TSTP Solution File: GRP665+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP665+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:44:46 EDT 2022
% Result : Theorem 0.20s 0.55s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 60
% Syntax : Number of formulae : 274 ( 162 unt; 0 def)
% Number of atoms : 440 ( 437 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 336 ( 170 ~; 152 |; 10 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 357 ( 0 sgn 73 !; 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(f07,axiom,
! [C,B,A] : mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)) ).
fof(f08,axiom,
! [C,B,A] : mult(mult(A,B),C) = mult(mult(A,C),ld(C,mult(B,C))) ).
fof(f09,axiom,
! [A] : mult(op_c,A) = mult(A,op_c) ).
fof(goals,conjecture,
! [X0,X1] :
( mult(op_c,mult(X0,X1)) = mult(mult(op_c,X0),X1)
& mult(mult(X0,op_c),X1) = mult(X0,mult(op_c,X1))
& mult(mult(X0,X1),op_c) = mult(X0,mult(X1,op_c)) ) ).
fof(subgoal_0,plain,
! [X0,X1] : mult(op_c,mult(X0,X1)) = mult(mult(op_c,X0),X1),
inference(strip,[],[goals]) ).
fof(subgoal_1,plain,
! [X0,X1] :
( mult(op_c,mult(X0,X1)) = mult(mult(op_c,X0),X1)
=> mult(mult(X0,op_c),X1) = mult(X0,mult(op_c,X1)) ),
inference(strip,[],[goals]) ).
fof(subgoal_2,plain,
! [X0,X1] :
( ( mult(op_c,mult(X0,X1)) = mult(mult(op_c,X0),X1)
& mult(mult(X0,op_c),X1) = mult(X0,mult(op_c,X1)) )
=> mult(mult(X0,X1),op_c) = mult(X0,mult(X1,op_c)) ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0,X1] : mult(op_c,mult(X0,X1)) = mult(mult(op_c,X0),X1),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0,X1] : mult(op_c,mult(X0,X1)) != mult(mult(op_c,X0),X1),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != mult(mult(op_c,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B,C] : mult(mult(A,B),C) = mult(mult(A,C),ld(C,mult(B,C))),
inference(canonicalize,[],[f08]) ).
fof(normalize_0_3,plain,
! [A,B,C] : mult(mult(A,B),C) = mult(mult(A,C),ld(C,mult(B,C))),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A] : mult(op_c,A) = mult(A,op_c),
inference(canonicalize,[],[f09]) ).
fof(normalize_0_5,plain,
! [A] : mult(op_c,A) = mult(A,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] : ld(A,mult(A,B)) = B,
inference(canonicalize,[],[f02]) ).
fof(normalize_0_9,plain,
! [A,B] : ld(A,mult(A,B)) = B,
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B,C] : mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)),
inference(canonicalize,[],[f07]) ).
fof(normalize_0_11,plain,
! [A,B,C] : mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B] : rd(mult(A,B),B) = A,
inference(canonicalize,[],[f04]) ).
fof(normalize_0_13,plain,
! [A,B] : rd(mult(A,B),B) = A,
inference(specialize,[],[normalize_0_12]) ).
cnf(refute_0_0,plain,
mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != mult(mult(op_c,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
mult(mult(A,B),C) = mult(mult(A,C),ld(C,mult(B,C))),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
mult(mult(op_c,X_61),X_62) = mult(mult(op_c,X_62),ld(X_62,mult(X_61,X_62))),
inference(subst,[],[refute_0_1:[bind(A,$fot(op_c)),bind(B,$fot(X_61)),bind(C,$fot(X_62))]]) ).
cnf(refute_0_3,plain,
mult(op_c,A) = mult(A,op_c),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
mult(op_c,X_62) = mult(X_62,op_c),
inference(subst,[],[refute_0_3:[bind(A,$fot(X_62))]]) ).
cnf(refute_0_5,plain,
( mult(mult(op_c,X_61),X_62) != mult(mult(op_c,X_62),ld(X_62,mult(X_61,X_62)))
| mult(op_c,X_62) != mult(X_62,op_c)
| mult(mult(op_c,X_61),X_62) = mult(mult(X_62,op_c),ld(X_62,mult(X_61,X_62))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(op_c,X_61),X_62),mult(mult(op_c,X_62),ld(X_62,mult(X_61,X_62)))) ),[1,0],$fot(mult(X_62,op_c))]]) ).
cnf(refute_0_6,plain,
( mult(mult(op_c,X_61),X_62) != mult(mult(op_c,X_62),ld(X_62,mult(X_61,X_62)))
| mult(mult(op_c,X_61),X_62) = mult(mult(X_62,op_c),ld(X_62,mult(X_61,X_62))) ),
inference(resolve,[$cnf( $equal(mult(op_c,X_62),mult(X_62,op_c)) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
mult(mult(op_c,X_61),X_62) = mult(mult(X_62,op_c),ld(X_62,mult(X_61,X_62))),
inference(resolve,[$cnf( $equal(mult(mult(op_c,X_61),X_62),mult(mult(op_c,X_62),ld(X_62,mult(X_61,X_62)))) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
mult(A,ld(A,B)) = B,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_9,plain,
mult(X_62,ld(X_62,mult(X_61,X_62))) = mult(X_61,X_62),
inference(subst,[],[refute_0_8:[bind(A,$fot(X_62)),bind(B,$fot(mult(X_61,X_62)))]]) ).
cnf(refute_0_10,plain,
mult(op_c,mult(X_62,ld(X_62,mult(X_61,X_62)))) = mult(op_c,mult(X_62,ld(X_62,mult(X_61,X_62)))),
introduced(tautology,[refl,[$fot(mult(op_c,mult(X_62,ld(X_62,mult(X_61,X_62)))))]]) ).
cnf(refute_0_11,plain,
( mult(X_62,ld(X_62,mult(X_61,X_62))) != mult(X_61,X_62)
| mult(op_c,mult(X_62,ld(X_62,mult(X_61,X_62)))) != mult(op_c,mult(X_62,ld(X_62,mult(X_61,X_62))))
| mult(op_c,mult(X_62,ld(X_62,mult(X_61,X_62)))) = mult(op_c,mult(X_61,X_62)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_c,mult(X_62,ld(X_62,mult(X_61,X_62)))),mult(op_c,mult(X_62,ld(X_62,mult(X_61,X_62))))) ),[1,1],$fot(mult(X_61,X_62))]]) ).
cnf(refute_0_12,plain,
( mult(X_62,ld(X_62,mult(X_61,X_62))) != mult(X_61,X_62)
| mult(op_c,mult(X_62,ld(X_62,mult(X_61,X_62)))) = mult(op_c,mult(X_61,X_62)) ),
inference(resolve,[$cnf( $equal(mult(op_c,mult(X_62,ld(X_62,mult(X_61,X_62)))),mult(op_c,mult(X_62,ld(X_62,mult(X_61,X_62))))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
mult(op_c,mult(X_62,ld(X_62,mult(X_61,X_62)))) = mult(op_c,mult(X_61,X_62)),
inference(resolve,[$cnf( $equal(mult(X_62,ld(X_62,mult(X_61,X_62))),mult(X_61,X_62)) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
mult(mult(X_60,X_61),op_c) = mult(mult(X_60,op_c),ld(op_c,mult(X_61,op_c))),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_60)),bind(B,$fot(X_61)),bind(C,$fot(op_c))]]) ).
cnf(refute_0_15,plain,
mult(op_c,mult(X_60,X_61)) = mult(mult(X_60,X_61),op_c),
inference(subst,[],[refute_0_3:[bind(A,$fot(mult(X_60,X_61)))]]) ).
cnf(refute_0_16,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_17,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_18,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( mult(op_c,mult(X_60,X_61)) != mult(mult(X_60,X_61),op_c)
| mult(mult(X_60,X_61),op_c) = mult(op_c,mult(X_60,X_61)) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(mult(op_c,mult(X_60,X_61)))),bind(Y,$fot(mult(mult(X_60,X_61),op_c)))]]) ).
cnf(refute_0_20,plain,
mult(mult(X_60,X_61),op_c) = mult(op_c,mult(X_60,X_61)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(X_60,X_61)),mult(mult(X_60,X_61),op_c)) )],[refute_0_15,refute_0_19]) ).
cnf(refute_0_21,plain,
( mult(mult(X_60,X_61),op_c) != mult(mult(X_60,op_c),ld(op_c,mult(X_61,op_c)))
| mult(mult(X_60,X_61),op_c) != mult(op_c,mult(X_60,X_61))
| mult(op_c,mult(X_60,X_61)) = mult(mult(X_60,op_c),ld(op_c,mult(X_61,op_c))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(X_60,X_61),op_c),mult(mult(X_60,op_c),ld(op_c,mult(X_61,op_c)))) ),[0],$fot(mult(op_c,mult(X_60,X_61)))]]) ).
