refute_1_225,plain,
( mult(skolemFOFtoCNF_X5_1,op_f) != mult(skolemFOFtoCNF_X5_1,op_f)
| op_f != op_c
| mult(skolemFOFtoCNF_X5_1,op_f) = mult(skolemFOFtoCNF_X5_1,op_c) ),
introduced(tautology,[equality,[$cnf( $equal(mult(skolemFOFtoCNF_X5_1,op_f),mult(skolemFOFtoCNF_X5_1,op_f)) ),[1,1],$fot(op_c)]]) ).
cnf(refute_1_226,plain,
( op_f != op_c
| mult(skolemFOFtoCNF_X5_1,op_f) = mult(skolemFOFtoCNF_X5_1,op_c) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X5_1,op_f),mult(skolemFOFtoCNF_X5_1,op_f)) )],[refute_1_224,refute_1_225]) ).
cnf(refute_1_227,plain,
mult(skolemFOFtoCNF_X5_1,op_f) = mult(skolemFOFtoCNF_X5_1,op_c),
inference(resolve,[$cnf( $equal(op_f,op_c) )],[refute_1_223,refute_1_226]) ).
cnf(refute_1_228,plain,
( mult(skolemFOFtoCNF_X5_1,op_c) != mult(op_c,skolemFOFtoCNF_X5_1)
| mult(skolemFOFtoCNF_X5_1,op_f) != mult(skolemFOFtoCNF_X5_1,op_c)
| mult(skolemFOFtoCNF_X5_1,op_f) = mult(op_c,skolemFOFtoCNF_X5_1) ),
inference(subst,[],[refute_1_87:[bind(X,$fot(mult(skolemFOFtoCNF_X5_1,op_f))),bind(Y,$fot(mult(skolemFOFtoCNF_X5_1,op_c))),bind(Z,$fot(mult(op_c,skolemFOFtoCNF_X5_1)))]]) ).
cnf(refute_1_229,plain,
( mult(skolemFOFtoCNF_X5_1,op_c) != mult(op_c,skolemFOFtoCNF_X5_1)
| mult(skolemFOFtoCNF_X5_1,op_f) = mult(op_c,skolemFOFtoCNF_X5_1) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X5_1,op_f),mult(skolemFOFtoCNF_X5_1,op_c)) )],[refute_1_227,refute_1_228]) ).
cnf(refute_1_230,plain,
mult(skolemFOFtoCNF_X5_1,op_f) = mult(op_c,skolemFOFtoCNF_X5_1),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X5_1,op_c),mult(op_c,skolemFOFtoCNF_X5_1)) )],[refute_1_59,refute_1_229]) ).
cnf(refute_1_231,plain,
mult(skolemFOFtoCNF_X4_1,mult(skolemFOFtoCNF_X5_1,op_f)) = mult(skolemFOFtoCNF_X4_1,mult(skolemFOFtoCNF_X5_1,op_f)),
introduced(tautology,[refl,[$fot(mult(skolemFOFtoCNF_X4_1,mult(skolemFOFtoCNF_X5_1,op_f)))]]) ).
cnf(refute_1_232,plain,
( mult(skolemFOFtoCNF_X4_1,mult(skolemFOFtoCNF_X5_1,op_f)) != mult(skolemFOFtoCNF_X4_1,mult(skolemFOFtoCNF_X5_1,op_f))
| mult(skolemFOFtoCNF_X5_1,op_f) != mult(op_c,skolemFOFtoCNF_X5_1)
| mult(skolemFOFtoCNF_X4_1,mult(skolemFOFtoCNF_X5_1,op_f)) = mult(skolemFOFtoCNF_X4_1,mult(op_c,skolemFOFtoCNF_X5_1)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(skolemFOFtoCNF_X4_1,mult(skolemFOFtoCNF_X5_1,op_f)),mult(skolemFOFtoCNF_X4_1,mult(skolemFOFtoCNF_X5_1,op_f))) ),[1,1],$fot(mult(op_c,skolemFOFtoCNF_X5_1))]]) ).
