TSTP Solution File: GRP703+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP703+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 10:50:21 EDT 2022
% Result : Theorem 0.20s 0.49s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 85
% Syntax : Number of formulae : 361 ( 214 unt; 0 def)
% Number of atoms : 576 ( 573 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 434 ( 219 ~; 201 |; 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 : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 353 ( 0 sgn 101 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f01,axiom,
! [B,A] : mult(A,ld(A,B)) = B ).
fof(f03,axiom,
! [B,A] : mult(rd(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(goals,conjecture,
! [X2,X3] :
( mult(op_e,mult(X2,X3)) = mult(mult(op_e,X2),X3)
& mult(X2,mult(X3,op_e)) = mult(mult(X2,X3),op_e)
& mult(X2,mult(op_e,X3)) = mult(mult(X2,op_e),X3) ) ).
fof(subgoal_0,plain,
! [X2,X3] : mult(op_e,mult(X2,X3)) = mult(mult(op_e,X2),X3),
inference(strip,[],[goals]) ).
fof(subgoal_1,plain,
! [X2,X3] :
( mult(op_e,mult(X2,X3)) = mult(mult(op_e,X2),X3)
=> mult(X2,mult(X3,op_e)) = mult(mult(X2,X3),op_e) ),
inference(strip,[],[goals]) ).
fof(subgoal_2,plain,
! [X2,X3] :
( ( mult(op_e,mult(X2,X3)) = mult(mult(op_e,X2),X3)
& mult(X2,mult(X3,op_e)) = mult(mult(X2,X3),op_e) )
=> mult(X2,mult(op_e,X3)) = mult(mult(X2,op_e),X3) ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X2,X3] : mult(op_e,mult(X2,X3)) = mult(mult(op_e,X2),X3),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X2,X3] : mult(op_e,mult(X2,X3)) != mult(mult(op_e,X2),X3),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
mult(op_e,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)) != mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] : mult(A,ld(A,B)) = B,
inference(canonicalize,[],[f01]) ).
fof(normalize_0_3,plain,
! [A,B] : mult(A,ld(A,B)) = B,
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A] : op_d = ld(A,mult(op_c,A)),
inference(canonicalize,[],[f11]) ).
fof(normalize_0_5,plain,
! [A] : op_d = ld(A,mult(op_c,A)),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A] : mult(A,unit) = A,
inference(canonicalize,[],[f05]) ).
fof(normalize_0_7,plain,
! [A] : mult(A,unit) = A,
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A] : mult(unit,A) = A,
inference(canonicalize,[],[f06]) ).
fof(normalize_0_9,plain,
! [A] : mult(unit,A) = A,
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B] : op_e = mult(mult(rd(op_c,mult(A,B)),B),A),
inference(canonicalize,[],[f12]) ).
fof(normalize_0_11,plain,
! [A,B] : op_e = mult(mult(rd(op_c,mult(A,B)),B),A),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B] : mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
inference(canonicalize,[],[f10]) ).
fof(normalize_0_13,plain,
! [A,B] : mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,B] : mult(rd(A,B),B) = A,
inference(canonicalize,[],[f03]) ).
fof(normalize_0_15,plain,
! [A,B] : mult(rd(A,B),B) = A,
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [A,B] : mult(A,mult(B,op_c)) = mult(mult(A,B),op_c),
inference(canonicalize,[],[f09]) ).
fof(normalize_0_17,plain,
! [A,B] : mult(A,mult(B,op_c)) = mult(mult(A,B),op_c),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [A,B] : mult(op_c,mult(A,B)) = mult(mult(op_c,A),B),
inference(canonicalize,[],[f08]) ).
fof(normalize_0_19,plain,
! [A,B] : mult(op_c,mult(A,B)) = mult(mult(op_c,A),B),
inference(specialize,[],[normalize_0_18]) ).
cnf(refute_0_0,plain,
mult(op_e,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)) != mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
mult(A,ld(A,B)) = B,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
mult(X_3,ld(X_3,mult(op_c,X_3))) = mult(op_c,X_3),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_3)),bind(B,$fot(mult(op_c,X_3)))]]) ).
cnf(refute_0_3,plain,
op_d = ld(A,mult(op_c,A)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
op_d = ld(X_3,mult(op_c,X_3)),
inference(subst,[],[refute_0_3:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_5,plain,
X = X,
introduced(tautology,[refl,[$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( $equal(X,X) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( op_d != ld(X_3,mult(op_c,X_3))
| ld(X_3,mult(op_c,X_3)) = op_d ),
inference(subst,[],[refute_0_7:[bind(X,$fot(op_d)),bind(Y,$fot(ld(X_3,mult(op_c,X_3))))]]) ).
cnf(refute_0_9,plain,
ld(X_3,mult(op_c,X_3)) = op_d,
inference(resolve,[$cnf( $equal(op_d,ld(X_3,mult(op_c,X_3))) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( ld(X_3,mult(op_c,X_3)) != op_d
| mult(X_3,ld(X_3,mult(op_c,X_3))) != mult(op_c,X_3)
| mult(X_3,op_d) = mult(op_c,X_3) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_3,ld(X_3,mult(op_c,X_3))),mult(op_c,X_3)) ),[0,1],$fot(op_d)]]) ).
cnf(refute_0_11,plain,
( mult(X_3,ld(X_3,mult(op_c,X_3))) != mult(op_c,X_3)
| mult(X_3,op_d) = mult(op_c,X_3) ),
inference(resolve,[$cnf( $equal(ld(X_3,mult(op_c,X_3)),op_d) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
mult(X_3,op_d) = mult(op_c,X_3),
inference(resolve,[$cnf( $equal(mult(X_3,ld(X_3,mult(op_c,X_3))),mult(op_c,X_3)) )],[refute_0_2,refute_0_11]) ).
cnf(refute_0_13,plain,
mult(unit,ld(unit,op_c)) = op_c,
inference(subst,[],[refute_0_1:[bind(A,$fot(unit)),bind(B,$fot(op_c))]]) ).
cnf(refute_0_14,plain,
op_d = ld(unit,mult(op_c,unit)),
inference(subst,[],[refute_0_3:[bind(A,$fot(unit))]]) ).
cnf(refute_0_15,plain,
mult(A,unit) = A,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_16,plain,
mult(op_c,unit) = op_c,
inference(subst,[],[refute_0_15:[bind(A,$fot(op_c))]]) ).
cnf(refute_0_17,plain,
( mult(op_c,unit) != op_c
| op_d != ld(unit,mult(op_c,unit))
| op_d = ld(unit,op_c) ),
introduced(tautology,[equality,[$cnf( $equal(op_d,ld(unit,mult(op_c,unit))) ),[1,1],$fot(op_c)]]) ).
cnf(refute_0_18,plain,
( op_d != ld(unit,mult(op_c,unit))
| op_d = ld(unit,op_c) ),
inference(resolve,[$cnf( $equal(mult(op_c,unit),op_c) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
op_d = ld(unit,op_c),
inference(resolve,[$cnf( $equal(op_d,ld(unit,mult(op_c,unit))) )],[refute_0_14,refute_0_18]) ).
cnf(refute_0_20,plain,
( op_d != ld(unit,op_c)
| ld(unit,op_c) = op_d ),
inference(subst,[],[refute_0_7:[bind(X,$fot(op_d)),bind(Y,$fot(ld(unit,op_c)))]]) ).
cnf(refute_0_21,plain,
ld(unit,op_c) = op_d,
inference(resolve,[$cnf( $equal(op_d,ld(unit,op_c)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( ld(unit,op_c) != op_d
| mult(unit,ld(unit,op_c)) != op_c
| mult(unit,op_d) = op_c ),
introduced(tautology,[equality,[$cnf( $equal(mult(unit,ld(unit,op_c)),op_c) ),[0,1],$fot(op_d)]]) ).
cnf(refute_0_23,plain,
( mult(unit,ld(unit,op_c)) != op_c
| mult(unit,op_d) = op_c ),
inference(resolve,[$cnf( $equal(ld(unit,op_c),op_d) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
mult(unit,op_d) = op_c,
inference(resolve,[$cnf( $equal(mult(unit,ld(unit,op_c)),op_c) )],[refute_0_13,refute_0_23]) ).
cnf(refute_0_25,plain,
mult(unit,A) = A,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_26,plain,
mult(unit,op_d) = op_d,
inference(subst,[],[refute_0_25:[bind(A,$fot(op_d))]]) ).
cnf(refute_0_27,plain,
( mult(unit,op_d) != op_c
| mult(unit,op_d) != op_d
| op_d = op_c ),
introduced(tautology,[equality,[$cnf( $equal(mult(unit,op_d),op_c) ),[0],$fot(op_d)]]) ).
cnf(refute_0_28,plain,
( mult(unit,op_d) != op_c
| op_d = op_c ),
inference(resolve,[$cnf( $equal(mult(unit,op_d),op_d) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
op_d = op_c,
inference(resolve,[$cnf( $equal(mult(unit,op_d),op_c) )],[refute_0_24,refute_0_28]) ).
cnf(refute_0_30,plain,
mult(X_3,op_d) = mult(X_3,op_d),
introduced(tautology,[refl,[$fot(mult(X_3,op_d))]]) ).
cnf(refute_0_31,plain,
( mult(X_3,op_d) != mult(X_3,op_d)
| op_d != op_c
| mult(X_3,op_d) = mult(X_3,op_c) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_3,op_d),mult(X_3,op_d)) ),[1,1],$fot(op_c)]]) ).
cnf(refute_0_32,plain,
( op_d != op_c
| mult(X_3,op_d) = mult(X_3,op_c) ),
inference(resolve,[$cnf( $equal(mult(X_3,op_d),mult(X_3,op_d)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
mult(X_3,op_d) = mult(X_3,op_c),
inference(resolve,[$cnf( $equal(op_d,op_c) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
( mult(X_3,op_d) != mult(X_3,op_c)
| mult(X_3,op_d) != mult(op_c,X_3)
| mult(X_3,op_c) = mult(op_c,X_3) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_3,op_d),mult(op_c,X_3)) ),[0],$fot(mult(X_3,op_c))]]) ).
cnf(refute_0_35,plain,
( mult(X_3,op_d) != mult(op_c,X_3)
| mult(X_3,op_c) = mult(op_c,X_3) ),
inference(resolve,[$cnf( $equal(mult(X_3,op_d),mult(X_3,op_c)) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
mult(X_3,op_c) = mult(op_c,X_3),
inference(resolve,[$cnf( $equal(mult(X_3,op_d),mult(op_c,X_3)) )],[refute_0_12,refute_0_35]) ).
cnf(refute_0_37,plain,
mult(mult(rd(op_c,mult(op_c,X_36)),X_36),op_c) = mult(op_c,mult(rd(op_c,mult(op_c,X_36)),X_36)),
inference(subst,[],[refute_0_36:[bind(X_3,$fot(mult(rd(op_c,mult(op_c,X_36)),X_36)))]]) ).
cnf(refute_0_38,plain,
op_e = mult(mult(rd(op_c,mult(A,B)),B),A),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_39,plain,
op_e = mult(mult(rd(op_c,mult(op_c,X_36)),X_36),op_c),
inference(subst,[],[refute_0_38:[bind(A,$fot(op_c)),bind(B,$fot(X_36))]]) ).