cnf(refute_0_22,plain,
( mult(mult(X_60,X_61),op_c) != mult(mult(X_60,op_c),ld(op_c,mult(X_61,op_c)))
| mult(op_c,mult(X_60,X_61)) = mult(mult(X_60,op_c),ld(op_c,mult(X_61,op_c))) ),
inference(resolve,[$cnf( $equal(mult(mult(X_60,X_61),op_c),mult(op_c,mult(X_60,X_61))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
mult(op_c,mult(X_60,X_61)) = mult(mult(X_60,op_c),ld(op_c,mult(X_61,op_c))),
inference(resolve,[$cnf( $equal(mult(mult(X_60,X_61),op_c),mult(mult(X_60,op_c),ld(op_c,mult(X_61,op_c)))) )],[refute_0_14,refute_0_22]) ).
cnf(refute_0_24,plain,
ld(A,mult(A,B)) = B,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_25,plain,
ld(op_c,mult(op_c,mult(X_30,X_31))) = mult(X_30,X_31),
inference(subst,[],[refute_0_24:[bind(A,$fot(op_c)),bind(B,$fot(mult(X_30,X_31)))]]) ).
cnf(refute_0_26,plain,
mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_27,plain,
mult(op_c,mult(X_28,X_29)) = mult(rd(mult(op_c,X_28),op_c),mult(op_c,X_29)),
inference(subst,[],[refute_0_26:[bind(A,$fot(op_c)),bind(B,$fot(X_28)),bind(C,$fot(X_29))]]) ).
cnf(refute_0_28,plain,
mult(op_c,X_29) = mult(X_29,op_c),
inference(subst,[],[refute_0_3:[bind(A,$fot(X_29))]]) ).
cnf(refute_0_29,plain,
( mult(op_c,X_29) != mult(X_29,op_c)
| mult(op_c,mult(X_28,X_29)) != mult(rd(mult(op_c,X_28),op_c),mult(op_c,X_29))
| mult(op_c,mult(X_28,X_29)) = mult(rd(mult(op_c,X_28),op_c),mult(X_29,op_c)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_c,mult(X_28,X_29)),mult(rd(mult(op_c,X_28),op_c),mult(op_c,X_29))) ),[1,1],$fot(mult(X_29,op_c))]]) ).
cnf(refute_0_30,plain,
( mult(op_c,mult(X_28,X_29)) != mult(rd(mult(op_c,X_28),op_c),mult(op_c,X_29))
| mult(op_c,mult(X_28,X_29)) = mult(rd(mult(op_c,X_28),op_c),mult(X_29,op_c)) ),
inference(resolve,[$cnf( $equal(mult(op_c,X_29),mult(X_29,op_c)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
mult(op_c,mult(X_28,X_29)) = mult(rd(mult(op_c,X_28),op_c),mult(X_29,op_c)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(X_28,X_29)),mult(rd(mult(op_c,X_28),op_c),mult(op_c,X_29))) )],[refute_0_27,refute_0_30]) ).
cnf(refute_0_32,plain,
ld(op_c,mult(op_c,X_28)) = X_28,
inference(subst,[],[refute_0_24:[bind(A,$fot(op_c)),bind(B,$fot(X_28))]]) ).
cnf(refute_0_33,plain,
rd(mult(A,B),B) = A,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_34,plain,
rd(mult(X_7,op_c),op_c) = X_7,
inference(subst,[],[refute_0_33:[bind(A,$fot(X_7)),bind(B,$fot(op_c))]]) ).
cnf(refute_0_35,plain,
mult(op_c,X_7) = mult(X_7,op_c),
inference(subst,[],[refute_0_3:[bind(A,$fot(X_7))]]) ).
cnf(refute_0_36,plain,
( mult(op_c,X_7) != mult(X_7,op_c)
| mult(X_7,op_c) = mult(op_c,X_7) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(mult(op_c,X_7))),bind(Y,$fot(mult(X_7,op_c)))]]) ).
cnf(refute_0_37,plain,
mult(X_7,op_c) = mult(op_c,X_7),
inference(resolve,[$cnf( $equal(mult(op_c,X_7),mult(X_7,op_c)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( mult(X_7,op_c) != mult(op_c,X_7)
| rd(mult(X_7,op_c),op_c) != X_7
| rd(mult(op_c,X_7),op_c) = X_7 ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(X_7,op_c),op_c),X_7) ),[0,0],$fot(mult(op_c,X_7))]]) ).
cnf(refute_0_39,plain,
( rd(mult(X_7,op_c),op_c) != X_7
| rd(mult(op_c,X_7),op_c) = X_7 ),
inference(resolve,[$cnf( $equal(mult(X_7,op_c),mult(op_c,X_7)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
rd(mult(op_c,X_7),op_c) = X_7,
inference(resolve,[$cnf( $equal(rd(mult(X_7,op_c),op_c),X_7) )],[refute_0_34,refute_0_39]) ).
cnf(refute_0_41,plain,
rd(mult(op_c,ld(op_c,X_14)),op_c) = ld(op_c,X_14),
inference(subst,[],[refute_0_40:[bind(X_7,$fot(ld(op_c,X_14)))]]) ).
cnf(refute_0_42,plain,
mult(op_c,ld(op_c,X_14)) = X_14,
inference(subst,[],[refute_0_8:[bind(A,$fot(op_c)),bind(B,$fot(X_14))]]) ).
cnf(refute_0_43,plain,
( mult(op_c,ld(op_c,X_14)) != X_14
| rd(mult(op_c,ld(op_c,X_14)),op_c) != ld(op_c,X_14)
| rd(X_14,op_c) = ld(op_c,X_14) ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(op_c,ld(op_c,X_14)),op_c),ld(op_c,X_14)) ),[0,0],$fot(X_14)]]) ).
cnf(refute_0_44,plain,
( rd(mult(op_c,ld(op_c,X_14)),op_c) != ld(op_c,X_14)
| rd(X_14,op_c) = ld(op_c,X_14) ),
inference(resolve,[$cnf( $equal(mult(op_c,ld(op_c,X_14)),X_14) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
rd(X_14,op_c) = ld(op_c,X_14),
inference(resolve,[$cnf( $equal(rd(mult(op_c,ld(op_c,X_14)),op_c),ld(op_c,X_14)) )],[refute_0_41,refute_0_44]) ).
cnf(refute_0_46,plain,
rd(mult(op_c,X_28),op_c) = ld(op_c,mult(op_c,X_28)),
inference(subst,[],[refute_0_45:[bind(X_14,$fot(mult(op_c,X_28)))]]) ).
cnf(refute_0_47,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_48,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_18,refute_0_47]) ).
cnf(refute_0_49,plain,
( ld(op_c,mult(op_c,X_28)) != X_28
| rd(mult(op_c,X_28),op_c) != ld(op_c,mult(op_c,X_28))
| rd(mult(op_c,X_28),op_c) = X_28 ),
inference(subst,[],[refute_0_48:[bind(X,$fot(rd(mult(op_c,X_28),op_c))),bind(Y,$fot(ld(op_c,mult(op_c,X_28)))),bind(Z,$fot(X_28))]]) ).
cnf(refute_0_50,plain,
( ld(op_c,mult(op_c,X_28)) != X_28
| rd(mult(op_c,X_28),op_c) = X_28 ),
inference(resolve,[$cnf( $equal(rd(mult(op_c,X_28),op_c),ld(op_c,mult(op_c,X_28))) )],[refute_0_46,refute_0_49]) ).
cnf(refute_0_51,plain,
rd(mult(op_c,X_28),op_c) = X_28,
inference(resolve,[$cnf( $equal(ld(op_c,mult(op_c,X_28)),X_28) )],[refute_0_32,refute_0_50]) ).
cnf(refute_0_52,plain,
mult(rd(mult(op_c,X_28),op_c),mult(X_29,op_c)) = mult(rd(mult(op_c,X_28),op_c),mult(X_29,op_c)),
introduced(tautology,[refl,[$fot(mult(rd(mult(op_c,X_28),op_c),mult(X_29,op_c)))]]) ).
cnf(refute_0_53,plain,
( mult(rd(mult(op_c,X_28),op_c),mult(X_29,op_c)) != mult(rd(mult(op_c,X_28),op_c),mult(X_29,op_c))
| rd(mult(op_c,X_28),op_c) != X_28
| mult(rd(mult(op_c,X_28),op_c),mult(X_29,op_c)) = mult(X_28,mult(X_29,op_c)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(rd(mult(op_c,X_28),op_c),mult(X_29,op_c)),mult(rd(mult(op_c,X_28),op_c),mult(X_29,op_c))) ),[1,0],$fot(X_28)]]) ).
