TSTP Solution File: GRP671-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP671-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:44:50 EDT 2022
% Result : Unsatisfiable 0.21s 0.39s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 22
% Syntax : Number of clauses : 55 ( 28 unt; 0 nHn; 29 RR)
% Number of literals : 95 ( 94 equ; 42 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 94 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c05,axiom,
mult(A,unit) = A ).
cnf(c06,axiom,
mult(unit,A) = A ).
cnf(c09,axiom,
mult(mult(A,B),mult(C,mult(A,B))) = mult(mult(mult(A,mult(B,C)),A),B) ).
cnf(goals,negated_conjecture,
mult(mult(a,b),a) != mult(a,mult(b,a)) ).
cnf(refute_0_0,plain,
mult(mult(mult(X_52,mult(unit,X_54)),X_52),unit) = mult(mult(X_52,mult(unit,X_54)),X_52),
inference(subst,[],[c05:[bind(A,$fot(mult(mult(X_52,mult(unit,X_54)),X_52)))]]) ).
cnf(refute_0_1,plain,
mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))) = mult(mult(mult(X_52,mult(unit,X_54)),X_52),unit),
inference(subst,[],[c09:[bind(A,$fot(X_52)),bind(B,$fot(unit)),bind(C,$fot(X_54))]]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))) != mult(mult(mult(X_52,mult(unit,X_54)),X_52),unit)
| mult(mult(mult(X_52,mult(unit,X_54)),X_52),unit) = mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))))),bind(Y,$fot(mult(mult(mult(X_52,mult(unit,X_54)),X_52),unit)))]]) ).
cnf(refute_0_6,plain,
mult(mult(mult(X_52,mult(unit,X_54)),X_52),unit) = mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))),
inference(resolve,[$cnf( $equal(mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))),mult(mult(mult(X_52,mult(unit,X_54)),X_52),unit)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( mult(mult(mult(X_52,mult(unit,X_54)),X_52),unit) != mult(mult(X_52,mult(unit,X_54)),X_52)
| mult(mult(mult(X_52,mult(unit,X_54)),X_52),unit) != mult(mult(X_52,unit),mult(X_54,mult(X_52,unit)))
| mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))) = mult(mult(X_52,mult(unit,X_54)),X_52) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(mult(X_52,mult(unit,X_54)),X_52),unit),mult(mult(X_52,mult(unit,X_54)),X_52)) ),[0],$fot(mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))))]]) ).
cnf(refute_0_8,plain,
( mult(mult(mult(X_52,mult(unit,X_54)),X_52),unit) != mult(mult(X_52,mult(unit,X_54)),X_52)
| mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))) = mult(mult(X_52,mult(unit,X_54)),X_52) ),
inference(resolve,[$cnf( $equal(mult(mult(mult(X_52,mult(unit,X_54)),X_52),unit),mult(mult(X_52,unit),mult(X_54,mult(X_52,unit)))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))) = mult(mult(X_52,mult(unit,X_54)),X_52),
inference(resolve,[$cnf( $equal(mult(mult(mult(X_52,mult(unit,X_54)),X_52),unit),mult(mult(X_52,mult(unit,X_54)),X_52)) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
mult(X_52,unit) = X_52,
inference(subst,[],[c05:[bind(A,$fot(X_52))]]) ).
cnf(refute_0_11,plain,
mult(X_54,mult(X_52,unit)) = mult(X_54,mult(X_52,unit)),
introduced(tautology,[refl,[$fot(mult(X_54,mult(X_52,unit)))]]) ).
cnf(refute_0_12,plain,
( mult(X_52,unit) != X_52
| mult(X_54,mult(X_52,unit)) != mult(X_54,mult(X_52,unit))
| mult(X_54,mult(X_52,unit)) = mult(X_54,X_52) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_54,mult(X_52,unit)),mult(X_54,mult(X_52,unit))) ),[1,1],$fot(X_52)]]) ).
