TSTP Solution File: GRP703-12 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP703-12 : 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 10:50:21 EDT 2022
% Result : Unsatisfiable 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 26
% Syntax : Number of clauses : 64 ( 33 unt; 0 nHn; 46 RR)
% Number of literals : 110 ( 109 equ; 48 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 : 45 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(f03,axiom,
mult(rd(A,B),B) = A ).
cnf(f05,axiom,
mult(A,unit) = A ).
cnf(f06,axiom,
mult(unit,A) = A ).
cnf(f10,axiom,
mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ).
cnf(f12,axiom,
op_e = mult(mult(rd(op_c,mult(A,B)),B),A) ).
cnf(goal,negated_conjecture,
mult(x2,mult(op_e,x3)) != mult(mult(x2,op_e),x3) ).
cnf(refute_0_0,plain,
mult(mult(rd(op_c,mult(unit,X_13)),X_13),unit) = mult(rd(op_c,mult(unit,X_13)),X_13),
inference(subst,[],[f05:[bind(A,$fot(mult(rd(op_c,mult(unit,X_13)),X_13)))]]) ).
cnf(refute_0_1,plain,
op_e = mult(mult(rd(op_c,mult(unit,X_13)),X_13),unit),
inference(subst,[],[f12:[bind(A,$fot(unit)),bind(B,$fot(X_13))]]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$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( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( op_e != mult(mult(rd(op_c,mult(unit,X_13)),X_13),unit)
| mult(mult(rd(op_c,mult(unit,X_13)),X_13),unit) = op_e ),
inference(subst,[],[refute_0_4:[bind(X,$fot(op_e)),bind(Y,$fot(mult(mult(rd(op_c,mult(unit,X_13)),X_13),unit)))]]) ).
cnf(refute_0_6,plain,
mult(mult(rd(op_c,mult(unit,X_13)),X_13),unit) = op_e,
inference(resolve,[$cnf( $equal(op_e,mult(mult(rd(op_c,mult(unit,X_13)),X_13),unit)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( mult(mult(rd(op_c,mult(unit,X_13)),X_13),unit) != mult(rd(op_c,mult(unit,X_13)),X_13)
| mult(mult(rd(op_c,mult(unit,X_13)),X_13),unit) != op_e
| op_e = mult(rd(op_c,mult(unit,X_13)),X_13) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(rd(op_c,mult(unit,X_13)),X_13),unit),mult(rd(op_c,mult(unit,X_13)),X_13)) ),[0],$fot(op_e)]]) ).
cnf(refute_0_8,plain,
( mult(mult(rd(op_c,mult(unit,X_13)),X_13),unit) != mult(rd(op_c,mult(unit,X_13)),X_13)
| op_e = mult(rd(op_c,mult(unit,X_13)),X_13) ),
inference(resolve,[$cnf( $equal(mult(mult(rd(op_c,mult(unit,X_13)),X_13),unit),op_e) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
op_e = mult(rd(op_c,mult(unit,X_13)),X_13),
inference(resolve,[$cnf( $equal(mult(mult(rd(op_c,mult(unit,X_13)),X_13),unit),mult(rd(op_c,mult(unit,X_13)),X_13)) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
mult(rd(op_c,X_13),X_13) = op_c,
inference(subst,[],[f03:[bind(A,$fot(op_c)),bind(B,$fot(X_13))]]) ).
cnf(refute_0_11,plain,
mult(unit,X_13) = X_13,
inference(subst,[],[f06:[bind(A,$fot(X_13))]]) ).
cnf(refute_0_12,plain,
rd(op_c,mult(unit,X_13)) = rd(op_c,mult(unit,X_13)),
introduced(tautology,[refl,[$fot(rd(op_c,mult(unit,X_13)))]]) ).
cnf(refute_0_13,plain,
( mult(unit,X_13) != X_13
| rd(op_c,mult(unit,X_13)) != rd(op_c,mult(unit,X_13))
| rd(op_c,mult(unit,X_13)) = rd(op_c,X_13) ),
introduced(tautology,[equality,[$cnf( $equal(rd(op_c,mult(unit,X_13)),rd(op_c,mult(unit,X_13))) ),[1,1],$fot(X_13)]]) ).