cnf(refute_0_54,plain,
( rd(mult(op_c,X_28),op_c) != X_28
| mult(rd(mult(op_c,X_28),op_c),mult(X_29,op_c)) = mult(X_28,mult(X_29,op_c)) ),
inference(resolve,[$cnf( $equal(mult(rd(mult(op_c,X_28),op_c),mult(X_29,op_c)),mult(rd(mult(op_c,X_28),op_c),mult(X_29,op_c))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
mult(rd(mult(op_c,X_28),op_c),mult(X_29,op_c)) = mult(X_28,mult(X_29,op_c)),
inference(resolve,[$cnf( $equal(rd(mult(op_c,X_28),op_c),X_28) )],[refute_0_51,refute_0_54]) ).
cnf(refute_0_56,plain,
( mult(op_c,mult(X_28,X_29)) != mult(rd(mult(op_c,X_28),op_c),mult(X_29,op_c))
| mult(rd(mult(op_c,X_28),op_c),mult(X_29,op_c)) != mult(X_28,mult(X_29,op_c))
| mult(op_c,mult(X_28,X_29)) = mult(X_28,mult(X_29,op_c)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(op_c,mult(X_28,X_29)),mult(X_28,mult(X_29,op_c))) ),[0],$fot(mult(rd(mult(op_c,X_28),op_c),mult(X_29,op_c)))]]) ).
cnf(refute_0_57,plain,
( mult(op_c,mult(X_28,X_29)) != mult(rd(mult(op_c,X_28),op_c),mult(X_29,op_c))
| mult(op_c,mult(X_28,X_29)) = mult(X_28,mult(X_29,op_c)) ),
inference(resolve,[$cnf( $equal(mult(rd(mult(op_c,X_28),op_c),mult(X_29,op_c)),mult(X_28,mult(X_29,op_c))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
mult(op_c,mult(X_28,X_29)) = mult(X_28,mult(X_29,op_c)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(X_28,X_29)),mult(rd(mult(op_c,X_28),op_c),mult(X_29,op_c))) )],[refute_0_31,refute_0_57]) ).
cnf(refute_0_59,plain,
mult(op_c,mult(X_30,X_31)) = mult(X_30,mult(X_31,op_c)),
inference(subst,[],[refute_0_58:[bind(X_28,$fot(X_30)),bind(X_29,$fot(X_31))]]) ).
cnf(refute_0_60,plain,
( ld(op_c,mult(op_c,mult(X_30,X_31))) != mult(X_30,X_31)
| mult(op_c,mult(X_30,X_31)) != mult(X_30,mult(X_31,op_c))
| ld(op_c,mult(X_30,mult(X_31,op_c))) = mult(X_30,X_31) ),
introduced(tautology,[equality,[$cnf( $equal(ld(op_c,mult(op_c,mult(X_30,X_31))),mult(X_30,X_31)) ),[0,1],$fot(mult(X_30,mult(X_31,op_c)))]]) ).
cnf(refute_0_61,plain,
( ld(op_c,mult(op_c,mult(X_30,X_31))) != mult(X_30,X_31)
| ld(op_c,mult(X_30,mult(X_31,op_c))) = mult(X_30,X_31) ),
inference(resolve,[$cnf( $equal(mult(op_c,mult(X_30,X_31)),mult(X_30,mult(X_31,op_c))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
ld(op_c,mult(X_30,mult(X_31,op_c))) = mult(X_30,X_31),
inference(resolve,[$cnf( $equal(ld(op_c,mult(op_c,mult(X_30,X_31))),mult(X_30,X_31)) )],[refute_0_25,refute_0_61]) ).
cnf(refute_0_63,plain,
ld(op_c,mult(mult(X_60,op_c),mult(X_61,op_c))) = mult(mult(X_60,op_c),X_61),
inference(subst,[],[refute_0_62:[bind(X_30,$fot(mult(X_60,op_c))),bind(X_31,$fot(X_61))]]) ).
cnf(refute_0_64,plain,
ld(op_c,mult(op_c,mult(X_32,X_33))) = mult(X_32,X_33),
inference(subst,[],[refute_0_24:[bind(A,$fot(op_c)),bind(B,$fot(mult(X_32,X_33)))]]) ).
cnf(refute_0_65,plain,
mult(op_c,X_28) = mult(X_28,op_c),
inference(subst,[],[refute_0_3:[bind(A,$fot(X_28))]]) ).
cnf(refute_0_66,plain,
( mult(op_c,X_28) != mult(X_28,op_c)
| mult(op_c,mult(X_28,X_29)) != mult(rd(mult(op_c,X_28),op_c),mult(op_c,X_29))
| mult(op_c,mult(X_28,X_29)) = mult(rd(mult(X_28,op_c),op_c),mult(op_c,X_29)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_c,mult(X_28,X_29)),mult(rd(mult(op_c,X_28),op_c),mult(op_c,X_29))) ),[1,0,0],$fot(mult(X_28,op_c))]]) ).
cnf(refute_0_67,plain,
( mult(op_c,mult(X_28,X_29)) != mult(rd(mult(op_c,X_28),op_c),mult(op_c,X_29))
| mult(op_c,mult(X_28,X_29)) = mult(rd(mult(X_28,op_c),op_c),mult(op_c,X_29)) ),
inference(resolve,[$cnf( $equal(mult(op_c,X_28),mult(X_28,op_c)) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
mult(op_c,mult(X_28,X_29)) = mult(rd(mult(X_28,op_c),op_c),mult(op_c,X_29)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(X_28,X_29)),mult(rd(mult(op_c,X_28),op_c),mult(op_c,X_29))) )],[refute_0_27,refute_0_67]) ).
cnf(refute_0_69,plain,
rd(mult(A,op_c),op_c) = A,
inference(subst,[],[refute_0_33:[bind(B,$fot(op_c))]]) ).
cnf(refute_0_70,plain,
rd(mult(A,op_c),op_c) = ld(op_c,mult(A,op_c)),
inference(subst,[],[refute_0_45:[bind(X_14,$fot(mult(A,op_c)))]]) ).
cnf(refute_0_71,plain,
( rd(mult(A,op_c),op_c) != A
| rd(mult(A,op_c),op_c) != ld(op_c,mult(A,op_c))
| ld(op_c,mult(A,op_c)) = A ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(A,op_c),op_c),A) ),[0],$fot(ld(op_c,mult(A,op_c)))]]) ).
cnf(refute_0_72,plain,
( rd(mult(A,op_c),op_c) != A
| ld(op_c,mult(A,op_c)) = A ),
inference(resolve,[$cnf( $equal(rd(mult(A,op_c),op_c),ld(op_c,mult(A,op_c))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
ld(op_c,mult(A,op_c)) = A,
inference(resolve,[$cnf( $equal(rd(mult(A,op_c),op_c),A) )],[refute_0_69,refute_0_72]) ).
cnf(refute_0_74,plain,
ld(op_c,mult(X_28,op_c)) = X_28,
inference(subst,[],[refute_0_73:[bind(A,$fot(X_28))]]) ).
cnf(refute_0_75,plain,
rd(mult(X_28,op_c),op_c) = ld(op_c,mult(X_28,op_c)),
inference(subst,[],[refute_0_45:[bind(X_14,$fot(mult(X_28,op_c)))]]) ).
cnf(refute_0_76,plain,
( ld(op_c,mult(X_28,op_c)) != X_28
| rd(mult(X_28,op_c),op_c) != ld(op_c,mult(X_28,op_c))
| rd(mult(X_28,op_c),op_c) = X_28 ),
inference(subst,[],[refute_0_48:[bind(X,$fot(rd(mult(X_28,op_c),op_c))),bind(Y,$fot(ld(op_c,mult(X_28,op_c)))),bind(Z,$fot(X_28))]]) ).
cnf(refute_0_77,plain,
( ld(op_c,mult(X_28,op_c)) != X_28
| rd(mult(X_28,op_c),op_c) = X_28 ),
inference(resolve,[$cnf( $equal(rd(mult(X_28,op_c),op_c),ld(op_c,mult(X_28,op_c))) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
rd(mult(X_28,op_c),op_c) = X_28,
inference(resolve,[$cnf( $equal(ld(op_c,mult(X_28,op_c)),X_28) )],[refute_0_74,refute_0_77]) ).
cnf(refute_0_79,plain,
mult(rd(mult(X_28,op_c),op_c),mult(op_c,X_29)) = mult(rd(mult(X_28,op_c),op_c),mult(op_c,X_29)),
introduced(tautology,[refl,[$fot(mult(rd(mult(X_28,op_c),op_c),mult(op_c,X_29)))]]) ).
cnf(refute_0_80,plain,
( mult(rd(mult(X_28,op_c),op_c),mult(op_c,X_29)) != mult(rd(mult(X_28,op_c),op_c),mult(op_c,X_29))
| rd(mult(X_28,op_c),op_c) != X_28
| mult(rd(mult(X_28,op_c),op_c),mult(op_c,X_29)) = mult(X_28,mult(op_c,X_29)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(rd(mult(X_28,op_c),op_c),mult(op_c,X_29)),mult(rd(mult(X_28,op_c),op_c),mult(op_c,X_29))) ),[1,0],$fot(X_28)]]) ).