cnf(refute_0_13,plain,
( mult(X_52,unit) != X_52
| mult(X_54,mult(X_52,unit)) = mult(X_54,X_52) ),
inference(resolve,[$cnf( $equal(mult(X_54,mult(X_52,unit)),mult(X_54,mult(X_52,unit))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
mult(X_54,mult(X_52,unit)) = mult(X_54,X_52),
inference(resolve,[$cnf( $equal(mult(X_52,unit),X_52) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
mult(X_52,mult(X_54,mult(X_52,unit))) = mult(X_52,mult(X_54,mult(X_52,unit))),
introduced(tautology,[refl,[$fot(mult(X_52,mult(X_54,mult(X_52,unit))))]]) ).
cnf(refute_0_16,plain,
( mult(X_52,mult(X_54,mult(X_52,unit))) != mult(X_52,mult(X_54,mult(X_52,unit)))
| mult(X_54,mult(X_52,unit)) != mult(X_54,X_52)
| mult(X_52,mult(X_54,mult(X_52,unit))) = mult(X_52,mult(X_54,X_52)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_52,mult(X_54,mult(X_52,unit))),mult(X_52,mult(X_54,mult(X_52,unit)))) ),[1,1],$fot(mult(X_54,X_52))]]) ).
cnf(refute_0_17,plain,
( mult(X_54,mult(X_52,unit)) != mult(X_54,X_52)
| mult(X_52,mult(X_54,mult(X_52,unit))) = mult(X_52,mult(X_54,X_52)) ),
inference(resolve,[$cnf( $equal(mult(X_52,mult(X_54,mult(X_52,unit))),mult(X_52,mult(X_54,mult(X_52,unit)))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
mult(X_52,mult(X_54,mult(X_52,unit))) = mult(X_52,mult(X_54,X_52)),
inference(resolve,[$cnf( $equal(mult(X_54,mult(X_52,unit)),mult(X_54,X_52)) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))) = mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))),
introduced(tautology,[refl,[$fot(mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))))]]) ).
cnf(refute_0_20,plain,
( mult(X_52,unit) != X_52
| mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))) != mult(mult(X_52,unit),mult(X_54,mult(X_52,unit)))
| mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))) = mult(X_52,mult(X_54,mult(X_52,unit))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))),mult(mult(X_52,unit),mult(X_54,mult(X_52,unit)))) ),[1,0],$fot(X_52)]]) ).
cnf(refute_0_21,plain,
( mult(X_52,unit) != X_52
| mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))) = mult(X_52,mult(X_54,mult(X_52,unit))) ),
inference(resolve,[$cnf( $equal(mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))),mult(mult(X_52,unit),mult(X_54,mult(X_52,unit)))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))) = mult(X_52,mult(X_54,mult(X_52,unit))),
inference(resolve,[$cnf( $equal(mult(X_52,unit),X_52) )],[refute_0_10,refute_0_21]) ).
cnf(refute_0_23,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_24,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_23]) ).
cnf(refute_0_25,plain,
( mult(X_52,mult(X_54,mult(X_52,unit))) != mult(X_52,mult(X_54,X_52))
| mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))) != mult(X_52,mult(X_54,mult(X_52,unit)))
| mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))) = mult(X_52,mult(X_54,X_52)) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))))),bind(Y,$fot(mult(X_52,mult(X_54,mult(X_52,unit))))),bind(Z,$fot(mult(X_52,mult(X_54,X_52))))]]) ).
cnf(refute_0_26,plain,
( mult(X_52,mult(X_54,mult(X_52,unit))) != mult(X_52,mult(X_54,X_52))
| mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))) = mult(X_52,mult(X_54,X_52)) ),
inference(resolve,[$cnf( $equal(mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))),mult(X_52,mult(X_54,mult(X_52,unit)))) )],[refute_0_22,refute_0_25]) ).