cnf(refute_0_40,plain,
( op_e != mult(mult(rd(op_c,mult(op_c,X_36)),X_36),op_c)
| mult(mult(rd(op_c,mult(op_c,X_36)),X_36),op_c) = op_e ),
inference(subst,[],[refute_0_7:[bind(X,$fot(op_e)),bind(Y,$fot(mult(mult(rd(op_c,mult(op_c,X_36)),X_36),op_c)))]]) ).
cnf(refute_0_41,plain,
mult(mult(rd(op_c,mult(op_c,X_36)),X_36),op_c) = op_e,
inference(resolve,[$cnf( $equal(op_e,mult(mult(rd(op_c,mult(op_c,X_36)),X_36),op_c)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( mult(mult(rd(op_c,mult(op_c,X_36)),X_36),op_c) != mult(op_c,mult(rd(op_c,mult(op_c,X_36)),X_36))
| mult(mult(rd(op_c,mult(op_c,X_36)),X_36),op_c) != op_e
| op_e = mult(op_c,mult(rd(op_c,mult(op_c,X_36)),X_36)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(rd(op_c,mult(op_c,X_36)),X_36),op_c),mult(op_c,mult(rd(op_c,mult(op_c,X_36)),X_36))) ),[0],$fot(op_e)]]) ).
cnf(refute_0_43,plain,
( mult(mult(rd(op_c,mult(op_c,X_36)),X_36),op_c) != mult(op_c,mult(rd(op_c,mult(op_c,X_36)),X_36))
| op_e = mult(op_c,mult(rd(op_c,mult(op_c,X_36)),X_36)) ),
inference(resolve,[$cnf( $equal(mult(mult(rd(op_c,mult(op_c,X_36)),X_36),op_c),op_e) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
op_e = mult(op_c,mult(rd(op_c,mult(op_c,X_36)),X_36)),
inference(resolve,[$cnf( $equal(mult(mult(rd(op_c,mult(op_c,X_36)),X_36),op_c),mult(op_c,mult(rd(op_c,mult(op_c,X_36)),X_36))) )],[refute_0_37,refute_0_43]) ).
cnf(refute_0_45,plain,
mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_46,plain,
mult(rd(A,mult(op_c,X_34)),mult(op_c,X_34)) = mult(mult(rd(A,mult(op_c,X_34)),op_c),X_34),
inference(subst,[],[refute_0_45:[bind(A,$fot(rd(A,mult(op_c,X_34)))),bind(B,$fot(X_34))]]) ).
cnf(refute_0_47,plain,
mult(rd(A,B),B) = A,
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_48,plain,
mult(rd(A,mult(op_c,X_34)),mult(op_c,X_34)) = A,
inference(subst,[],[refute_0_47:[bind(B,$fot(mult(op_c,X_34)))]]) ).
cnf(refute_0_49,plain,
( mult(rd(A,mult(op_c,X_34)),mult(op_c,X_34)) != A
| mult(rd(A,mult(op_c,X_34)),mult(op_c,X_34)) != mult(mult(rd(A,mult(op_c,X_34)),op_c),X_34)
| A = mult(mult(rd(A,mult(op_c,X_34)),op_c),X_34) ),
introduced(tautology,[equality,[$cnf( $equal(mult(rd(A,mult(op_c,X_34)),mult(op_c,X_34)),mult(mult(rd(A,mult(op_c,X_34)),op_c),X_34)) ),[0],$fot(A)]]) ).
cnf(refute_0_50,plain,
( mult(rd(A,mult(op_c,X_34)),mult(op_c,X_34)) != mult(mult(rd(A,mult(op_c,X_34)),op_c),X_34)
| A = mult(mult(rd(A,mult(op_c,X_34)),op_c),X_34) ),
inference(resolve,[$cnf( $equal(mult(rd(A,mult(op_c,X_34)),mult(op_c,X_34)),A) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
A = mult(mult(rd(A,mult(op_c,X_34)),op_c),X_34),
inference(resolve,[$cnf( $equal(mult(rd(A,mult(op_c,X_34)),mult(op_c,X_34)),mult(mult(rd(A,mult(op_c,X_34)),op_c),X_34)) )],[refute_0_46,refute_0_50]) ).
cnf(refute_0_52,plain,
mult(A,mult(B,op_c)) = mult(mult(A,B),op_c),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_53,plain,
mult(mult(A,B),op_c) = mult(op_c,mult(A,B)),
inference(subst,[],[refute_0_36:[bind(X_3,$fot(mult(A,B)))]]) ).
cnf(refute_0_54,plain,
( mult(A,mult(B,op_c)) != mult(mult(A,B),op_c)
| mult(mult(A,B),op_c) != mult(op_c,mult(A,B))
| mult(A,mult(B,op_c)) = mult(op_c,mult(A,B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(A,mult(B,op_c)),mult(op_c,mult(A,B))) ),[0],$fot(mult(mult(A,B),op_c))]]) ).
cnf(refute_0_55,plain,
( mult(A,mult(B,op_c)) != mult(mult(A,B),op_c)
| mult(A,mult(B,op_c)) = mult(op_c,mult(A,B)) ),
inference(resolve,[$cnf( $equal(mult(mult(A,B),op_c),mult(op_c,mult(A,B))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
mult(A,mult(B,op_c)) = mult(op_c,mult(A,B)),
inference(resolve,[$cnf( $equal(mult(A,mult(B,op_c)),mult(mult(A,B),op_c)) )],[refute_0_52,refute_0_55]) ).
cnf(refute_0_57,plain,
mult(X_31,mult(X_32,op_c)) = mult(op_c,mult(X_31,X_32)),
inference(subst,[],[refute_0_56:[bind(A,$fot(X_31)),bind(B,$fot(X_32))]]) ).
cnf(refute_0_58,plain,
mult(X_32,op_c) = mult(op_c,X_32),
inference(subst,[],[refute_0_36:[bind(X_3,$fot(X_32))]]) ).
cnf(refute_0_59,plain,
( mult(X_31,mult(X_32,op_c)) != mult(op_c,mult(X_31,X_32))
| mult(X_32,op_c) != mult(op_c,X_32)
| mult(X_31,mult(op_c,X_32)) = mult(op_c,mult(X_31,X_32)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_31,mult(X_32,op_c)),mult(op_c,mult(X_31,X_32))) ),[0,1],$fot(mult(op_c,X_32))]]) ).
cnf(refute_0_60,plain,
( mult(X_31,mult(X_32,op_c)) != mult(op_c,mult(X_31,X_32))
| mult(X_31,mult(op_c,X_32)) = mult(op_c,mult(X_31,X_32)) ),
inference(resolve,[$cnf( $equal(mult(X_32,op_c),mult(op_c,X_32)) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
mult(X_31,mult(op_c,X_32)) = mult(op_c,mult(X_31,X_32)),
inference(resolve,[$cnf( $equal(mult(X_31,mult(X_32,op_c)),mult(op_c,mult(X_31,X_32))) )],[refute_0_57,refute_0_60]) ).
cnf(refute_0_62,plain,
mult(rd(A,mult(op_c,X_34)),mult(op_c,X_34)) = mult(op_c,mult(rd(A,mult(op_c,X_34)),X_34)),
inference(subst,[],[refute_0_61:[bind(X_31,$fot(rd(A,mult(op_c,X_34)))),bind(X_32,$fot(X_34))]]) ).
cnf(refute_0_63,plain,
( mult(A,mult(op_c,B)) != mult(mult(A,op_c),B)
| mult(mult(A,op_c),B) = mult(A,mult(op_c,B)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(mult(A,mult(op_c,B)))),bind(Y,$fot(mult(mult(A,op_c),B)))]]) ).
cnf(refute_0_64,plain,
mult(mult(A,op_c),B) = mult(A,mult(op_c,B)),
inference(resolve,[$cnf( $equal(mult(A,mult(op_c,B)),mult(mult(A,op_c),B)) )],[refute_0_45,refute_0_63]) ).
cnf(refute_0_65,plain,
mult(mult(rd(A,mult(op_c,X_34)),op_c),X_34) = mult(rd(A,mult(op_c,X_34)),mult(op_c,X_34)),
inference(subst,[],[refute_0_64:[bind(A,$fot(rd(A,mult(op_c,X_34)))),bind(B,$fot(X_34))]]) ).
cnf(refute_0_66,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_67,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_7,refute_0_66]) ).
cnf(refute_0_68,plain,
( mult(mult(rd(A,mult(op_c,X_34)),op_c),X_34) != mult(rd(A,mult(op_c,X_34)),mult(op_c,X_34))
| mult(rd(A,mult(op_c,X_34)),mult(op_c,X_34)) != mult(op_c,mult(rd(A,mult(op_c,X_34)),X_34))
| mult(mult(rd(A,mult(op_c,X_34)),op_c),X_34) = mult(op_c,mult(rd(A,mult(op_c,X_34)),X_34)) ),
inference(subst,[],[refute_0_67:[bind(X,$fot(mult(mult(rd(A,mult(op_c,X_34)),op_c),X_34))),bind(Y,$fot(mult(rd(A,mult(op_c,X_34)),mult(op_c,X_34)))),bind(Z,$fot(mult(op_c,mult(rd(A,mult(op_c,X_34)),X_34))))]]) ).
cnf(refute_0_69,plain,
( mult(rd(A,mult(op_c,X_34)),mult(op_c,X_34)) != mult(op_c,mult(rd(A,mult(op_c,X_34)),X_34))
| mult(mult(rd(A,mult(op_c,X_34)),op_c),X_34) = mult(op_c,mult(rd(A,mult(op_c,X_34)),X_34)) ),
inference(resolve,[$cnf( $equal(mult(mult(rd(A,mult(op_c,X_34)),op_c),X_34),mult(rd(A,mult(op_c,X_34)),mult(op_c,X_34))) )],[refute_0_65,refute_0_68]) ).
cnf(refute_0_70,plain,
mult(mult(rd(A,mult(op_c,X_34)),op_c),X_34) = mult(op_c,mult(rd(A,mult(op_c,X_34)),X_34)),
inference(resolve,[$cnf( $equal(mult(rd(A,mult(op_c,X_34)),mult(op_c,X_34)),mult(op_c,mult(rd(A,mult(op_c,X_34)),X_34))) )],[refute_0_62,refute_0_69]) ).
cnf(refute_0_71,plain,
( A != mult(mult(rd(A,mult(op_c,X_34)),op_c),X_34)
| mult(mult(rd(A,mult(op_c,X_34)),op_c),X_34) != mult(op_c,mult(rd(A,mult(op_c,X_34)),X_34))
| A = mult(op_c,mult(rd(A,mult(op_c,X_34)),X_34)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(A,mult(op_c,mult(rd(A,mult(op_c,X_34)),X_34))) ),[0],$fot(mult(mult(rd(A,mult(op_c,X_34)),op_c),X_34))]]) ).
cnf(refute_0_72,plain,
( A != mult(mult(rd(A,mult(op_c,X_34)),op_c),X_34)
| A = mult(op_c,mult(rd(A,mult(op_c,X_34)),X_34)) ),
inference(resolve,[$cnf( $equal(mult(mult(rd(A,mult(op_c,X_34)),op_c),X_34),mult(op_c,mult(rd(A,mult(op_c,X_34)),X_34))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
A = mult(op_c,mult(rd(A,mult(op_c,X_34)),X_34)),
inference(resolve,[$cnf( $equal(A,mult(mult(rd(A,mult(op_c,X_34)),op_c),X_34)) )],[refute_0_51,refute_0_72]) ).
