TSTP Solution File: GRP700+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP700+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 10:50:03 EDT 2022
% Result : Theorem 0.19s 0.55s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 22
% Syntax : Number of formulae : 93 ( 55 unt; 0 def)
% Number of atoms : 144 ( 143 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 109 ( 58 ~; 48 |; 3 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 129 ( 0 sgn 33 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f03,axiom,
! [B,A] : mult(rd(A,B),B) = A ).
fof(f04,axiom,
! [B,A] : rd(mult(A,B),B) = A ).
fof(f05,axiom,
! [A] : mult(A,unit) = A ).
fof(f06,axiom,
! [A] : mult(unit,A) = A ).
fof(f07,axiom,
! [C,B,A] : mult(mult(mult(A,B),A),mult(A,C)) = mult(A,mult(mult(mult(B,A),A),C)) ).
fof(goals,conjecture,
! [X0] :
? [X1] :
( mult(X1,X0) = unit
& mult(X0,X1) = unit ) ).
fof(subgoal_0,plain,
! [X0] :
? [X1] :
( mult(X1,X0) = unit
& mult(X0,X1) = unit ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0] :
? [X1] :
( mult(X1,X0) = unit
& mult(X0,X1) = unit ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0] :
! [X1] :
( mult(X0,X1) != unit
| mult(X1,X0) != unit ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [X1] :
( mult(X1,skolemFOFtoCNF_X0) != unit
| mult(skolemFOFtoCNF_X0,X1) != unit ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X1] :
( mult(X1,skolemFOFtoCNF_X0) != unit
| mult(skolemFOFtoCNF_X0,X1) != unit ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] : mult(rd(A,B),B) = A,
inference(canonicalize,[],[f03]) ).
fof(normalize_0_4,plain,
! [A,B] : mult(rd(A,B),B) = A,
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B] : rd(mult(A,B),B) = A,
inference(canonicalize,[],[f04]) ).
fof(normalize_0_6,plain,
! [A,B] : rd(mult(A,B),B) = A,
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C] : mult(mult(mult(A,B),A),mult(A,C)) = mult(A,mult(mult(mult(B,A),A),C)),
inference(canonicalize,[],[f07]) ).
fof(normalize_0_8,plain,
! [A,B,C] : mult(mult(mult(A,B),A),mult(A,C)) = mult(A,mult(mult(mult(B,A),A),C)),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A] : mult(A,unit) = A,
inference(canonicalize,[],[f05]) ).
fof(normalize_0_10,plain,
! [A] : mult(A,unit) = A,
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A] : mult(unit,A) = A,
inference(canonicalize,[],[f06]) ).
fof(normalize_0_12,plain,
! [A] : mult(unit,A) = A,
inference(specialize,[],[normalize_0_11]) ).
cnf(refute_0_0,plain,
( mult(X1,skolemFOFtoCNF_X0) != unit
| mult(skolemFOFtoCNF_X0,X1) != unit ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( mult(rd(A,skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) != unit
| mult(skolemFOFtoCNF_X0,rd(A,skolemFOFtoCNF_X0)) != unit ),
inference(subst,[],[refute_0_0:[bind(X1,$fot(rd(A,skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_2,plain,
mult(rd(A,B),B) = A,
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
mult(rd(A,skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) = A,
inference(subst,[],[refute_0_2:[bind(B,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_4,plain,
( A != unit
| mult(rd(A,skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) != A
| mult(rd(A,skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) = unit ),
introduced(tautology,[equality,[$cnf( $equal(mult(rd(A,skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),A) ),[1],$fot(unit)]]) ).
cnf(refute_0_5,plain,
( A != unit
| mult(rd(A,skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) = unit ),
inference(resolve,[$cnf( $equal(mult(rd(A,skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),A) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( A != unit
| mult(skolemFOFtoCNF_X0,rd(A,skolemFOFtoCNF_X0)) != unit ),
inference(resolve,[$cnf( $equal(mult(rd(A,skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),unit) )],[refute_0_5,refute_0_1]) ).
cnf(refute_0_7,plain,
( mult(skolemFOFtoCNF_X0,rd(unit,skolemFOFtoCNF_X0)) != unit
| unit != unit ),
inference(subst,[],[refute_0_6:[bind(A,$fot(unit))]]) ).
cnf(refute_0_8,plain,
unit = unit,
introduced(tautology,[refl,[$fot(unit)]]) ).