cnf(refute_0_27,plain,
mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))) = mult(X_52,mult(X_54,X_52)),
inference(resolve,[$cnf( $equal(mult(X_52,mult(X_54,mult(X_52,unit))),mult(X_52,mult(X_54,X_52))) )],[refute_0_18,refute_0_26]) ).
cnf(refute_0_28,plain,
( mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))) != mult(X_52,mult(X_54,X_52))
| mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))) != mult(mult(X_52,mult(unit,X_54)),X_52)
| mult(X_52,mult(X_54,X_52)) = mult(mult(X_52,mult(unit,X_54)),X_52) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))),mult(mult(X_52,mult(unit,X_54)),X_52)) ),[0],$fot(mult(X_52,mult(X_54,X_52)))]]) ).
cnf(refute_0_29,plain,
( mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))) != mult(mult(X_52,mult(unit,X_54)),X_52)
| mult(X_52,mult(X_54,X_52)) = mult(mult(X_52,mult(unit,X_54)),X_52) ),
inference(resolve,[$cnf( $equal(mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))),mult(X_52,mult(X_54,X_52))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
mult(unit,X_54) = X_54,
inference(subst,[],[c06:[bind(A,$fot(X_54))]]) ).
cnf(refute_0_31,plain,
mult(X_52,mult(unit,X_54)) = mult(X_52,mult(unit,X_54)),
introduced(tautology,[refl,[$fot(mult(X_52,mult(unit,X_54)))]]) ).
cnf(refute_0_32,plain,
( mult(X_52,mult(unit,X_54)) != mult(X_52,mult(unit,X_54))
| mult(unit,X_54) != X_54
| mult(X_52,mult(unit,X_54)) = mult(X_52,X_54) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_52,mult(unit,X_54)),mult(X_52,mult(unit,X_54))) ),[1,1],$fot(X_54)]]) ).
cnf(refute_0_33,plain,
( mult(unit,X_54) != X_54
| mult(X_52,mult(unit,X_54)) = mult(X_52,X_54) ),
inference(resolve,[$cnf( $equal(mult(X_52,mult(unit,X_54)),mult(X_52,mult(unit,X_54))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
mult(X_52,mult(unit,X_54)) = mult(X_52,X_54),
inference(resolve,[$cnf( $equal(mult(unit,X_54),X_54) )],[refute_0_30,refute_0_33]) ).
cnf(refute_0_35,plain,
mult(mult(X_52,mult(unit,X_54)),X_52) = mult(mult(X_52,mult(unit,X_54)),X_52),
introduced(tautology,[refl,[$fot(mult(mult(X_52,mult(unit,X_54)),X_52))]]) ).
cnf(refute_0_36,plain,
( mult(X_52,mult(unit,X_54)) != mult(X_52,X_54)
| mult(mult(X_52,mult(unit,X_54)),X_52) != mult(mult(X_52,mult(unit,X_54)),X_52)
| mult(mult(X_52,mult(unit,X_54)),X_52) = mult(mult(X_52,X_54),X_52) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(X_52,mult(unit,X_54)),X_52),mult(mult(X_52,mult(unit,X_54)),X_52)) ),[1,0],$fot(mult(X_52,X_54))]]) ).
cnf(refute_0_37,plain,
( mult(X_52,mult(unit,X_54)) != mult(X_52,X_54)
| mult(mult(X_52,mult(unit,X_54)),X_52) = mult(mult(X_52,X_54),X_52) ),
inference(resolve,[$cnf( $equal(mult(mult(X_52,mult(unit,X_54)),X_52),mult(mult(X_52,mult(unit,X_54)),X_52)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
mult(mult(X_52,mult(unit,X_54)),X_52) = mult(mult(X_52,X_54),X_52),
inference(resolve,[$cnf( $equal(mult(X_52,mult(unit,X_54)),mult(X_52,X_54)) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
( mult(X_52,mult(X_54,X_52)) != mult(mult(X_52,mult(unit,X_54)),X_52)
| mult(mult(X_52,mult(unit,X_54)),X_52) != mult(mult(X_52,X_54),X_52)
| mult(X_52,mult(X_54,X_52)) = mult(mult(X_52,X_54),X_52) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(X_52,mult(X_54,X_52)),mult(mult(X_52,X_54),X_52)) ),[0],$fot(mult(mult(X_52,mult(unit,X_54)),X_52))]]) ).