cnf(refute_1_233,plain,
( mult(skolemFOFtoCNF_X5_1,op_f) != mult(op_c,skolemFOFtoCNF_X5_1)
| mult(skolemFOFtoCNF_X4_1,mult(skolemFOFtoCNF_X5_1,op_f)) = mult(skolemFOFtoCNF_X4_1,mult(op_c,skolemFOFtoCNF_X5_1)) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X4_1,mult(skolemFOFtoCNF_X5_1,op_f)),mult(skolemFOFtoCNF_X4_1,mult(skolemFOFtoCNF_X5_1,op_f))) )],[refute_1_231,refute_1_232]) ).
cnf(refute_1_234,plain,
mult(skolemFOFtoCNF_X4_1,mult(skolemFOFtoCNF_X5_1,op_f)) = mult(skolemFOFtoCNF_X4_1,mult(op_c,skolemFOFtoCNF_X5_1)),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X5_1,op_f),mult(op_c,skolemFOFtoCNF_X5_1)) )],[refute_1_230,refute_1_233]) ).
cnf(refute_1_235,plain,
( mult(skolemFOFtoCNF_X4_1,mult(op_c,skolemFOFtoCNF_X5_1)) != mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1))
| mult(skolemFOFtoCNF_X4_1,mult(skolemFOFtoCNF_X5_1,op_f)) != mult(skolemFOFtoCNF_X4_1,mult(op_c,skolemFOFtoCNF_X5_1))
| mult(skolemFOFtoCNF_X4_1,mult(skolemFOFtoCNF_X5_1,op_f)) = mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1)) ),
inference(subst,[],[refute_1_87:[bind(X,$fot(mult(skolemFOFtoCNF_X4_1,mult(skolemFOFtoCNF_X5_1,op_f)))),bind(Y,$fot(mult(skolemFOFtoCNF_X4_1,mult(op_c,skolemFOFtoCNF_X5_1)))),bind(Z,$fot(mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1))))]]) ).
cnf(refute_1_236,plain,
( mult(skolemFOFtoCNF_X4_1,mult(op_c,skolemFOFtoCNF_X5_1)) != mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1))
| mult(skolemFOFtoCNF_X4_1,mult(skolemFOFtoCNF_X5_1,op_f)) = mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1)) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X4_1,mult(skolemFOFtoCNF_X5_1,op_f)),mult(skolemFOFtoCNF_X4_1,mult(op_c,skolemFOFtoCNF_X5_1))) )],[refute_1_234,refute_1_235]) ).
cnf(refute_1_237,plain,
mult(skolemFOFtoCNF_X4_1,mult(skolemFOFtoCNF_X5_1,op_f)) = mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1)),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X4_1,mult(op_c,skolemFOFtoCNF_X5_1)),mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1))) )],[refute_1_58,refute_1_236]) ).
cnf(refute_1_238,plain,
( mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1)) != mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f)
| mult(skolemFOFtoCNF_X4_1,mult(skolemFOFtoCNF_X5_1,op_f)) != mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1))
| mult(skolemFOFtoCNF_X4_1,mult(skolemFOFtoCNF_X5_1,op_f)) = mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f) ),
introduced(tautology,[equality,[$cnf( $equal(mult(skolemFOFtoCNF_X4_1,mult(skolemFOFtoCNF_X5_1,op_f)),mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1))) ),[1],$fot(mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f))]]) ).
cnf(refute_1_239,plain,
( mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1)) != mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f)
| mult(skolemFOFtoCNF_X4_1,mult(skolemFOFtoCNF_X5_1,op_f)) = mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X4_1,mult(skolemFOFtoCNF_X5_1,op_f)),mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1))) )],[refute_1_237,refute_1_238]) ).
cnf(refute_1_240,plain,
mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_c) = mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1)),
inference(subst,[],[refute_1_40:[bind(X_28,$fot(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1)))]]) ).
cnf(refute_1_241,plain,
mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f) = mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f),
introduced(tautology,[refl,[$fot(mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f))]]) ).
cnf(refute_1_242,plain,
( mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f) != mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f)
| op_f != op_c
| mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f) = mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_c) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f),mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f)) ),[1,1],$fot(op_c)]]) ).