cnf(refute_0_81,plain,
( rd(mult(X_28,op_c),op_c) != X_28
| mult(rd(mult(X_28,op_c),op_c),mult(op_c,X_29)) = mult(X_28,mult(op_c,X_29)) ),
inference(resolve,[$cnf( $equal(mult(rd(mult(X_28,op_c),op_c),mult(op_c,X_29)),mult(rd(mult(X_28,op_c),op_c),mult(op_c,X_29))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
mult(rd(mult(X_28,op_c),op_c),mult(op_c,X_29)) = mult(X_28,mult(op_c,X_29)),
inference(resolve,[$cnf( $equal(rd(mult(X_28,op_c),op_c),X_28) )],[refute_0_78,refute_0_81]) ).
cnf(refute_0_83,plain,
( mult(op_c,mult(X_28,X_29)) != mult(rd(mult(X_28,op_c),op_c),mult(op_c,X_29))
| mult(rd(mult(X_28,op_c),op_c),mult(op_c,X_29)) != mult(X_28,mult(op_c,X_29))
| mult(op_c,mult(X_28,X_29)) = mult(X_28,mult(op_c,X_29)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(op_c,mult(X_28,X_29)),mult(X_28,mult(op_c,X_29))) ),[0],$fot(mult(rd(mult(X_28,op_c),op_c),mult(op_c,X_29)))]]) ).
cnf(refute_0_84,plain,
( mult(op_c,mult(X_28,X_29)) != mult(rd(mult(X_28,op_c),op_c),mult(op_c,X_29))
| mult(op_c,mult(X_28,X_29)) = mult(X_28,mult(op_c,X_29)) ),
inference(resolve,[$cnf( $equal(mult(rd(mult(X_28,op_c),op_c),mult(op_c,X_29)),mult(X_28,mult(op_c,X_29))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
mult(op_c,mult(X_28,X_29)) = mult(X_28,mult(op_c,X_29)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(X_28,X_29)),mult(rd(mult(X_28,op_c),op_c),mult(op_c,X_29))) )],[refute_0_68,refute_0_84]) ).
cnf(refute_0_86,plain,
mult(op_c,mult(X_32,X_33)) = mult(X_32,mult(op_c,X_33)),
inference(subst,[],[refute_0_85:[bind(X_28,$fot(X_32)),bind(X_29,$fot(X_33))]]) ).
cnf(refute_0_87,plain,
( ld(op_c,mult(op_c,mult(X_32,X_33))) != mult(X_32,X_33)
| mult(op_c,mult(X_32,X_33)) != mult(X_32,mult(op_c,X_33))
| ld(op_c,mult(X_32,mult(op_c,X_33))) = mult(X_32,X_33) ),
introduced(tautology,[equality,[$cnf( $equal(ld(op_c,mult(op_c,mult(X_32,X_33))),mult(X_32,X_33)) ),[0,1],$fot(mult(X_32,mult(op_c,X_33)))]]) ).
cnf(refute_0_88,plain,
( ld(op_c,mult(op_c,mult(X_32,X_33))) != mult(X_32,X_33)
| ld(op_c,mult(X_32,mult(op_c,X_33))) = mult(X_32,X_33) ),
inference(resolve,[$cnf( $equal(mult(op_c,mult(X_32,X_33)),mult(X_32,mult(op_c,X_33))) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
ld(op_c,mult(X_32,mult(op_c,X_33))) = mult(X_32,X_33),
inference(resolve,[$cnf( $equal(ld(op_c,mult(op_c,mult(X_32,X_33))),mult(X_32,X_33)) )],[refute_0_64,refute_0_88]) ).
cnf(refute_0_90,plain,
ld(op_c,mult(X_41,mult(op_c,ld(op_c,B)))) = mult(X_41,ld(op_c,B)),
inference(subst,[],[refute_0_89:[bind(X_32,$fot(X_41)),bind(X_33,$fot(ld(op_c,B)))]]) ).
cnf(refute_0_91,plain,
mult(op_c,ld(op_c,B)) = B,
inference(subst,[],[refute_0_8:[bind(A,$fot(op_c))]]) ).
cnf(refute_0_92,plain,
( ld(op_c,mult(X_41,mult(op_c,ld(op_c,B)))) != mult(X_41,ld(op_c,B))
| mult(op_c,ld(op_c,B)) != B
| ld(op_c,mult(X_41,B)) = mult(X_41,ld(op_c,B)) ),
introduced(tautology,[equality,[$cnf( $equal(ld(op_c,mult(X_41,mult(op_c,ld(op_c,B)))),mult(X_41,ld(op_c,B))) ),[0,1,1],$fot(B)]]) ).
cnf(refute_0_93,plain,
( ld(op_c,mult(X_41,mult(op_c,ld(op_c,B)))) != mult(X_41,ld(op_c,B))
| ld(op_c,mult(X_41,B)) = mult(X_41,ld(op_c,B)) ),
inference(resolve,[$cnf( $equal(mult(op_c,ld(op_c,B)),B) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
ld(op_c,mult(X_41,B)) = mult(X_41,ld(op_c,B)),
inference(resolve,[$cnf( $equal(ld(op_c,mult(X_41,mult(op_c,ld(op_c,B)))),mult(X_41,ld(op_c,B))) )],[refute_0_90,refute_0_93]) ).
cnf(refute_0_95,plain,
( ld(op_c,mult(X_41,B)) != mult(X_41,ld(op_c,B))
| mult(X_41,ld(op_c,B)) = ld(op_c,mult(X_41,B)) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(ld(op_c,mult(X_41,B)))),bind(Y,$fot(mult(X_41,ld(op_c,B))))]]) ).
cnf(refute_0_96,plain,
mult(X_41,ld(op_c,B)) = ld(op_c,mult(X_41,B)),
inference(resolve,[$cnf( $equal(ld(op_c,mult(X_41,B)),mult(X_41,ld(op_c,B))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
mult(mult(X_60,op_c),ld(op_c,mult(X_61,op_c))) = ld(op_c,mult(mult(X_60,op_c),mult(X_61,op_c))),
inference(subst,[],[refute_0_96:[bind(B,$fot(mult(X_61,op_c))),bind(X_41,$fot(mult(X_60,op_c)))]]) ).
cnf(refute_0_98,plain,
( ld(op_c,mult(mult(X_60,op_c),mult(X_61,op_c))) != mult(mult(X_60,op_c),X_61)
| mult(mult(X_60,op_c),ld(op_c,mult(X_61,op_c))) != ld(op_c,mult(mult(X_60,op_c),mult(X_61,op_c)))
| mult(mult(X_60,op_c),ld(op_c,mult(X_61,op_c))) = mult(mult(X_60,op_c),X_61) ),
inference(subst,[],[refute_0_48:[bind(X,$fot(mult(mult(X_60,op_c),ld(op_c,mult(X_61,op_c))))),bind(Y,$fot(ld(op_c,mult(mult(X_60,op_c),mult(X_61,op_c))))),bind(Z,$fot(mult(mult(X_60,op_c),X_61)))]]) ).
cnf(refute_0_99,plain,
( ld(op_c,mult(mult(X_60,op_c),mult(X_61,op_c))) != mult(mult(X_60,op_c),X_61)
| mult(mult(X_60,op_c),ld(op_c,mult(X_61,op_c))) = mult(mult(X_60,op_c),X_61) ),
inference(resolve,[$cnf( $equal(mult(mult(X_60,op_c),ld(op_c,mult(X_61,op_c))),ld(op_c,mult(mult(X_60,op_c),mult(X_61,op_c)))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
mult(mult(X_60,op_c),ld(op_c,mult(X_61,op_c))) = mult(mult(X_60,op_c),X_61),
inference(resolve,[$cnf( $equal(ld(op_c,mult(mult(X_60,op_c),mult(X_61,op_c))),mult(mult(X_60,op_c),X_61)) )],[refute_0_63,refute_0_99]) ).
cnf(refute_0_101,plain,
( mult(mult(X_60,op_c),ld(op_c,mult(X_61,op_c))) != mult(mult(X_60,op_c),X_61)
| mult(op_c,mult(X_60,X_61)) != mult(mult(X_60,op_c),ld(op_c,mult(X_61,op_c)))
| mult(op_c,mult(X_60,X_61)) = mult(mult(X_60,op_c),X_61) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_c,mult(X_60,X_61)),mult(mult(X_60,op_c),ld(op_c,mult(X_61,op_c)))) ),[1],$fot(mult(mult(X_60,op_c),X_61))]]) ).