cnf(refute_0_40,plain,
( mult(X_52,mult(X_54,X_52)) != mult(mult(X_52,mult(unit,X_54)),X_52)
| mult(X_52,mult(X_54,X_52)) = mult(mult(X_52,X_54),X_52) ),
inference(resolve,[$cnf( $equal(mult(mult(X_52,mult(unit,X_54)),X_52),mult(mult(X_52,X_54),X_52)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))) != mult(mult(X_52,mult(unit,X_54)),X_52)
| mult(X_52,mult(X_54,X_52)) = mult(mult(X_52,X_54),X_52) ),
inference(resolve,[$cnf( $equal(mult(X_52,mult(X_54,X_52)),mult(mult(X_52,mult(unit,X_54)),X_52)) )],[refute_0_29,refute_0_40]) ).
cnf(refute_0_42,plain,
mult(X_52,mult(X_54,X_52)) = mult(mult(X_52,X_54),X_52),
inference(resolve,[$cnf( $equal(mult(mult(X_52,unit),mult(X_54,mult(X_52,unit))),mult(mult(X_52,mult(unit,X_54)),X_52)) )],[refute_0_9,refute_0_41]) ).
cnf(refute_0_43,plain,
( mult(X_52,mult(X_54,X_52)) != mult(mult(X_52,X_54),X_52)
| mult(mult(X_52,X_54),X_52) = mult(X_52,mult(X_54,X_52)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(mult(X_52,mult(X_54,X_52)))),bind(Y,$fot(mult(mult(X_52,X_54),X_52)))]]) ).
cnf(refute_0_44,plain,
mult(mult(X_52,X_54),X_52) = mult(X_52,mult(X_54,X_52)),
inference(resolve,[$cnf( $equal(mult(X_52,mult(X_54,X_52)),mult(mult(X_52,X_54),X_52)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
mult(mult(a,b),a) = mult(a,mult(b,a)),
inference(subst,[],[refute_0_44:[bind(X_52,$fot(a)),bind(X_54,$fot(b))]]) ).
cnf(refute_0_46,plain,
( mult(a,mult(b,a)) != mult(a,mult(b,a))
| mult(mult(a,b),a) != mult(a,mult(b,a))
| mult(mult(a,b),a) = mult(a,mult(b,a)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(a,b),a),mult(a,mult(b,a))) ),[1],$fot(mult(a,mult(b,a)))]]) ).
cnf(refute_0_47,plain,
( mult(a,mult(b,a)) != mult(a,mult(b,a))
| mult(mult(a,b),a) = mult(a,mult(b,a)) ),
inference(resolve,[$cnf( $equal(mult(mult(a,b),a),mult(a,mult(b,a))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
mult(a,mult(b,a)) != mult(a,mult(b,a)),
inference(resolve,[$cnf( $equal(mult(mult(a,b),a),mult(a,mult(b,a))) )],[refute_0_47,goals]) ).
cnf(refute_0_49,plain,
mult(a,mult(b,a)) = mult(a,mult(b,a)),
introduced(tautology,[refl,[$fot(mult(a,mult(b,a)))]]) ).
cnf(refute_0_50,plain,
$false,
inference(resolve,[$cnf( $equal(mult(a,mult(b,a)),mult(a,mult(b,a))) )],[refute_0_49,refute_0_48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP671-1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 08:07:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.39 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.39
% 0.21/0.39 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.21/0.40
%------------------------------------------------------------------------------