cnf(refute_0_9,plain,
mult(skolemFOFtoCNF_X0,rd(unit,skolemFOFtoCNF_X0)) != unit,
inference(resolve,[$cnf( $equal(unit,unit) )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
rd(mult(A,B),B) = A,
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_11,plain,
rd(mult(mult(B,rd(unit,B)),B),B) = mult(B,rd(unit,B)),
inference(subst,[],[refute_0_10:[bind(A,$fot(mult(B,rd(unit,B))))]]) ).
cnf(refute_0_12,plain,
rd(mult(mult(mult(B,X_23),B),B),B) = mult(mult(B,X_23),B),
inference(subst,[],[refute_0_10:[bind(A,$fot(mult(mult(B,X_23),B)))]]) ).
cnf(refute_0_13,plain,
mult(mult(mult(A,B),A),mult(A,C)) = mult(A,mult(mult(mult(B,A),A),C)),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_14,plain,
mult(mult(mult(X_19,X_20),X_19),mult(X_19,unit)) = mult(X_19,mult(mult(mult(X_20,X_19),X_19),unit)),
inference(subst,[],[refute_0_13:[bind(A,$fot(X_19)),bind(B,$fot(X_20)),bind(C,$fot(unit))]]) ).
cnf(refute_0_15,plain,
mult(A,unit) = A,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_16,plain,
mult(X_19,unit) = X_19,
inference(subst,[],[refute_0_15:[bind(A,$fot(X_19))]]) ).
cnf(refute_0_17,plain,
( mult(X_19,unit) != X_19
| mult(mult(mult(X_19,X_20),X_19),mult(X_19,unit)) != mult(X_19,mult(mult(mult(X_20,X_19),X_19),unit))
| mult(mult(mult(X_19,X_20),X_19),X_19) = mult(X_19,mult(mult(mult(X_20,X_19),X_19),unit)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(mult(X_19,X_20),X_19),mult(X_19,unit)),mult(X_19,mult(mult(mult(X_20,X_19),X_19),unit))) ),[0,1],$fot(X_19)]]) ).
cnf(refute_0_18,plain,
( mult(mult(mult(X_19,X_20),X_19),mult(X_19,unit)) != mult(X_19,mult(mult(mult(X_20,X_19),X_19),unit))
| mult(mult(mult(X_19,X_20),X_19),X_19) = mult(X_19,mult(mult(mult(X_20,X_19),X_19),unit)) ),
inference(resolve,[$cnf( $equal(mult(X_19,unit),X_19) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
mult(mult(mult(X_19,X_20),X_19),X_19) = mult(X_19,mult(mult(mult(X_20,X_19),X_19),unit)),
inference(resolve,[$cnf( $equal(mult(mult(mult(X_19,X_20),X_19),mult(X_19,unit)),mult(X_19,mult(mult(mult(X_20,X_19),X_19),unit))) )],[refute_0_14,refute_0_18]) ).
cnf(refute_0_20,plain,
mult(mult(mult(X_20,X_19),X_19),unit) = mult(mult(X_20,X_19),X_19),
inference(subst,[],[refute_0_15:[bind(A,$fot(mult(mult(X_20,X_19),X_19)))]]) ).
cnf(refute_0_21,plain,
mult(X_19,mult(mult(mult(X_20,X_19),X_19),unit)) = mult(X_19,mult(mult(mult(X_20,X_19),X_19),unit)),
introduced(tautology,[refl,[$fot(mult(X_19,mult(mult(mult(X_20,X_19),X_19),unit)))]]) ).
cnf(refute_0_22,plain,
( mult(X_19,mult(mult(mult(X_20,X_19),X_19),unit)) != mult(X_19,mult(mult(mult(X_20,X_19),X_19),unit))
| mult(mult(mult(X_20,X_19),X_19),unit) != mult(mult(X_20,X_19),X_19)
| mult(X_19,mult(mult(mult(X_20,X_19),X_19),unit)) = mult(X_19,mult(mult(X_20,X_19),X_19)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_19,mult(mult(mult(X_20,X_19),X_19),unit)),mult(X_19,mult(mult(mult(X_20,X_19),X_19),unit))) ),[1,1],$fot(mult(mult(X_20,X_19),X_19))]]) ).
