TSTP Solution File: GRP665-12 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP665-12 : 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 10:44:46 EDT 2022
% Result : Unsatisfiable 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 20
% Syntax : Number of clauses : 61 ( 33 unt; 0 nHn; 37 RR)
% Number of literals : 102 ( 101 equ; 44 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(f02,axiom,
ld(A,mult(A,B)) = B ).
cnf(f03,axiom,
mult(rd(A,B),B) = A ).
cnf(f07,axiom,
mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)) ).
cnf(f09,axiom,
mult(op_c,A) = mult(A,op_c) ).
cnf(goal,negated_conjecture,
mult(mult(x0,x1),op_c) != mult(x0,mult(x1,op_c)) ).
cnf(refute_0_0,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_1,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_2,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( mult(op_c,A) != mult(A,op_c)
| mult(A,op_c) = mult(op_c,A) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(mult(op_c,A))),bind(Y,$fot(mult(A,op_c)))]]) ).
cnf(refute_0_4,plain,
mult(A,op_c) = mult(op_c,A),
inference(resolve,[$cnf( $equal(mult(op_c,A),mult(A,op_c)) )],[f09,refute_0_3]) ).
cnf(refute_0_5,plain,
mult(mult(x0,x1),op_c) = mult(op_c,mult(x0,x1)),
inference(subst,[],[refute_0_4:[bind(A,$fot(mult(x0,x1)))]]) ).
cnf(refute_0_6,plain,
( mult(mult(x0,x1),op_c) != mult(op_c,mult(x0,x1))
| mult(op_c,mult(x0,x1)) != mult(x0,mult(x1,op_c))
| mult(mult(x0,x1),op_c) = mult(x0,mult(x1,op_c)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(mult(x0,x1),op_c),mult(x0,mult(x1,op_c))) ),[0],$fot(mult(op_c,mult(x0,x1)))]]) ).
cnf(refute_0_7,plain,
( mult(op_c,mult(x0,x1)) != mult(x0,mult(x1,op_c))
| mult(mult(x0,x1),op_c) = mult(x0,mult(x1,op_c)) ),
inference(resolve,[$cnf( $equal(mult(mult(x0,x1),op_c),mult(op_c,mult(x0,x1))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
mult(x1,op_c) = mult(op_c,x1),
inference(subst,[],[refute_0_4:[bind(A,$fot(x1))]]) ).
cnf(refute_0_9,plain,
mult(x0,mult(x1,op_c)) = mult(x0,mult(x1,op_c)),
introduced(tautology,[refl,[$fot(mult(x0,mult(x1,op_c)))]]) ).
cnf(refute_0_10,plain,
( mult(x0,mult(x1,op_c)) != mult(x0,mult(x1,op_c))
| mult(x1,op_c) != mult(op_c,x1)
| mult(x0,mult(x1,op_c)) = mult(x0,mult(op_c,x1)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(x0,mult(x1,op_c)),mult(x0,mult(x1,op_c))) ),[1,1],$fot(mult(op_c,x1))]]) ).
cnf(refute_0_11,plain,
( mult(x1,op_c) != mult(op_c,x1)
| mult(x0,mult(x1,op_c)) = mult(x0,mult(op_c,x1)) ),
inference(resolve,[$cnf( $equal(mult(x0,mult(x1,op_c)),mult(x0,mult(x1,op_c))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
mult(x0,mult(x1,op_c)) = mult(x0,mult(op_c,x1)),
inference(resolve,[$cnf( $equal(mult(x1,op_c),mult(op_c,x1)) )],[refute_0_8,refute_0_11]) ).
cnf(refute_0_13,plain,
( mult(op_c,mult(x0,x1)) != mult(x0,mult(op_c,x1))
| mult(x0,mult(x1,op_c)) != mult(x0,mult(op_c,x1))
| mult(op_c,mult(x0,x1)) = mult(x0,mult(x1,op_c)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(op_c,mult(x0,x1)),mult(x0,mult(x1,op_c))) ),[1],$fot(mult(x0,mult(op_c,x1)))]]) ).