cnf(refute_0_102,plain,
( mult(op_c,mult(X_60,X_61)) != mult(mult(X_60,op_c),ld(op_c,mult(X_61,op_c)))
| mult(op_c,mult(X_60,X_61)) = mult(mult(X_60,op_c),X_61) ),
inference(resolve,[$cnf( $equal(mult(mult(X_60,op_c),ld(op_c,mult(X_61,op_c))),mult(mult(X_60,op_c),X_61)) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
mult(op_c,mult(X_60,X_61)) = mult(mult(X_60,op_c),X_61),
inference(resolve,[$cnf( $equal(mult(op_c,mult(X_60,X_61)),mult(mult(X_60,op_c),ld(op_c,mult(X_61,op_c)))) )],[refute_0_23,refute_0_102]) ).
cnf(refute_0_104,plain,
( mult(op_c,mult(X_60,X_61)) != mult(mult(X_60,op_c),X_61)
| mult(mult(X_60,op_c),X_61) = mult(op_c,mult(X_60,X_61)) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(mult(op_c,mult(X_60,X_61)))),bind(Y,$fot(mult(mult(X_60,op_c),X_61)))]]) ).
cnf(refute_0_105,plain,
mult(mult(X_60,op_c),X_61) = mult(op_c,mult(X_60,X_61)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(X_60,X_61)),mult(mult(X_60,op_c),X_61)) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
mult(mult(X_62,op_c),ld(X_62,mult(X_61,X_62))) = mult(op_c,mult(X_62,ld(X_62,mult(X_61,X_62)))),
inference(subst,[],[refute_0_105:[bind(X_60,$fot(X_62)),bind(X_61,$fot(ld(X_62,mult(X_61,X_62))))]]) ).
cnf(refute_0_107,plain,
( mult(mult(X_62,op_c),ld(X_62,mult(X_61,X_62))) != mult(op_c,mult(X_62,ld(X_62,mult(X_61,X_62))))
| mult(op_c,mult(X_62,ld(X_62,mult(X_61,X_62)))) != mult(op_c,mult(X_61,X_62))
| mult(mult(X_62,op_c),ld(X_62,mult(X_61,X_62))) = mult(op_c,mult(X_61,X_62)) ),
inference(subst,[],[refute_0_48:[bind(X,$fot(mult(mult(X_62,op_c),ld(X_62,mult(X_61,X_62))))),bind(Y,$fot(mult(op_c,mult(X_62,ld(X_62,mult(X_61,X_62)))))),bind(Z,$fot(mult(op_c,mult(X_61,X_62))))]]) ).
cnf(refute_0_108,plain,
( mult(op_c,mult(X_62,ld(X_62,mult(X_61,X_62)))) != mult(op_c,mult(X_61,X_62))
| mult(mult(X_62,op_c),ld(X_62,mult(X_61,X_62))) = mult(op_c,mult(X_61,X_62)) ),
inference(resolve,[$cnf( $equal(mult(mult(X_62,op_c),ld(X_62,mult(X_61,X_62))),mult(op_c,mult(X_62,ld(X_62,mult(X_61,X_62))))) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
mult(mult(X_62,op_c),ld(X_62,mult(X_61,X_62))) = mult(op_c,mult(X_61,X_62)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(X_62,ld(X_62,mult(X_61,X_62)))),mult(op_c,mult(X_61,X_62))) )],[refute_0_13,refute_0_108]) ).
cnf(refute_0_110,plain,
( mult(mult(X_62,op_c),ld(X_62,mult(X_61,X_62))) != mult(op_c,mult(X_61,X_62))
| mult(mult(op_c,X_61),X_62) != mult(mult(X_62,op_c),ld(X_62,mult(X_61,X_62)))
| mult(mult(op_c,X_61),X_62) = mult(op_c,mult(X_61,X_62)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(op_c,X_61),X_62),mult(mult(X_62,op_c),ld(X_62,mult(X_61,X_62)))) ),[1],$fot(mult(op_c,mult(X_61,X_62)))]]) ).
cnf(refute_0_111,plain,
( mult(mult(op_c,X_61),X_62) != mult(mult(X_62,op_c),ld(X_62,mult(X_61,X_62)))
| mult(mult(op_c,X_61),X_62) = mult(op_c,mult(X_61,X_62)) ),
inference(resolve,[$cnf( $equal(mult(mult(X_62,op_c),ld(X_62,mult(X_61,X_62))),mult(op_c,mult(X_61,X_62))) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
mult(mult(op_c,X_61),X_62) = mult(op_c,mult(X_61,X_62)),
inference(resolve,[$cnf( $equal(mult(mult(op_c,X_61),X_62),mult(mult(X_62,op_c),ld(X_62,mult(X_61,X_62)))) )],[refute_0_7,refute_0_111]) ).
cnf(refute_0_113,plain,
mult(mult(op_c,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) = mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),
inference(subst,[],[refute_0_112:[bind(X_61,$fot(skolemFOFtoCNF_X0)),bind(X_62,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_114,plain,
( mult(mult(op_c,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) != mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = mult(mult(op_c,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),mult(mult(op_c,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)) ),[1],$fot(mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_115,plain,
( mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = mult(mult(op_c,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) ),
inference(resolve,[$cnf( $equal(mult(mult(op_c,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1),mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),mult(mult(op_c,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)) )],[refute_0_115,refute_0_0]) ).
cnf(refute_0_117,plain,
mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),
introduced(tautology,[refl,[$fot(mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_118,plain,
$false,
inference(resolve,[$cnf( $equal(mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) )],[refute_0_117,refute_0_116]) ).
fof(negate_1_0,plain,
~ ! [X0,X1] :
( mult(op_c,mult(X0,X1)) = mult(mult(op_c,X0),X1)
=> mult(mult(X0,op_c),X1) = mult(X0,mult(op_c,X1)) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [X0,X1] :
( mult(mult(X0,op_c),X1) != mult(X0,mult(op_c,X1))
& mult(op_c,mult(X0,X1)) = mult(mult(op_c,X0),X1) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( mult(mult(skolemFOFtoCNF_X0_1,op_c),skolemFOFtoCNF_X1_1) != mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1))
& mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)) = mult(mult(op_c,skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_1) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
mult(mult(skolemFOFtoCNF_X0_1,op_c),skolemFOFtoCNF_X1_1) != mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1)),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)) = mult(mult(op_c,skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_1),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_4,plain,
! [A] : mult(op_c,A) = mult(A,op_c),
inference(canonicalize,[],[f09]) ).
fof(normalize_1_5,plain,
! [A] : mult(op_c,A) = mult(A,op_c),
inference(specialize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [A,B,C] : mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)),
inference(canonicalize,[],[f07]) ).
fof(normalize_1_7,plain,
! [A,B,C] : mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)),
inference(specialize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
! [A,B] : ld(A,mult(A,B)) = B,
inference(canonicalize,[],[f02]) ).
fof(normalize_1_9,plain,
! [A,B] : ld(A,mult(A,B)) = B,
inference(specialize,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
! [A,B] : mult(rd(A,B),B) = A,
inference(canonicalize,[],[f03]) ).
fof(normalize_1_11,plain,
! [A,B] : mult(rd(A,B),B) = A,
inference(specialize,[],[normalize_1_10]) ).
cnf(refute_1_0,plain,
mult(mult(skolemFOFtoCNF_X0_1,op_c),skolemFOFtoCNF_X1_1) != mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1)),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)) = mult(mult(op_c,skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_1),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_2,refute_1_3]) ).
cnf(refute_1_5,plain,
( mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)) != mult(mult(op_c,skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_1)
| mult(mult(op_c,skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_1) = mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)) ),
inference(subst,[],[refute_1_4:[bind(X,$fot(mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)))),bind(Y,$fot(mult(mult(op_c,skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_1_6,plain,
mult(mult(op_c,skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_1) = mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)),mult(mult(op_c,skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_1)) )],[refute_1_1,refute_1_5]) ).
cnf(refute_1_7,plain,
mult(op_c,A) = mult(A,op_c),
inference(canonicalize,[],[normalize_1_5]) ).
cnf(refute_1_8,plain,
( mult(op_c,A) != mult(A,op_c)
| mult(A,op_c) = mult(op_c,A) ),
inference(subst,[],[refute_1_4:[bind(X,$fot(mult(op_c,A))),bind(Y,$fot(mult(A,op_c)))]]) ).
cnf(refute_1_9,plain,
mult(A,op_c) = mult(op_c,A),
inference(resolve,[$cnf( $equal(mult(op_c,A),mult(A,op_c)) )],[refute_1_7,refute_1_8]) ).
cnf(refute_1_10,plain,
mult(skolemFOFtoCNF_X0_1,op_c) = mult(op_c,skolemFOFtoCNF_X0_1),
inference(subst,[],[refute_1_9:[bind(A,$fot(skolemFOFtoCNF_X0_1))]]) ).