cnf(refute_1_243,plain,
( op_f != op_c
| mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f) = mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_c) ),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f),mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f)) )],[refute_1_241,refute_1_242]) ).
cnf(refute_1_244,plain,
mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f) = mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_c),
inference(resolve,[$cnf( $equal(op_f,op_c) )],[refute_1_223,refute_1_243]) ).
cnf(refute_1_245,plain,
( mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_c) != mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1))
| mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f) != mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_c)
| mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f) = mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1)) ),
inference(subst,[],[refute_1_87:[bind(X,$fot(mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f))),bind(Y,$fot(mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_c))),bind(Z,$fot(mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1))))]]) ).
cnf(refute_1_246,plain,
( mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_c) != mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1))
| mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f) = mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1)) ),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f),mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_c)) )],[refute_1_244,refute_1_245]) ).
cnf(refute_1_247,plain,
mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f) = mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1)),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_c),mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1))) )],[refute_1_240,refute_1_246]) ).
cnf(refute_1_248,plain,
( mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f) != mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1))
| mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1)) != mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1))
| mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1)) = mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1)),mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f)) ),[1],$fot(mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1)))]]) ).
cnf(refute_1_249,plain,
( mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1)) != mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1))
| mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1)) = mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f) ),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f),mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1))) )],[refute_1_247,refute_1_248]) ).
cnf(refute_1_250,plain,
( mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1)) != mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1))
| mult(skolemFOFtoCNF_X4_1,mult(skolemFOFtoCNF_X5_1,op_f)) = mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f) ),
inference(resolve,[$cnf( $equal(mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1)),mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f)) )],[refute_1_249,refute_1_239]) ).
cnf(refute_1_251,plain,
mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1)) != mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1)),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X4_1,mult(skolemFOFtoCNF_X5_1,op_f)),mult(mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1),op_f)) )],[refute_1_250,refute_1_0]) ).
cnf(refute_1_252,plain,
mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1)) = mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1)),
introduced(tautology,[refl,[$fot(mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1)))]]) ).
cnf(refute_1_253,plain,
$false,
inference(resolve,[$cnf( $equal(mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1)),mult(op_c,mult(skolemFOFtoCNF_X4_1,skolemFOFtoCNF_X5_1))) )],[refute_1_252,refute_1_251]) ).
fof(negate_2_0,plain,
~ ! [X4,X5] :
( ( mult(op_f,mult(X4,X5)) = mult(mult(op_f,X4),X5)
& mult(X4,mult(X5,op_f)) = mult(mult(X4,X5),op_f) )
=> mult(X4,mult(op_f,X5)) = mult(mult(X4,op_f),X5) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
? [X4,X5] :
( mult(X4,mult(op_f,X5)) != mult(mult(X4,op_f),X5)
& mult(X4,mult(X5,op_f)) = mult(mult(X4,X5),op_f)
& mult(op_f,mult(X4,X5)) = mult(mult(op_f,X4),X5) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_1,plain,
( mult(skolemFOFtoCNF_X4_2,mult(op_f,skolemFOFtoCNF_X5_2)) != mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2)
& mult(op_f,mult(skolemFOFtoCNF_X4_2,skolemFOFtoCNF_X5_2)) = mult(mult(op_f,skolemFOFtoCNF_X4_2),skolemFOFtoCNF_X5_2)
& mult(skolemFOFtoCNF_X4_2,mult(skolemFOFtoCNF_X5_2,op_f)) = mult(mult(skolemFOFtoCNF_X4_2,skolemFOFtoCNF_X5_2),op_f) ),
inference(skolemize,[],[normalize_2_0]) ).
fof(normalize_2_2,plain,
mult(skolemFOFtoCNF_X4_2,mult(op_f,skolemFOFtoCNF_X5_2)) != mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2),
inference(conjunct,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
! [A] : mult(unit,A) = A,
inference(canonicalize,[],[f06]) ).
fof(normalize_2_4,plain,
! [A] : mult(unit,A) = A,
inference(specialize,[],[normalize_2_3]) ).
fof(normalize_2_5,plain,
! [A,B] : op_f = mult(A,mult(B,ld(mult(A,B),op_c))),
inference(canonicalize,[],[f13]) ).