cnf(refute_0_14,plain,
( mult(op_c,mult(x0,x1)) != mult(x0,mult(op_c,x1))
| mult(op_c,mult(x0,x1)) = mult(x0,mult(x1,op_c)) ),
inference(resolve,[$cnf( $equal(mult(x0,mult(x1,op_c)),mult(x0,mult(op_c,x1))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( mult(op_c,mult(x0,x1)) != mult(x0,mult(op_c,x1))
| mult(mult(x0,x1),op_c) = mult(x0,mult(x1,op_c)) ),
inference(resolve,[$cnf( $equal(mult(op_c,mult(x0,x1)),mult(x0,mult(x1,op_c))) )],[refute_0_14,refute_0_7]) ).
cnf(refute_0_16,plain,
mult(op_c,mult(x0,x1)) != mult(x0,mult(op_c,x1)),
inference(resolve,[$cnf( $equal(mult(mult(x0,x1),op_c),mult(x0,mult(x1,op_c))) )],[refute_0_15,goal]) ).
cnf(refute_0_17,plain,
mult(op_c,mult(X_25,X_26)) = mult(rd(mult(op_c,X_25),op_c),mult(op_c,X_26)),
inference(subst,[],[f07:[bind(A,$fot(op_c)),bind(B,$fot(X_25)),bind(C,$fot(X_26))]]) ).
cnf(refute_0_18,plain,
mult(op_c,X_25) = mult(X_25,op_c),
inference(subst,[],[f09:[bind(A,$fot(X_25))]]) ).
cnf(refute_0_19,plain,
( mult(op_c,X_25) != mult(X_25,op_c)
| mult(op_c,mult(X_25,X_26)) != mult(rd(mult(op_c,X_25),op_c),mult(op_c,X_26))
| mult(op_c,mult(X_25,X_26)) = mult(rd(mult(X_25,op_c),op_c),mult(op_c,X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_c,mult(X_25,X_26)),mult(rd(mult(op_c,X_25),op_c),mult(op_c,X_26))) ),[1,0,0],$fot(mult(X_25,op_c))]]) ).
cnf(refute_0_20,plain,
( mult(op_c,mult(X_25,X_26)) != mult(rd(mult(op_c,X_25),op_c),mult(op_c,X_26))
| mult(op_c,mult(X_25,X_26)) = mult(rd(mult(X_25,op_c),op_c),mult(op_c,X_26)) ),
inference(resolve,[$cnf( $equal(mult(op_c,X_25),mult(X_25,op_c)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
mult(op_c,mult(X_25,X_26)) = mult(rd(mult(X_25,op_c),op_c),mult(op_c,X_26)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(X_25,X_26)),mult(rd(mult(op_c,X_25),op_c),mult(op_c,X_26))) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
ld(op_c,mult(op_c,X_4)) = X_4,
inference(subst,[],[f02:[bind(A,$fot(op_c)),bind(B,$fot(X_4))]]) ).
cnf(refute_0_23,plain,
mult(op_c,X_4) = mult(X_4,op_c),
inference(subst,[],[f09:[bind(A,$fot(X_4))]]) ).
cnf(refute_0_24,plain,
( ld(op_c,mult(op_c,X_4)) != X_4
| mult(op_c,X_4) != mult(X_4,op_c)
| ld(op_c,mult(X_4,op_c)) = X_4 ),
introduced(tautology,[equality,[$cnf( $equal(ld(op_c,mult(op_c,X_4)),X_4) ),[0,1],$fot(mult(X_4,op_c))]]) ).
cnf(refute_0_25,plain,
( ld(op_c,mult(op_c,X_4)) != X_4
| ld(op_c,mult(X_4,op_c)) = X_4 ),
inference(resolve,[$cnf( $equal(mult(op_c,X_4),mult(X_4,op_c)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
ld(op_c,mult(X_4,op_c)) = X_4,
inference(resolve,[$cnf( $equal(ld(op_c,mult(op_c,X_4)),X_4) )],[refute_0_22,refute_0_25]) ).
cnf(refute_0_27,plain,
ld(op_c,mult(X_25,op_c)) = X_25,
inference(subst,[],[refute_0_26:[bind(X_4,$fot(X_25))]]) ).
cnf(refute_0_28,plain,
ld(op_c,mult(rd(X_12,op_c),op_c)) = rd(X_12,op_c),
inference(subst,[],[refute_0_26:[bind(X_4,$fot(rd(X_12,op_c)))]]) ).
