TSTP Solution File: GRP702+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP702+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 10:50:20 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 60
% Syntax : Number of formulae : 234 ( 136 unt; 0 def)
% Number of atoms : 379 ( 376 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 294 ( 149 ~; 131 |; 10 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 176 ( 0 sgn 67 !; 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(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(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(goals,conjecture,
! [X0,X1] :
( mult(op_d,mult(X0,X1)) = mult(mult(op_d,X0),X1)
& mult(X0,mult(X1,op_d)) = mult(mult(X0,X1),op_d)
& mult(X0,mult(op_d,X1)) = mult(mult(X0,op_d),X1) ) ).
fof(subgoal_0,plain,
! [X0,X1] : mult(op_d,mult(X0,X1)) = mult(mult(op_d,X0),X1),
inference(strip,[],[goals]) ).
fof(subgoal_1,plain,
! [X0,X1] :
( mult(op_d,mult(X0,X1)) = mult(mult(op_d,X0),X1)
=> mult(X0,mult(X1,op_d)) = mult(mult(X0,X1),op_d) ),
inference(strip,[],[goals]) ).
fof(subgoal_2,plain,
! [X0,X1] :
( ( mult(op_d,mult(X0,X1)) = mult(mult(op_d,X0),X1)
& mult(X0,mult(X1,op_d)) = mult(mult(X0,X1),op_d) )
=> mult(X0,mult(op_d,X1)) = mult(mult(X0,op_d),X1) ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0,X1] : mult(op_d,mult(X0,X1)) = mult(mult(op_d,X0),X1),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0,X1] : mult(op_d,mult(X0,X1)) != mult(mult(op_d,X0),X1),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
mult(op_d,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1),
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] : mult(op_c,mult(A,B)) = mult(mult(op_c,A),B),
inference(canonicalize,[],[f08]) ).
fof(normalize_0_11,plain,
! [A,B] : mult(op_c,mult(A,B)) = mult(mult(op_c,A),B),
inference(specialize,[],[normalize_0_10]) ).
cnf(refute_0_0,plain,
mult(op_d,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1),
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(unit,ld(unit,op_c)) = op_c,
inference(subst,[],[refute_0_1:[bind(A,$fot(unit)),bind(B,$fot(op_c))]]) ).
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(unit,mult(op_c,unit)),
inference(subst,[],[refute_0_3:[bind(A,$fot(unit))]]) ).
cnf(refute_0_5,plain,
mult(A,unit) = A,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_6,plain,
mult(op_c,unit) = op_c,
inference(subst,[],[refute_0_5:[bind(A,$fot(op_c))]]) ).
cnf(refute_0_7,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_8,plain,
( op_d != ld(unit,mult(op_c,unit))
| op_d = ld(unit,op_c) ),
inference(resolve,[$cnf( $equal(mult(op_c,unit),op_c) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
op_d = ld(unit,op_c),
inference(resolve,[$cnf( $equal(op_d,ld(unit,mult(op_c,unit))) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_11,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_12,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( op_d != ld(unit,op_c)
| ld(unit,op_c) = op_d ),
inference(subst,[],[refute_0_12:[bind(X,$fot(op_d)),bind(Y,$fot(ld(unit,op_c)))]]) ).
cnf(refute_0_14,plain,
ld(unit,op_c) = op_d,
inference(resolve,[$cnf( $equal(op_d,ld(unit,op_c)) )],[refute_0_9,refute_0_13]) ).
cnf(refute_0_15,plain,
( ld(unit,op_c) != op_d
| mult(unit,ld(unit,op_c)) != op_c
| mult(unit,op_d) = op_c ),
introduced(tautology,[equality,[$cnf( $equal(mult(unit,ld(unit,op_c)),op_c) ),[0,1],$fot(op_d)]]) ).
cnf(refute_0_16,plain,
( mult(unit,ld(unit,op_c)) != op_c
| mult(unit,op_d) = op_c ),
inference(resolve,[$cnf( $equal(ld(unit,op_c),op_d) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
mult(unit,op_d) = op_c,
inference(resolve,[$cnf( $equal(mult(unit,ld(unit,op_c)),op_c) )],[refute_0_2,refute_0_16]) ).
cnf(refute_0_18,plain,
mult(unit,A) = A,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_19,plain,
mult(unit,op_d) = op_d,
inference(subst,[],[refute_0_18:[bind(A,$fot(op_d))]]) ).
cnf(refute_0_20,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_21,plain,
( mult(unit,op_d) != op_c
| op_d = op_c ),
inference(resolve,[$cnf( $equal(mult(unit,op_d),op_d) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
op_d = op_c,
inference(resolve,[$cnf( $equal(mult(unit,op_d),op_c) )],[refute_0_17,refute_0_21]) ).
cnf(refute_0_23,plain,
mult(op_d,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = mult(op_d,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),
introduced(tautology,[refl,[$fot(mult(op_d,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_24,plain,
( mult(op_d,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != mult(op_d,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| op_d != op_c
| mult(op_d,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_d,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),mult(op_d,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) ),[1,0],$fot(op_c)]]) ).
cnf(refute_0_25,plain,
( op_d != op_c
| mult(op_d,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) ),
inference(resolve,[$cnf( $equal(mult(op_d,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),mult(op_d,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
mult(op_d,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),
inference(resolve,[$cnf( $equal(op_d,op_c) )],[refute_0_22,refute_0_25]) ).
cnf(refute_0_27,plain,
( mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)
| mult(op_d,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| mult(op_d,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_d,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) ),[1],$fot(mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_28,plain,
( mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)
| mult(op_d,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) ),
inference(resolve,[$cnf( $equal(mult(op_d,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
mult(op_c,mult(A,B)) = mult(mult(op_c,A),B),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_30,plain,
( mult(op_c,mult(A,B)) != mult(mult(op_c,A),B)
| mult(mult(op_c,A),B) = mult(op_c,mult(A,B)) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(mult(op_c,mult(A,B)))),bind(Y,$fot(mult(mult(op_c,A),B)))]]) ).
