TSTP Solution File: GRP704-10 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP704-10 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n014.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 10:50:22 EDT 2022
% Result : Unsatisfiable 0.12s 0.37s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 23
% Syntax : Number of clauses : 59 ( 30 unt; 0 nHn; 42 RR)
% Number of literals : 102 ( 101 equ; 45 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(f01,axiom,
mult(A,ld(A,B)) = B ).
cnf(f06,axiom,
mult(unit,A) = A ).
cnf(f08,axiom,
mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ).
cnf(f13,axiom,
op_f = mult(A,mult(B,ld(mult(A,B),op_c))) ).
cnf(goal,negated_conjecture,
mult(op_f,mult(x4,x5)) != mult(mult(op_f,x4),x5) ).
cnf(refute_0_0,plain,
mult(unit,mult(X_14,ld(mult(unit,X_14),op_c))) = mult(X_14,ld(mult(unit,X_14),op_c)),
inference(subst,[],[f06:[bind(A,$fot(mult(X_14,ld(mult(unit,X_14),op_c))))]]) ).
cnf(refute_0_1,plain,
op_f = mult(unit,mult(X_14,ld(mult(unit,X_14),op_c))),
inference(subst,[],[f13:[bind(A,$fot(unit)),bind(B,$fot(X_14))]]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$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( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( op_f != mult(unit,mult(X_14,ld(mult(unit,X_14),op_c)))
| mult(unit,mult(X_14,ld(mult(unit,X_14),op_c))) = op_f ),
inference(subst,[],[refute_0_4:[bind(X,$fot(op_f)),bind(Y,$fot(mult(unit,mult(X_14,ld(mult(unit,X_14),op_c)))))]]) ).
cnf(refute_0_6,plain,
mult(unit,mult(X_14,ld(mult(unit,X_14),op_c))) = op_f,
inference(resolve,[$cnf( $equal(op_f,mult(unit,mult(X_14,ld(mult(unit,X_14),op_c)))) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( mult(unit,mult(X_14,ld(mult(unit,X_14),op_c))) != mult(X_14,ld(mult(unit,X_14),op_c))
| mult(unit,mult(X_14,ld(mult(unit,X_14),op_c))) != op_f
| op_f = mult(X_14,ld(mult(unit,X_14),op_c)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(unit,mult(X_14,ld(mult(unit,X_14),op_c))),mult(X_14,ld(mult(unit,X_14),op_c))) ),[0],$fot(op_f)]]) ).
cnf(refute_0_8,plain,
( mult(unit,mult(X_14,ld(mult(unit,X_14),op_c))) != mult(X_14,ld(mult(unit,X_14),op_c))
| op_f = mult(X_14,ld(mult(unit,X_14),op_c)) ),
inference(resolve,[$cnf( $equal(mult(unit,mult(X_14,ld(mult(unit,X_14),op_c))),op_f) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
op_f = mult(X_14,ld(mult(unit,X_14),op_c)),
inference(resolve,[$cnf( $equal(mult(unit,mult(X_14,ld(mult(unit,X_14),op_c))),mult(X_14,ld(mult(unit,X_14),op_c))) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
mult(X_14,ld(X_14,op_c)) = op_c,
inference(subst,[],[f01:[bind(A,$fot(X_14)),bind(B,$fot(op_c))]]) ).
cnf(refute_0_11,plain,
mult(unit,X_14) = X_14,
inference(subst,[],[f06:[bind(A,$fot(X_14))]]) ).
cnf(refute_0_12,plain,
ld(mult(unit,X_14),op_c) = ld(mult(unit,X_14),op_c),
introduced(tautology,[refl,[$fot(ld(mult(unit,X_14),op_c))]]) ).
cnf(refute_0_13,plain,
( ld(mult(unit,X_14),op_c) != ld(mult(unit,X_14),op_c)
| mult(unit,X_14) != X_14
| ld(mult(unit,X_14),op_c) = ld(X_14,op_c) ),
introduced(tautology,[equality,[$cnf( $equal(ld(mult(unit,X_14),op_c),ld(mult(unit,X_14),op_c)) ),[1,0],$fot(X_14)]]) ).