cnf(refute_1_11,plain,
mult(mult(skolemFOFtoCNF_X0_1,op_c),skolemFOFtoCNF_X1_1) = mult(mult(skolemFOFtoCNF_X0_1,op_c),skolemFOFtoCNF_X1_1),
introduced(tautology,[refl,[$fot(mult(mult(skolemFOFtoCNF_X0_1,op_c),skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_1_12,plain,
( mult(mult(skolemFOFtoCNF_X0_1,op_c),skolemFOFtoCNF_X1_1) != mult(mult(skolemFOFtoCNF_X0_1,op_c),skolemFOFtoCNF_X1_1)
| mult(skolemFOFtoCNF_X0_1,op_c) != mult(op_c,skolemFOFtoCNF_X0_1)
| mult(mult(skolemFOFtoCNF_X0_1,op_c),skolemFOFtoCNF_X1_1) = mult(mult(op_c,skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_1) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X0_1,op_c),skolemFOFtoCNF_X1_1),mult(mult(skolemFOFtoCNF_X0_1,op_c),skolemFOFtoCNF_X1_1)) ),[1,0],$fot(mult(op_c,skolemFOFtoCNF_X0_1))]]) ).
cnf(refute_1_13,plain,
( mult(skolemFOFtoCNF_X0_1,op_c) != mult(op_c,skolemFOFtoCNF_X0_1)
| mult(mult(skolemFOFtoCNF_X0_1,op_c),skolemFOFtoCNF_X1_1) = mult(mult(op_c,skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_1) ),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X0_1,op_c),skolemFOFtoCNF_X1_1),mult(mult(skolemFOFtoCNF_X0_1,op_c),skolemFOFtoCNF_X1_1)) )],[refute_1_11,refute_1_12]) ).
cnf(refute_1_14,plain,
mult(mult(skolemFOFtoCNF_X0_1,op_c),skolemFOFtoCNF_X1_1) = mult(mult(op_c,skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_1),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X0_1,op_c),mult(op_c,skolemFOFtoCNF_X0_1)) )],[refute_1_10,refute_1_13]) ).
cnf(refute_1_15,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_1_16,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_1_4,refute_1_15]) ).
cnf(refute_1_17,plain,
( mult(mult(op_c,skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_1) != mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1))
| mult(mult(skolemFOFtoCNF_X0_1,op_c),skolemFOFtoCNF_X1_1) != mult(mult(op_c,skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_1)
| mult(mult(skolemFOFtoCNF_X0_1,op_c),skolemFOFtoCNF_X1_1) = mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)) ),
inference(subst,[],[refute_1_16:[bind(X,$fot(mult(mult(skolemFOFtoCNF_X0_1,op_c),skolemFOFtoCNF_X1_1))),bind(Y,$fot(mult(mult(op_c,skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_1))),bind(Z,$fot(mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1))))]]) ).
cnf(refute_1_18,plain,
( mult(mult(op_c,skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_1) != mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1))
| mult(mult(skolemFOFtoCNF_X0_1,op_c),skolemFOFtoCNF_X1_1) = mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)) ),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X0_1,op_c),skolemFOFtoCNF_X1_1),mult(mult(op_c,skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_1)) )],[refute_1_14,refute_1_17]) ).
cnf(refute_1_19,plain,
mult(mult(skolemFOFtoCNF_X0_1,op_c),skolemFOFtoCNF_X1_1) = mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)),
inference(resolve,[$cnf( $equal(mult(mult(op_c,skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_1),mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1))) )],[refute_1_6,refute_1_18]) ).
cnf(refute_1_20,plain,
( mult(mult(skolemFOFtoCNF_X0_1,op_c),skolemFOFtoCNF_X1_1) != mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1))
| mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)) != mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1))
| mult(mult(skolemFOFtoCNF_X0_1,op_c),skolemFOFtoCNF_X1_1) = mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(mult(skolemFOFtoCNF_X0_1,op_c),skolemFOFtoCNF_X1_1),mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1))) ),[0],$fot(mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_1_21,plain,
( mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)) != mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1))
| mult(mult(skolemFOFtoCNF_X0_1,op_c),skolemFOFtoCNF_X1_1) = mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1)) ),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X0_1,op_c),skolemFOFtoCNF_X1_1),mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1))) )],[refute_1_19,refute_1_20]) ).
cnf(refute_1_22,plain,
mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)) != mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1)),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X0_1,op_c),skolemFOFtoCNF_X1_1),mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1))) )],[refute_1_21,refute_1_0]) ).
cnf(refute_1_23,plain,
mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_24,plain,
mult(op_c,mult(X_94,X_95)) = mult(rd(mult(op_c,X_94),op_c),mult(op_c,X_95)),
inference(subst,[],[refute_1_23:[bind(A,$fot(op_c)),bind(B,$fot(X_94)),bind(C,$fot(X_95))]]) ).
cnf(refute_1_25,plain,
mult(op_c,X_94) = mult(X_94,op_c),
inference(subst,[],[refute_1_7:[bind(A,$fot(X_94))]]) ).
cnf(refute_1_26,plain,
( mult(op_c,X_94) != mult(X_94,op_c)
| mult(op_c,mult(X_94,X_95)) != mult(rd(mult(op_c,X_94),op_c),mult(op_c,X_95))
| mult(op_c,mult(X_94,X_95)) = mult(rd(mult(X_94,op_c),op_c),mult(op_c,X_95)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_c,mult(X_94,X_95)),mult(rd(mult(op_c,X_94),op_c),mult(op_c,X_95))) ),[1,0,0],$fot(mult(X_94,op_c))]]) ).
cnf(refute_1_27,plain,
( mult(op_c,mult(X_94,X_95)) != mult(rd(mult(op_c,X_94),op_c),mult(op_c,X_95))
| mult(op_c,mult(X_94,X_95)) = mult(rd(mult(X_94,op_c),op_c),mult(op_c,X_95)) ),
inference(resolve,[$cnf( $equal(mult(op_c,X_94),mult(X_94,op_c)) )],[refute_1_25,refute_1_26]) ).
cnf(refute_1_28,plain,
mult(op_c,mult(X_94,X_95)) = mult(rd(mult(X_94,op_c),op_c),mult(op_c,X_95)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(X_94,X_95)),mult(rd(mult(op_c,X_94),op_c),mult(op_c,X_95))) )],[refute_1_24,refute_1_27]) ).
cnf(refute_1_29,plain,
ld(A,mult(A,B)) = B,
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_30,plain,
ld(op_c,mult(op_c,X_74)) = X_74,
inference(subst,[],[refute_1_29:[bind(A,$fot(op_c)),bind(B,$fot(X_74))]]) ).
cnf(refute_1_31,plain,
mult(op_c,X_74) = mult(X_74,op_c),
inference(subst,[],[refute_1_7:[bind(A,$fot(X_74))]]) ).
cnf(refute_1_32,plain,
( ld(op_c,mult(op_c,X_74)) != X_74
| mult(op_c,X_74) != mult(X_74,op_c)
| ld(op_c,mult(X_74,op_c)) = X_74 ),
introduced(tautology,[equality,[$cnf( $equal(ld(op_c,mult(op_c,X_74)),X_74) ),[0,1],$fot(mult(X_74,op_c))]]) ).
cnf(refute_1_33,plain,
( ld(op_c,mult(op_c,X_74)) != X_74
| ld(op_c,mult(X_74,op_c)) = X_74 ),
inference(resolve,[$cnf( $equal(mult(op_c,X_74),mult(X_74,op_c)) )],[refute_1_31,refute_1_32]) ).
cnf(refute_1_34,plain,
ld(op_c,mult(X_74,op_c)) = X_74,
inference(resolve,[$cnf( $equal(ld(op_c,mult(op_c,X_74)),X_74) )],[refute_1_30,refute_1_33]) ).
cnf(refute_1_35,plain,
ld(op_c,mult(X_94,op_c)) = X_94,
inference(subst,[],[refute_1_34:[bind(X_74,$fot(X_94))]]) ).
cnf(refute_1_36,plain,
ld(op_c,mult(op_c,rd(X_69,op_c))) = rd(X_69,op_c),
inference(subst,[],[refute_1_29:[bind(A,$fot(op_c)),bind(B,$fot(rd(X_69,op_c)))]]) ).
cnf(refute_1_37,plain,
mult(op_c,rd(X_69,op_c)) = mult(rd(X_69,op_c),op_c),
inference(subst,[],[refute_1_7:[bind(A,$fot(rd(X_69,op_c)))]]) ).
cnf(refute_1_38,plain,
mult(rd(A,B),B) = A,
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_39,plain,
mult(rd(X_69,op_c),op_c) = X_69,
inference(subst,[],[refute_1_38:[bind(A,$fot(X_69)),bind(B,$fot(op_c))]]) ).
cnf(refute_1_40,plain,
( mult(op_c,rd(X_69,op_c)) != mult(rd(X_69,op_c),op_c)
| mult(rd(X_69,op_c),op_c) != X_69
| mult(op_c,rd(X_69,op_c)) = X_69 ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(op_c,rd(X_69,op_c)),X_69) ),[0],$fot(mult(rd(X_69,op_c),op_c))]]) ).