cnf(refute_0_29,plain,
mult(rd(X_12,op_c),op_c) = X_12,
inference(subst,[],[f03:[bind(A,$fot(X_12)),bind(B,$fot(op_c))]]) ).
cnf(refute_0_30,plain,
( ld(op_c,mult(rd(X_12,op_c),op_c)) != rd(X_12,op_c)
| mult(rd(X_12,op_c),op_c) != X_12
| ld(op_c,X_12) = rd(X_12,op_c) ),
introduced(tautology,[equality,[$cnf( $equal(ld(op_c,mult(rd(X_12,op_c),op_c)),rd(X_12,op_c)) ),[0,1],$fot(X_12)]]) ).
cnf(refute_0_31,plain,
( ld(op_c,mult(rd(X_12,op_c),op_c)) != rd(X_12,op_c)
| ld(op_c,X_12) = rd(X_12,op_c) ),
inference(resolve,[$cnf( $equal(mult(rd(X_12,op_c),op_c),X_12) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
ld(op_c,X_12) = rd(X_12,op_c),
inference(resolve,[$cnf( $equal(ld(op_c,mult(rd(X_12,op_c),op_c)),rd(X_12,op_c)) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
( ld(op_c,X_12) != rd(X_12,op_c)
| rd(X_12,op_c) = ld(op_c,X_12) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(ld(op_c,X_12))),bind(Y,$fot(rd(X_12,op_c)))]]) ).
cnf(refute_0_34,plain,
rd(X_12,op_c) = ld(op_c,X_12),
inference(resolve,[$cnf( $equal(ld(op_c,X_12),rd(X_12,op_c)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
rd(mult(X_25,op_c),op_c) = ld(op_c,mult(X_25,op_c)),
inference(subst,[],[refute_0_34:[bind(X_12,$fot(mult(X_25,op_c)))]]) ).
cnf(refute_0_36,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_37,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_36]) ).
cnf(refute_0_38,plain,
( ld(op_c,mult(X_25,op_c)) != X_25
| rd(mult(X_25,op_c),op_c) != ld(op_c,mult(X_25,op_c))
| rd(mult(X_25,op_c),op_c) = X_25 ),
inference(subst,[],[refute_0_37:[bind(X,$fot(rd(mult(X_25,op_c),op_c))),bind(Y,$fot(ld(op_c,mult(X_25,op_c)))),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_39,plain,
( ld(op_c,mult(X_25,op_c)) != X_25
| rd(mult(X_25,op_c),op_c) = X_25 ),
inference(resolve,[$cnf( $equal(rd(mult(X_25,op_c),op_c),ld(op_c,mult(X_25,op_c))) )],[refute_0_35,refute_0_38]) ).
cnf(refute_0_40,plain,
rd(mult(X_25,op_c),op_c) = X_25,
inference(resolve,[$cnf( $equal(ld(op_c,mult(X_25,op_c)),X_25) )],[refute_0_27,refute_0_39]) ).
cnf(refute_0_41,plain,
mult(rd(mult(X_25,op_c),op_c),mult(op_c,X_26)) = mult(rd(mult(X_25,op_c),op_c),mult(op_c,X_26)),
introduced(tautology,[refl,[$fot(mult(rd(mult(X_25,op_c),op_c),mult(op_c,X_26)))]]) ).
cnf(refute_0_42,plain,
( mult(rd(mult(X_25,op_c),op_c),mult(op_c,X_26)) != mult(rd(mult(X_25,op_c),op_c),mult(op_c,X_26))
| rd(mult(X_25,op_c),op_c) != X_25
| mult(rd(mult(X_25,op_c),op_c),mult(op_c,X_26)) = mult(X_25,mult(op_c,X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(rd(mult(X_25,op_c),op_c),mult(op_c,X_26)),mult(rd(mult(X_25,op_c),op_c),mult(op_c,X_26))) ),[1,0],$fot(X_25)]]) ).