cnf(refute_0_14,plain,
( mult(unit,X_14) != X_14
| ld(mult(unit,X_14),op_c) = ld(X_14,op_c) ),
inference(resolve,[$cnf( $equal(ld(mult(unit,X_14),op_c),ld(mult(unit,X_14),op_c)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
ld(mult(unit,X_14),op_c) = ld(X_14,op_c),
inference(resolve,[$cnf( $equal(mult(unit,X_14),X_14) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
mult(X_14,ld(mult(unit,X_14),op_c)) = mult(X_14,ld(mult(unit,X_14),op_c)),
introduced(tautology,[refl,[$fot(mult(X_14,ld(mult(unit,X_14),op_c)))]]) ).
cnf(refute_0_17,plain,
( ld(mult(unit,X_14),op_c) != ld(X_14,op_c)
| mult(X_14,ld(mult(unit,X_14),op_c)) != mult(X_14,ld(mult(unit,X_14),op_c))
| mult(X_14,ld(mult(unit,X_14),op_c)) = mult(X_14,ld(X_14,op_c)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_14,ld(mult(unit,X_14),op_c)),mult(X_14,ld(mult(unit,X_14),op_c))) ),[1,1],$fot(ld(X_14,op_c))]]) ).
cnf(refute_0_18,plain,
( ld(mult(unit,X_14),op_c) != ld(X_14,op_c)
| mult(X_14,ld(mult(unit,X_14),op_c)) = mult(X_14,ld(X_14,op_c)) ),
inference(resolve,[$cnf( $equal(mult(X_14,ld(mult(unit,X_14),op_c)),mult(X_14,ld(mult(unit,X_14),op_c))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
mult(X_14,ld(mult(unit,X_14),op_c)) = mult(X_14,ld(X_14,op_c)),
inference(resolve,[$cnf( $equal(ld(mult(unit,X_14),op_c),ld(X_14,op_c)) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_21,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_20]) ).
cnf(refute_0_22,plain,
( mult(X_14,ld(X_14,op_c)) != op_c
| mult(X_14,ld(mult(unit,X_14),op_c)) != mult(X_14,ld(X_14,op_c))
| mult(X_14,ld(mult(unit,X_14),op_c)) = op_c ),
inference(subst,[],[refute_0_21:[bind(X,$fot(mult(X_14,ld(mult(unit,X_14),op_c)))),bind(Y,$fot(mult(X_14,ld(X_14,op_c)))),bind(Z,$fot(op_c))]]) ).
cnf(refute_0_23,plain,
( mult(X_14,ld(X_14,op_c)) != op_c
| mult(X_14,ld(mult(unit,X_14),op_c)) = op_c ),
inference(resolve,[$cnf( $equal(mult(X_14,ld(mult(unit,X_14),op_c)),mult(X_14,ld(X_14,op_c))) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
mult(X_14,ld(mult(unit,X_14),op_c)) = op_c,
inference(resolve,[$cnf( $equal(mult(X_14,ld(X_14,op_c)),op_c) )],[refute_0_10,refute_0_23]) ).
cnf(refute_0_25,plain,
( mult(X_14,ld(mult(unit,X_14),op_c)) != op_c
| op_f != mult(X_14,ld(mult(unit,X_14),op_c))
| op_f = op_c ),
introduced(tautology,[equality,[$cnf( $equal(op_f,mult(X_14,ld(mult(unit,X_14),op_c))) ),[1],$fot(op_c)]]) ).
cnf(refute_0_26,plain,
( op_f != mult(X_14,ld(mult(unit,X_14),op_c))
| op_f = op_c ),
inference(resolve,[$cnf( $equal(mult(X_14,ld(mult(unit,X_14),op_c)),op_c) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
op_f = op_c,
inference(resolve,[$cnf( $equal(op_f,mult(X_14,ld(mult(unit,X_14),op_c))) )],[refute_0_9,refute_0_26]) ).