cnf(refute_0_74,plain,
( A != mult(op_c,mult(rd(A,mult(op_c,X_34)),X_34))
| mult(op_c,mult(rd(A,mult(op_c,X_34)),X_34)) = A ),
inference(subst,[],[refute_0_7:[bind(X,$fot(A)),bind(Y,$fot(mult(op_c,mult(rd(A,mult(op_c,X_34)),X_34))))]]) ).
cnf(refute_0_75,plain,
mult(op_c,mult(rd(A,mult(op_c,X_34)),X_34)) = A,
inference(resolve,[$cnf( $equal(A,mult(op_c,mult(rd(A,mult(op_c,X_34)),X_34))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
mult(op_c,mult(rd(op_c,mult(op_c,X_36)),X_36)) = op_c,
inference(subst,[],[refute_0_75:[bind(A,$fot(op_c)),bind(X_34,$fot(X_36))]]) ).
cnf(refute_0_77,plain,
( mult(op_c,mult(rd(op_c,mult(op_c,X_36)),X_36)) != op_c
| op_e != mult(op_c,mult(rd(op_c,mult(op_c,X_36)),X_36))
| op_e = op_c ),
introduced(tautology,[equality,[$cnf( $equal(op_e,mult(op_c,mult(rd(op_c,mult(op_c,X_36)),X_36))) ),[1],$fot(op_c)]]) ).
cnf(refute_0_78,plain,
( op_e != mult(op_c,mult(rd(op_c,mult(op_c,X_36)),X_36))
| op_e = op_c ),
inference(resolve,[$cnf( $equal(mult(op_c,mult(rd(op_c,mult(op_c,X_36)),X_36)),op_c) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
op_e = op_c,
inference(resolve,[$cnf( $equal(op_e,mult(op_c,mult(rd(op_c,mult(op_c,X_36)),X_36))) )],[refute_0_44,refute_0_78]) ).
cnf(refute_0_80,plain,
mult(op_e,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)) = mult(op_e,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)),
introduced(tautology,[refl,[$fot(mult(op_e,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)))]]) ).
cnf(refute_0_81,plain,
( mult(op_e,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)) != mult(op_e,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3))
| op_e != op_c
| mult(op_e,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)) = mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_e,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)),mult(op_e,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3))) ),[1,0],$fot(op_c)]]) ).
cnf(refute_0_82,plain,
( op_e != op_c
| mult(op_e,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)) = mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)) ),
inference(resolve,[$cnf( $equal(mult(op_e,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)),mult(op_e,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
mult(op_e,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)) = mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)),
inference(resolve,[$cnf( $equal(op_e,op_c) )],[refute_0_79,refute_0_82]) ).
cnf(refute_0_84,plain,
( mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)) != mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3)
| mult(op_e,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)) != mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3))
| mult(op_e,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)) = mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_e,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)),mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3))) ),[1],$fot(mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3))]]) ).
cnf(refute_0_85,plain,
( mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)) != mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3)
| mult(op_e,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)) = mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3) ),
inference(resolve,[$cnf( $equal(mult(op_e,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)),mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
mult(op_c,mult(A,B)) = mult(mult(op_c,A),B),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_87,plain,
( mult(op_c,mult(A,B)) != mult(mult(op_c,A),B)
| mult(mult(op_c,A),B) = mult(op_c,mult(A,B)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(mult(op_c,mult(A,B)))),bind(Y,$fot(mult(mult(op_c,A),B)))]]) ).
cnf(refute_0_88,plain,
mult(mult(op_c,A),B) = mult(op_c,mult(A,B)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(A,B)),mult(mult(op_c,A),B)) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
mult(mult(op_c,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3) = mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)),
inference(subst,[],[refute_0_88:[bind(A,$fot(skolemFOFtoCNF_X2)),bind(B,$fot(skolemFOFtoCNF_X3))]]) ).
cnf(refute_0_90,plain,
mult(op_e,skolemFOFtoCNF_X2) = mult(op_e,skolemFOFtoCNF_X2),
introduced(tautology,[refl,[$fot(mult(op_e,skolemFOFtoCNF_X2))]]) ).
cnf(refute_0_91,plain,
( mult(op_e,skolemFOFtoCNF_X2) != mult(op_e,skolemFOFtoCNF_X2)
| op_e != op_c
| mult(op_e,skolemFOFtoCNF_X2) = mult(op_c,skolemFOFtoCNF_X2) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_e,skolemFOFtoCNF_X2),mult(op_e,skolemFOFtoCNF_X2)) ),[1,0],$fot(op_c)]]) ).
cnf(refute_0_92,plain,
( op_e != op_c
| mult(op_e,skolemFOFtoCNF_X2) = mult(op_c,skolemFOFtoCNF_X2) ),
inference(resolve,[$cnf( $equal(mult(op_e,skolemFOFtoCNF_X2),mult(op_e,skolemFOFtoCNF_X2)) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
mult(op_e,skolemFOFtoCNF_X2) = mult(op_c,skolemFOFtoCNF_X2),
inference(resolve,[$cnf( $equal(op_e,op_c) )],[refute_0_79,refute_0_92]) ).
cnf(refute_0_94,plain,
mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3) = mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3),
introduced(tautology,[refl,[$fot(mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3))]]) ).
cnf(refute_0_95,plain,
( mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3) != mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3)
| mult(op_e,skolemFOFtoCNF_X2) != mult(op_c,skolemFOFtoCNF_X2)
| mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3) = mult(mult(op_c,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3),mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3)) ),[1,0],$fot(mult(op_c,skolemFOFtoCNF_X2))]]) ).
cnf(refute_0_96,plain,
( mult(op_e,skolemFOFtoCNF_X2) != mult(op_c,skolemFOFtoCNF_X2)
| mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3) = mult(mult(op_c,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3) ),
inference(resolve,[$cnf( $equal(mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3),mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3)) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3) = mult(mult(op_c,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3),
inference(resolve,[$cnf( $equal(mult(op_e,skolemFOFtoCNF_X2),mult(op_c,skolemFOFtoCNF_X2)) )],[refute_0_93,refute_0_96]) ).
cnf(refute_0_98,plain,
( mult(mult(op_c,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3) != mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3))
| mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3) != mult(mult(op_c,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3)
| mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3) = mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)) ),
inference(subst,[],[refute_0_67:[bind(X,$fot(mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3))),bind(Y,$fot(mult(mult(op_c,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3))),bind(Z,$fot(mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3))))]]) ).
cnf(refute_0_99,plain,
( mult(mult(op_c,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3) != mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3))
| mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3) = mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)) ),
inference(resolve,[$cnf( $equal(mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3),mult(mult(op_c,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3)) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3) = mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)),
inference(resolve,[$cnf( $equal(mult(mult(op_c,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3),mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3))) )],[refute_0_89,refute_0_99]) ).
cnf(refute_0_101,plain,
( mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3) != mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3))
| mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)) != mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3))
| mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)) = mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)),mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3)) ),[1],$fot(mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)))]]) ).
cnf(refute_0_102,plain,
( mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)) != mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3))
| mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)) = mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3) ),
inference(resolve,[$cnf( $equal(mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3),mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3))) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
( mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)) != mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3))
| mult(op_e,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)) = mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3) ),
inference(resolve,[$cnf( $equal(mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)),mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3)) )],[refute_0_102,refute_0_85]) ).
cnf(refute_0_104,plain,
mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)) != mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)),
inference(resolve,[$cnf( $equal(mult(op_e,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)),mult(mult(op_e,skolemFOFtoCNF_X2),skolemFOFtoCNF_X3)) )],[refute_0_103,refute_0_0]) ).
cnf(refute_0_105,plain,
mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)) = mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)),
introduced(tautology,[refl,[$fot(mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)))]]) ).
cnf(refute_0_106,plain,
$false,
inference(resolve,[$cnf( $equal(mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3)),mult(op_c,mult(skolemFOFtoCNF_X2,skolemFOFtoCNF_X3))) )],[refute_0_105,refute_0_104]) ).
fof(negate_1_0,plain,
~ ! [X2,X3] :
( mult(op_e,mult(X2,X3)) = mult(mult(op_e,X2),X3)
=> mult(X2,mult(X3,op_e)) = mult(mult(X2,X3),op_e) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [X2,X3] :
( mult(X2,mult(X3,op_e)) != mult(mult(X2,X3),op_e)
& mult(op_e,mult(X2,X3)) = mult(mult(op_e,X2),X3) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( mult(skolemFOFtoCNF_X2_1,mult(skolemFOFtoCNF_X3_1,op_e)) != mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e)
& mult(op_e,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1)) = mult(mult(op_e,skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X3_1) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
mult(skolemFOFtoCNF_X2_1,mult(skolemFOFtoCNF_X3_1,op_e)) != mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A,B] : mult(A,ld(A,B)) = B,
inference(canonicalize,[],[f01]) ).
fof(normalize_1_4,plain,
! [A,B] : mult(A,ld(A,B)) = B,
inference(specialize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [A] : op_d = ld(A,mult(op_c,A)),
inference(canonicalize,[],[f11]) ).
fof(normalize_1_6,plain,
! [A] : op_d = ld(A,mult(op_c,A)),
inference(specialize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [A] : mult(A,unit) = A,
inference(canonicalize,[],[f05]) ).
fof(normalize_1_8,plain,
! [A] : mult(A,unit) = A,
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [A] : mult(unit,A) = A,
inference(canonicalize,[],[f06]) ).
fof(normalize_1_10,plain,
! [A] : mult(unit,A) = A,
inference(specialize,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [A,B] : op_e = mult(mult(rd(op_c,mult(A,B)),B),A),
inference(canonicalize,[],[f12]) ).
fof(normalize_1_12,plain,
! [A,B] : op_e = mult(mult(rd(op_c,mult(A,B)),B),A),
inference(specialize,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
! [A,B] : mult(rd(A,B),B) = A,
inference(canonicalize,[],[f03]) ).
fof(normalize_1_14,plain,
! [A,B] : mult(rd(A,B),B) = A,
inference(specialize,[],[normalize_1_13]) ).
fof(normalize_1_15,plain,
! [A,B] : mult(op_c,mult(A,B)) = mult(mult(op_c,A),B),
inference(canonicalize,[],[f08]) ).
fof(normalize_1_16,plain,
! [A,B] : mult(op_c,mult(A,B)) = mult(mult(op_c,A),B),
inference(specialize,[],[normalize_1_15]) ).
fof(normalize_1_17,plain,
! [A,B] : mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
inference(canonicalize,[],[f10]) ).
fof(normalize_1_18,plain,
! [A,B] : mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
inference(specialize,[],[normalize_1_17]) ).
cnf(refute_1_0,plain,
mult(skolemFOFtoCNF_X2_1,mult(skolemFOFtoCNF_X3_1,op_e)) != mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
mult(A,ld(A,B)) = B,
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_2,plain,
mult(A,ld(A,mult(op_c,A))) = mult(op_c,A),
inference(subst,[],[refute_1_1:[bind(B,$fot(mult(op_c,A)))]]) ).
cnf(refute_1_3,plain,
op_d = ld(A,mult(op_c,A)),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_4,plain,
mult(unit,ld(unit,op_c)) = op_c,
inference(subst,[],[refute_1_1:[bind(A,$fot(unit)),bind(B,$fot(op_c))]]) ).
cnf(refute_1_5,plain,
op_d = ld(unit,mult(op_c,unit)),
inference(subst,[],[refute_1_3:[bind(A,$fot(unit))]]) ).