cnf(refute_0_43,plain,
( rd(mult(X_25,op_c),op_c) != X_25
| mult(rd(mult(X_25,op_c),op_c),mult(op_c,X_26)) = mult(X_25,mult(op_c,X_26)) ),
inference(resolve,[$cnf( $equal(mult(rd(mult(X_25,op_c),op_c),mult(op_c,X_26)),mult(rd(mult(X_25,op_c),op_c),mult(op_c,X_26))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
mult(rd(mult(X_25,op_c),op_c),mult(op_c,X_26)) = mult(X_25,mult(op_c,X_26)),
inference(resolve,[$cnf( $equal(rd(mult(X_25,op_c),op_c),X_25) )],[refute_0_40,refute_0_43]) ).
cnf(refute_0_45,plain,
( mult(op_c,mult(X_25,X_26)) != mult(rd(mult(X_25,op_c),op_c),mult(op_c,X_26))
| mult(rd(mult(X_25,op_c),op_c),mult(op_c,X_26)) != mult(X_25,mult(op_c,X_26))
| mult(op_c,mult(X_25,X_26)) = mult(X_25,mult(op_c,X_26)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(op_c,mult(X_25,X_26)),mult(X_25,mult(op_c,X_26))) ),[0],$fot(mult(rd(mult(X_25,op_c),op_c),mult(op_c,X_26)))]]) ).
cnf(refute_0_46,plain,
( mult(op_c,mult(X_25,X_26)) != mult(rd(mult(X_25,op_c),op_c),mult(op_c,X_26))
| mult(op_c,mult(X_25,X_26)) = mult(X_25,mult(op_c,X_26)) ),
inference(resolve,[$cnf( $equal(mult(rd(mult(X_25,op_c),op_c),mult(op_c,X_26)),mult(X_25,mult(op_c,X_26))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
mult(op_c,mult(X_25,X_26)) = mult(X_25,mult(op_c,X_26)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(X_25,X_26)),mult(rd(mult(X_25,op_c),op_c),mult(op_c,X_26))) )],[refute_0_21,refute_0_46]) ).
cnf(refute_0_48,plain,
( mult(op_c,mult(X_25,X_26)) != mult(X_25,mult(op_c,X_26))
| mult(X_25,mult(op_c,X_26)) = mult(op_c,mult(X_25,X_26)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(mult(op_c,mult(X_25,X_26)))),bind(Y,$fot(mult(X_25,mult(op_c,X_26))))]]) ).
cnf(refute_0_49,plain,
mult(X_25,mult(op_c,X_26)) = mult(op_c,mult(X_25,X_26)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(X_25,X_26)),mult(X_25,mult(op_c,X_26))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
mult(x0,mult(op_c,x1)) = mult(op_c,mult(x0,x1)),
inference(subst,[],[refute_0_49:[bind(X_25,$fot(x0)),bind(X_26,$fot(x1))]]) ).
cnf(refute_0_51,plain,
( mult(op_c,mult(x0,x1)) != mult(op_c,mult(x0,x1))
| mult(x0,mult(op_c,x1)) != mult(op_c,mult(x0,x1))
| mult(op_c,mult(x0,x1)) = mult(x0,mult(op_c,x1)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(op_c,mult(x0,x1)),mult(x0,mult(op_c,x1))) ),[1],$fot(mult(op_c,mult(x0,x1)))]]) ).
cnf(refute_0_52,plain,
( mult(op_c,mult(x0,x1)) != mult(op_c,mult(x0,x1))
| mult(op_c,mult(x0,x1)) = mult(x0,mult(op_c,x1)) ),
inference(resolve,[$cnf( $equal(mult(x0,mult(op_c,x1)),mult(op_c,mult(x0,x1))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
mult(op_c,mult(x0,x1)) != mult(op_c,mult(x0,x1)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(x0,x1)),mult(x0,mult(op_c,x1))) )],[refute_0_52,refute_0_16]) ).
cnf(refute_0_54,plain,
mult(op_c,mult(x0,x1)) = mult(op_c,mult(x0,x1)),
introduced(tautology,[refl,[$fot(mult(op_c,mult(x0,x1)))]]) ).
cnf(refute_0_55,plain,
$false,
inference(resolve,[$cnf( $equal(mult(op_c,mult(x0,x1)),mult(op_c,mult(x0,x1))) )],[refute_0_54,refute_0_53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP665-12 : TPTP v8.1.0. Released v8.1.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n014.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 : Mon Jun 13 19:50:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.37
%------------------------------------------------------------------------------