cnf(refute_0_23,plain,
( mult(mult(mult(X_20,X_19),X_19),unit) != mult(mult(X_20,X_19),X_19)
| mult(X_19,mult(mult(mult(X_20,X_19),X_19),unit)) = mult(X_19,mult(mult(X_20,X_19),X_19)) ),
inference(resolve,[$cnf( $equal(mult(X_19,mult(mult(mult(X_20,X_19),X_19),unit)),mult(X_19,mult(mult(mult(X_20,X_19),X_19),unit))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
mult(X_19,mult(mult(mult(X_20,X_19),X_19),unit)) = mult(X_19,mult(mult(X_20,X_19),X_19)),
inference(resolve,[$cnf( $equal(mult(mult(mult(X_20,X_19),X_19),unit),mult(mult(X_20,X_19),X_19)) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
( mult(X_19,mult(mult(mult(X_20,X_19),X_19),unit)) != mult(X_19,mult(mult(X_20,X_19),X_19))
| mult(mult(mult(X_19,X_20),X_19),X_19) != mult(X_19,mult(mult(mult(X_20,X_19),X_19),unit))
| mult(mult(mult(X_19,X_20),X_19),X_19) = mult(X_19,mult(mult(X_20,X_19),X_19)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(mult(X_19,X_20),X_19),X_19),mult(X_19,mult(mult(mult(X_20,X_19),X_19),unit))) ),[1],$fot(mult(X_19,mult(mult(X_20,X_19),X_19)))]]) ).
cnf(refute_0_26,plain,
( mult(mult(mult(X_19,X_20),X_19),X_19) != mult(X_19,mult(mult(mult(X_20,X_19),X_19),unit))
| mult(mult(mult(X_19,X_20),X_19),X_19) = mult(X_19,mult(mult(X_20,X_19),X_19)) ),
inference(resolve,[$cnf( $equal(mult(X_19,mult(mult(mult(X_20,X_19),X_19),unit)),mult(X_19,mult(mult(X_20,X_19),X_19))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
mult(mult(mult(X_19,X_20),X_19),X_19) = mult(X_19,mult(mult(X_20,X_19),X_19)),
inference(resolve,[$cnf( $equal(mult(mult(mult(X_19,X_20),X_19),X_19),mult(X_19,mult(mult(mult(X_20,X_19),X_19),unit))) )],[refute_0_19,refute_0_26]) ).
cnf(refute_0_28,plain,
mult(mult(mult(B,X_23),B),B) = mult(B,mult(mult(X_23,B),B)),
inference(subst,[],[refute_0_27:[bind(X_19,$fot(B)),bind(X_20,$fot(X_23))]]) ).
cnf(refute_0_29,plain,
( mult(mult(mult(B,X_23),B),B) != mult(B,mult(mult(X_23,B),B))
| rd(mult(mult(mult(B,X_23),B),B),B) != mult(mult(B,X_23),B)
| rd(mult(B,mult(mult(X_23,B),B)),B) = mult(mult(B,X_23),B) ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(mult(mult(B,X_23),B),B),B),mult(mult(B,X_23),B)) ),[0,0],$fot(mult(B,mult(mult(X_23,B),B)))]]) ).
cnf(refute_0_30,plain,
( rd(mult(mult(mult(B,X_23),B),B),B) != mult(mult(B,X_23),B)
| rd(mult(B,mult(mult(X_23,B),B)),B) = mult(mult(B,X_23),B) ),
inference(resolve,[$cnf( $equal(mult(mult(mult(B,X_23),B),B),mult(B,mult(mult(X_23,B),B))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
rd(mult(B,mult(mult(X_23,B),B)),B) = mult(mult(B,X_23),B),
inference(resolve,[$cnf( $equal(rd(mult(mult(mult(B,X_23),B),B),B),mult(mult(B,X_23),B)) )],[refute_0_12,refute_0_30]) ).
cnf(refute_0_32,plain,
rd(mult(X_27,mult(mult(rd(A,X_27),X_27),X_27)),X_27) = mult(mult(X_27,rd(A,X_27)),X_27),
inference(subst,[],[refute_0_31:[bind(B,$fot(X_27)),bind(X_23,$fot(rd(A,X_27)))]]) ).
cnf(refute_0_33,plain,
mult(rd(A,X_27),X_27) = A,
inference(subst,[],[refute_0_2:[bind(B,$fot(X_27))]]) ).
cnf(refute_0_34,plain,
( mult(rd(A,X_27),X_27) != A
| rd(mult(X_27,mult(mult(rd(A,X_27),X_27),X_27)),X_27) != mult(mult(X_27,rd(A,X_27)),X_27)
| rd(mult(X_27,mult(A,X_27)),X_27) = mult(mult(X_27,rd(A,X_27)),X_27) ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(X_27,mult(mult(rd(A,X_27),X_27),X_27)),X_27),mult(mult(X_27,rd(A,X_27)),X_27)) ),[0,0,1,0],$fot(A)]]) ).