fof(normalize_2_6,plain,
! [A,B] : op_f = mult(A,mult(B,ld(mult(A,B),op_c))),
inference(specialize,[],[normalize_2_5]) ).
fof(normalize_2_7,plain,
! [A,B] : mult(A,ld(A,B)) = B,
inference(canonicalize,[],[f01]) ).
fof(normalize_2_8,plain,
! [A,B] : mult(A,ld(A,B)) = B,
inference(specialize,[],[normalize_2_7]) ).
fof(normalize_2_9,plain,
! [A,B] : mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
inference(canonicalize,[],[f10]) ).
fof(normalize_2_10,plain,
! [A,B] : mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
inference(specialize,[],[normalize_2_9]) ).
cnf(refute_2_0,plain,
mult(skolemFOFtoCNF_X4_2,mult(op_f,skolemFOFtoCNF_X5_2)) != mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2),
inference(canonicalize,[],[normalize_2_2]) ).
cnf(refute_2_1,plain,
mult(unit,A) = A,
inference(canonicalize,[],[normalize_2_4]) ).
cnf(refute_2_2,plain,
mult(unit,mult(X_81,ld(mult(unit,X_81),op_c))) = mult(X_81,ld(mult(unit,X_81),op_c)),
inference(subst,[],[refute_2_1:[bind(A,$fot(mult(X_81,ld(mult(unit,X_81),op_c))))]]) ).
cnf(refute_2_3,plain,
op_f = mult(A,mult(B,ld(mult(A,B),op_c))),
inference(canonicalize,[],[normalize_2_6]) ).
cnf(refute_2_4,plain,
op_f = mult(unit,mult(X_81,ld(mult(unit,X_81),op_c))),
inference(subst,[],[refute_2_3:[bind(A,$fot(unit)),bind(B,$fot(X_81))]]) ).
cnf(refute_2_5,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_2_6,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_2_7,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_2_5,refute_2_6]) ).
cnf(refute_2_8,plain,
( op_f != mult(unit,mult(X_81,ld(mult(unit,X_81),op_c)))
| mult(unit,mult(X_81,ld(mult(unit,X_81),op_c))) = op_f ),
inference(subst,[],[refute_2_7:[bind(X,$fot(op_f)),bind(Y,$fot(mult(unit,mult(X_81,ld(mult(unit,X_81),op_c)))))]]) ).
cnf(refute_2_9,plain,
mult(unit,mult(X_81,ld(mult(unit,X_81),op_c))) = op_f,
inference(resolve,[$cnf( $equal(op_f,mult(unit,mult(X_81,ld(mult(unit,X_81),op_c)))) )],[refute_2_4,refute_2_8]) ).
cnf(refute_2_10,plain,
( mult(unit,mult(X_81,ld(mult(unit,X_81),op_c))) != mult(X_81,ld(mult(unit,X_81),op_c))
| mult(unit,mult(X_81,ld(mult(unit,X_81),op_c))) != op_f
| op_f = mult(X_81,ld(mult(unit,X_81),op_c)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(unit,mult(X_81,ld(mult(unit,X_81),op_c))),mult(X_81,ld(mult(unit,X_81),op_c))) ),[0],$fot(op_f)]]) ).
cnf(refute_2_11,plain,
( mult(unit,mult(X_81,ld(mult(unit,X_81),op_c))) != mult(X_81,ld(mult(unit,X_81),op_c))
| op_f = mult(X_81,ld(mult(unit,X_81),op_c)) ),
inference(resolve,[$cnf( $equal(mult(unit,mult(X_81,ld(mult(unit,X_81),op_c))),op_f) )],[refute_2_9,refute_2_10]) ).
cnf(refute_2_12,plain,
op_f = mult(X_81,ld(mult(unit,X_81),op_c)),
inference(resolve,[$cnf( $equal(mult(unit,mult(X_81,ld(mult(unit,X_81),op_c))),mult(X_81,ld(mult(unit,X_81),op_c))) )],[refute_2_2,refute_2_11]) ).
cnf(refute_2_13,plain,
mult(A,ld(A,B)) = B,
inference(canonicalize,[],[normalize_2_8]) ).