cnf(refute_0_31,plain,
mult(mult(op_c,A),B) = mult(op_c,mult(A,B)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(A,B)),mult(mult(op_c,A),B)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
mult(mult(op_c,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) = mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),
inference(subst,[],[refute_0_31:[bind(A,$fot(skolemFOFtoCNF_X0)),bind(B,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_33,plain,
mult(op_d,skolemFOFtoCNF_X0) = mult(op_d,skolemFOFtoCNF_X0),
introduced(tautology,[refl,[$fot(mult(op_d,skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_34,plain,
( mult(op_d,skolemFOFtoCNF_X0) != mult(op_d,skolemFOFtoCNF_X0)
| op_d != op_c
| mult(op_d,skolemFOFtoCNF_X0) = mult(op_c,skolemFOFtoCNF_X0) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_d,skolemFOFtoCNF_X0),mult(op_d,skolemFOFtoCNF_X0)) ),[1,0],$fot(op_c)]]) ).
cnf(refute_0_35,plain,
( op_d != op_c
| mult(op_d,skolemFOFtoCNF_X0) = mult(op_c,skolemFOFtoCNF_X0) ),
inference(resolve,[$cnf( $equal(mult(op_d,skolemFOFtoCNF_X0),mult(op_d,skolemFOFtoCNF_X0)) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
mult(op_d,skolemFOFtoCNF_X0) = mult(op_c,skolemFOFtoCNF_X0),
inference(resolve,[$cnf( $equal(op_d,op_c) )],[refute_0_22,refute_0_35]) ).
cnf(refute_0_37,plain,
mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) = mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1),
introduced(tautology,[refl,[$fot(mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_38,plain,
( mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) != mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)
| mult(op_d,skolemFOFtoCNF_X0) != mult(op_c,skolemFOFtoCNF_X0)
| mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) = mult(mult(op_c,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1),mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)) ),[1,0],$fot(mult(op_c,skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_39,plain,
( mult(op_d,skolemFOFtoCNF_X0) != mult(op_c,skolemFOFtoCNF_X0)
| mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) = mult(mult(op_c,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) ),
inference(resolve,[$cnf( $equal(mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1),mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) = mult(mult(op_c,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1),
inference(resolve,[$cnf( $equal(mult(op_d,skolemFOFtoCNF_X0),mult(op_c,skolemFOFtoCNF_X0)) )],[refute_0_36,refute_0_39]) ).
cnf(refute_0_41,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_42,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_12,refute_0_41]) ).
cnf(refute_0_43,plain,
( mult(mult(op_c,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) != mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) != mult(mult(op_c,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)
| mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) = mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) ),
inference(subst,[],[refute_0_42:[bind(X,$fot(mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1))),bind(Y,$fot(mult(mult(op_c,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1))),bind(Z,$fot(mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))))]]) ).
cnf(refute_0_44,plain,
( mult(mult(op_c,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) != mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) = mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) ),
inference(resolve,[$cnf( $equal(mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1),mult(mult(op_c,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)) )],[refute_0_40,refute_0_43]) ).
cnf(refute_0_45,plain,
mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) = mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),
inference(resolve,[$cnf( $equal(mult(mult(op_c,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1),mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) )],[refute_0_32,refute_0_44]) ).
cnf(refute_0_46,plain,
( mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) != mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)) ),[1],$fot(mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_47,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_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) ),
inference(resolve,[$cnf( $equal(mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1),mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| mult(op_d,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) ),
inference(resolve,[$cnf( $equal(mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)) )],[refute_0_47,refute_0_28]) ).
cnf(refute_0_49,plain,
mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),
inference(resolve,[$cnf( $equal(mult(op_d,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),mult(mult(op_d,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)) )],[refute_0_48,refute_0_0]) ).
cnf(refute_0_50,plain,
mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),
introduced(tautology,[refl,[$fot(mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_51,plain,
$false,
inference(resolve,[$cnf( $equal(mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),mult(op_c,mult(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) )],[refute_0_50,refute_0_49]) ).
fof(negate_1_0,plain,
~ ! [X0,X1] :
( mult(op_d,mult(X0,X1)) = mult(mult(op_d,X0),X1)
=> mult(X0,mult(X1,op_d)) = mult(mult(X0,X1),op_d) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [X0,X1] :
( mult(X0,mult(X1,op_d)) != mult(mult(X0,X1),op_d)
& mult(op_d,mult(X0,X1)) = mult(mult(op_d,X0),X1) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( mult(skolemFOFtoCNF_X0_1,mult(skolemFOFtoCNF_X1_1,op_d)) != mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d)
& mult(op_d,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)) = mult(mult(op_d,skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_1) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
mult(skolemFOFtoCNF_X0_1,mult(skolemFOFtoCNF_X1_1,op_d)) != mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d),
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] : mult(op_c,mult(A,B)) = mult(mult(op_c,A),B),
inference(canonicalize,[],[f08]) ).
fof(normalize_1_12,plain,
! [A,B] : mult(op_c,mult(A,B)) = mult(mult(op_c,A),B),
inference(specialize,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
! [A,B] : mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
inference(canonicalize,[],[f10]) ).
fof(normalize_1_14,plain,
! [A,B] : mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
inference(specialize,[],[normalize_1_13]) ).
cnf(refute_1_0,plain,
mult(skolemFOFtoCNF_X0_1,mult(skolemFOFtoCNF_X1_1,op_d)) != mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d),
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(X_12,ld(X_12,mult(op_c,X_12))) = mult(op_c,X_12),
inference(subst,[],[refute_1_1:[bind(A,$fot(X_12)),bind(B,$fot(mult(op_c,X_12)))]]) ).
cnf(refute_1_3,plain,
op_d = ld(A,mult(op_c,A)),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_4,plain,
op_d = ld(X_12,mult(op_c,X_12)),
inference(subst,[],[refute_1_3:[bind(A,$fot(X_12))]]) ).
