TSTP Solution File: GRP657-10 by Metis---2.4

View Problem - Process Solution 
%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP657-10 : TPTP v8.1.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n020.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 10:44:36 EDT 2022

% Result   : Unsatisfiable 0.13s 0.39s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   18
% Syntax   : Number of clauses     :   56 (  34 unt;   0 nHn;  25 RR)
%            Number of literals    :   88 (  87 equ;  36 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   0 con; 1-2 aty)
%            Number of variables   :  105 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(f02,axiom,
    ld(A,mult(A,B)) = B ).

cnf(f03,axiom,
    mult(rd(A,B),B) = A ).

cnf(f04,axiom,
    rd(mult(A,B),B) = A ).

cnf(f05,axiom,
    mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)) ).

cnf(goal,negated_conjecture,
    tuple(mult(X0,x1(X0)),mult(x1_2(X0),X0)) != tuple(x1(X0),x1_2(X0)) ).

cnf(refute_0_0,plain,
    tuple(mult(ld(X_40,X_40),x1(ld(X_40,X_40))),mult(x1_2(ld(X_40,X_40)),ld(X_40,X_40))) != tuple(x1(ld(X_40,X_40)),x1_2(ld(X_40,X_40))),
    inference(subst,[],[goal:[bind(X0,$fot(ld(X_40,X_40)))]]) ).

cnf(refute_0_1,plain,
    rd(mult(A,mult(X_28,A)),mult(X_28,A)) = A,
    inference(subst,[],[f04:[bind(B,$fot(mult(X_28,A)))]]) ).

cnf(refute_0_2,plain,
    rd(mult(mult(X_13,X_14),mult(X_15,X_13)),mult(X_15,X_13)) = mult(X_13,X_14),
    inference(subst,[],[f04:[bind(A,$fot(mult(X_13,X_14))),bind(B,$fot(mult(X_15,X_13)))]]) ).

cnf(refute_0_3,plain,
    mult(mult(X_13,X_14),mult(X_15,X_13)) = mult(X_13,mult(mult(X_14,X_15),X_13)),
    inference(subst,[],[f05:[bind(A,$fot(X_13)),bind(B,$fot(X_14)),bind(C,$fot(X_15))]]) ).

cnf(refute_0_4,plain,
    ( mult(mult(X_13,X_14),mult(X_15,X_13)) != mult(X_13,mult(mult(X_14,X_15),X_13))
    | rd(mult(mult(X_13,X_14),mult(X_15,X_13)),mult(X_15,X_13)) != mult(X_13,X_14)
    | rd(mult(X_13,mult(mult(X_14,X_15),X_13)),mult(X_15,X_13)) = mult(X_13,X_14) ),
    introduced(tautology,[equality,[$cnf( $equal(rd(mult(mult(X_13,X_14),mult(X_15,X_13)),mult(X_15,X_13)),mult(X_13,X_14)) ),[0,0],$fot(mult(X_13,mult(mult(X_14,X_15),X_13)))]]) ).

cnf(refute_0_5,plain,
    ( rd(mult(mult(X_13,X_14),mult(X_15,X_13)),mult(X_15,X_13)) != mult(X_13,X_14)
    | rd(mult(X_13,mult(mult(X_14,X_15),X_13)),mult(X_15,X_13)) = mult(X_13,X_14) ),
    inference(resolve,[$cnf( $equal(mult(mult(X_13,X_14),mult(X_15,X_13)),mult(X_13,mult(mult(X_14,X_15),X_13))) )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
    rd(mult(X_13,mult(mult(X_14,X_15),X_13)),mult(X_15,X_13)) = mult(X_13,X_14),
    inference(resolve,[$cnf( $equal(rd(mult(mult(X_13,X_14),mult(X_15,X_13)),mult(X_15,X_13)),mult(X_13,X_14)) )],[refute_0_2,refute_0_5]) ).

cnf(refute_0_7,plain,
    rd(mult(X_16,mult(mult(rd(A,X_18),X_18),X_16)),mult(X_18,X_16)) = mult(X_16,rd(A,X_18)),
    inference(subst,[],[refute_0_6:[bind(X_13,$fot(X_16)),bind(X_14,$fot(rd(A,X_18))),bind(X_15,$fot(X_18))]]) ).