cnf(refute_2_14,plain,
mult(X_81,ld(X_81,op_c)) = op_c,
inference(subst,[],[refute_2_13:[bind(A,$fot(X_81)),bind(B,$fot(op_c))]]) ).
cnf(refute_2_15,plain,
mult(unit,X_81) = X_81,
inference(subst,[],[refute_2_1:[bind(A,$fot(X_81))]]) ).
cnf(refute_2_16,plain,
ld(mult(unit,X_81),op_c) = ld(mult(unit,X_81),op_c),
introduced(tautology,[refl,[$fot(ld(mult(unit,X_81),op_c))]]) ).
cnf(refute_2_17,plain,
( ld(mult(unit,X_81),op_c) != ld(mult(unit,X_81),op_c)
| mult(unit,X_81) != X_81
| ld(mult(unit,X_81),op_c) = ld(X_81,op_c) ),
introduced(tautology,[equality,[$cnf( $equal(ld(mult(unit,X_81),op_c),ld(mult(unit,X_81),op_c)) ),[1,0],$fot(X_81)]]) ).
cnf(refute_2_18,plain,
( mult(unit,X_81) != X_81
| ld(mult(unit,X_81),op_c) = ld(X_81,op_c) ),
inference(resolve,[$cnf( $equal(ld(mult(unit,X_81),op_c),ld(mult(unit,X_81),op_c)) )],[refute_2_16,refute_2_17]) ).
cnf(refute_2_19,plain,
ld(mult(unit,X_81),op_c) = ld(X_81,op_c),
inference(resolve,[$cnf( $equal(mult(unit,X_81),X_81) )],[refute_2_15,refute_2_18]) ).
cnf(refute_2_20,plain,
mult(X_81,ld(mult(unit,X_81),op_c)) = mult(X_81,ld(mult(unit,X_81),op_c)),
introduced(tautology,[refl,[$fot(mult(X_81,ld(mult(unit,X_81),op_c)))]]) ).
cnf(refute_2_21,plain,
( ld(mult(unit,X_81),op_c) != ld(X_81,op_c)
| mult(X_81,ld(mult(unit,X_81),op_c)) != mult(X_81,ld(mult(unit,X_81),op_c))
| mult(X_81,ld(mult(unit,X_81),op_c)) = mult(X_81,ld(X_81,op_c)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_81,ld(mult(unit,X_81),op_c)),mult(X_81,ld(mult(unit,X_81),op_c))) ),[1,1],$fot(ld(X_81,op_c))]]) ).
cnf(refute_2_22,plain,
( ld(mult(unit,X_81),op_c) != ld(X_81,op_c)
| mult(X_81,ld(mult(unit,X_81),op_c)) = mult(X_81,ld(X_81,op_c)) ),
inference(resolve,[$cnf( $equal(mult(X_81,ld(mult(unit,X_81),op_c)),mult(X_81,ld(mult(unit,X_81),op_c))) )],[refute_2_20,refute_2_21]) ).
cnf(refute_2_23,plain,
mult(X_81,ld(mult(unit,X_81),op_c)) = mult(X_81,ld(X_81,op_c)),
inference(resolve,[$cnf( $equal(ld(mult(unit,X_81),op_c),ld(X_81,op_c)) )],[refute_2_19,refute_2_22]) ).
cnf(refute_2_24,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_2_25,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_2_7,refute_2_24]) ).
cnf(refute_2_26,plain,
( mult(X_81,ld(X_81,op_c)) != op_c
| mult(X_81,ld(mult(unit,X_81),op_c)) != mult(X_81,ld(X_81,op_c))
| mult(X_81,ld(mult(unit,X_81),op_c)) = op_c ),
inference(subst,[],[refute_2_25:[bind(X,$fot(mult(X_81,ld(mult(unit,X_81),op_c)))),bind(Y,$fot(mult(X_81,ld(X_81,op_c)))),bind(Z,$fot(op_c))]]) ).