cnf(refute_1_41,plain,
( mult(op_c,rd(X_69,op_c)) != mult(rd(X_69,op_c),op_c)
| mult(op_c,rd(X_69,op_c)) = X_69 ),
inference(resolve,[$cnf( $equal(mult(rd(X_69,op_c),op_c),X_69) )],[refute_1_39,refute_1_40]) ).
cnf(refute_1_42,plain,
mult(op_c,rd(X_69,op_c)) = X_69,
inference(resolve,[$cnf( $equal(mult(op_c,rd(X_69,op_c)),mult(rd(X_69,op_c),op_c)) )],[refute_1_37,refute_1_41]) ).
cnf(refute_1_43,plain,
( ld(op_c,mult(op_c,rd(X_69,op_c))) != rd(X_69,op_c)
| mult(op_c,rd(X_69,op_c)) != X_69
| ld(op_c,X_69) = rd(X_69,op_c) ),
introduced(tautology,[equality,[$cnf( $equal(ld(op_c,mult(op_c,rd(X_69,op_c))),rd(X_69,op_c)) ),[0,1],$fot(X_69)]]) ).
cnf(refute_1_44,plain,
( ld(op_c,mult(op_c,rd(X_69,op_c))) != rd(X_69,op_c)
| ld(op_c,X_69) = rd(X_69,op_c) ),
inference(resolve,[$cnf( $equal(mult(op_c,rd(X_69,op_c)),X_69) )],[refute_1_42,refute_1_43]) ).
cnf(refute_1_45,plain,
ld(op_c,X_69) = rd(X_69,op_c),
inference(resolve,[$cnf( $equal(ld(op_c,mult(op_c,rd(X_69,op_c))),rd(X_69,op_c)) )],[refute_1_36,refute_1_44]) ).
cnf(refute_1_46,plain,
( ld(op_c,X_69) != rd(X_69,op_c)
| rd(X_69,op_c) = ld(op_c,X_69) ),
inference(subst,[],[refute_1_4:[bind(X,$fot(ld(op_c,X_69))),bind(Y,$fot(rd(X_69,op_c)))]]) ).
cnf(refute_1_47,plain,
rd(X_69,op_c) = ld(op_c,X_69),
inference(resolve,[$cnf( $equal(ld(op_c,X_69),rd(X_69,op_c)) )],[refute_1_45,refute_1_46]) ).
cnf(refute_1_48,plain,
rd(mult(X_94,op_c),op_c) = ld(op_c,mult(X_94,op_c)),
inference(subst,[],[refute_1_47:[bind(X_69,$fot(mult(X_94,op_c)))]]) ).
cnf(refute_1_49,plain,
( ld(op_c,mult(X_94,op_c)) != X_94
| rd(mult(X_94,op_c),op_c) != ld(op_c,mult(X_94,op_c))
| rd(mult(X_94,op_c),op_c) = X_94 ),
inference(subst,[],[refute_1_16:[bind(X,$fot(rd(mult(X_94,op_c),op_c))),bind(Y,$fot(ld(op_c,mult(X_94,op_c)))),bind(Z,$fot(X_94))]]) ).
cnf(refute_1_50,plain,
( ld(op_c,mult(X_94,op_c)) != X_94
| rd(mult(X_94,op_c),op_c) = X_94 ),
inference(resolve,[$cnf( $equal(rd(mult(X_94,op_c),op_c),ld(op_c,mult(X_94,op_c))) )],[refute_1_48,refute_1_49]) ).
cnf(refute_1_51,plain,
rd(mult(X_94,op_c),op_c) = X_94,
inference(resolve,[$cnf( $equal(ld(op_c,mult(X_94,op_c)),X_94) )],[refute_1_35,refute_1_50]) ).
cnf(refute_1_52,plain,
mult(rd(mult(X_94,op_c),op_c),mult(op_c,X_95)) = mult(rd(mult(X_94,op_c),op_c),mult(op_c,X_95)),
introduced(tautology,[refl,[$fot(mult(rd(mult(X_94,op_c),op_c),mult(op_c,X_95)))]]) ).
cnf(refute_1_53,plain,
( mult(rd(mult(X_94,op_c),op_c),mult(op_c,X_95)) != mult(rd(mult(X_94,op_c),op_c),mult(op_c,X_95))
| rd(mult(X_94,op_c),op_c) != X_94
| mult(rd(mult(X_94,op_c),op_c),mult(op_c,X_95)) = mult(X_94,mult(op_c,X_95)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(rd(mult(X_94,op_c),op_c),mult(op_c,X_95)),mult(rd(mult(X_94,op_c),op_c),mult(op_c,X_95))) ),[1,0],$fot(X_94)]]) ).
cnf(refute_1_54,plain,
( rd(mult(X_94,op_c),op_c) != X_94
| mult(rd(mult(X_94,op_c),op_c),mult(op_c,X_95)) = mult(X_94,mult(op_c,X_95)) ),
inference(resolve,[$cnf( $equal(mult(rd(mult(X_94,op_c),op_c),mult(op_c,X_95)),mult(rd(mult(X_94,op_c),op_c),mult(op_c,X_95))) )],[refute_1_52,refute_1_53]) ).
cnf(refute_1_55,plain,
mult(rd(mult(X_94,op_c),op_c),mult(op_c,X_95)) = mult(X_94,mult(op_c,X_95)),
inference(resolve,[$cnf( $equal(rd(mult(X_94,op_c),op_c),X_94) )],[refute_1_51,refute_1_54]) ).
cnf(refute_1_56,plain,
( mult(op_c,mult(X_94,X_95)) != mult(rd(mult(X_94,op_c),op_c),mult(op_c,X_95))
| mult(rd(mult(X_94,op_c),op_c),mult(op_c,X_95)) != mult(X_94,mult(op_c,X_95))
| mult(op_c,mult(X_94,X_95)) = mult(X_94,mult(op_c,X_95)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(op_c,mult(X_94,X_95)),mult(X_94,mult(op_c,X_95))) ),[0],$fot(mult(rd(mult(X_94,op_c),op_c),mult(op_c,X_95)))]]) ).
cnf(refute_1_57,plain,
( mult(op_c,mult(X_94,X_95)) != mult(rd(mult(X_94,op_c),op_c),mult(op_c,X_95))
| mult(op_c,mult(X_94,X_95)) = mult(X_94,mult(op_c,X_95)) ),
inference(resolve,[$cnf( $equal(mult(rd(mult(X_94,op_c),op_c),mult(op_c,X_95)),mult(X_94,mult(op_c,X_95))) )],[refute_1_55,refute_1_56]) ).
cnf(refute_1_58,plain,
mult(op_c,mult(X_94,X_95)) = mult(X_94,mult(op_c,X_95)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(X_94,X_95)),mult(rd(mult(X_94,op_c),op_c),mult(op_c,X_95))) )],[refute_1_28,refute_1_57]) ).
cnf(refute_1_59,plain,
( mult(op_c,mult(X_94,X_95)) != mult(X_94,mult(op_c,X_95))
| mult(X_94,mult(op_c,X_95)) = mult(op_c,mult(X_94,X_95)) ),
inference(subst,[],[refute_1_4:[bind(X,$fot(mult(op_c,mult(X_94,X_95)))),bind(Y,$fot(mult(X_94,mult(op_c,X_95))))]]) ).
cnf(refute_1_60,plain,
mult(X_94,mult(op_c,X_95)) = mult(op_c,mult(X_94,X_95)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(X_94,X_95)),mult(X_94,mult(op_c,X_95))) )],[refute_1_58,refute_1_59]) ).
cnf(refute_1_61,plain,
mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1)) = mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)),
inference(subst,[],[refute_1_60:[bind(X_94,$fot(skolemFOFtoCNF_X0_1)),bind(X_95,$fot(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_1_62,plain,
( mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)) != mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1))
| mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1)) != mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1))
| mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)) = mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)),mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1))) ),[1],$fot(mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_1_63,plain,
( mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)) != mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1))
| mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)) = mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1)) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1)),mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1))) )],[refute_1_61,refute_1_62]) ).
cnf(refute_1_64,plain,
mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)) != mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)),mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1))) )],[refute_1_63,refute_1_22]) ).
cnf(refute_1_65,plain,
mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)) = mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)),
introduced(tautology,[refl,[$fot(mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_1_66,plain,
$false,
inference(resolve,[$cnf( $equal(mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)),mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1))) )],[refute_1_65,refute_1_64]) ).