cnf(refute_0_28,plain,
mult(op_f,mult(x4,x5)) = mult(op_f,mult(x4,x5)),
introduced(tautology,[refl,[$fot(mult(op_f,mult(x4,x5)))]]) ).
cnf(refute_0_29,plain,
( mult(op_f,mult(x4,x5)) != mult(op_f,mult(x4,x5))
| op_f != op_c
| mult(op_f,mult(x4,x5)) = mult(op_c,mult(x4,x5)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_f,mult(x4,x5)),mult(op_f,mult(x4,x5))) ),[1,0],$fot(op_c)]]) ).
cnf(refute_0_30,plain,
( op_f != op_c
| mult(op_f,mult(x4,x5)) = mult(op_c,mult(x4,x5)) ),
inference(resolve,[$cnf( $equal(mult(op_f,mult(x4,x5)),mult(op_f,mult(x4,x5))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
mult(op_f,mult(x4,x5)) = mult(op_c,mult(x4,x5)),
inference(resolve,[$cnf( $equal(op_f,op_c) )],[refute_0_27,refute_0_30]) ).
cnf(refute_0_32,plain,
( mult(op_c,mult(x4,x5)) != mult(mult(op_f,x4),x5)
| mult(op_f,mult(x4,x5)) != mult(op_c,mult(x4,x5))
| mult(op_f,mult(x4,x5)) = mult(mult(op_f,x4),x5) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_f,mult(x4,x5)),mult(op_c,mult(x4,x5))) ),[1],$fot(mult(mult(op_f,x4),x5))]]) ).
cnf(refute_0_33,plain,
( mult(op_c,mult(x4,x5)) != mult(mult(op_f,x4),x5)
| mult(op_f,mult(x4,x5)) = mult(mult(op_f,x4),x5) ),
inference(resolve,[$cnf( $equal(mult(op_f,mult(x4,x5)),mult(op_c,mult(x4,x5))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( mult(op_c,mult(A,B)) != mult(mult(op_c,A),B)
| mult(mult(op_c,A),B) = mult(op_c,mult(A,B)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(mult(op_c,mult(A,B)))),bind(Y,$fot(mult(mult(op_c,A),B)))]]) ).
cnf(refute_0_35,plain,
mult(mult(op_c,A),B) = mult(op_c,mult(A,B)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(A,B)),mult(mult(op_c,A),B)) )],[f08,refute_0_34]) ).
cnf(refute_0_36,plain,
mult(mult(op_c,x4),x5) = mult(op_c,mult(x4,x5)),
inference(subst,[],[refute_0_35:[bind(A,$fot(x4)),bind(B,$fot(x5))]]) ).
cnf(refute_0_37,plain,
mult(op_f,x4) = mult(op_f,x4),
introduced(tautology,[refl,[$fot(mult(op_f,x4))]]) ).
cnf(refute_0_38,plain,
( mult(op_f,x4) != mult(op_f,x4)
| op_f != op_c
| mult(op_f,x4) = mult(op_c,x4) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_f,x4),mult(op_f,x4)) ),[1,0],$fot(op_c)]]) ).
cnf(refute_0_39,plain,
( op_f != op_c
| mult(op_f,x4) = mult(op_c,x4) ),
inference(resolve,[$cnf( $equal(mult(op_f,x4),mult(op_f,x4)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
mult(op_f,x4) = mult(op_c,x4),
inference(resolve,[$cnf( $equal(op_f,op_c) )],[refute_0_27,refute_0_39]) ).
cnf(refute_0_41,plain,
mult(mult(op_f,x4),x5) = mult(mult(op_f,x4),x5),
introduced(tautology,[refl,[$fot(mult(mult(op_f,x4),x5))]]) ).