cnf(refute_2_27,plain,
( mult(X_81,ld(X_81,op_c)) != op_c
| mult(X_81,ld(mult(unit,X_81),op_c)) = op_c ),
inference(resolve,[$cnf( $equal(mult(X_81,ld(mult(unit,X_81),op_c)),mult(X_81,ld(X_81,op_c))) )],[refute_2_23,refute_2_26]) ).
cnf(refute_2_28,plain,
mult(X_81,ld(mult(unit,X_81),op_c)) = op_c,
inference(resolve,[$cnf( $equal(mult(X_81,ld(X_81,op_c)),op_c) )],[refute_2_14,refute_2_27]) ).
cnf(refute_2_29,plain,
( mult(X_81,ld(mult(unit,X_81),op_c)) != op_c
| op_f != mult(X_81,ld(mult(unit,X_81),op_c))
| op_f = op_c ),
introduced(tautology,[equality,[$cnf( $equal(op_f,mult(X_81,ld(mult(unit,X_81),op_c))) ),[1],$fot(op_c)]]) ).
cnf(refute_2_30,plain,
( op_f != mult(X_81,ld(mult(unit,X_81),op_c))
| op_f = op_c ),
inference(resolve,[$cnf( $equal(mult(X_81,ld(mult(unit,X_81),op_c)),op_c) )],[refute_2_28,refute_2_29]) ).
cnf(refute_2_31,plain,
op_f = op_c,
inference(resolve,[$cnf( $equal(op_f,mult(X_81,ld(mult(unit,X_81),op_c))) )],[refute_2_12,refute_2_30]) ).
cnf(refute_2_32,plain,
mult(op_f,skolemFOFtoCNF_X5_2) = mult(op_f,skolemFOFtoCNF_X5_2),
introduced(tautology,[refl,[$fot(mult(op_f,skolemFOFtoCNF_X5_2))]]) ).
cnf(refute_2_33,plain,
( mult(op_f,skolemFOFtoCNF_X5_2) != mult(op_f,skolemFOFtoCNF_X5_2)
| op_f != op_c
| mult(op_f,skolemFOFtoCNF_X5_2) = mult(op_c,skolemFOFtoCNF_X5_2) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_f,skolemFOFtoCNF_X5_2),mult(op_f,skolemFOFtoCNF_X5_2)) ),[1,0],$fot(op_c)]]) ).
cnf(refute_2_34,plain,
( op_f != op_c
| mult(op_f,skolemFOFtoCNF_X5_2) = mult(op_c,skolemFOFtoCNF_X5_2) ),
inference(resolve,[$cnf( $equal(mult(op_f,skolemFOFtoCNF_X5_2),mult(op_f,skolemFOFtoCNF_X5_2)) )],[refute_2_32,refute_2_33]) ).
cnf(refute_2_35,plain,
mult(op_f,skolemFOFtoCNF_X5_2) = mult(op_c,skolemFOFtoCNF_X5_2),
inference(resolve,[$cnf( $equal(op_f,op_c) )],[refute_2_31,refute_2_34]) ).
cnf(refute_2_36,plain,
mult(skolemFOFtoCNF_X4_2,mult(op_f,skolemFOFtoCNF_X5_2)) = mult(skolemFOFtoCNF_X4_2,mult(op_f,skolemFOFtoCNF_X5_2)),
introduced(tautology,[refl,[$fot(mult(skolemFOFtoCNF_X4_2,mult(op_f,skolemFOFtoCNF_X5_2)))]]) ).
cnf(refute_2_37,plain,
( mult(op_f,skolemFOFtoCNF_X5_2) != mult(op_c,skolemFOFtoCNF_X5_2)
| mult(skolemFOFtoCNF_X4_2,mult(op_f,skolemFOFtoCNF_X5_2)) != mult(skolemFOFtoCNF_X4_2,mult(op_f,skolemFOFtoCNF_X5_2))
| mult(skolemFOFtoCNF_X4_2,mult(op_f,skolemFOFtoCNF_X5_2)) = mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(skolemFOFtoCNF_X4_2,mult(op_f,skolemFOFtoCNF_X5_2)),mult(skolemFOFtoCNF_X4_2,mult(op_f,skolemFOFtoCNF_X5_2))) ),[1,1],$fot(mult(op_c,skolemFOFtoCNF_X5_2))]]) ).