fof(negate_2_0,plain,
~ ! [X0,X1] :
( ( mult(op_c,mult(X0,X1)) = mult(mult(op_c,X0),X1)
& mult(mult(X0,op_c),X1) = mult(X0,mult(op_c,X1)) )
=> mult(mult(X0,X1),op_c) = mult(X0,mult(X1,op_c)) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
? [X0,X1] :
( mult(mult(X0,X1),op_c) != mult(X0,mult(X1,op_c))
& mult(mult(X0,op_c),X1) = mult(X0,mult(op_c,X1))
& mult(op_c,mult(X0,X1)) = mult(mult(op_c,X0),X1) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_1,plain,
( mult(mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2),op_c) != mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c))
& mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2) = mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2))
& mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)) = mult(mult(op_c,skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X1_2) ),
inference(skolemize,[],[normalize_2_0]) ).
fof(normalize_2_2,plain,
mult(mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2),op_c) != mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c)),
inference(conjunct,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
! [A] : mult(op_c,A) = mult(A,op_c),
inference(canonicalize,[],[f09]) ).
fof(normalize_2_4,plain,
! [A] : mult(op_c,A) = mult(A,op_c),
inference(specialize,[],[normalize_2_3]) ).
fof(normalize_2_5,plain,
mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)) = mult(mult(op_c,skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X1_2),
inference(conjunct,[],[normalize_2_1]) ).
fof(normalize_2_6,plain,
mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2) = mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)),
inference(conjunct,[],[normalize_2_1]) ).
cnf(refute_2_0,plain,
mult(mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2),op_c) != mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c)),
inference(canonicalize,[],[normalize_2_2]) ).
cnf(refute_2_1,plain,
mult(op_c,A) = mult(A,op_c),
inference(canonicalize,[],[normalize_2_4]) ).
cnf(refute_2_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_2_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_2_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_2_2,refute_2_3]) ).
cnf(refute_2_5,plain,
( mult(op_c,A) != mult(A,op_c)
| mult(A,op_c) = mult(op_c,A) ),
inference(subst,[],[refute_2_4:[bind(X,$fot(mult(op_c,A))),bind(Y,$fot(mult(A,op_c)))]]) ).
cnf(refute_2_6,plain,
mult(A,op_c) = mult(op_c,A),
inference(resolve,[$cnf( $equal(mult(op_c,A),mult(A,op_c)) )],[refute_2_1,refute_2_5]) ).
cnf(refute_2_7,plain,
mult(mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2),op_c) = mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)),
inference(subst,[],[refute_2_6:[bind(A,$fot(mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)))]]) ).
cnf(refute_2_8,plain,
( mult(mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2),op_c) != mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2))
| mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)) != mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c))
| mult(mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2),op_c) = mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2),op_c),mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c))) ),[0],$fot(mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)))]]) ).
cnf(refute_2_9,plain,
( mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)) != mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c))
| mult(mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2),op_c) = mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c)) ),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2),op_c),mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2))) )],[refute_2_7,refute_2_8]) ).
cnf(refute_2_10,plain,
mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)) = mult(mult(op_c,skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X1_2),
inference(canonicalize,[],[normalize_2_5]) ).
cnf(refute_2_11,plain,
mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2) = mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)),
inference(canonicalize,[],[normalize_2_6]) ).
cnf(refute_2_12,plain,
mult(skolemFOFtoCNF_X0_2,op_c) = mult(op_c,skolemFOFtoCNF_X0_2),
inference(subst,[],[refute_2_6:[bind(A,$fot(skolemFOFtoCNF_X0_2))]]) ).
cnf(refute_2_13,plain,
mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2) = mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2),
introduced(tautology,[refl,[$fot(mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2))]]) ).
cnf(refute_2_14,plain,
( mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2) != mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2)
| mult(skolemFOFtoCNF_X0_2,op_c) != mult(op_c,skolemFOFtoCNF_X0_2)
| mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2) = mult(mult(op_c,skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X1_2) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2),mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2)) ),[1,0],$fot(mult(op_c,skolemFOFtoCNF_X0_2))]]) ).
cnf(refute_2_15,plain,
( mult(skolemFOFtoCNF_X0_2,op_c) != mult(op_c,skolemFOFtoCNF_X0_2)
| mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2) = mult(mult(op_c,skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X1_2) ),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2),mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2)) )],[refute_2_13,refute_2_14]) ).
cnf(refute_2_16,plain,
mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2) = mult(mult(op_c,skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X1_2),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X0_2,op_c),mult(op_c,skolemFOFtoCNF_X0_2)) )],[refute_2_12,refute_2_15]) ).
cnf(refute_2_17,plain,
( mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2) != mult(mult(op_c,skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X1_2)
| mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2) != mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2))
| mult(mult(op_c,skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X1_2) = mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2),mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2))) ),[0],$fot(mult(mult(op_c,skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X1_2))]]) ).
cnf(refute_2_18,plain,
( mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2) != mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2))
| mult(mult(op_c,skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X1_2) = mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)) ),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2),mult(mult(op_c,skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X1_2)) )],[refute_2_16,refute_2_17]) ).
cnf(refute_2_19,plain,
mult(mult(op_c,skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X1_2) = mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2),mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2))) )],[refute_2_11,refute_2_18]) ).
cnf(refute_2_20,plain,
( mult(mult(op_c,skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X1_2) != mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2))
| mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)) != mult(mult(op_c,skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X1_2)
| mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)) = mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)),mult(mult(op_c,skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X1_2)) ),[1],$fot(mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)))]]) ).
cnf(refute_2_21,plain,
( mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)) != mult(mult(op_c,skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X1_2)
| mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)) = mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)) ),
inference(resolve,[$cnf( $equal(mult(mult(op_c,skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X1_2),mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2))) )],[refute_2_19,refute_2_20]) ).
cnf(refute_2_22,plain,
mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)) = mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)),mult(mult(op_c,skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X1_2)) )],[refute_2_10,refute_2_21]) ).
cnf(refute_2_23,plain,
( mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)) != mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2))
| mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)) = mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)) ),
inference(subst,[],[refute_2_4:[bind(X,$fot(mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)))),bind(Y,$fot(mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2))))]]) ).
cnf(refute_2_24,plain,
mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)) = mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)),mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2))) )],[refute_2_22,refute_2_23]) ).
cnf(refute_2_25,plain,
mult(skolemFOFtoCNF_X1_2,op_c) = mult(op_c,skolemFOFtoCNF_X1_2),
inference(subst,[],[refute_2_6:[bind(A,$fot(skolemFOFtoCNF_X1_2))]]) ).
cnf(refute_2_26,plain,
mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c)) = mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c)),
introduced(tautology,[refl,[$fot(mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c)))]]) ).
cnf(refute_2_27,plain,
( mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c)) != mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c))
| mult(skolemFOFtoCNF_X1_2,op_c) != mult(op_c,skolemFOFtoCNF_X1_2)
| mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c)) = mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c)),mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c))) ),[1,1],$fot(mult(op_c,skolemFOFtoCNF_X1_2))]]) ).
cnf(refute_2_28,plain,
( mult(skolemFOFtoCNF_X1_2,op_c) != mult(op_c,skolemFOFtoCNF_X1_2)
| mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c)) = mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c)),mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c))) )],[refute_2_26,refute_2_27]) ).
cnf(refute_2_29,plain,
mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c)) = mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X1_2,op_c),mult(op_c,skolemFOFtoCNF_X1_2)) )],[refute_2_25,refute_2_28]) ).
cnf(refute_2_30,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_2_31,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_2_4,refute_2_30]) ).
cnf(refute_2_32,plain,
( mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)) != mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2))
| mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c)) != mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2))
| mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c)) = mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)) ),
inference(subst,[],[refute_2_31:[bind(X,$fot(mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c)))),bind(Y,$fot(mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)))),bind(Z,$fot(mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2))))]]) ).
cnf(refute_2_33,plain,
( mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)) != mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2))
| mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c)) = mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c)),mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2))) )],[refute_2_29,refute_2_32]) ).
cnf(refute_2_34,plain,
mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c)) = mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)),mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2))) )],[refute_2_24,refute_2_33]) ).
cnf(refute_2_35,plain,
( mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)) != mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2))
| mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c)) != mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2))
| mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)) = mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)),mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c))) ),[1],$fot(mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)))]]) ).
cnf(refute_2_36,plain,
( mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)) != mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2))
| mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)) = mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c)) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c)),mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2))) )],[refute_2_34,refute_2_35]) ).
cnf(refute_2_37,plain,
( mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)) != mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2))
| mult(mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2),op_c) = mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c)) ),
inference(resolve,[$cnf( $equal(mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)),mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c))) )],[refute_2_36,refute_2_9]) ).
cnf(refute_2_38,plain,
mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)) != mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2),op_c),mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_c))) )],[refute_2_37,refute_2_0]) ).
cnf(refute_2_39,plain,
mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)) = mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)),
introduced(tautology,[refl,[$fot(mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)))]]) ).
cnf(refute_2_40,plain,
$false,
inference(resolve,[$cnf( $equal(mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)),mult(op_c,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2))) )],[refute_2_39,refute_2_38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP665+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 00:19:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.55
% 0.20/0.55 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.58
%------------------------------------------------------------------------------