cnf(refute_0_14,plain,
( mult(unit,X_13) != X_13
| rd(op_c,mult(unit,X_13)) = rd(op_c,X_13) ),
inference(resolve,[$cnf( $equal(rd(op_c,mult(unit,X_13)),rd(op_c,mult(unit,X_13))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
rd(op_c,mult(unit,X_13)) = rd(op_c,X_13),
inference(resolve,[$cnf( $equal(mult(unit,X_13),X_13) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
mult(rd(op_c,mult(unit,X_13)),X_13) = mult(rd(op_c,mult(unit,X_13)),X_13),
introduced(tautology,[refl,[$fot(mult(rd(op_c,mult(unit,X_13)),X_13))]]) ).
cnf(refute_0_17,plain,
( mult(rd(op_c,mult(unit,X_13)),X_13) != mult(rd(op_c,mult(unit,X_13)),X_13)
| rd(op_c,mult(unit,X_13)) != rd(op_c,X_13)
| mult(rd(op_c,mult(unit,X_13)),X_13) = mult(rd(op_c,X_13),X_13) ),
introduced(tautology,[equality,[$cnf( $equal(mult(rd(op_c,mult(unit,X_13)),X_13),mult(rd(op_c,mult(unit,X_13)),X_13)) ),[1,0],$fot(rd(op_c,X_13))]]) ).
cnf(refute_0_18,plain,
( rd(op_c,mult(unit,X_13)) != rd(op_c,X_13)
| mult(rd(op_c,mult(unit,X_13)),X_13) = mult(rd(op_c,X_13),X_13) ),
inference(resolve,[$cnf( $equal(mult(rd(op_c,mult(unit,X_13)),X_13),mult(rd(op_c,mult(unit,X_13)),X_13)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
mult(rd(op_c,mult(unit,X_13)),X_13) = mult(rd(op_c,X_13),X_13),
inference(resolve,[$cnf( $equal(rd(op_c,mult(unit,X_13)),rd(op_c,X_13)) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_21,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_20]) ).
cnf(refute_0_22,plain,
( mult(rd(op_c,X_13),X_13) != op_c
| mult(rd(op_c,mult(unit,X_13)),X_13) != mult(rd(op_c,X_13),X_13)
| mult(rd(op_c,mult(unit,X_13)),X_13) = op_c ),
inference(subst,[],[refute_0_21:[bind(X,$fot(mult(rd(op_c,mult(unit,X_13)),X_13))),bind(Y,$fot(mult(rd(op_c,X_13),X_13))),bind(Z,$fot(op_c))]]) ).
cnf(refute_0_23,plain,
( mult(rd(op_c,X_13),X_13) != op_c
| mult(rd(op_c,mult(unit,X_13)),X_13) = op_c ),
inference(resolve,[$cnf( $equal(mult(rd(op_c,mult(unit,X_13)),X_13),mult(rd(op_c,X_13),X_13)) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
mult(rd(op_c,mult(unit,X_13)),X_13) = op_c,
inference(resolve,[$cnf( $equal(mult(rd(op_c,X_13),X_13),op_c) )],[refute_0_10,refute_0_23]) ).
cnf(refute_0_25,plain,
( mult(rd(op_c,mult(unit,X_13)),X_13) != op_c
| op_e != mult(rd(op_c,mult(unit,X_13)),X_13)
| op_e = op_c ),
introduced(tautology,[equality,[$cnf( $equal(op_e,mult(rd(op_c,mult(unit,X_13)),X_13)) ),[1],$fot(op_c)]]) ).
cnf(refute_0_26,plain,
( op_e != mult(rd(op_c,mult(unit,X_13)),X_13)
| op_e = op_c ),
inference(resolve,[$cnf( $equal(mult(rd(op_c,mult(unit,X_13)),X_13),op_c) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
op_e = op_c,
inference(resolve,[$cnf( $equal(op_e,mult(rd(op_c,mult(unit,X_13)),X_13)) )],[refute_0_9,refute_0_26]) ).
cnf(refute_0_28,plain,
mult(op_e,x3) = mult(op_e,x3),
introduced(tautology,[refl,[$fot(mult(op_e,x3))]]) ).
cnf(refute_0_29,plain,
( mult(op_e,x3) != mult(op_e,x3)
| op_e != op_c
| mult(op_e,x3) = mult(op_c,x3) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_e,x3),mult(op_e,x3)) ),[1,0],$fot(op_c)]]) ).