cnf(refute_1_6,plain,
mult(A,unit) = A,
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_7,plain,
mult(op_c,unit) = op_c,
inference(subst,[],[refute_1_6:[bind(A,$fot(op_c))]]) ).
cnf(refute_1_8,plain,
( mult(op_c,unit) != op_c
| op_d != ld(unit,mult(op_c,unit))
| op_d = ld(unit,op_c) ),
introduced(tautology,[equality,[$cnf( $equal(op_d,ld(unit,mult(op_c,unit))) ),[1,1],$fot(op_c)]]) ).
cnf(refute_1_9,plain,
( op_d != ld(unit,mult(op_c,unit))
| op_d = ld(unit,op_c) ),
inference(resolve,[$cnf( $equal(mult(op_c,unit),op_c) )],[refute_1_7,refute_1_8]) ).
cnf(refute_1_10,plain,
op_d = ld(unit,op_c),
inference(resolve,[$cnf( $equal(op_d,ld(unit,mult(op_c,unit))) )],[refute_1_5,refute_1_9]) ).
cnf(refute_1_11,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_12,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_13,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_11,refute_1_12]) ).
cnf(refute_1_14,plain,
( op_d != ld(unit,op_c)
| ld(unit,op_c) = op_d ),
inference(subst,[],[refute_1_13:[bind(X,$fot(op_d)),bind(Y,$fot(ld(unit,op_c)))]]) ).
cnf(refute_1_15,plain,
ld(unit,op_c) = op_d,
inference(resolve,[$cnf( $equal(op_d,ld(unit,op_c)) )],[refute_1_10,refute_1_14]) ).
cnf(refute_1_16,plain,
( ld(unit,op_c) != op_d
| mult(unit,ld(unit,op_c)) != op_c
| mult(unit,op_d) = op_c ),
introduced(tautology,[equality,[$cnf( $equal(mult(unit,ld(unit,op_c)),op_c) ),[0,1],$fot(op_d)]]) ).
cnf(refute_1_17,plain,
( mult(unit,ld(unit,op_c)) != op_c
| mult(unit,op_d) = op_c ),
inference(resolve,[$cnf( $equal(ld(unit,op_c),op_d) )],[refute_1_15,refute_1_16]) ).
cnf(refute_1_18,plain,
mult(unit,op_d) = op_c,
inference(resolve,[$cnf( $equal(mult(unit,ld(unit,op_c)),op_c) )],[refute_1_4,refute_1_17]) ).
cnf(refute_1_19,plain,
mult(unit,A) = A,
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_20,plain,
mult(unit,op_d) = op_d,
inference(subst,[],[refute_1_19:[bind(A,$fot(op_d))]]) ).
cnf(refute_1_21,plain,
( mult(unit,op_d) != op_c
| mult(unit,op_d) != op_d
| op_d = op_c ),
introduced(tautology,[equality,[$cnf( $equal(mult(unit,op_d),op_c) ),[0],$fot(op_d)]]) ).
cnf(refute_1_22,plain,
( mult(unit,op_d) != op_c
| op_d = op_c ),
inference(resolve,[$cnf( $equal(mult(unit,op_d),op_d) )],[refute_1_20,refute_1_21]) ).
cnf(refute_1_23,plain,
op_d = op_c,
inference(resolve,[$cnf( $equal(mult(unit,op_d),op_c) )],[refute_1_18,refute_1_22]) ).
cnf(refute_1_24,plain,
( op_d != ld(A,mult(op_c,A))
| op_d != op_c
| op_c = ld(A,mult(op_c,A)) ),
introduced(tautology,[equality,[$cnf( $equal(op_d,ld(A,mult(op_c,A))) ),[0],$fot(op_c)]]) ).
cnf(refute_1_25,plain,
( op_d != ld(A,mult(op_c,A))
| op_c = ld(A,mult(op_c,A)) ),
inference(resolve,[$cnf( $equal(op_d,op_c) )],[refute_1_23,refute_1_24]) ).
cnf(refute_1_26,plain,
op_c = ld(A,mult(op_c,A)),
inference(resolve,[$cnf( $equal(op_d,ld(A,mult(op_c,A))) )],[refute_1_3,refute_1_25]) ).
cnf(refute_1_27,plain,
( op_c != ld(A,mult(op_c,A))
| ld(A,mult(op_c,A)) = op_c ),
inference(subst,[],[refute_1_13:[bind(X,$fot(op_c)),bind(Y,$fot(ld(A,mult(op_c,A))))]]) ).
cnf(refute_1_28,plain,
ld(A,mult(op_c,A)) = op_c,
inference(resolve,[$cnf( $equal(op_c,ld(A,mult(op_c,A))) )],[refute_1_26,refute_1_27]) ).
cnf(refute_1_29,plain,
( ld(A,mult(op_c,A)) != op_c
| mult(A,ld(A,mult(op_c,A))) != mult(op_c,A)
| mult(A,op_c) = mult(op_c,A) ),
introduced(tautology,[equality,[$cnf( $equal(mult(A,ld(A,mult(op_c,A))),mult(op_c,A)) ),[0,1],$fot(op_c)]]) ).
cnf(refute_1_30,plain,
( mult(A,ld(A,mult(op_c,A))) != mult(op_c,A)
| mult(A,op_c) = mult(op_c,A) ),
inference(resolve,[$cnf( $equal(ld(A,mult(op_c,A)),op_c) )],[refute_1_28,refute_1_29]) ).
cnf(refute_1_31,plain,
mult(A,op_c) = mult(op_c,A),
inference(resolve,[$cnf( $equal(mult(A,ld(A,mult(op_c,A))),mult(op_c,A)) )],[refute_1_2,refute_1_30]) ).
cnf(refute_1_32,plain,
mult(skolemFOFtoCNF_X3_1,op_c) = mult(op_c,skolemFOFtoCNF_X3_1),
inference(subst,[],[refute_1_31:[bind(A,$fot(skolemFOFtoCNF_X3_1))]]) ).
cnf(refute_1_33,plain,
mult(mult(rd(op_c,mult(unit,X_47)),X_47),unit) = mult(rd(op_c,mult(unit,X_47)),X_47),
inference(subst,[],[refute_1_6:[bind(A,$fot(mult(rd(op_c,mult(unit,X_47)),X_47)))]]) ).
cnf(refute_1_34,plain,
op_e = mult(mult(rd(op_c,mult(A,B)),B),A),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_35,plain,
op_e = mult(mult(rd(op_c,mult(unit,X_47)),X_47),unit),
inference(subst,[],[refute_1_34:[bind(A,$fot(unit)),bind(B,$fot(X_47))]]) ).
cnf(refute_1_36,plain,
( op_e != mult(mult(rd(op_c,mult(unit,X_47)),X_47),unit)
| mult(mult(rd(op_c,mult(unit,X_47)),X_47),unit) = op_e ),
inference(subst,[],[refute_1_13:[bind(X,$fot(op_e)),bind(Y,$fot(mult(mult(rd(op_c,mult(unit,X_47)),X_47),unit)))]]) ).
cnf(refute_1_37,plain,
mult(mult(rd(op_c,mult(unit,X_47)),X_47),unit) = op_e,
inference(resolve,[$cnf( $equal(op_e,mult(mult(rd(op_c,mult(unit,X_47)),X_47),unit)) )],[refute_1_35,refute_1_36]) ).
cnf(refute_1_38,plain,
( mult(mult(rd(op_c,mult(unit,X_47)),X_47),unit) != mult(rd(op_c,mult(unit,X_47)),X_47)
| mult(mult(rd(op_c,mult(unit,X_47)),X_47),unit) != op_e
| op_e = mult(rd(op_c,mult(unit,X_47)),X_47) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(rd(op_c,mult(unit,X_47)),X_47),unit),mult(rd(op_c,mult(unit,X_47)),X_47)) ),[0],$fot(op_e)]]) ).
cnf(refute_1_39,plain,
( mult(mult(rd(op_c,mult(unit,X_47)),X_47),unit) != mult(rd(op_c,mult(unit,X_47)),X_47)
| op_e = mult(rd(op_c,mult(unit,X_47)),X_47) ),
inference(resolve,[$cnf( $equal(mult(mult(rd(op_c,mult(unit,X_47)),X_47),unit),op_e) )],[refute_1_37,refute_1_38]) ).
cnf(refute_1_40,plain,
op_e = mult(rd(op_c,mult(unit,X_47)),X_47),
inference(resolve,[$cnf( $equal(mult(mult(rd(op_c,mult(unit,X_47)),X_47),unit),mult(rd(op_c,mult(unit,X_47)),X_47)) )],[refute_1_33,refute_1_39]) ).
cnf(refute_1_41,plain,
mult(rd(A,B),B) = A,
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_42,plain,
mult(rd(op_c,X_47),X_47) = op_c,
inference(subst,[],[refute_1_41:[bind(A,$fot(op_c)),bind(B,$fot(X_47))]]) ).
cnf(refute_1_43,plain,
mult(unit,X_47) = X_47,
inference(subst,[],[refute_1_19:[bind(A,$fot(X_47))]]) ).
cnf(refute_1_44,plain,
rd(op_c,mult(unit,X_47)) = rd(op_c,mult(unit,X_47)),
introduced(tautology,[refl,[$fot(rd(op_c,mult(unit,X_47)))]]) ).
cnf(refute_1_45,plain,
( mult(unit,X_47) != X_47
| rd(op_c,mult(unit,X_47)) != rd(op_c,mult(unit,X_47))
| rd(op_c,mult(unit,X_47)) = rd(op_c,X_47) ),
introduced(tautology,[equality,[$cnf( $equal(rd(op_c,mult(unit,X_47)),rd(op_c,mult(unit,X_47))) ),[1,1],$fot(X_47)]]) ).
cnf(refute_1_46,plain,
( mult(unit,X_47) != X_47
| rd(op_c,mult(unit,X_47)) = rd(op_c,X_47) ),
inference(resolve,[$cnf( $equal(rd(op_c,mult(unit,X_47)),rd(op_c,mult(unit,X_47))) )],[refute_1_44,refute_1_45]) ).
cnf(refute_1_47,plain,
rd(op_c,mult(unit,X_47)) = rd(op_c,X_47),
inference(resolve,[$cnf( $equal(mult(unit,X_47),X_47) )],[refute_1_43,refute_1_46]) ).
cnf(refute_1_48,plain,
mult(rd(op_c,mult(unit,X_47)),X_47) = mult(rd(op_c,mult(unit,X_47)),X_47),
introduced(tautology,[refl,[$fot(mult(rd(op_c,mult(unit,X_47)),X_47))]]) ).
cnf(refute_1_49,plain,
( mult(rd(op_c,mult(unit,X_47)),X_47) != mult(rd(op_c,mult(unit,X_47)),X_47)
| rd(op_c,mult(unit,X_47)) != rd(op_c,X_47)
| mult(rd(op_c,mult(unit,X_47)),X_47) = mult(rd(op_c,X_47),X_47) ),
introduced(tautology,[equality,[$cnf( $equal(mult(rd(op_c,mult(unit,X_47)),X_47),mult(rd(op_c,mult(unit,X_47)),X_47)) ),[1,0],$fot(rd(op_c,X_47))]]) ).