cnf(refute_2_38,plain,
( mult(op_f,skolemFOFtoCNF_X5_2) != mult(op_c,skolemFOFtoCNF_X5_2)
| mult(skolemFOFtoCNF_X4_2,mult(op_f,skolemFOFtoCNF_X5_2)) = mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2)) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X4_2,mult(op_f,skolemFOFtoCNF_X5_2)),mult(skolemFOFtoCNF_X4_2,mult(op_f,skolemFOFtoCNF_X5_2))) )],[refute_2_36,refute_2_37]) ).
cnf(refute_2_39,plain,
mult(skolemFOFtoCNF_X4_2,mult(op_f,skolemFOFtoCNF_X5_2)) = mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2)),
inference(resolve,[$cnf( $equal(mult(op_f,skolemFOFtoCNF_X5_2),mult(op_c,skolemFOFtoCNF_X5_2)) )],[refute_2_35,refute_2_38]) ).
cnf(refute_2_40,plain,
( mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2)) != mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2)
| mult(skolemFOFtoCNF_X4_2,mult(op_f,skolemFOFtoCNF_X5_2)) != mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2))
| mult(skolemFOFtoCNF_X4_2,mult(op_f,skolemFOFtoCNF_X5_2)) = mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2) ),
introduced(tautology,[equality,[$cnf( $equal(mult(skolemFOFtoCNF_X4_2,mult(op_f,skolemFOFtoCNF_X5_2)),mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2))) ),[1],$fot(mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2))]]) ).
cnf(refute_2_41,plain,
( mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2)) != mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2)
| mult(skolemFOFtoCNF_X4_2,mult(op_f,skolemFOFtoCNF_X5_2)) = mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X4_2,mult(op_f,skolemFOFtoCNF_X5_2)),mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2))) )],[refute_2_39,refute_2_40]) ).
cnf(refute_2_42,plain,
mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
inference(canonicalize,[],[normalize_2_10]) ).
cnf(refute_2_43,plain,
( mult(A,mult(op_c,B)) != mult(mult(A,op_c),B)
| mult(mult(A,op_c),B) = mult(A,mult(op_c,B)) ),
inference(subst,[],[refute_2_7:[bind(X,$fot(mult(A,mult(op_c,B)))),bind(Y,$fot(mult(mult(A,op_c),B)))]]) ).
cnf(refute_2_44,plain,
mult(mult(A,op_c),B) = mult(A,mult(op_c,B)),
inference(resolve,[$cnf( $equal(mult(A,mult(op_c,B)),mult(mult(A,op_c),B)) )],[refute_2_42,refute_2_43]) ).
cnf(refute_2_45,plain,
mult(mult(skolemFOFtoCNF_X4_2,op_c),skolemFOFtoCNF_X5_2) = mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2)),
inference(subst,[],[refute_2_44:[bind(A,$fot(skolemFOFtoCNF_X4_2)),bind(B,$fot(skolemFOFtoCNF_X5_2))]]) ).
cnf(refute_2_46,plain,
mult(skolemFOFtoCNF_X4_2,op_f) = mult(skolemFOFtoCNF_X4_2,op_f),
introduced(tautology,[refl,[$fot(mult(skolemFOFtoCNF_X4_2,op_f))]]) ).
cnf(refute_2_47,plain,
( mult(skolemFOFtoCNF_X4_2,op_f) != mult(skolemFOFtoCNF_X4_2,op_f)
| op_f != op_c
| mult(skolemFOFtoCNF_X4_2,op_f) = mult(skolemFOFtoCNF_X4_2,op_c) ),
introduced(tautology,[equality,[$cnf( $equal(mult(skolemFOFtoCNF_X4_2,op_f),mult(skolemFOFtoCNF_X4_2,op_f)) ),[1,1],$fot(op_c)]]) ).
cnf(refute_2_48,plain,
( op_f != op_c
| mult(skolemFOFtoCNF_X4_2,op_f) = mult(skolemFOFtoCNF_X4_2,op_c) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X4_2,op_f),mult(skolemFOFtoCNF_X4_2,op_f)) )],[refute_2_46,refute_2_47]) ).