cnf(refute_1_5,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_6,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_7,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_5,refute_1_6]) ).
cnf(refute_1_8,plain,
( op_d != ld(X_12,mult(op_c,X_12))
| ld(X_12,mult(op_c,X_12)) = op_d ),
inference(subst,[],[refute_1_7:[bind(X,$fot(op_d)),bind(Y,$fot(ld(X_12,mult(op_c,X_12))))]]) ).
cnf(refute_1_9,plain,
ld(X_12,mult(op_c,X_12)) = op_d,
inference(resolve,[$cnf( $equal(op_d,ld(X_12,mult(op_c,X_12))) )],[refute_1_4,refute_1_8]) ).
cnf(refute_1_10,plain,
( ld(X_12,mult(op_c,X_12)) != op_d
| mult(X_12,ld(X_12,mult(op_c,X_12))) != mult(op_c,X_12)
| mult(X_12,op_d) = mult(op_c,X_12) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_12,ld(X_12,mult(op_c,X_12))),mult(op_c,X_12)) ),[0,1],$fot(op_d)]]) ).
cnf(refute_1_11,plain,
( mult(X_12,ld(X_12,mult(op_c,X_12))) != mult(op_c,X_12)
| mult(X_12,op_d) = mult(op_c,X_12) ),
inference(resolve,[$cnf( $equal(ld(X_12,mult(op_c,X_12)),op_d) )],[refute_1_9,refute_1_10]) ).
cnf(refute_1_12,plain,
mult(X_12,op_d) = mult(op_c,X_12),
inference(resolve,[$cnf( $equal(mult(X_12,ld(X_12,mult(op_c,X_12))),mult(op_c,X_12)) )],[refute_1_2,refute_1_11]) ).
cnf(refute_1_13,plain,
mult(unit,ld(unit,op_c)) = op_c,
inference(subst,[],[refute_1_1:[bind(A,$fot(unit)),bind(B,$fot(op_c))]]) ).
cnf(refute_1_14,plain,
op_d = ld(unit,mult(op_c,unit)),
inference(subst,[],[refute_1_3:[bind(A,$fot(unit))]]) ).
cnf(refute_1_15,plain,
mult(A,unit) = A,
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_16,plain,
mult(op_c,unit) = op_c,
inference(subst,[],[refute_1_15:[bind(A,$fot(op_c))]]) ).
cnf(refute_1_17,plain,
( mult(op_c,unit) != op_c
| op_d != ld(unit,mult(op_c,unit))
| op_d = ld(unit,op_c) ),
introduced(tautology,[equality,[$cnf( $equal(op_d,ld(unit,mult(op_c,unit))) ),[1,1],$fot(op_c)]]) ).
cnf(refute_1_18,plain,
( op_d != ld(unit,mult(op_c,unit))
| op_d = ld(unit,op_c) ),
inference(resolve,[$cnf( $equal(mult(op_c,unit),op_c) )],[refute_1_16,refute_1_17]) ).
cnf(refute_1_19,plain,
op_d = ld(unit,op_c),
inference(resolve,[$cnf( $equal(op_d,ld(unit,mult(op_c,unit))) )],[refute_1_14,refute_1_18]) ).
cnf(refute_1_20,plain,
( op_d != ld(unit,op_c)
| ld(unit,op_c) = op_d ),
inference(subst,[],[refute_1_7:[bind(X,$fot(op_d)),bind(Y,$fot(ld(unit,op_c)))]]) ).
cnf(refute_1_21,plain,
ld(unit,op_c) = op_d,
inference(resolve,[$cnf( $equal(op_d,ld(unit,op_c)) )],[refute_1_19,refute_1_20]) ).
cnf(refute_1_22,plain,
( ld(unit,op_c) != op_d
| mult(unit,ld(unit,op_c)) != op_c
| mult(unit,op_d) = op_c ),
introduced(tautology,[equality,[$cnf( $equal(mult(unit,ld(unit,op_c)),op_c) ),[0,1],$fot(op_d)]]) ).
cnf(refute_1_23,plain,
( mult(unit,ld(unit,op_c)) != op_c
| mult(unit,op_d) = op_c ),
inference(resolve,[$cnf( $equal(ld(unit,op_c),op_d) )],[refute_1_21,refute_1_22]) ).
cnf(refute_1_24,plain,
mult(unit,op_d) = op_c,
inference(resolve,[$cnf( $equal(mult(unit,ld(unit,op_c)),op_c) )],[refute_1_13,refute_1_23]) ).
cnf(refute_1_25,plain,
mult(unit,A) = A,
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_26,plain,
mult(unit,op_d) = op_d,
inference(subst,[],[refute_1_25:[bind(A,$fot(op_d))]]) ).
cnf(refute_1_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_1_28,plain,
( mult(unit,op_d) != op_c
| op_d = op_c ),
inference(resolve,[$cnf( $equal(mult(unit,op_d),op_d) )],[refute_1_26,refute_1_27]) ).
cnf(refute_1_29,plain,
op_d = op_c,
inference(resolve,[$cnf( $equal(mult(unit,op_d),op_c) )],[refute_1_24,refute_1_28]) ).
cnf(refute_1_30,plain,
mult(X_12,op_d) = mult(X_12,op_d),
introduced(tautology,[refl,[$fot(mult(X_12,op_d))]]) ).
cnf(refute_1_31,plain,
( mult(X_12,op_d) != mult(X_12,op_d)
| op_d != op_c
| mult(X_12,op_d) = mult(X_12,op_c) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_12,op_d),mult(X_12,op_d)) ),[1,1],$fot(op_c)]]) ).
cnf(refute_1_32,plain,
( op_d != op_c
| mult(X_12,op_d) = mult(X_12,op_c) ),
inference(resolve,[$cnf( $equal(mult(X_12,op_d),mult(X_12,op_d)) )],[refute_1_30,refute_1_31]) ).