cnf(refute_1_50,plain,
( rd(op_c,mult(unit,X_47)) != rd(op_c,X_47)
| mult(rd(op_c,mult(unit,X_47)),X_47) = mult(rd(op_c,X_47),X_47) ),
inference(resolve,[$cnf( $equal(mult(rd(op_c,mult(unit,X_47)),X_47),mult(rd(op_c,mult(unit,X_47)),X_47)) )],[refute_1_48,refute_1_49]) ).
cnf(refute_1_51,plain,
mult(rd(op_c,mult(unit,X_47)),X_47) = mult(rd(op_c,X_47),X_47),
inference(resolve,[$cnf( $equal(rd(op_c,mult(unit,X_47)),rd(op_c,X_47)) )],[refute_1_47,refute_1_50]) ).
cnf(refute_1_52,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_1_53,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_1_13,refute_1_52]) ).
cnf(refute_1_54,plain,
( mult(rd(op_c,X_47),X_47) != op_c
| mult(rd(op_c,mult(unit,X_47)),X_47) != mult(rd(op_c,X_47),X_47)
| mult(rd(op_c,mult(unit,X_47)),X_47) = op_c ),
inference(subst,[],[refute_1_53:[bind(X,$fot(mult(rd(op_c,mult(unit,X_47)),X_47))),bind(Y,$fot(mult(rd(op_c,X_47),X_47))),bind(Z,$fot(op_c))]]) ).
cnf(refute_1_55,plain,
( mult(rd(op_c,X_47),X_47) != op_c
| mult(rd(op_c,mult(unit,X_47)),X_47) = op_c ),
inference(resolve,[$cnf( $equal(mult(rd(op_c,mult(unit,X_47)),X_47),mult(rd(op_c,X_47),X_47)) )],[refute_1_51,refute_1_54]) ).
cnf(refute_1_56,plain,
mult(rd(op_c,mult(unit,X_47)),X_47) = op_c,
inference(resolve,[$cnf( $equal(mult(rd(op_c,X_47),X_47),op_c) )],[refute_1_42,refute_1_55]) ).
cnf(refute_1_57,plain,
( mult(rd(op_c,mult(unit,X_47)),X_47) != op_c
| op_e != mult(rd(op_c,mult(unit,X_47)),X_47)
| op_e = op_c ),
introduced(tautology,[equality,[$cnf( $equal(op_e,mult(rd(op_c,mult(unit,X_47)),X_47)) ),[1],$fot(op_c)]]) ).
cnf(refute_1_58,plain,
( op_e != mult(rd(op_c,mult(unit,X_47)),X_47)
| op_e = op_c ),
inference(resolve,[$cnf( $equal(mult(rd(op_c,mult(unit,X_47)),X_47),op_c) )],[refute_1_56,refute_1_57]) ).
cnf(refute_1_59,plain,
op_e = op_c,
inference(resolve,[$cnf( $equal(op_e,mult(rd(op_c,mult(unit,X_47)),X_47)) )],[refute_1_40,refute_1_58]) ).
cnf(refute_1_60,plain,
mult(skolemFOFtoCNF_X3_1,op_e) = mult(skolemFOFtoCNF_X3_1,op_e),
introduced(tautology,[refl,[$fot(mult(skolemFOFtoCNF_X3_1,op_e))]]) ).
cnf(refute_1_61,plain,
( mult(skolemFOFtoCNF_X3_1,op_e) != mult(skolemFOFtoCNF_X3_1,op_e)
| op_e != op_c
| mult(skolemFOFtoCNF_X3_1,op_e) = mult(skolemFOFtoCNF_X3_1,op_c) ),
introduced(tautology,[equality,[$cnf( $equal(mult(skolemFOFtoCNF_X3_1,op_e),mult(skolemFOFtoCNF_X3_1,op_e)) ),[1,1],$fot(op_c)]]) ).
cnf(refute_1_62,plain,
( op_e != op_c
| mult(skolemFOFtoCNF_X3_1,op_e) = mult(skolemFOFtoCNF_X3_1,op_c) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X3_1,op_e),mult(skolemFOFtoCNF_X3_1,op_e)) )],[refute_1_60,refute_1_61]) ).
cnf(refute_1_63,plain,
mult(skolemFOFtoCNF_X3_1,op_e) = mult(skolemFOFtoCNF_X3_1,op_c),
inference(resolve,[$cnf( $equal(op_e,op_c) )],[refute_1_59,refute_1_62]) ).
cnf(refute_1_64,plain,
( mult(skolemFOFtoCNF_X3_1,op_c) != mult(op_c,skolemFOFtoCNF_X3_1)
| mult(skolemFOFtoCNF_X3_1,op_e) != mult(skolemFOFtoCNF_X3_1,op_c)
| mult(skolemFOFtoCNF_X3_1,op_e) = mult(op_c,skolemFOFtoCNF_X3_1) ),
inference(subst,[],[refute_1_53:[bind(X,$fot(mult(skolemFOFtoCNF_X3_1,op_e))),bind(Y,$fot(mult(skolemFOFtoCNF_X3_1,op_c))),bind(Z,$fot(mult(op_c,skolemFOFtoCNF_X3_1)))]]) ).
cnf(refute_1_65,plain,
( mult(skolemFOFtoCNF_X3_1,op_c) != mult(op_c,skolemFOFtoCNF_X3_1)
| mult(skolemFOFtoCNF_X3_1,op_e) = mult(op_c,skolemFOFtoCNF_X3_1) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X3_1,op_e),mult(skolemFOFtoCNF_X3_1,op_c)) )],[refute_1_63,refute_1_64]) ).
cnf(refute_1_66,plain,
mult(skolemFOFtoCNF_X3_1,op_e) = mult(op_c,skolemFOFtoCNF_X3_1),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X3_1,op_c),mult(op_c,skolemFOFtoCNF_X3_1)) )],[refute_1_32,refute_1_65]) ).
cnf(refute_1_67,plain,
mult(skolemFOFtoCNF_X2_1,mult(skolemFOFtoCNF_X3_1,op_e)) = mult(skolemFOFtoCNF_X2_1,mult(skolemFOFtoCNF_X3_1,op_e)),
introduced(tautology,[refl,[$fot(mult(skolemFOFtoCNF_X2_1,mult(skolemFOFtoCNF_X3_1,op_e)))]]) ).
cnf(refute_1_68,plain,
( mult(skolemFOFtoCNF_X2_1,mult(skolemFOFtoCNF_X3_1,op_e)) != mult(skolemFOFtoCNF_X2_1,mult(skolemFOFtoCNF_X3_1,op_e))
| mult(skolemFOFtoCNF_X3_1,op_e) != mult(op_c,skolemFOFtoCNF_X3_1)
| mult(skolemFOFtoCNF_X2_1,mult(skolemFOFtoCNF_X3_1,op_e)) = mult(skolemFOFtoCNF_X2_1,mult(op_c,skolemFOFtoCNF_X3_1)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(skolemFOFtoCNF_X2_1,mult(skolemFOFtoCNF_X3_1,op_e)),mult(skolemFOFtoCNF_X2_1,mult(skolemFOFtoCNF_X3_1,op_e))) ),[1,1],$fot(mult(op_c,skolemFOFtoCNF_X3_1))]]) ).
cnf(refute_1_69,plain,
( mult(skolemFOFtoCNF_X3_1,op_e) != mult(op_c,skolemFOFtoCNF_X3_1)
| mult(skolemFOFtoCNF_X2_1,mult(skolemFOFtoCNF_X3_1,op_e)) = mult(skolemFOFtoCNF_X2_1,mult(op_c,skolemFOFtoCNF_X3_1)) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X2_1,mult(skolemFOFtoCNF_X3_1,op_e)),mult(skolemFOFtoCNF_X2_1,mult(skolemFOFtoCNF_X3_1,op_e))) )],[refute_1_67,refute_1_68]) ).
cnf(refute_1_70,plain,
mult(skolemFOFtoCNF_X2_1,mult(skolemFOFtoCNF_X3_1,op_e)) = mult(skolemFOFtoCNF_X2_1,mult(op_c,skolemFOFtoCNF_X3_1)),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X3_1,op_e),mult(op_c,skolemFOFtoCNF_X3_1)) )],[refute_1_66,refute_1_69]) ).
cnf(refute_1_71,plain,
( mult(skolemFOFtoCNF_X2_1,mult(op_c,skolemFOFtoCNF_X3_1)) != mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e)
| mult(skolemFOFtoCNF_X2_1,mult(skolemFOFtoCNF_X3_1,op_e)) != mult(skolemFOFtoCNF_X2_1,mult(op_c,skolemFOFtoCNF_X3_1))
| mult(skolemFOFtoCNF_X2_1,mult(skolemFOFtoCNF_X3_1,op_e)) = mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e) ),
introduced(tautology,[equality,[$cnf( $equal(mult(skolemFOFtoCNF_X2_1,mult(skolemFOFtoCNF_X3_1,op_e)),mult(skolemFOFtoCNF_X2_1,mult(op_c,skolemFOFtoCNF_X3_1))) ),[1],$fot(mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e))]]) ).
cnf(refute_1_72,plain,
( mult(skolemFOFtoCNF_X2_1,mult(op_c,skolemFOFtoCNF_X3_1)) != mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e)
| mult(skolemFOFtoCNF_X2_1,mult(skolemFOFtoCNF_X3_1,op_e)) = mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X2_1,mult(skolemFOFtoCNF_X3_1,op_e)),mult(skolemFOFtoCNF_X2_1,mult(op_c,skolemFOFtoCNF_X3_1))) )],[refute_1_70,refute_1_71]) ).
cnf(refute_1_73,plain,
mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_c) = mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1)),
inference(subst,[],[refute_1_31:[bind(A,$fot(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1)))]]) ).
cnf(refute_1_74,plain,
mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e) = mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e),
introduced(tautology,[refl,[$fot(mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e))]]) ).
cnf(refute_1_75,plain,
( mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e) != mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e)
| op_e != op_c
| mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e) = mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_c) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e),mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e)) ),[1,1],$fot(op_c)]]) ).
cnf(refute_1_76,plain,
( op_e != op_c
| mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e) = mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_c) ),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e),mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e)) )],[refute_1_74,refute_1_75]) ).
cnf(refute_1_77,plain,
mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e) = mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_c),
inference(resolve,[$cnf( $equal(op_e,op_c) )],[refute_1_59,refute_1_76]) ).
cnf(refute_1_78,plain,
( mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_c) != mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1))
| mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e) != mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_c)
| mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e) = mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1)) ),
inference(subst,[],[refute_1_53:[bind(X,$fot(mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e))),bind(Y,$fot(mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_c))),bind(Z,$fot(mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1))))]]) ).
cnf(refute_1_79,plain,
( mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_c) != mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1))
| mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e) = mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1)) ),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e),mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_c)) )],[refute_1_77,refute_1_78]) ).
cnf(refute_1_80,plain,
mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e) = mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1)),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_c),mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1))) )],[refute_1_73,refute_1_79]) ).
cnf(refute_1_81,plain,
( mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e) != mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1))
| mult(skolemFOFtoCNF_X2_1,mult(op_c,skolemFOFtoCNF_X3_1)) != mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1))
| mult(skolemFOFtoCNF_X2_1,mult(op_c,skolemFOFtoCNF_X3_1)) = mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(skolemFOFtoCNF_X2_1,mult(op_c,skolemFOFtoCNF_X3_1)),mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e)) ),[1],$fot(mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1)))]]) ).