cnf(refute_0_8,plain,
    mult(rd(A,X_18),X_18) = A,
    inference(subst,[],[f03:[bind(B,$fot(X_18))]]) ).

cnf(refute_0_9,plain,
    ( mult(rd(A,X_18),X_18) != A
    | rd(mult(X_16,mult(mult(rd(A,X_18),X_18),X_16)),mult(X_18,X_16)) != mult(X_16,rd(A,X_18))
    | rd(mult(X_16,mult(A,X_16)),mult(X_18,X_16)) = mult(X_16,rd(A,X_18)) ),
    introduced(tautology,[equality,[$cnf( $equal(rd(mult(X_16,mult(mult(rd(A,X_18),X_18),X_16)),mult(X_18,X_16)),mult(X_16,rd(A,X_18))) ),[0,0,1,0],$fot(A)]]) ).

cnf(refute_0_10,plain,
    ( rd(mult(X_16,mult(mult(rd(A,X_18),X_18),X_16)),mult(X_18,X_16)) != mult(X_16,rd(A,X_18))
    | rd(mult(X_16,mult(A,X_16)),mult(X_18,X_16)) = mult(X_16,rd(A,X_18)) ),
    inference(resolve,[$cnf( $equal(mult(rd(A,X_18),X_18),A) )],[refute_0_8,refute_0_9]) ).

cnf(refute_0_11,plain,
    rd(mult(X_16,mult(A,X_16)),mult(X_18,X_16)) = mult(X_16,rd(A,X_18)),
    inference(resolve,[$cnf( $equal(rd(mult(X_16,mult(mult(rd(A,X_18),X_18),X_16)),mult(X_18,X_16)),mult(X_16,rd(A,X_18))) )],[refute_0_7,refute_0_10]) ).

cnf(refute_0_12,plain,
    rd(mult(A,mult(X_28,A)),mult(X_28,A)) = mult(A,rd(X_28,X_28)),
    inference(subst,[],[refute_0_11:[bind(A,$fot(X_28)),bind(X_16,$fot(A)),bind(X_18,$fot(X_28))]]) ).

cnf(refute_0_13,plain,
    ( rd(mult(A,mult(X_28,A)),mult(X_28,A)) != A
    | rd(mult(A,mult(X_28,A)),mult(X_28,A)) != mult(A,rd(X_28,X_28))
    | mult(A,rd(X_28,X_28)) = A ),
    introduced(tautology,[equality,[$cnf( $equal(rd(mult(A,mult(X_28,A)),mult(X_28,A)),A) ),[0],$fot(mult(A,rd(X_28,X_28)))]]) ).

cnf(refute_0_14,plain,
    ( rd(mult(A,mult(X_28,A)),mult(X_28,A)) != A
    | mult(A,rd(X_28,X_28)) = A ),
    inference(resolve,[$cnf( $equal(rd(mult(A,mult(X_28,A)),mult(X_28,A)),mult(A,rd(X_28,X_28))) )],[refute_0_12,refute_0_13]) ).

cnf(refute_0_15,plain,
    mult(A,rd(X_28,X_28)) = A,
    inference(resolve,[$cnf( $equal(rd(mult(A,mult(X_28,A)),mult(X_28,A)),A) )],[refute_0_1,refute_0_14]) ).

cnf(refute_0_16,plain,
    ld(A,mult(A,rd(X_32,X_32))) = rd(X_32,X_32),
    inference(subst,[],[f02:[bind(B,$fot(rd(X_32,X_32)))]]) ).

cnf(refute_0_17,plain,
    mult(A,rd(X_32,X_32)) = A,
    inference(subst,[],[refute_0_15:[bind(X_28,$fot(X_32))]]) ).

cnf(refute_0_18,plain,
    ( ld(A,mult(A,rd(X_32,X_32))) != rd(X_32,X_32)
    | mult(A,rd(X_32,X_32)) != A
    | ld(A,A) = rd(X_32,X_32) ),
    introduced(tautology,[equality,[$cnf( $equal(ld(A,mult(A,rd(X_32,X_32))),rd(X_32,X_32)) ),[0,1],$fot(A)]]) ).

cnf(refute_0_19,plain,
    ( ld(A,mult(A,rd(X_32,X_32))) != rd(X_32,X_32)
    | ld(A,A) = rd(X_32,X_32) ),
    inference(resolve,[$cnf( $equal(mult(A,rd(X_32,X_32)),A) )],[refute_0_17,refute_0_18]) ).