cnf(refute_1_33,plain,
mult(X_12,op_d) = mult(X_12,op_c),
inference(resolve,[$cnf( $equal(op_d,op_c) )],[refute_1_29,refute_1_32]) ).
cnf(refute_1_34,plain,
( mult(X_12,op_d) != mult(X_12,op_c)
| mult(X_12,op_d) != mult(op_c,X_12)
| mult(X_12,op_c) = mult(op_c,X_12) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_12,op_d),mult(op_c,X_12)) ),[0],$fot(mult(X_12,op_c))]]) ).
cnf(refute_1_35,plain,
( mult(X_12,op_d) != mult(op_c,X_12)
| mult(X_12,op_c) = mult(op_c,X_12) ),
inference(resolve,[$cnf( $equal(mult(X_12,op_d),mult(X_12,op_c)) )],[refute_1_33,refute_1_34]) ).
cnf(refute_1_36,plain,
mult(X_12,op_c) = mult(op_c,X_12),
inference(resolve,[$cnf( $equal(mult(X_12,op_d),mult(op_c,X_12)) )],[refute_1_12,refute_1_35]) ).
cnf(refute_1_37,plain,
mult(skolemFOFtoCNF_X1_1,op_c) = mult(op_c,skolemFOFtoCNF_X1_1),
inference(subst,[],[refute_1_36:[bind(X_12,$fot(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_1_38,plain,
mult(skolemFOFtoCNF_X1_1,op_d) = mult(skolemFOFtoCNF_X1_1,op_d),
introduced(tautology,[refl,[$fot(mult(skolemFOFtoCNF_X1_1,op_d))]]) ).
cnf(refute_1_39,plain,
( mult(skolemFOFtoCNF_X1_1,op_d) != mult(skolemFOFtoCNF_X1_1,op_d)
| op_d != op_c
| mult(skolemFOFtoCNF_X1_1,op_d) = mult(skolemFOFtoCNF_X1_1,op_c) ),
introduced(tautology,[equality,[$cnf( $equal(mult(skolemFOFtoCNF_X1_1,op_d),mult(skolemFOFtoCNF_X1_1,op_d)) ),[1,1],$fot(op_c)]]) ).
cnf(refute_1_40,plain,
( op_d != op_c
| mult(skolemFOFtoCNF_X1_1,op_d) = mult(skolemFOFtoCNF_X1_1,op_c) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X1_1,op_d),mult(skolemFOFtoCNF_X1_1,op_d)) )],[refute_1_38,refute_1_39]) ).
cnf(refute_1_41,plain,
mult(skolemFOFtoCNF_X1_1,op_d) = mult(skolemFOFtoCNF_X1_1,op_c),
inference(resolve,[$cnf( $equal(op_d,op_c) )],[refute_1_29,refute_1_40]) ).
cnf(refute_1_42,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_1_43,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_1_7,refute_1_42]) ).
cnf(refute_1_44,plain,
( mult(skolemFOFtoCNF_X1_1,op_c) != mult(op_c,skolemFOFtoCNF_X1_1)
| mult(skolemFOFtoCNF_X1_1,op_d) != mult(skolemFOFtoCNF_X1_1,op_c)
| mult(skolemFOFtoCNF_X1_1,op_d) = mult(op_c,skolemFOFtoCNF_X1_1) ),
inference(subst,[],[refute_1_43:[bind(X,$fot(mult(skolemFOFtoCNF_X1_1,op_d))),bind(Y,$fot(mult(skolemFOFtoCNF_X1_1,op_c))),bind(Z,$fot(mult(op_c,skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_1_45,plain,
( mult(skolemFOFtoCNF_X1_1,op_c) != mult(op_c,skolemFOFtoCNF_X1_1)
| mult(skolemFOFtoCNF_X1_1,op_d) = mult(op_c,skolemFOFtoCNF_X1_1) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X1_1,op_d),mult(skolemFOFtoCNF_X1_1,op_c)) )],[refute_1_41,refute_1_44]) ).
cnf(refute_1_46,plain,
mult(skolemFOFtoCNF_X1_1,op_d) = mult(op_c,skolemFOFtoCNF_X1_1),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X1_1,op_c),mult(op_c,skolemFOFtoCNF_X1_1)) )],[refute_1_37,refute_1_45]) ).
cnf(refute_1_47,plain,
mult(skolemFOFtoCNF_X0_1,mult(skolemFOFtoCNF_X1_1,op_d)) = mult(skolemFOFtoCNF_X0_1,mult(skolemFOFtoCNF_X1_1,op_d)),
introduced(tautology,[refl,[$fot(mult(skolemFOFtoCNF_X0_1,mult(skolemFOFtoCNF_X1_1,op_d)))]]) ).
cnf(refute_1_48,plain,
( mult(skolemFOFtoCNF_X0_1,mult(skolemFOFtoCNF_X1_1,op_d)) != mult(skolemFOFtoCNF_X0_1,mult(skolemFOFtoCNF_X1_1,op_d))
| mult(skolemFOFtoCNF_X1_1,op_d) != mult(op_c,skolemFOFtoCNF_X1_1)
| mult(skolemFOFtoCNF_X0_1,mult(skolemFOFtoCNF_X1_1,op_d)) = mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(skolemFOFtoCNF_X0_1,mult(skolemFOFtoCNF_X1_1,op_d)),mult(skolemFOFtoCNF_X0_1,mult(skolemFOFtoCNF_X1_1,op_d))) ),[1,1],$fot(mult(op_c,skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_1_49,plain,
( mult(skolemFOFtoCNF_X1_1,op_d) != mult(op_c,skolemFOFtoCNF_X1_1)
| mult(skolemFOFtoCNF_X0_1,mult(skolemFOFtoCNF_X1_1,op_d)) = mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1)) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X0_1,mult(skolemFOFtoCNF_X1_1,op_d)),mult(skolemFOFtoCNF_X0_1,mult(skolemFOFtoCNF_X1_1,op_d))) )],[refute_1_47,refute_1_48]) ).