cnf(refute_1_82,plain,
( mult(skolemFOFtoCNF_X2_1,mult(op_c,skolemFOFtoCNF_X3_1)) != mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1))
| mult(skolemFOFtoCNF_X2_1,mult(op_c,skolemFOFtoCNF_X3_1)) = mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e) ),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e),mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1))) )],[refute_1_80,refute_1_81]) ).
cnf(refute_1_83,plain,
( mult(skolemFOFtoCNF_X2_1,mult(op_c,skolemFOFtoCNF_X3_1)) != mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1))
| mult(skolemFOFtoCNF_X2_1,mult(skolemFOFtoCNF_X3_1,op_e)) = mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X2_1,mult(op_c,skolemFOFtoCNF_X3_1)),mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e)) )],[refute_1_82,refute_1_72]) ).
cnf(refute_1_84,plain,
mult(skolemFOFtoCNF_X2_1,mult(op_c,skolemFOFtoCNF_X3_1)) != mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1)),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X2_1,mult(skolemFOFtoCNF_X3_1,op_e)),mult(mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1),op_e)) )],[refute_1_83,refute_1_0]) ).
cnf(refute_1_85,plain,
mult(op_c,mult(A,B)) = mult(mult(op_c,A),B),
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_86,plain,
mult(op_c,mult(X_69,X_70)) = mult(mult(op_c,X_69),X_70),
inference(subst,[],[refute_1_85:[bind(A,$fot(X_69)),bind(B,$fot(X_70))]]) ).
cnf(refute_1_87,plain,
mult(X_40,ld(X_40,mult(op_c,X_40))) = mult(op_c,X_40),
inference(subst,[],[refute_1_1:[bind(A,$fot(X_40)),bind(B,$fot(mult(op_c,X_40)))]]) ).
cnf(refute_1_88,plain,
op_d = ld(X_40,mult(op_c,X_40)),
inference(subst,[],[refute_1_3:[bind(A,$fot(X_40))]]) ).
cnf(refute_1_89,plain,
( op_d != ld(X_40,mult(op_c,X_40))
| ld(X_40,mult(op_c,X_40)) = op_d ),
inference(subst,[],[refute_1_13:[bind(X,$fot(op_d)),bind(Y,$fot(ld(X_40,mult(op_c,X_40))))]]) ).
cnf(refute_1_90,plain,
ld(X_40,mult(op_c,X_40)) = op_d,
inference(resolve,[$cnf( $equal(op_d,ld(X_40,mult(op_c,X_40))) )],[refute_1_88,refute_1_89]) ).
cnf(refute_1_91,plain,
( ld(X_40,mult(op_c,X_40)) != op_d
| mult(X_40,ld(X_40,mult(op_c,X_40))) != mult(op_c,X_40)
| mult(X_40,op_d) = mult(op_c,X_40) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_40,ld(X_40,mult(op_c,X_40))),mult(op_c,X_40)) ),[0,1],$fot(op_d)]]) ).
cnf(refute_1_92,plain,
( mult(X_40,ld(X_40,mult(op_c,X_40))) != mult(op_c,X_40)
| mult(X_40,op_d) = mult(op_c,X_40) ),
inference(resolve,[$cnf( $equal(ld(X_40,mult(op_c,X_40)),op_d) )],[refute_1_90,refute_1_91]) ).
cnf(refute_1_93,plain,
mult(X_40,op_d) = mult(op_c,X_40),
inference(resolve,[$cnf( $equal(mult(X_40,ld(X_40,mult(op_c,X_40))),mult(op_c,X_40)) )],[refute_1_87,refute_1_92]) ).
cnf(refute_1_94,plain,
mult(X_40,op_d) = mult(X_40,op_d),
introduced(tautology,[refl,[$fot(mult(X_40,op_d))]]) ).
cnf(refute_1_95,plain,
( mult(X_40,op_d) != mult(X_40,op_d)
| op_d != op_c
| mult(X_40,op_d) = mult(X_40,op_c) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_40,op_d),mult(X_40,op_d)) ),[1,1],$fot(op_c)]]) ).
cnf(refute_1_96,plain,
( op_d != op_c
| mult(X_40,op_d) = mult(X_40,op_c) ),
inference(resolve,[$cnf( $equal(mult(X_40,op_d),mult(X_40,op_d)) )],[refute_1_94,refute_1_95]) ).
cnf(refute_1_97,plain,
mult(X_40,op_d) = mult(X_40,op_c),
inference(resolve,[$cnf( $equal(op_d,op_c) )],[refute_1_23,refute_1_96]) ).
cnf(refute_1_98,plain,
( mult(X_40,op_d) != mult(X_40,op_c)
| mult(X_40,op_d) != mult(op_c,X_40)
| mult(X_40,op_c) = mult(op_c,X_40) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_40,op_d),mult(op_c,X_40)) ),[0],$fot(mult(X_40,op_c))]]) ).
cnf(refute_1_99,plain,
( mult(X_40,op_d) != mult(op_c,X_40)
| mult(X_40,op_c) = mult(op_c,X_40) ),
inference(resolve,[$cnf( $equal(mult(X_40,op_d),mult(X_40,op_c)) )],[refute_1_97,refute_1_98]) ).
cnf(refute_1_100,plain,
mult(X_40,op_c) = mult(op_c,X_40),
inference(resolve,[$cnf( $equal(mult(X_40,op_d),mult(op_c,X_40)) )],[refute_1_93,refute_1_99]) ).
cnf(refute_1_101,plain,
mult(X_69,op_c) = mult(op_c,X_69),
inference(subst,[],[refute_1_100:[bind(X_40,$fot(X_69))]]) ).
cnf(refute_1_102,plain,
( mult(X_69,op_c) != mult(op_c,X_69)
| mult(op_c,X_69) = mult(X_69,op_c) ),
inference(subst,[],[refute_1_13:[bind(X,$fot(mult(X_69,op_c))),bind(Y,$fot(mult(op_c,X_69)))]]) ).
cnf(refute_1_103,plain,
mult(op_c,X_69) = mult(X_69,op_c),
inference(resolve,[$cnf( $equal(mult(X_69,op_c),mult(op_c,X_69)) )],[refute_1_101,refute_1_102]) ).
cnf(refute_1_104,plain,
( mult(op_c,X_69) != mult(X_69,op_c)
| mult(op_c,mult(X_69,X_70)) != mult(mult(op_c,X_69),X_70)
| mult(op_c,mult(X_69,X_70)) = mult(mult(X_69,op_c),X_70) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_c,mult(X_69,X_70)),mult(mult(op_c,X_69),X_70)) ),[1,0],$fot(mult(X_69,op_c))]]) ).
cnf(refute_1_105,plain,
( mult(op_c,mult(X_69,X_70)) != mult(mult(op_c,X_69),X_70)
| mult(op_c,mult(X_69,X_70)) = mult(mult(X_69,op_c),X_70) ),
inference(resolve,[$cnf( $equal(mult(op_c,X_69),mult(X_69,op_c)) )],[refute_1_103,refute_1_104]) ).
cnf(refute_1_106,plain,
mult(op_c,mult(X_69,X_70)) = mult(mult(X_69,op_c),X_70),
inference(resolve,[$cnf( $equal(mult(op_c,mult(X_69,X_70)),mult(mult(op_c,X_69),X_70)) )],[refute_1_86,refute_1_105]) ).
cnf(refute_1_107,plain,
mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
inference(canonicalize,[],[normalize_1_18]) ).
cnf(refute_1_108,plain,
( mult(A,mult(op_c,B)) != mult(mult(A,op_c),B)
| mult(mult(A,op_c),B) = mult(A,mult(op_c,B)) ),
inference(subst,[],[refute_1_13:[bind(X,$fot(mult(A,mult(op_c,B)))),bind(Y,$fot(mult(mult(A,op_c),B)))]]) ).
cnf(refute_1_109,plain,
mult(mult(A,op_c),B) = mult(A,mult(op_c,B)),
inference(resolve,[$cnf( $equal(mult(A,mult(op_c,B)),mult(mult(A,op_c),B)) )],[refute_1_107,refute_1_108]) ).
cnf(refute_1_110,plain,
mult(mult(X_69,op_c),X_70) = mult(X_69,mult(op_c,X_70)),
inference(subst,[],[refute_1_109:[bind(A,$fot(X_69)),bind(B,$fot(X_70))]]) ).
cnf(refute_1_111,plain,
( mult(mult(X_69,op_c),X_70) != mult(X_69,mult(op_c,X_70))
| mult(op_c,mult(X_69,X_70)) != mult(mult(X_69,op_c),X_70)
| mult(op_c,mult(X_69,X_70)) = mult(X_69,mult(op_c,X_70)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_c,mult(X_69,X_70)),mult(mult(X_69,op_c),X_70)) ),[1],$fot(mult(X_69,mult(op_c,X_70)))]]) ).
cnf(refute_1_112,plain,
( mult(op_c,mult(X_69,X_70)) != mult(mult(X_69,op_c),X_70)
| mult(op_c,mult(X_69,X_70)) = mult(X_69,mult(op_c,X_70)) ),
inference(resolve,[$cnf( $equal(mult(mult(X_69,op_c),X_70),mult(X_69,mult(op_c,X_70))) )],[refute_1_110,refute_1_111]) ).
cnf(refute_1_113,plain,
mult(op_c,mult(X_69,X_70)) = mult(X_69,mult(op_c,X_70)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(X_69,X_70)),mult(mult(X_69,op_c),X_70)) )],[refute_1_106,refute_1_112]) ).
cnf(refute_1_114,plain,
( mult(op_c,mult(X_69,X_70)) != mult(X_69,mult(op_c,X_70))
| mult(X_69,mult(op_c,X_70)) = mult(op_c,mult(X_69,X_70)) ),
inference(subst,[],[refute_1_13:[bind(X,$fot(mult(op_c,mult(X_69,X_70)))),bind(Y,$fot(mult(X_69,mult(op_c,X_70))))]]) ).
cnf(refute_1_115,plain,
mult(X_69,mult(op_c,X_70)) = mult(op_c,mult(X_69,X_70)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(X_69,X_70)),mult(X_69,mult(op_c,X_70))) )],[refute_1_113,refute_1_114]) ).
cnf(refute_1_116,plain,
mult(skolemFOFtoCNF_X2_1,mult(op_c,skolemFOFtoCNF_X3_1)) = mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1)),
inference(subst,[],[refute_1_115:[bind(X_69,$fot(skolemFOFtoCNF_X2_1)),bind(X_70,$fot(skolemFOFtoCNF_X3_1))]]) ).
cnf(refute_1_117,plain,
( mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1)) != mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1))
| mult(skolemFOFtoCNF_X2_1,mult(op_c,skolemFOFtoCNF_X3_1)) != mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1))
| mult(skolemFOFtoCNF_X2_1,mult(op_c,skolemFOFtoCNF_X3_1)) = mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(skolemFOFtoCNF_X2_1,mult(op_c,skolemFOFtoCNF_X3_1)),mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1))) ),[1],$fot(mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1)))]]) ).
cnf(refute_1_118,plain,
( mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1)) != mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1))
| mult(skolemFOFtoCNF_X2_1,mult(op_c,skolemFOFtoCNF_X3_1)) = mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1)) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X2_1,mult(op_c,skolemFOFtoCNF_X3_1)),mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1))) )],[refute_1_116,refute_1_117]) ).