cnf(refute_0_20,plain,
    ld(A,A) = rd(X_32,X_32),
    inference(resolve,[$cnf( $equal(ld(A,mult(A,rd(X_32,X_32))),rd(X_32,X_32)) )],[refute_0_16,refute_0_19]) ).

cnf(refute_0_21,plain,
    ld(X_35,X_35) = rd(X_28,X_28),
    inference(subst,[],[refute_0_20:[bind(A,$fot(X_35)),bind(X_32,$fot(X_28))]]) ).

cnf(refute_0_22,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_23,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_24,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_22,refute_0_23]) ).

cnf(refute_0_25,plain,
    ( ld(X_35,X_35) != rd(X_28,X_28)
    | rd(X_28,X_28) = ld(X_35,X_35) ),
    inference(subst,[],[refute_0_24:[bind(X,$fot(ld(X_35,X_35))),bind(Y,$fot(rd(X_28,X_28)))]]) ).

cnf(refute_0_26,plain,
    rd(X_28,X_28) = ld(X_35,X_35),
    inference(resolve,[$cnf( $equal(ld(X_35,X_35),rd(X_28,X_28)) )],[refute_0_21,refute_0_25]) ).

cnf(refute_0_27,plain,
    ( mult(A,rd(X_28,X_28)) != A
    | rd(X_28,X_28) != ld(X_35,X_35)
    | mult(A,ld(X_35,X_35)) = A ),
    introduced(tautology,[equality,[$cnf( $equal(mult(A,rd(X_28,X_28)),A) ),[0,1],$fot(ld(X_35,X_35))]]) ).

cnf(refute_0_28,plain,
    ( mult(A,rd(X_28,X_28)) != A
    | mult(A,ld(X_35,X_35)) = A ),
    inference(resolve,[$cnf( $equal(rd(X_28,X_28),ld(X_35,X_35)) )],[refute_0_26,refute_0_27]) ).

cnf(refute_0_29,plain,
    mult(A,ld(X_35,X_35)) = A,
    inference(resolve,[$cnf( $equal(mult(A,rd(X_28,X_28)),A) )],[refute_0_15,refute_0_28]) ).

cnf(refute_0_30,plain,
    mult(x1_2(ld(X_40,X_40)),ld(X_40,X_40)) = x1_2(ld(X_40,X_40)),
    inference(subst,[],[refute_0_29:[bind(A,$fot(x1_2(ld(X_40,X_40)))),bind(X_35,$fot(X_40))]]) ).

cnf(refute_0_31,plain,
    ( mult(x1_2(ld(X_40,X_40)),ld(X_40,X_40)) != x1_2(ld(X_40,X_40))
    | tuple(mult(ld(X_40,X_40),x1(ld(X_40,X_40))),x1_2(ld(X_40,X_40))) != tuple(x1(ld(X_40,X_40)),x1_2(ld(X_40,X_40)))
    | tuple(mult(ld(X_40,X_40),x1(ld(X_40,X_40))),mult(x1_2(ld(X_40,X_40)),ld(X_40,X_40))) = tuple(x1(ld(X_40,X_40)),x1_2(ld(X_40,X_40))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(tuple(mult(ld(X_40,X_40),x1(ld(X_40,X_40))),mult(x1_2(ld(X_40,X_40)),ld(X_40,X_40))),tuple(x1(ld(X_40,X_40)),x1_2(ld(X_40,X_40)))) ),[0,1],$fot(x1_2(ld(X_40,X_40)))]]) ).

cnf(refute_0_32,plain,
    ( tuple(mult(ld(X_40,X_40),x1(ld(X_40,X_40))),x1_2(ld(X_40,X_40))) != tuple(x1(ld(X_40,X_40)),x1_2(ld(X_40,X_40)))
    | tuple(mult(ld(X_40,X_40),x1(ld(X_40,X_40))),mult(x1_2(ld(X_40,X_40)),ld(X_40,X_40))) = tuple(x1(ld(X_40,X_40)),x1_2(ld(X_40,X_40))) ),
    inference(resolve,[$cnf( $equal(mult(x1_2(ld(X_40,X_40)),ld(X_40,X_40)),x1_2(ld(X_40,X_40))) )],[refute_0_30,refute_0_31]) ).