cnf(refute_1_50,plain,
mult(skolemFOFtoCNF_X0_1,mult(skolemFOFtoCNF_X1_1,op_d)) = mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1)),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X1_1,op_d),mult(op_c,skolemFOFtoCNF_X1_1)) )],[refute_1_46,refute_1_49]) ).
cnf(refute_1_51,plain,
( mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1)) != mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d)
| mult(skolemFOFtoCNF_X0_1,mult(skolemFOFtoCNF_X1_1,op_d)) != mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1))
| mult(skolemFOFtoCNF_X0_1,mult(skolemFOFtoCNF_X1_1,op_d)) = mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d) ),
introduced(tautology,[equality,[$cnf( $equal(mult(skolemFOFtoCNF_X0_1,mult(skolemFOFtoCNF_X1_1,op_d)),mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1))) ),[1],$fot(mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d))]]) ).
cnf(refute_1_52,plain,
( mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1)) != mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d)
| mult(skolemFOFtoCNF_X0_1,mult(skolemFOFtoCNF_X1_1,op_d)) = mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X0_1,mult(skolemFOFtoCNF_X1_1,op_d)),mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1))) )],[refute_1_50,refute_1_51]) ).
cnf(refute_1_53,plain,
mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_c) = mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)),
inference(subst,[],[refute_1_36:[bind(X_12,$fot(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_1_54,plain,
mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d) = mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d),
introduced(tautology,[refl,[$fot(mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d))]]) ).
cnf(refute_1_55,plain,
( mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d) != mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d)
| op_d != op_c
| mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d) = mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_c) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d),mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d)) ),[1,1],$fot(op_c)]]) ).
cnf(refute_1_56,plain,
( op_d != op_c
| mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d) = mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_c) ),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d),mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d)) )],[refute_1_54,refute_1_55]) ).
cnf(refute_1_57,plain,
mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d) = mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_c),
inference(resolve,[$cnf( $equal(op_d,op_c) )],[refute_1_29,refute_1_56]) ).
cnf(refute_1_58,plain,
( mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_c) != mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1))
| mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d) != mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_c)
| mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d) = mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)) ),
inference(subst,[],[refute_1_43:[bind(X,$fot(mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d))),bind(Y,$fot(mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_c))),bind(Z,$fot(mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1))))]]) ).
cnf(refute_1_59,plain,
( mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_c) != mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1))
| mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d) = mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)) ),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d),mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_c)) )],[refute_1_57,refute_1_58]) ).
cnf(refute_1_60,plain,
mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d) = mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_c),mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1))) )],[refute_1_53,refute_1_59]) ).
cnf(refute_1_61,plain,
( mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d) != mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1))
| mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1)) != mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1))
| mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1)) = mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1)),mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d)) ),[1],$fot(mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_1_62,plain,
( mult(skolemFOFtoCNF_X0_1,mult(op_c,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,skolemFOFtoCNF_X1_1),op_d) ),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d),mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1))) )],[refute_1_60,refute_1_61]) ).
cnf(refute_1_63,plain,
( mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1)) != mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1))
| mult(skolemFOFtoCNF_X0_1,mult(skolemFOFtoCNF_X1_1,op_d)) = mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1)),mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d)) )],[refute_1_62,refute_1_52]) ).
cnf(refute_1_64,plain,
mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1)) != mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X0_1,mult(skolemFOFtoCNF_X1_1,op_d)),mult(mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1),op_d)) )],[refute_1_63,refute_1_0]) ).
cnf(refute_1_65,plain,
mult(op_c,mult(A,B)) = mult(mult(op_c,A),B),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_66,plain,
mult(op_c,mult(X_23,X_24)) = mult(mult(op_c,X_23),X_24),
inference(subst,[],[refute_1_65:[bind(A,$fot(X_23)),bind(B,$fot(X_24))]]) ).
cnf(refute_1_67,plain,
mult(X_23,op_c) = mult(op_c,X_23),
inference(subst,[],[refute_1_36:[bind(X_12,$fot(X_23))]]) ).
cnf(refute_1_68,plain,
( mult(X_23,op_c) != mult(op_c,X_23)
| mult(op_c,X_23) = mult(X_23,op_c) ),
inference(subst,[],[refute_1_7:[bind(X,$fot(mult(X_23,op_c))),bind(Y,$fot(mult(op_c,X_23)))]]) ).
cnf(refute_1_69,plain,
mult(op_c,X_23) = mult(X_23,op_c),
inference(resolve,[$cnf( $equal(mult(X_23,op_c),mult(op_c,X_23)) )],[refute_1_67,refute_1_68]) ).
cnf(refute_1_70,plain,
( mult(op_c,X_23) != mult(X_23,op_c)
| mult(op_c,mult(X_23,X_24)) != mult(mult(op_c,X_23),X_24)
| mult(op_c,mult(X_23,X_24)) = mult(mult(X_23,op_c),X_24) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_c,mult(X_23,X_24)),mult(mult(op_c,X_23),X_24)) ),[1,0],$fot(mult(X_23,op_c))]]) ).
cnf(refute_1_71,plain,
( mult(op_c,mult(X_23,X_24)) != mult(mult(op_c,X_23),X_24)
| mult(op_c,mult(X_23,X_24)) = mult(mult(X_23,op_c),X_24) ),
inference(resolve,[$cnf( $equal(mult(op_c,X_23),mult(X_23,op_c)) )],[refute_1_69,refute_1_70]) ).
cnf(refute_1_72,plain,
mult(op_c,mult(X_23,X_24)) = mult(mult(X_23,op_c),X_24),
inference(resolve,[$cnf( $equal(mult(op_c,mult(X_23,X_24)),mult(mult(op_c,X_23),X_24)) )],[refute_1_66,refute_1_71]) ).