cnf(refute_1_119,plain,
mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1)) != mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1)),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X2_1,mult(op_c,skolemFOFtoCNF_X3_1)),mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1))) )],[refute_1_118,refute_1_84]) ).
cnf(refute_1_120,plain,
mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1)) = mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1)),
introduced(tautology,[refl,[$fot(mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1)))]]) ).
cnf(refute_1_121,plain,
$false,
inference(resolve,[$cnf( $equal(mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1)),mult(op_c,mult(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X3_1))) )],[refute_1_120,refute_1_119]) ).
fof(negate_2_0,plain,
~ ! [X2,X3] :
( ( mult(op_e,mult(X2,X3)) = mult(mult(op_e,X2),X3)
& mult(X2,mult(X3,op_e)) = mult(mult(X2,X3),op_e) )
=> mult(X2,mult(op_e,X3)) = mult(mult(X2,op_e),X3) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
? [X2,X3] :
( mult(X2,mult(op_e,X3)) != mult(mult(X2,op_e),X3)
& mult(X2,mult(X3,op_e)) = mult(mult(X2,X3),op_e)
& mult(op_e,mult(X2,X3)) = mult(mult(op_e,X2),X3) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_1,plain,
( mult(skolemFOFtoCNF_X2_2,mult(op_e,skolemFOFtoCNF_X3_2)) != mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2)
& mult(op_e,mult(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X3_2)) = mult(mult(op_e,skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X3_2)
& mult(skolemFOFtoCNF_X2_2,mult(skolemFOFtoCNF_X3_2,op_e)) = mult(mult(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X3_2),op_e) ),
inference(skolemize,[],[normalize_2_0]) ).
fof(normalize_2_2,plain,
mult(skolemFOFtoCNF_X2_2,mult(op_e,skolemFOFtoCNF_X3_2)) != mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2),
inference(conjunct,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
! [A] : mult(A,unit) = A,
inference(canonicalize,[],[f05]) ).
fof(normalize_2_4,plain,
! [A] : mult(A,unit) = A,
inference(specialize,[],[normalize_2_3]) ).
fof(normalize_2_5,plain,
! [A,B] : op_e = mult(mult(rd(op_c,mult(A,B)),B),A),
inference(canonicalize,[],[f12]) ).
fof(normalize_2_6,plain,
! [A,B] : op_e = mult(mult(rd(op_c,mult(A,B)),B),A),
inference(specialize,[],[normalize_2_5]) ).
fof(normalize_2_7,plain,
! [A,B] : mult(rd(A,B),B) = A,
inference(canonicalize,[],[f03]) ).
fof(normalize_2_8,plain,
! [A,B] : mult(rd(A,B),B) = A,
inference(specialize,[],[normalize_2_7]) ).
fof(normalize_2_9,plain,
! [A] : mult(unit,A) = A,
inference(canonicalize,[],[f06]) ).
fof(normalize_2_10,plain,
! [A] : mult(unit,A) = A,
inference(specialize,[],[normalize_2_9]) ).
fof(normalize_2_11,plain,
! [A,B] : mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
inference(canonicalize,[],[f10]) ).
fof(normalize_2_12,plain,
! [A,B] : mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
inference(specialize,[],[normalize_2_11]) ).
cnf(refute_2_0,plain,
mult(skolemFOFtoCNF_X2_2,mult(op_e,skolemFOFtoCNF_X3_2)) != mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2),
inference(canonicalize,[],[normalize_2_2]) ).
cnf(refute_2_1,plain,
mult(A,unit) = A,
inference(canonicalize,[],[normalize_2_4]) ).
cnf(refute_2_2,plain,
mult(mult(rd(op_c,mult(unit,X_77)),X_77),unit) = mult(rd(op_c,mult(unit,X_77)),X_77),
inference(subst,[],[refute_2_1:[bind(A,$fot(mult(rd(op_c,mult(unit,X_77)),X_77)))]]) ).
cnf(refute_2_3,plain,
op_e = mult(mult(rd(op_c,mult(A,B)),B),A),
inference(canonicalize,[],[normalize_2_6]) ).
cnf(refute_2_4,plain,
op_e = mult(mult(rd(op_c,mult(unit,X_77)),X_77),unit),
inference(subst,[],[refute_2_3:[bind(A,$fot(unit)),bind(B,$fot(X_77))]]) ).
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( $equal(X,X) )],[refute_2_5,refute_2_6]) ).
cnf(refute_2_8,plain,
( op_e != mult(mult(rd(op_c,mult(unit,X_77)),X_77),unit)
| mult(mult(rd(op_c,mult(unit,X_77)),X_77),unit) = op_e ),
inference(subst,[],[refute_2_7:[bind(X,$fot(op_e)),bind(Y,$fot(mult(mult(rd(op_c,mult(unit,X_77)),X_77),unit)))]]) ).
cnf(refute_2_9,plain,
mult(mult(rd(op_c,mult(unit,X_77)),X_77),unit) = op_e,
inference(resolve,[$cnf( $equal(op_e,mult(mult(rd(op_c,mult(unit,X_77)),X_77),unit)) )],[refute_2_4,refute_2_8]) ).
cnf(refute_2_10,plain,
( mult(mult(rd(op_c,mult(unit,X_77)),X_77),unit) != mult(rd(op_c,mult(unit,X_77)),X_77)
| mult(mult(rd(op_c,mult(unit,X_77)),X_77),unit) != op_e
| op_e = mult(rd(op_c,mult(unit,X_77)),X_77) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(rd(op_c,mult(unit,X_77)),X_77),unit),mult(rd(op_c,mult(unit,X_77)),X_77)) ),[0],$fot(op_e)]]) ).
cnf(refute_2_11,plain,
( mult(mult(rd(op_c,mult(unit,X_77)),X_77),unit) != mult(rd(op_c,mult(unit,X_77)),X_77)
| op_e = mult(rd(op_c,mult(unit,X_77)),X_77) ),
inference(resolve,[$cnf( $equal(mult(mult(rd(op_c,mult(unit,X_77)),X_77),unit),op_e) )],[refute_2_9,refute_2_10]) ).
cnf(refute_2_12,plain,
op_e = mult(rd(op_c,mult(unit,X_77)),X_77),
inference(resolve,[$cnf( $equal(mult(mult(rd(op_c,mult(unit,X_77)),X_77),unit),mult(rd(op_c,mult(unit,X_77)),X_77)) )],[refute_2_2,refute_2_11]) ).
cnf(refute_2_13,plain,
mult(rd(A,B),B) = A,
inference(canonicalize,[],[normalize_2_8]) ).
cnf(refute_2_14,plain,
mult(rd(op_c,X_77),X_77) = op_c,
inference(subst,[],[refute_2_13:[bind(A,$fot(op_c)),bind(B,$fot(X_77))]]) ).
cnf(refute_2_15,plain,
mult(unit,A) = A,
inference(canonicalize,[],[normalize_2_10]) ).
cnf(refute_2_16,plain,
mult(unit,X_77) = X_77,
inference(subst,[],[refute_2_15:[bind(A,$fot(X_77))]]) ).
cnf(refute_2_17,plain,
rd(op_c,mult(unit,X_77)) = rd(op_c,mult(unit,X_77)),
introduced(tautology,[refl,[$fot(rd(op_c,mult(unit,X_77)))]]) ).
cnf(refute_2_18,plain,
( mult(unit,X_77) != X_77
| rd(op_c,mult(unit,X_77)) != rd(op_c,mult(unit,X_77))
| rd(op_c,mult(unit,X_77)) = rd(op_c,X_77) ),
introduced(tautology,[equality,[$cnf( $equal(rd(op_c,mult(unit,X_77)),rd(op_c,mult(unit,X_77))) ),[1,1],$fot(X_77)]]) ).
cnf(refute_2_19,plain,
( mult(unit,X_77) != X_77
| rd(op_c,mult(unit,X_77)) = rd(op_c,X_77) ),
inference(resolve,[$cnf( $equal(rd(op_c,mult(unit,X_77)),rd(op_c,mult(unit,X_77))) )],[refute_2_17,refute_2_18]) ).
cnf(refute_2_20,plain,
rd(op_c,mult(unit,X_77)) = rd(op_c,X_77),
inference(resolve,[$cnf( $equal(mult(unit,X_77),X_77) )],[refute_2_16,refute_2_19]) ).
cnf(refute_2_21,plain,
mult(rd(op_c,mult(unit,X_77)),X_77) = mult(rd(op_c,mult(unit,X_77)),X_77),
introduced(tautology,[refl,[$fot(mult(rd(op_c,mult(unit,X_77)),X_77))]]) ).
cnf(refute_2_22,plain,
( mult(rd(op_c,mult(unit,X_77)),X_77) != mult(rd(op_c,mult(unit,X_77)),X_77)
| rd(op_c,mult(unit,X_77)) != rd(op_c,X_77)
| mult(rd(op_c,mult(unit,X_77)),X_77) = mult(rd(op_c,X_77),X_77) ),
introduced(tautology,[equality,[$cnf( $equal(mult(rd(op_c,mult(unit,X_77)),X_77),mult(rd(op_c,mult(unit,X_77)),X_77)) ),[1,0],$fot(rd(op_c,X_77))]]) ).
cnf(refute_2_23,plain,
( rd(op_c,mult(unit,X_77)) != rd(op_c,X_77)
| mult(rd(op_c,mult(unit,X_77)),X_77) = mult(rd(op_c,X_77),X_77) ),
inference(resolve,[$cnf( $equal(mult(rd(op_c,mult(unit,X_77)),X_77),mult(rd(op_c,mult(unit,X_77)),X_77)) )],[refute_2_21,refute_2_22]) ).
cnf(refute_2_24,plain,
mult(rd(op_c,mult(unit,X_77)),X_77) = mult(rd(op_c,X_77),X_77),
inference(resolve,[$cnf( $equal(rd(op_c,mult(unit,X_77)),rd(op_c,X_77)) )],[refute_2_20,refute_2_23]) ).
cnf(refute_2_25,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_2_26,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_2_7,refute_2_25]) ).
cnf(refute_2_27,plain,
( mult(rd(op_c,X_77),X_77) != op_c
| mult(rd(op_c,mult(unit,X_77)),X_77) != mult(rd(op_c,X_77),X_77)
| mult(rd(op_c,mult(unit,X_77)),X_77) = op_c ),
inference(subst,[],[refute_2_26:[bind(X,$fot(mult(rd(op_c,mult(unit,X_77)),X_77))),bind(Y,$fot(mult(rd(op_c,X_77),X_77))),bind(Z,$fot(op_c))]]) ).
cnf(refute_2_28,plain,
( mult(rd(op_c,X_77),X_77) != op_c
| mult(rd(op_c,mult(unit,X_77)),X_77) = op_c ),
inference(resolve,[$cnf( $equal(mult(rd(op_c,mult(unit,X_77)),X_77),mult(rd(op_c,X_77),X_77)) )],[refute_2_24,refute_2_27]) ).
cnf(refute_2_29,plain,
mult(rd(op_c,mult(unit,X_77)),X_77) = op_c,
inference(resolve,[$cnf( $equal(mult(rd(op_c,X_77),X_77),op_c) )],[refute_2_14,refute_2_28]) ).
cnf(refute_2_30,plain,
( mult(rd(op_c,mult(unit,X_77)),X_77) != op_c
| op_e != mult(rd(op_c,mult(unit,X_77)),X_77)
| op_e = op_c ),
introduced(tautology,[equality,[$cnf( $equal(op_e,mult(rd(op_c,mult(unit,X_77)),X_77)) ),[1],$fot(op_c)]]) ).