cnf(refute_0_33,plain,
    tuple(mult(ld(X_40,X_40),x1(ld(X_40,X_40))),x1_2(ld(X_40,X_40))) != tuple(x1(ld(X_40,X_40)),x1_2(ld(X_40,X_40))),
    inference(resolve,[$cnf( $equal(tuple(mult(ld(X_40,X_40),x1(ld(X_40,X_40))),mult(x1_2(ld(X_40,X_40)),ld(X_40,X_40))),tuple(x1(ld(X_40,X_40)),x1_2(ld(X_40,X_40)))) )],[refute_0_32,refute_0_0]) ).

cnf(refute_0_34,plain,
    mult(rd(B,B),B) = B,
    inference(subst,[],[f03:[bind(A,$fot(B))]]) ).

cnf(refute_0_35,plain,
    ld(X_35,X_35) = rd(B,B),
    inference(subst,[],[refute_0_20:[bind(A,$fot(X_35)),bind(X_32,$fot(B))]]) ).

cnf(refute_0_36,plain,
    ( ld(X_35,X_35) != rd(B,B)
    | rd(B,B) = ld(X_35,X_35) ),
    inference(subst,[],[refute_0_24:[bind(X,$fot(ld(X_35,X_35))),bind(Y,$fot(rd(B,B)))]]) ).

cnf(refute_0_37,plain,
    rd(B,B) = ld(X_35,X_35),
    inference(resolve,[$cnf( $equal(ld(X_35,X_35),rd(B,B)) )],[refute_0_35,refute_0_36]) ).

cnf(refute_0_38,plain,
    ( mult(rd(B,B),B) != B
    | rd(B,B) != ld(X_35,X_35)
    | mult(ld(X_35,X_35),B) = B ),
    introduced(tautology,[equality,[$cnf( $equal(mult(rd(B,B),B),B) ),[0,0],$fot(ld(X_35,X_35))]]) ).

cnf(refute_0_39,plain,
    ( mult(rd(B,B),B) != B
    | mult(ld(X_35,X_35),B) = B ),
    inference(resolve,[$cnf( $equal(rd(B,B),ld(X_35,X_35)) )],[refute_0_37,refute_0_38]) ).

cnf(refute_0_40,plain,
    mult(ld(X_35,X_35),B) = B,
    inference(resolve,[$cnf( $equal(mult(rd(B,B),B),B) )],[refute_0_34,refute_0_39]) ).

cnf(refute_0_41,plain,
    mult(ld(X_40,X_40),x1(ld(X_40,X_40))) = x1(ld(X_40,X_40)),
    inference(subst,[],[refute_0_40:[bind(B,$fot(x1(ld(X_40,X_40)))),bind(X_35,$fot(X_40))]]) ).

cnf(refute_0_42,plain,
    tuple(mult(ld(X_40,X_40),x1(ld(X_40,X_40))),x1_2(ld(X_40,X_40))) = tuple(mult(ld(X_40,X_40),x1(ld(X_40,X_40))),x1_2(ld(X_40,X_40))),
    introduced(tautology,[refl,[$fot(tuple(mult(ld(X_40,X_40),x1(ld(X_40,X_40))),x1_2(ld(X_40,X_40))))]]) ).

cnf(refute_0_43,plain,
    ( mult(ld(X_40,X_40),x1(ld(X_40,X_40))) != x1(ld(X_40,X_40))
    | tuple(mult(ld(X_40,X_40),x1(ld(X_40,X_40))),x1_2(ld(X_40,X_40))) != tuple(mult(ld(X_40,X_40),x1(ld(X_40,X_40))),x1_2(ld(X_40,X_40)))
    | tuple(mult(ld(X_40,X_40),x1(ld(X_40,X_40))),x1_2(ld(X_40,X_40))) = tuple(x1(ld(X_40,X_40)),x1_2(ld(X_40,X_40))) ),
    introduced(tautology,[equality,[$cnf( $equal(tuple(mult(ld(X_40,X_40),x1(ld(X_40,X_40))),x1_2(ld(X_40,X_40))),tuple(mult(ld(X_40,X_40),x1(ld(X_40,X_40))),x1_2(ld(X_40,X_40)))) ),[1,0],$fot(x1(ld(X_40,X_40)))]]) ).