cnf(refute_2_49,plain,
mult(skolemFOFtoCNF_X4_2,op_f) = mult(skolemFOFtoCNF_X4_2,op_c),
inference(resolve,[$cnf( $equal(op_f,op_c) )],[refute_2_31,refute_2_48]) ).
cnf(refute_2_50,plain,
mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2) = mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2),
introduced(tautology,[refl,[$fot(mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2))]]) ).
cnf(refute_2_51,plain,
( mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2) != mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2)
| mult(skolemFOFtoCNF_X4_2,op_f) != mult(skolemFOFtoCNF_X4_2,op_c)
| mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2) = mult(mult(skolemFOFtoCNF_X4_2,op_c),skolemFOFtoCNF_X5_2) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2),mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2)) ),[1,0],$fot(mult(skolemFOFtoCNF_X4_2,op_c))]]) ).
cnf(refute_2_52,plain,
( mult(skolemFOFtoCNF_X4_2,op_f) != mult(skolemFOFtoCNF_X4_2,op_c)
| mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2) = mult(mult(skolemFOFtoCNF_X4_2,op_c),skolemFOFtoCNF_X5_2) ),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2),mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2)) )],[refute_2_50,refute_2_51]) ).
cnf(refute_2_53,plain,
mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2) = mult(mult(skolemFOFtoCNF_X4_2,op_c),skolemFOFtoCNF_X5_2),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X4_2,op_f),mult(skolemFOFtoCNF_X4_2,op_c)) )],[refute_2_49,refute_2_52]) ).
cnf(refute_2_54,plain,
( mult(mult(skolemFOFtoCNF_X4_2,op_c),skolemFOFtoCNF_X5_2) != mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2))
| mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2) != mult(mult(skolemFOFtoCNF_X4_2,op_c),skolemFOFtoCNF_X5_2)
| mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2) = mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2)) ),
inference(subst,[],[refute_2_25:[bind(X,$fot(mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2))),bind(Y,$fot(mult(mult(skolemFOFtoCNF_X4_2,op_c),skolemFOFtoCNF_X5_2))),bind(Z,$fot(mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2))))]]) ).
cnf(refute_2_55,plain,
( mult(mult(skolemFOFtoCNF_X4_2,op_c),skolemFOFtoCNF_X5_2) != mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2))
| mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2) = mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2)) ),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2),mult(mult(skolemFOFtoCNF_X4_2,op_c),skolemFOFtoCNF_X5_2)) )],[refute_2_53,refute_2_54]) ).
cnf(refute_2_56,plain,
mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2) = mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2)),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X4_2,op_c),skolemFOFtoCNF_X5_2),mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2))) )],[refute_2_45,refute_2_55]) ).
cnf(refute_2_57,plain,
( mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2) != mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2))
| mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2)) != mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2))
| mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2)) = mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2)),mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2)) ),[1],$fot(mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2)))]]) ).
cnf(refute_2_58,plain,
( mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2)) != mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2))
| mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2)) = mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2) ),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2),mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2))) )],[refute_2_56,refute_2_57]) ).
cnf(refute_2_59,plain,
( mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2)) != mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2))
| mult(skolemFOFtoCNF_X4_2,mult(op_f,skolemFOFtoCNF_X5_2)) = mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2)),mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2)) )],[refute_2_58,refute_2_41]) ).
cnf(refute_2_60,plain,
mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2)) != mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2)),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X4_2,mult(op_f,skolemFOFtoCNF_X5_2)),mult(mult(skolemFOFtoCNF_X4_2,op_f),skolemFOFtoCNF_X5_2)) )],[refute_2_59,refute_2_0]) ).
cnf(refute_2_61,plain,
mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2)) = mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2)),
introduced(tautology,[refl,[$fot(mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2)))]]) ).
cnf(refute_2_62,plain,
$false,
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2)),mult(skolemFOFtoCNF_X4_2,mult(op_c,skolemFOFtoCNF_X5_2))) )],[refute_2_61,refute_2_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP704+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n014.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 12:29:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.48
% 0.20/0.48 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.36/0.55
%------------------------------------------------------------------------------