cnf(refute_2_31,plain,
( op_e != mult(rd(op_c,mult(unit,X_77)),X_77)
| op_e = op_c ),
inference(resolve,[$cnf( $equal(mult(rd(op_c,mult(unit,X_77)),X_77),op_c) )],[refute_2_29,refute_2_30]) ).
cnf(refute_2_32,plain,
op_e = op_c,
inference(resolve,[$cnf( $equal(op_e,mult(rd(op_c,mult(unit,X_77)),X_77)) )],[refute_2_12,refute_2_31]) ).
cnf(refute_2_33,plain,
mult(op_e,skolemFOFtoCNF_X3_2) = mult(op_e,skolemFOFtoCNF_X3_2),
introduced(tautology,[refl,[$fot(mult(op_e,skolemFOFtoCNF_X3_2))]]) ).
cnf(refute_2_34,plain,
( mult(op_e,skolemFOFtoCNF_X3_2) != mult(op_e,skolemFOFtoCNF_X3_2)
| op_e != op_c
| mult(op_e,skolemFOFtoCNF_X3_2) = mult(op_c,skolemFOFtoCNF_X3_2) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_e,skolemFOFtoCNF_X3_2),mult(op_e,skolemFOFtoCNF_X3_2)) ),[1,0],$fot(op_c)]]) ).
cnf(refute_2_35,plain,
( op_e != op_c
| mult(op_e,skolemFOFtoCNF_X3_2) = mult(op_c,skolemFOFtoCNF_X3_2) ),
inference(resolve,[$cnf( $equal(mult(op_e,skolemFOFtoCNF_X3_2),mult(op_e,skolemFOFtoCNF_X3_2)) )],[refute_2_33,refute_2_34]) ).
cnf(refute_2_36,plain,
mult(op_e,skolemFOFtoCNF_X3_2) = mult(op_c,skolemFOFtoCNF_X3_2),
inference(resolve,[$cnf( $equal(op_e,op_c) )],[refute_2_32,refute_2_35]) ).
cnf(refute_2_37,plain,
mult(skolemFOFtoCNF_X2_2,mult(op_e,skolemFOFtoCNF_X3_2)) = mult(skolemFOFtoCNF_X2_2,mult(op_e,skolemFOFtoCNF_X3_2)),
introduced(tautology,[refl,[$fot(mult(skolemFOFtoCNF_X2_2,mult(op_e,skolemFOFtoCNF_X3_2)))]]) ).
cnf(refute_2_38,plain,
( mult(op_e,skolemFOFtoCNF_X3_2) != mult(op_c,skolemFOFtoCNF_X3_2)
| mult(skolemFOFtoCNF_X2_2,mult(op_e,skolemFOFtoCNF_X3_2)) != mult(skolemFOFtoCNF_X2_2,mult(op_e,skolemFOFtoCNF_X3_2))
| mult(skolemFOFtoCNF_X2_2,mult(op_e,skolemFOFtoCNF_X3_2)) = mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(skolemFOFtoCNF_X2_2,mult(op_e,skolemFOFtoCNF_X3_2)),mult(skolemFOFtoCNF_X2_2,mult(op_e,skolemFOFtoCNF_X3_2))) ),[1,1],$fot(mult(op_c,skolemFOFtoCNF_X3_2))]]) ).
cnf(refute_2_39,plain,
( mult(op_e,skolemFOFtoCNF_X3_2) != mult(op_c,skolemFOFtoCNF_X3_2)
| mult(skolemFOFtoCNF_X2_2,mult(op_e,skolemFOFtoCNF_X3_2)) = mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2)) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X2_2,mult(op_e,skolemFOFtoCNF_X3_2)),mult(skolemFOFtoCNF_X2_2,mult(op_e,skolemFOFtoCNF_X3_2))) )],[refute_2_37,refute_2_38]) ).
cnf(refute_2_40,plain,
mult(skolemFOFtoCNF_X2_2,mult(op_e,skolemFOFtoCNF_X3_2)) = mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2)),
inference(resolve,[$cnf( $equal(mult(op_e,skolemFOFtoCNF_X3_2),mult(op_c,skolemFOFtoCNF_X3_2)) )],[refute_2_36,refute_2_39]) ).
cnf(refute_2_41,plain,
( mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2)) != mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2)
| mult(skolemFOFtoCNF_X2_2,mult(op_e,skolemFOFtoCNF_X3_2)) != mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2))
| mult(skolemFOFtoCNF_X2_2,mult(op_e,skolemFOFtoCNF_X3_2)) = mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2) ),
introduced(tautology,[equality,[$cnf( $equal(mult(skolemFOFtoCNF_X2_2,mult(op_e,skolemFOFtoCNF_X3_2)),mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2))) ),[1],$fot(mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2))]]) ).
cnf(refute_2_42,plain,
( mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2)) != mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2)
| mult(skolemFOFtoCNF_X2_2,mult(op_e,skolemFOFtoCNF_X3_2)) = mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X2_2,mult(op_e,skolemFOFtoCNF_X3_2)),mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2))) )],[refute_2_40,refute_2_41]) ).
cnf(refute_2_43,plain,
mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
inference(canonicalize,[],[normalize_2_12]) ).
cnf(refute_2_44,plain,
( mult(A,mult(op_c,B)) != mult(mult(A,op_c),B)
| mult(mult(A,op_c),B) = mult(A,mult(op_c,B)) ),
inference(subst,[],[refute_2_7:[bind(X,$fot(mult(A,mult(op_c,B)))),bind(Y,$fot(mult(mult(A,op_c),B)))]]) ).
cnf(refute_2_45,plain,
mult(mult(A,op_c),B) = mult(A,mult(op_c,B)),
inference(resolve,[$cnf( $equal(mult(A,mult(op_c,B)),mult(mult(A,op_c),B)) )],[refute_2_43,refute_2_44]) ).
cnf(refute_2_46,plain,
mult(mult(skolemFOFtoCNF_X2_2,op_c),skolemFOFtoCNF_X3_2) = mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2)),
inference(subst,[],[refute_2_45:[bind(A,$fot(skolemFOFtoCNF_X2_2)),bind(B,$fot(skolemFOFtoCNF_X3_2))]]) ).
cnf(refute_2_47,plain,
mult(skolemFOFtoCNF_X2_2,op_e) = mult(skolemFOFtoCNF_X2_2,op_e),
introduced(tautology,[refl,[$fot(mult(skolemFOFtoCNF_X2_2,op_e))]]) ).
cnf(refute_2_48,plain,
( mult(skolemFOFtoCNF_X2_2,op_e) != mult(skolemFOFtoCNF_X2_2,op_e)
| op_e != op_c
| mult(skolemFOFtoCNF_X2_2,op_e) = mult(skolemFOFtoCNF_X2_2,op_c) ),
introduced(tautology,[equality,[$cnf( $equal(mult(skolemFOFtoCNF_X2_2,op_e),mult(skolemFOFtoCNF_X2_2,op_e)) ),[1,1],$fot(op_c)]]) ).
cnf(refute_2_49,plain,
( op_e != op_c
| mult(skolemFOFtoCNF_X2_2,op_e) = mult(skolemFOFtoCNF_X2_2,op_c) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X2_2,op_e),mult(skolemFOFtoCNF_X2_2,op_e)) )],[refute_2_47,refute_2_48]) ).
cnf(refute_2_50,plain,
mult(skolemFOFtoCNF_X2_2,op_e) = mult(skolemFOFtoCNF_X2_2,op_c),
inference(resolve,[$cnf( $equal(op_e,op_c) )],[refute_2_32,refute_2_49]) ).
cnf(refute_2_51,plain,
mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2) = mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2),
introduced(tautology,[refl,[$fot(mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2))]]) ).
cnf(refute_2_52,plain,
( mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2) != mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2)
| mult(skolemFOFtoCNF_X2_2,op_e) != mult(skolemFOFtoCNF_X2_2,op_c)
| mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2) = mult(mult(skolemFOFtoCNF_X2_2,op_c),skolemFOFtoCNF_X3_2) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2),mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2)) ),[1,0],$fot(mult(skolemFOFtoCNF_X2_2,op_c))]]) ).
cnf(refute_2_53,plain,
( mult(skolemFOFtoCNF_X2_2,op_e) != mult(skolemFOFtoCNF_X2_2,op_c)
| mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2) = mult(mult(skolemFOFtoCNF_X2_2,op_c),skolemFOFtoCNF_X3_2) ),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2),mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2)) )],[refute_2_51,refute_2_52]) ).
cnf(refute_2_54,plain,
mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2) = mult(mult(skolemFOFtoCNF_X2_2,op_c),skolemFOFtoCNF_X3_2),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X2_2,op_e),mult(skolemFOFtoCNF_X2_2,op_c)) )],[refute_2_50,refute_2_53]) ).
cnf(refute_2_55,plain,
( mult(mult(skolemFOFtoCNF_X2_2,op_c),skolemFOFtoCNF_X3_2) != mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2))
| mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2) != mult(mult(skolemFOFtoCNF_X2_2,op_c),skolemFOFtoCNF_X3_2)
| mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2) = mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2)) ),
inference(subst,[],[refute_2_26:[bind(X,$fot(mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2))),bind(Y,$fot(mult(mult(skolemFOFtoCNF_X2_2,op_c),skolemFOFtoCNF_X3_2))),bind(Z,$fot(mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2))))]]) ).
cnf(refute_2_56,plain,
( mult(mult(skolemFOFtoCNF_X2_2,op_c),skolemFOFtoCNF_X3_2) != mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2))
| mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2) = mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2)) ),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2),mult(mult(skolemFOFtoCNF_X2_2,op_c),skolemFOFtoCNF_X3_2)) )],[refute_2_54,refute_2_55]) ).
cnf(refute_2_57,plain,
mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2) = mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2)),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X2_2,op_c),skolemFOFtoCNF_X3_2),mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2))) )],[refute_2_46,refute_2_56]) ).
cnf(refute_2_58,plain,
( mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2) != mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2))
| mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2)) != mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2))
| mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2)) = mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2)),mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2)) ),[1],$fot(mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2)))]]) ).
cnf(refute_2_59,plain,
( mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2)) != mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2))
| mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2)) = mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2) ),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2),mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2))) )],[refute_2_57,refute_2_58]) ).
cnf(refute_2_60,plain,
( mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2)) != mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2))
| mult(skolemFOFtoCNF_X2_2,mult(op_e,skolemFOFtoCNF_X3_2)) = mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2)),mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2)) )],[refute_2_59,refute_2_42]) ).
cnf(refute_2_61,plain,
mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2)) != mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2)),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X2_2,mult(op_e,skolemFOFtoCNF_X3_2)),mult(mult(skolemFOFtoCNF_X2_2,op_e),skolemFOFtoCNF_X3_2)) )],[refute_2_60,refute_2_0]) ).
cnf(refute_2_62,plain,
mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2)) = mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2)),
introduced(tautology,[refl,[$fot(mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2)))]]) ).
cnf(refute_2_63,plain,
$false,
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2)),mult(skolemFOFtoCNF_X2_2,mult(op_c,skolemFOFtoCNF_X3_2))) )],[refute_2_62,refute_2_61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP703+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 01:15:08 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.49
% 0.20/0.49 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.51
%------------------------------------------------------------------------------