cnf(refute_0_35,plain,
( rd(mult(X_27,mult(mult(rd(A,X_27),X_27),X_27)),X_27) != mult(mult(X_27,rd(A,X_27)),X_27)
| rd(mult(X_27,mult(A,X_27)),X_27) = mult(mult(X_27,rd(A,X_27)),X_27) ),
inference(resolve,[$cnf( $equal(mult(rd(A,X_27),X_27),A) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
rd(mult(X_27,mult(A,X_27)),X_27) = mult(mult(X_27,rd(A,X_27)),X_27),
inference(resolve,[$cnf( $equal(rd(mult(X_27,mult(mult(rd(A,X_27),X_27),X_27)),X_27),mult(mult(X_27,rd(A,X_27)),X_27)) )],[refute_0_32,refute_0_35]) ).
cnf(refute_0_37,plain,
rd(mult(X_64,mult(unit,X_64)),X_64) = mult(mult(X_64,rd(unit,X_64)),X_64),
inference(subst,[],[refute_0_36:[bind(A,$fot(unit)),bind(X_27,$fot(X_64))]]) ).
cnf(refute_0_38,plain,
mult(unit,A) = A,
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_39,plain,
mult(unit,X_64) = X_64,
inference(subst,[],[refute_0_38:[bind(A,$fot(X_64))]]) ).
cnf(refute_0_40,plain,
( mult(unit,X_64) != X_64
| rd(mult(X_64,mult(unit,X_64)),X_64) != mult(mult(X_64,rd(unit,X_64)),X_64)
| rd(mult(X_64,X_64),X_64) = mult(mult(X_64,rd(unit,X_64)),X_64) ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(X_64,mult(unit,X_64)),X_64),mult(mult(X_64,rd(unit,X_64)),X_64)) ),[0,0,1],$fot(X_64)]]) ).
cnf(refute_0_41,plain,
( rd(mult(X_64,mult(unit,X_64)),X_64) != mult(mult(X_64,rd(unit,X_64)),X_64)
| rd(mult(X_64,X_64),X_64) = mult(mult(X_64,rd(unit,X_64)),X_64) ),
inference(resolve,[$cnf( $equal(mult(unit,X_64),X_64) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
rd(mult(X_64,X_64),X_64) = mult(mult(X_64,rd(unit,X_64)),X_64),
inference(resolve,[$cnf( $equal(rd(mult(X_64,mult(unit,X_64)),X_64),mult(mult(X_64,rd(unit,X_64)),X_64)) )],[refute_0_37,refute_0_41]) ).
cnf(refute_0_43,plain,
rd(mult(X_64,X_64),X_64) = X_64,
inference(subst,[],[refute_0_10:[bind(A,$fot(X_64)),bind(B,$fot(X_64))]]) ).
cnf(refute_0_44,plain,
( rd(mult(X_64,X_64),X_64) != X_64
| rd(mult(X_64,X_64),X_64) != mult(mult(X_64,rd(unit,X_64)),X_64)
| X_64 = mult(mult(X_64,rd(unit,X_64)),X_64) ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(X_64,X_64),X_64),mult(mult(X_64,rd(unit,X_64)),X_64)) ),[0],$fot(X_64)]]) ).
cnf(refute_0_45,plain,
( rd(mult(X_64,X_64),X_64) != mult(mult(X_64,rd(unit,X_64)),X_64)
| X_64 = mult(mult(X_64,rd(unit,X_64)),X_64) ),
inference(resolve,[$cnf( $equal(rd(mult(X_64,X_64),X_64),X_64) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
X_64 = mult(mult(X_64,rd(unit,X_64)),X_64),
inference(resolve,[$cnf( $equal(rd(mult(X_64,X_64),X_64),mult(mult(X_64,rd(unit,X_64)),X_64)) )],[refute_0_42,refute_0_45]) ).
cnf(refute_0_47,plain,
B = mult(mult(B,rd(unit,B)),B),
inference(subst,[],[refute_0_46:[bind(X_64,$fot(B))]]) ).
cnf(refute_0_48,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_49,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_50,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
( B != mult(mult(B,rd(unit,B)),B)
| mult(mult(B,rd(unit,B)),B) = B ),
inference(subst,[],[refute_0_50:[bind(X,$fot(B)),bind(Y,$fot(mult(mult(B,rd(unit,B)),B)))]]) ).
cnf(refute_0_52,plain,
mult(mult(B,rd(unit,B)),B) = B,
inference(resolve,[$cnf( $equal(B,mult(mult(B,rd(unit,B)),B)) )],[refute_0_47,refute_0_51]) ).