cnf(refute_0_44,plain,
    ( mult(ld(X_40,X_40),x1(ld(X_40,X_40))) != x1(ld(X_40,X_40))
    | tuple(mult(ld(X_40,X_40),x1(ld(X_40,X_40))),x1_2(ld(X_40,X_40))) = tuple(x1(ld(X_40,X_40)),x1_2(ld(X_40,X_40))) ),
    inference(resolve,[$cnf( $equal(tuple(mult(ld(X_40,X_40),x1(ld(X_40,X_40))),x1_2(ld(X_40,X_40))),tuple(mult(ld(X_40,X_40),x1(ld(X_40,X_40))),x1_2(ld(X_40,X_40)))) )],[refute_0_42,refute_0_43]) ).

cnf(refute_0_45,plain,
    tuple(mult(ld(X_40,X_40),x1(ld(X_40,X_40))),x1_2(ld(X_40,X_40))) = tuple(x1(ld(X_40,X_40)),x1_2(ld(X_40,X_40))),
    inference(resolve,[$cnf( $equal(mult(ld(X_40,X_40),x1(ld(X_40,X_40))),x1(ld(X_40,X_40))) )],[refute_0_41,refute_0_44]) ).

cnf(refute_0_46,plain,
    ( tuple(mult(ld(X_40,X_40),x1(ld(X_40,X_40))),x1_2(ld(X_40,X_40))) != tuple(x1(ld(X_40,X_40)),x1_2(ld(X_40,X_40)))
    | tuple(x1(ld(X_40,X_40)),x1_2(ld(X_40,X_40))) != tuple(x1(ld(X_40,X_40)),x1_2(ld(X_40,X_40)))
    | tuple(mult(ld(X_40,X_40),x1(ld(X_40,X_40))),x1_2(ld(X_40,X_40))) = tuple(x1(ld(X_40,X_40)),x1_2(ld(X_40,X_40))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(tuple(mult(ld(X_40,X_40),x1(ld(X_40,X_40))),x1_2(ld(X_40,X_40))),tuple(x1(ld(X_40,X_40)),x1_2(ld(X_40,X_40)))) ),[0],$fot(tuple(x1(ld(X_40,X_40)),x1_2(ld(X_40,X_40))))]]) ).

cnf(refute_0_47,plain,
    ( tuple(x1(ld(X_40,X_40)),x1_2(ld(X_40,X_40))) != tuple(x1(ld(X_40,X_40)),x1_2(ld(X_40,X_40)))
    | tuple(mult(ld(X_40,X_40),x1(ld(X_40,X_40))),x1_2(ld(X_40,X_40))) = tuple(x1(ld(X_40,X_40)),x1_2(ld(X_40,X_40))) ),
    inference(resolve,[$cnf( $equal(tuple(mult(ld(X_40,X_40),x1(ld(X_40,X_40))),x1_2(ld(X_40,X_40))),tuple(x1(ld(X_40,X_40)),x1_2(ld(X_40,X_40)))) )],[refute_0_45,refute_0_46]) ).

cnf(refute_0_48,plain,
    tuple(x1(ld(X_40,X_40)),x1_2(ld(X_40,X_40))) != tuple(x1(ld(X_40,X_40)),x1_2(ld(X_40,X_40))),
    inference(resolve,[$cnf( $equal(tuple(mult(ld(X_40,X_40),x1(ld(X_40,X_40))),x1_2(ld(X_40,X_40))),tuple(x1(ld(X_40,X_40)),x1_2(ld(X_40,X_40)))) )],[refute_0_47,refute_0_33]) ).

cnf(refute_0_49,plain,
    tuple(x1(ld(X_40,X_40)),x1_2(ld(X_40,X_40))) = tuple(x1(ld(X_40,X_40)),x1_2(ld(X_40,X_40))),
    introduced(tautology,[refl,[$fot(tuple(x1(ld(X_40,X_40)),x1_2(ld(X_40,X_40))))]]) ).

cnf(refute_0_50,plain,
    $false,
    inference(resolve,[$cnf( $equal(tuple(x1(ld(X_40,X_40)),x1_2(ld(X_40,X_40))),tuple(x1(ld(X_40,X_40)),x1_2(ld(X_40,X_40)))) )],[refute_0_49,refute_0_48]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP657-10 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n020.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 : Tue Jun 14 12:16:19 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.39  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.39  
% 0.13/0.39  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.40  
%------------------------------------------------------------------------------