cnf(refute_1_73,plain,
mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_74,plain,
( mult(A,mult(op_c,B)) != mult(mult(A,op_c),B)
| mult(mult(A,op_c),B) = mult(A,mult(op_c,B)) ),
inference(subst,[],[refute_1_7:[bind(X,$fot(mult(A,mult(op_c,B)))),bind(Y,$fot(mult(mult(A,op_c),B)))]]) ).
cnf(refute_1_75,plain,
mult(mult(A,op_c),B) = mult(A,mult(op_c,B)),
inference(resolve,[$cnf( $equal(mult(A,mult(op_c,B)),mult(mult(A,op_c),B)) )],[refute_1_73,refute_1_74]) ).
cnf(refute_1_76,plain,
mult(mult(X_23,op_c),X_24) = mult(X_23,mult(op_c,X_24)),
inference(subst,[],[refute_1_75:[bind(A,$fot(X_23)),bind(B,$fot(X_24))]]) ).
cnf(refute_1_77,plain,
( mult(mult(X_23,op_c),X_24) != mult(X_23,mult(op_c,X_24))
| mult(op_c,mult(X_23,X_24)) != mult(mult(X_23,op_c),X_24)
| mult(op_c,mult(X_23,X_24)) = mult(X_23,mult(op_c,X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_c,mult(X_23,X_24)),mult(mult(X_23,op_c),X_24)) ),[1],$fot(mult(X_23,mult(op_c,X_24)))]]) ).
cnf(refute_1_78,plain,
( mult(op_c,mult(X_23,X_24)) != mult(mult(X_23,op_c),X_24)
| mult(op_c,mult(X_23,X_24)) = mult(X_23,mult(op_c,X_24)) ),
inference(resolve,[$cnf( $equal(mult(mult(X_23,op_c),X_24),mult(X_23,mult(op_c,X_24))) )],[refute_1_76,refute_1_77]) ).
cnf(refute_1_79,plain,
mult(op_c,mult(X_23,X_24)) = mult(X_23,mult(op_c,X_24)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(X_23,X_24)),mult(mult(X_23,op_c),X_24)) )],[refute_1_72,refute_1_78]) ).
cnf(refute_1_80,plain,
( mult(op_c,mult(X_23,X_24)) != mult(X_23,mult(op_c,X_24))
| mult(X_23,mult(op_c,X_24)) = mult(op_c,mult(X_23,X_24)) ),
inference(subst,[],[refute_1_7:[bind(X,$fot(mult(op_c,mult(X_23,X_24)))),bind(Y,$fot(mult(X_23,mult(op_c,X_24))))]]) ).
cnf(refute_1_81,plain,
mult(X_23,mult(op_c,X_24)) = mult(op_c,mult(X_23,X_24)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(X_23,X_24)),mult(X_23,mult(op_c,X_24))) )],[refute_1_79,refute_1_80]) ).
cnf(refute_1_82,plain,
mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1)) = mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)),
inference(subst,[],[refute_1_81:[bind(X_23,$fot(skolemFOFtoCNF_X0_1)),bind(X_24,$fot(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_1_83,plain,
( mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)) != mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1))
| mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1)) != mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1))
| mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1)) = mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1)),mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1))) ),[1],$fot(mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_1_84,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)) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1)),mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1))) )],[refute_1_82,refute_1_83]) ).
cnf(refute_1_85,plain,
mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)) != mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X0_1,mult(op_c,skolemFOFtoCNF_X1_1)),mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1))) )],[refute_1_84,refute_1_64]) ).
cnf(refute_1_86,plain,
mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)) = mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)),
introduced(tautology,[refl,[$fot(mult(op_c,mult(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_1_87,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_86,refute_1_85]) ).
fof(negate_2_0,plain,
~ ! [X0,X1] :
( ( mult(op_d,mult(X0,X1)) = mult(mult(op_d,X0),X1)
& mult(X0,mult(X1,op_d)) = mult(mult(X0,X1),op_d) )
=> mult(X0,mult(op_d,X1)) = mult(mult(X0,op_d),X1) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
? [X0,X1] :
( mult(X0,mult(op_d,X1)) != mult(mult(X0,op_d),X1)
& mult(X0,mult(X1,op_d)) = mult(mult(X0,X1),op_d)
& mult(op_d,mult(X0,X1)) = mult(mult(op_d,X0),X1) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_1,plain,
( mult(skolemFOFtoCNF_X0_2,mult(op_d,skolemFOFtoCNF_X1_2)) != mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2)
& mult(op_d,mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2)) = mult(mult(op_d,skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X1_2)
& mult(skolemFOFtoCNF_X0_2,mult(skolemFOFtoCNF_X1_2,op_d)) = mult(mult(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_2),op_d) ),
inference(skolemize,[],[normalize_2_0]) ).
fof(normalize_2_2,plain,
mult(skolemFOFtoCNF_X0_2,mult(op_d,skolemFOFtoCNF_X1_2)) != mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2),
inference(conjunct,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
! [A] : op_d = ld(A,mult(op_c,A)),
inference(canonicalize,[],[f11]) ).
fof(normalize_2_4,plain,
! [A] : op_d = ld(A,mult(op_c,A)),
inference(specialize,[],[normalize_2_3]) ).
fof(normalize_2_5,plain,
! [A,B] : ld(A,mult(A,B)) = B,
inference(canonicalize,[],[f02]) ).
fof(normalize_2_6,plain,
! [A,B] : ld(A,mult(A,B)) = B,
inference(specialize,[],[normalize_2_5]) ).
fof(normalize_2_7,plain,
! [A,B] : mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
inference(canonicalize,[],[f10]) ).
fof(normalize_2_8,plain,
! [A,B] : mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
inference(specialize,[],[normalize_2_7]) ).