cnf(refute_0_53,plain,
( mult(mult(B,rd(unit,B)),B) != B
| rd(mult(mult(B,rd(unit,B)),B),B) != mult(B,rd(unit,B))
| rd(B,B) = mult(B,rd(unit,B)) ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(mult(B,rd(unit,B)),B),B),mult(B,rd(unit,B))) ),[0,0],$fot(B)]]) ).
cnf(refute_0_54,plain,
( rd(mult(mult(B,rd(unit,B)),B),B) != mult(B,rd(unit,B))
| rd(B,B) = mult(B,rd(unit,B)) ),
inference(resolve,[$cnf( $equal(mult(mult(B,rd(unit,B)),B),B) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
rd(B,B) = mult(B,rd(unit,B)),
inference(resolve,[$cnf( $equal(rd(mult(mult(B,rd(unit,B)),B),B),mult(B,rd(unit,B))) )],[refute_0_11,refute_0_54]) ).
cnf(refute_0_56,plain,
rd(mult(unit,X_7),X_7) = unit,
inference(subst,[],[refute_0_10:[bind(A,$fot(unit)),bind(B,$fot(X_7))]]) ).
cnf(refute_0_57,plain,
mult(unit,X_7) = X_7,
inference(subst,[],[refute_0_38:[bind(A,$fot(X_7))]]) ).
cnf(refute_0_58,plain,
( mult(unit,X_7) != X_7
| rd(mult(unit,X_7),X_7) != unit
| rd(X_7,X_7) = unit ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(unit,X_7),X_7),unit) ),[0,0],$fot(X_7)]]) ).
cnf(refute_0_59,plain,
( rd(mult(unit,X_7),X_7) != unit
| rd(X_7,X_7) = unit ),
inference(resolve,[$cnf( $equal(mult(unit,X_7),X_7) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
rd(X_7,X_7) = unit,
inference(resolve,[$cnf( $equal(rd(mult(unit,X_7),X_7),unit) )],[refute_0_56,refute_0_59]) ).
cnf(refute_0_61,plain,
rd(B,B) = unit,
inference(subst,[],[refute_0_60:[bind(X_7,$fot(B))]]) ).
cnf(refute_0_62,plain,
( rd(B,B) != mult(B,rd(unit,B))
| rd(B,B) != unit
| unit = mult(B,rd(unit,B)) ),
introduced(tautology,[equality,[$cnf( $equal(rd(B,B),mult(B,rd(unit,B))) ),[0],$fot(unit)]]) ).
cnf(refute_0_63,plain,
( rd(B,B) != mult(B,rd(unit,B))
| unit = mult(B,rd(unit,B)) ),
inference(resolve,[$cnf( $equal(rd(B,B),unit) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
unit = mult(B,rd(unit,B)),
inference(resolve,[$cnf( $equal(rd(B,B),mult(B,rd(unit,B))) )],[refute_0_55,refute_0_63]) ).
cnf(refute_0_65,plain,
( unit != mult(B,rd(unit,B))
| mult(B,rd(unit,B)) = unit ),
inference(subst,[],[refute_0_50:[bind(X,$fot(unit)),bind(Y,$fot(mult(B,rd(unit,B))))]]) ).
cnf(refute_0_66,plain,
mult(B,rd(unit,B)) = unit,
inference(resolve,[$cnf( $equal(unit,mult(B,rd(unit,B))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
mult(skolemFOFtoCNF_X0,rd(unit,skolemFOFtoCNF_X0)) = unit,
inference(subst,[],[refute_0_66:[bind(B,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_68,plain,
( mult(skolemFOFtoCNF_X0,rd(unit,skolemFOFtoCNF_X0)) != unit
| unit != unit
| mult(skolemFOFtoCNF_X0,rd(unit,skolemFOFtoCNF_X0)) = unit ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(skolemFOFtoCNF_X0,rd(unit,skolemFOFtoCNF_X0)),unit) ),[0],$fot(unit)]]) ).
cnf(refute_0_69,plain,
( unit != unit
| mult(skolemFOFtoCNF_X0,rd(unit,skolemFOFtoCNF_X0)) = unit ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X0,rd(unit,skolemFOFtoCNF_X0)),unit) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
unit != unit,
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X0,rd(unit,skolemFOFtoCNF_X0)),unit) )],[refute_0_69,refute_0_9]) ).
cnf(refute_0_71,plain,
$false,
inference(resolve,[$cnf( $equal(unit,unit) )],[refute_0_8,refute_0_70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP700+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 03:08:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.55
% 0.19/0.55 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.56
%------------------------------------------------------------------------------