cnf(refute_0_42,plain,
( mult(mult(op_f,x4),x5) != mult(mult(op_f,x4),x5)
| mult(op_f,x4) != mult(op_c,x4)
| mult(mult(op_f,x4),x5) = mult(mult(op_c,x4),x5) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(op_f,x4),x5),mult(mult(op_f,x4),x5)) ),[1,0],$fot(mult(op_c,x4))]]) ).
cnf(refute_0_43,plain,
( mult(op_f,x4) != mult(op_c,x4)
| mult(mult(op_f,x4),x5) = mult(mult(op_c,x4),x5) ),
inference(resolve,[$cnf( $equal(mult(mult(op_f,x4),x5),mult(mult(op_f,x4),x5)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
mult(mult(op_f,x4),x5) = mult(mult(op_c,x4),x5),
inference(resolve,[$cnf( $equal(mult(op_f,x4),mult(op_c,x4)) )],[refute_0_40,refute_0_43]) ).
cnf(refute_0_45,plain,
( mult(mult(op_c,x4),x5) != mult(op_c,mult(x4,x5))
| mult(mult(op_f,x4),x5) != mult(mult(op_c,x4),x5)
| mult(mult(op_f,x4),x5) = mult(op_c,mult(x4,x5)) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(mult(mult(op_f,x4),x5))),bind(Y,$fot(mult(mult(op_c,x4),x5))),bind(Z,$fot(mult(op_c,mult(x4,x5))))]]) ).
cnf(refute_0_46,plain,
( mult(mult(op_c,x4),x5) != mult(op_c,mult(x4,x5))
| mult(mult(op_f,x4),x5) = mult(op_c,mult(x4,x5)) ),
inference(resolve,[$cnf( $equal(mult(mult(op_f,x4),x5),mult(mult(op_c,x4),x5)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
mult(mult(op_f,x4),x5) = mult(op_c,mult(x4,x5)),
inference(resolve,[$cnf( $equal(mult(mult(op_c,x4),x5),mult(op_c,mult(x4,x5))) )],[refute_0_36,refute_0_46]) ).
cnf(refute_0_48,plain,
( mult(mult(op_f,x4),x5) != mult(op_c,mult(x4,x5))
| mult(op_c,mult(x4,x5)) != mult(op_c,mult(x4,x5))
| mult(op_c,mult(x4,x5)) = mult(mult(op_f,x4),x5) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(op_c,mult(x4,x5)),mult(mult(op_f,x4),x5)) ),[1],$fot(mult(op_c,mult(x4,x5)))]]) ).
cnf(refute_0_49,plain,
( mult(op_c,mult(x4,x5)) != mult(op_c,mult(x4,x5))
| mult(op_c,mult(x4,x5)) = mult(mult(op_f,x4),x5) ),
inference(resolve,[$cnf( $equal(mult(mult(op_f,x4),x5),mult(op_c,mult(x4,x5))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
( mult(op_c,mult(x4,x5)) != mult(op_c,mult(x4,x5))
| mult(op_f,mult(x4,x5)) = mult(mult(op_f,x4),x5) ),
inference(resolve,[$cnf( $equal(mult(op_c,mult(x4,x5)),mult(mult(op_f,x4),x5)) )],[refute_0_49,refute_0_33]) ).
cnf(refute_0_51,plain,
mult(op_c,mult(x4,x5)) != mult(op_c,mult(x4,x5)),
inference(resolve,[$cnf( $equal(mult(op_f,mult(x4,x5)),mult(mult(op_f,x4),x5)) )],[refute_0_50,goal]) ).
cnf(refute_0_52,plain,
mult(op_c,mult(x4,x5)) = mult(op_c,mult(x4,x5)),
introduced(tautology,[refl,[$fot(mult(op_c,mult(x4,x5)))]]) ).
cnf(refute_0_53,plain,
$false,
inference(resolve,[$cnf( $equal(mult(op_c,mult(x4,x5)),mult(op_c,mult(x4,x5))) )],[refute_0_52,refute_0_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP704-10 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 14:01:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.38
%------------------------------------------------------------------------------