cnf(refute_0_30,plain,
( op_e != op_c
| mult(op_e,x3) = mult(op_c,x3) ),
inference(resolve,[$cnf( $equal(mult(op_e,x3),mult(op_e,x3)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
mult(op_e,x3) = mult(op_c,x3),
inference(resolve,[$cnf( $equal(op_e,op_c) )],[refute_0_27,refute_0_30]) ).
cnf(refute_0_32,plain,
mult(x2,mult(op_e,x3)) = mult(x2,mult(op_e,x3)),
introduced(tautology,[refl,[$fot(mult(x2,mult(op_e,x3)))]]) ).
cnf(refute_0_33,plain,
( mult(op_e,x3) != mult(op_c,x3)
| mult(x2,mult(op_e,x3)) != mult(x2,mult(op_e,x3))
| mult(x2,mult(op_e,x3)) = mult(x2,mult(op_c,x3)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(x2,mult(op_e,x3)),mult(x2,mult(op_e,x3))) ),[1,1],$fot(mult(op_c,x3))]]) ).
cnf(refute_0_34,plain,
( mult(op_e,x3) != mult(op_c,x3)
| mult(x2,mult(op_e,x3)) = mult(x2,mult(op_c,x3)) ),
inference(resolve,[$cnf( $equal(mult(x2,mult(op_e,x3)),mult(x2,mult(op_e,x3))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
mult(x2,mult(op_e,x3)) = mult(x2,mult(op_c,x3)),
inference(resolve,[$cnf( $equal(mult(op_e,x3),mult(op_c,x3)) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
( mult(x2,mult(op_c,x3)) != mult(mult(x2,op_e),x3)
| mult(x2,mult(op_e,x3)) != mult(x2,mult(op_c,x3))
| mult(x2,mult(op_e,x3)) = mult(mult(x2,op_e),x3) ),
introduced(tautology,[equality,[$cnf( $equal(mult(x2,mult(op_e,x3)),mult(x2,mult(op_c,x3))) ),[1],$fot(mult(mult(x2,op_e),x3))]]) ).
cnf(refute_0_37,plain,
( mult(x2,mult(op_c,x3)) != mult(mult(x2,op_e),x3)
| mult(x2,mult(op_e,x3)) = mult(mult(x2,op_e),x3) ),
inference(resolve,[$cnf( $equal(mult(x2,mult(op_e,x3)),mult(x2,mult(op_c,x3))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( mult(A,mult(op_c,B)) != mult(mult(A,op_c),B)
| mult(mult(A,op_c),B) = mult(A,mult(op_c,B)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(mult(A,mult(op_c,B)))),bind(Y,$fot(mult(mult(A,op_c),B)))]]) ).
cnf(refute_0_39,plain,
mult(mult(A,op_c),B) = mult(A,mult(op_c,B)),
inference(resolve,[$cnf( $equal(mult(A,mult(op_c,B)),mult(mult(A,op_c),B)) )],[f10,refute_0_38]) ).
cnf(refute_0_40,plain,
mult(mult(x2,op_c),x3) = mult(x2,mult(op_c,x3)),
inference(subst,[],[refute_0_39:[bind(A,$fot(x2)),bind(B,$fot(x3))]]) ).
cnf(refute_0_41,plain,
mult(x2,op_e) = mult(x2,op_e),
introduced(tautology,[refl,[$fot(mult(x2,op_e))]]) ).
cnf(refute_0_42,plain,
( mult(x2,op_e) != mult(x2,op_e)
| op_e != op_c
| mult(x2,op_e) = mult(x2,op_c) ),
introduced(tautology,[equality,[$cnf( $equal(mult(x2,op_e),mult(x2,op_e)) ),[1,1],$fot(op_c)]]) ).
cnf(refute_0_43,plain,
( op_e != op_c
| mult(x2,op_e) = mult(x2,op_c) ),
inference(resolve,[$cnf( $equal(mult(x2,op_e),mult(x2,op_e)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
mult(x2,op_e) = mult(x2,op_c),
inference(resolve,[$cnf( $equal(op_e,op_c) )],[refute_0_27,refute_0_43]) ).