cnf(refute_2_0,plain,
mult(skolemFOFtoCNF_X0_2,mult(op_d,skolemFOFtoCNF_X1_2)) != mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2),
inference(canonicalize,[],[normalize_2_2]) ).
cnf(refute_2_1,plain,
op_d = ld(A,mult(op_c,A)),
inference(canonicalize,[],[normalize_2_4]) ).
cnf(refute_2_2,plain,
op_d = ld(op_c,mult(op_c,op_c)),
inference(subst,[],[refute_2_1:[bind(A,$fot(op_c))]]) ).
cnf(refute_2_3,plain,
ld(A,mult(A,B)) = B,
inference(canonicalize,[],[normalize_2_6]) ).
cnf(refute_2_4,plain,
ld(op_c,mult(op_c,op_c)) = op_c,
inference(subst,[],[refute_2_3:[bind(A,$fot(op_c)),bind(B,$fot(op_c))]]) ).
cnf(refute_2_5,plain,
( ld(op_c,mult(op_c,op_c)) != op_c
| op_d != ld(op_c,mult(op_c,op_c))
| op_d = op_c ),
introduced(tautology,[equality,[$cnf( $equal(op_d,ld(op_c,mult(op_c,op_c))) ),[1],$fot(op_c)]]) ).
cnf(refute_2_6,plain,
( op_d != ld(op_c,mult(op_c,op_c))
| op_d = op_c ),
inference(resolve,[$cnf( $equal(ld(op_c,mult(op_c,op_c)),op_c) )],[refute_2_4,refute_2_5]) ).
cnf(refute_2_7,plain,
op_d = op_c,
inference(resolve,[$cnf( $equal(op_d,ld(op_c,mult(op_c,op_c))) )],[refute_2_2,refute_2_6]) ).
cnf(refute_2_8,plain,
mult(op_d,skolemFOFtoCNF_X1_2) = mult(op_d,skolemFOFtoCNF_X1_2),
introduced(tautology,[refl,[$fot(mult(op_d,skolemFOFtoCNF_X1_2))]]) ).
cnf(refute_2_9,plain,
( mult(op_d,skolemFOFtoCNF_X1_2) != mult(op_d,skolemFOFtoCNF_X1_2)
| op_d != op_c
| mult(op_d,skolemFOFtoCNF_X1_2) = mult(op_c,skolemFOFtoCNF_X1_2) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_d,skolemFOFtoCNF_X1_2),mult(op_d,skolemFOFtoCNF_X1_2)) ),[1,0],$fot(op_c)]]) ).
cnf(refute_2_10,plain,
( op_d != op_c
| mult(op_d,skolemFOFtoCNF_X1_2) = mult(op_c,skolemFOFtoCNF_X1_2) ),
inference(resolve,[$cnf( $equal(mult(op_d,skolemFOFtoCNF_X1_2),mult(op_d,skolemFOFtoCNF_X1_2)) )],[refute_2_8,refute_2_9]) ).
cnf(refute_2_11,plain,
mult(op_d,skolemFOFtoCNF_X1_2) = mult(op_c,skolemFOFtoCNF_X1_2),
inference(resolve,[$cnf( $equal(op_d,op_c) )],[refute_2_7,refute_2_10]) ).
cnf(refute_2_12,plain,
mult(skolemFOFtoCNF_X0_2,mult(op_d,skolemFOFtoCNF_X1_2)) = mult(skolemFOFtoCNF_X0_2,mult(op_d,skolemFOFtoCNF_X1_2)),
introduced(tautology,[refl,[$fot(mult(skolemFOFtoCNF_X0_2,mult(op_d,skolemFOFtoCNF_X1_2)))]]) ).
cnf(refute_2_13,plain,
( mult(op_d,skolemFOFtoCNF_X1_2) != mult(op_c,skolemFOFtoCNF_X1_2)
| mult(skolemFOFtoCNF_X0_2,mult(op_d,skolemFOFtoCNF_X1_2)) != mult(skolemFOFtoCNF_X0_2,mult(op_d,skolemFOFtoCNF_X1_2))
| mult(skolemFOFtoCNF_X0_2,mult(op_d,skolemFOFtoCNF_X1_2)) = mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(skolemFOFtoCNF_X0_2,mult(op_d,skolemFOFtoCNF_X1_2)),mult(skolemFOFtoCNF_X0_2,mult(op_d,skolemFOFtoCNF_X1_2))) ),[1,1],$fot(mult(op_c,skolemFOFtoCNF_X1_2))]]) ).
cnf(refute_2_14,plain,
( mult(op_d,skolemFOFtoCNF_X1_2) != mult(op_c,skolemFOFtoCNF_X1_2)
| mult(skolemFOFtoCNF_X0_2,mult(op_d,skolemFOFtoCNF_X1_2)) = mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X0_2,mult(op_d,skolemFOFtoCNF_X1_2)),mult(skolemFOFtoCNF_X0_2,mult(op_d,skolemFOFtoCNF_X1_2))) )],[refute_2_12,refute_2_13]) ).
cnf(refute_2_15,plain,
mult(skolemFOFtoCNF_X0_2,mult(op_d,skolemFOFtoCNF_X1_2)) = mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)),
inference(resolve,[$cnf( $equal(mult(op_d,skolemFOFtoCNF_X1_2),mult(op_c,skolemFOFtoCNF_X1_2)) )],[refute_2_11,refute_2_14]) ).
cnf(refute_2_16,plain,
( mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)) != mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2)
| mult(skolemFOFtoCNF_X0_2,mult(op_d,skolemFOFtoCNF_X1_2)) != mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2))
| mult(skolemFOFtoCNF_X0_2,mult(op_d,skolemFOFtoCNF_X1_2)) = mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2) ),
introduced(tautology,[equality,[$cnf( $equal(mult(skolemFOFtoCNF_X0_2,mult(op_d,skolemFOFtoCNF_X1_2)),mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2))) ),[1],$fot(mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2))]]) ).