cnf(refute_0_45,plain,
mult(mult(x2,op_e),x3) = mult(mult(x2,op_e),x3),
introduced(tautology,[refl,[$fot(mult(mult(x2,op_e),x3))]]) ).
cnf(refute_0_46,plain,
( mult(mult(x2,op_e),x3) != mult(mult(x2,op_e),x3)
| mult(x2,op_e) != mult(x2,op_c)
| mult(mult(x2,op_e),x3) = mult(mult(x2,op_c),x3) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(x2,op_e),x3),mult(mult(x2,op_e),x3)) ),[1,0],$fot(mult(x2,op_c))]]) ).
cnf(refute_0_47,plain,
( mult(x2,op_e) != mult(x2,op_c)
| mult(mult(x2,op_e),x3) = mult(mult(x2,op_c),x3) ),
inference(resolve,[$cnf( $equal(mult(mult(x2,op_e),x3),mult(mult(x2,op_e),x3)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
mult(mult(x2,op_e),x3) = mult(mult(x2,op_c),x3),
inference(resolve,[$cnf( $equal(mult(x2,op_e),mult(x2,op_c)) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
( mult(mult(x2,op_c),x3) != mult(x2,mult(op_c,x3))
| mult(mult(x2,op_e),x3) != mult(mult(x2,op_c),x3)
| mult(mult(x2,op_e),x3) = mult(x2,mult(op_c,x3)) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(mult(mult(x2,op_e),x3))),bind(Y,$fot(mult(mult(x2,op_c),x3))),bind(Z,$fot(mult(x2,mult(op_c,x3))))]]) ).
cnf(refute_0_50,plain,
( mult(mult(x2,op_c),x3) != mult(x2,mult(op_c,x3))
| mult(mult(x2,op_e),x3) = mult(x2,mult(op_c,x3)) ),
inference(resolve,[$cnf( $equal(mult(mult(x2,op_e),x3),mult(mult(x2,op_c),x3)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
mult(mult(x2,op_e),x3) = mult(x2,mult(op_c,x3)),
inference(resolve,[$cnf( $equal(mult(mult(x2,op_c),x3),mult(x2,mult(op_c,x3))) )],[refute_0_40,refute_0_50]) ).
cnf(refute_0_52,plain,
( mult(mult(x2,op_e),x3) != mult(x2,mult(op_c,x3))
| mult(x2,mult(op_c,x3)) != mult(x2,mult(op_c,x3))
| mult(x2,mult(op_c,x3)) = mult(mult(x2,op_e),x3) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(x2,mult(op_c,x3)),mult(mult(x2,op_e),x3)) ),[1],$fot(mult(x2,mult(op_c,x3)))]]) ).
cnf(refute_0_53,plain,
( mult(x2,mult(op_c,x3)) != mult(x2,mult(op_c,x3))
| mult(x2,mult(op_c,x3)) = mult(mult(x2,op_e),x3) ),
inference(resolve,[$cnf( $equal(mult(mult(x2,op_e),x3),mult(x2,mult(op_c,x3))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
( mult(x2,mult(op_c,x3)) != mult(x2,mult(op_c,x3))
| mult(x2,mult(op_e,x3)) = mult(mult(x2,op_e),x3) ),
inference(resolve,[$cnf( $equal(mult(x2,mult(op_c,x3)),mult(mult(x2,op_e),x3)) )],[refute_0_53,refute_0_37]) ).
cnf(refute_0_55,plain,
mult(x2,mult(op_c,x3)) != mult(x2,mult(op_c,x3)),
inference(resolve,[$cnf( $equal(mult(x2,mult(op_e,x3)),mult(mult(x2,op_e),x3)) )],[refute_0_54,goal]) ).
cnf(refute_0_56,plain,
mult(x2,mult(op_c,x3)) = mult(x2,mult(op_c,x3)),
introduced(tautology,[refl,[$fot(mult(x2,mult(op_c,x3)))]]) ).
cnf(refute_0_57,plain,
$false,
inference(resolve,[$cnf( $equal(mult(x2,mult(op_c,x3)),mult(x2,mult(op_c,x3))) )],[refute_0_56,refute_0_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP703-12 : TPTP v8.1.0. Released v8.1.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n014.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 23:46:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36
% 0.13/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.37
%------------------------------------------------------------------------------