cnf(refute_2_17,plain,
( mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)) != mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2)
| mult(skolemFOFtoCNF_X0_2,mult(op_d,skolemFOFtoCNF_X1_2)) = mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X0_2,mult(op_d,skolemFOFtoCNF_X1_2)),mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2))) )],[refute_2_15,refute_2_16]) ).
cnf(refute_2_18,plain,
mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
inference(canonicalize,[],[normalize_2_8]) ).
cnf(refute_2_19,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_2_20,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_2_21,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_2_19,refute_2_20]) ).
cnf(refute_2_22,plain,
( mult(A,mult(op_c,B)) != mult(mult(A,op_c),B)
| mult(mult(A,op_c),B) = mult(A,mult(op_c,B)) ),
inference(subst,[],[refute_2_21:[bind(X,$fot(mult(A,mult(op_c,B)))),bind(Y,$fot(mult(mult(A,op_c),B)))]]) ).
cnf(refute_2_23,plain,
mult(mult(A,op_c),B) = mult(A,mult(op_c,B)),
inference(resolve,[$cnf( $equal(mult(A,mult(op_c,B)),mult(mult(A,op_c),B)) )],[refute_2_18,refute_2_22]) ).
cnf(refute_2_24,plain,
mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2) = mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)),
inference(subst,[],[refute_2_23:[bind(A,$fot(skolemFOFtoCNF_X0_2)),bind(B,$fot(skolemFOFtoCNF_X1_2))]]) ).
cnf(refute_2_25,plain,
mult(skolemFOFtoCNF_X0_2,op_d) = mult(skolemFOFtoCNF_X0_2,op_d),
introduced(tautology,[refl,[$fot(mult(skolemFOFtoCNF_X0_2,op_d))]]) ).
cnf(refute_2_26,plain,
( mult(skolemFOFtoCNF_X0_2,op_d) != mult(skolemFOFtoCNF_X0_2,op_d)
| op_d != op_c
| mult(skolemFOFtoCNF_X0_2,op_d) = mult(skolemFOFtoCNF_X0_2,op_c) ),
introduced(tautology,[equality,[$cnf( $equal(mult(skolemFOFtoCNF_X0_2,op_d),mult(skolemFOFtoCNF_X0_2,op_d)) ),[1,1],$fot(op_c)]]) ).
cnf(refute_2_27,plain,
( op_d != op_c
| mult(skolemFOFtoCNF_X0_2,op_d) = mult(skolemFOFtoCNF_X0_2,op_c) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X0_2,op_d),mult(skolemFOFtoCNF_X0_2,op_d)) )],[refute_2_25,refute_2_26]) ).
cnf(refute_2_28,plain,
mult(skolemFOFtoCNF_X0_2,op_d) = mult(skolemFOFtoCNF_X0_2,op_c),
inference(resolve,[$cnf( $equal(op_d,op_c) )],[refute_2_7,refute_2_27]) ).
cnf(refute_2_29,plain,
mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2) = mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2),
introduced(tautology,[refl,[$fot(mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2))]]) ).
cnf(refute_2_30,plain,
( mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2) != mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2)
| mult(skolemFOFtoCNF_X0_2,op_d) != mult(skolemFOFtoCNF_X0_2,op_c)
| mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2) = mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2),mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2)) ),[1,0],$fot(mult(skolemFOFtoCNF_X0_2,op_c))]]) ).
cnf(refute_2_31,plain,
( mult(skolemFOFtoCNF_X0_2,op_d) != mult(skolemFOFtoCNF_X0_2,op_c)
| mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2) = mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2) ),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2),mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2)) )],[refute_2_29,refute_2_30]) ).
cnf(refute_2_32,plain,
mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2) = mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X0_2,op_d),mult(skolemFOFtoCNF_X0_2,op_c)) )],[refute_2_28,refute_2_31]) ).
cnf(refute_2_33,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_2_34,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_2_21,refute_2_33]) ).
cnf(refute_2_35,plain,
( mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2) != mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2))
| mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2) != mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2)
| mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2) = mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)) ),
inference(subst,[],[refute_2_34:[bind(X,$fot(mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2))),bind(Y,$fot(mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2))),bind(Z,$fot(mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2))))]]) ).
cnf(refute_2_36,plain,
( mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2) != mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2))
| mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2) = mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)) ),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2),mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2)) )],[refute_2_32,refute_2_35]) ).
cnf(refute_2_37,plain,
mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2) = mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X0_2,op_c),skolemFOFtoCNF_X1_2),mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2))) )],[refute_2_24,refute_2_36]) ).
cnf(refute_2_38,plain,
( mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2) != mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2))
| mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)) != mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2))
| mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)) = mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)),mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2)) ),[1],$fot(mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)))]]) ).
cnf(refute_2_39,plain,
( mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)) != mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2))
| mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)) = mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2) ),
inference(resolve,[$cnf( $equal(mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2),mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2))) )],[refute_2_37,refute_2_38]) ).
cnf(refute_2_40,plain,
( mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)) != mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2))
| mult(skolemFOFtoCNF_X0_2,mult(op_d,skolemFOFtoCNF_X1_2)) = mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)),mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2)) )],[refute_2_39,refute_2_17]) ).
cnf(refute_2_41,plain,
mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)) != mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X0_2,mult(op_d,skolemFOFtoCNF_X1_2)),mult(mult(skolemFOFtoCNF_X0_2,op_d),skolemFOFtoCNF_X1_2)) )],[refute_2_40,refute_2_0]) ).
cnf(refute_2_42,plain,
mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)) = mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)),
introduced(tautology,[refl,[$fot(mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)))]]) ).
cnf(refute_2_43,plain,
$false,
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2)),mult(skolemFOFtoCNF_X0_2,mult(op_c,skolemFOFtoCNF_X1_2))) )],[refute_2_42,refute_2_41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP702+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n013.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 13 12:24:14 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.41
% 0.20/0.41 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.43
%------------------------------------------------------------------------------