TSTP Solution File: GRP665-10 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP665-10 : TPTP v8.1.0. Released v8.1.0.
% 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 10:44:46 EDT 2022
% Result : Unsatisfiable 0.13s 0.44s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 18
% Syntax : Number of clauses : 51 ( 28 unt; 0 nHn; 27 RR)
% Number of literals : 86 ( 85 equ; 37 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 85 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(f01,axiom,
mult(A,ld(A,B)) = B ).
cnf(f02,axiom,
ld(A,mult(A,B)) = B ).
cnf(f08,axiom,
mult(mult(A,B),C) = mult(mult(A,C),ld(C,mult(B,C))) ).
cnf(f09,axiom,
mult(op_c,A) = mult(A,op_c) ).
cnf(goal,negated_conjecture,
mult(op_c,mult(x0,x1)) != mult(mult(op_c,x0),x1) ).
cnf(refute_0_0,plain,
mult(mult(op_c,X_53),X_54) = mult(mult(op_c,X_54),ld(X_54,mult(X_53,X_54))),
inference(subst,[],[f08:[bind(A,$fot(op_c)),bind(B,$fot(X_53)),bind(C,$fot(X_54))]]) ).
cnf(refute_0_1,plain,
mult(op_c,X_54) = mult(X_54,op_c),
inference(subst,[],[f09:[bind(A,$fot(X_54))]]) ).
cnf(refute_0_2,plain,
( mult(mult(op_c,X_53),X_54) != mult(mult(op_c,X_54),ld(X_54,mult(X_53,X_54)))
| mult(op_c,X_54) != mult(X_54,op_c)
| mult(mult(op_c,X_53),X_54) = mult(mult(X_54,op_c),ld(X_54,mult(X_53,X_54))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(op_c,X_53),X_54),mult(mult(op_c,X_54),ld(X_54,mult(X_53,X_54)))) ),[1,0],$fot(mult(X_54,op_c))]]) ).
cnf(refute_0_3,plain,
( mult(mult(op_c,X_53),X_54) != mult(mult(op_c,X_54),ld(X_54,mult(X_53,X_54)))
| mult(mult(op_c,X_53),X_54) = mult(mult(X_54,op_c),ld(X_54,mult(X_53,X_54))) ),
inference(resolve,[$cnf( $equal(mult(op_c,X_54),mult(X_54,op_c)) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
mult(mult(op_c,X_53),X_54) = mult(mult(X_54,op_c),ld(X_54,mult(X_53,X_54))),
inference(resolve,[$cnf( $equal(mult(mult(op_c,X_53),X_54),mult(mult(op_c,X_54),ld(X_54,mult(X_53,X_54)))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
mult(X_54,ld(X_54,mult(X_53,X_54))) = mult(X_53,X_54),
inference(subst,[],[f01:[bind(A,$fot(X_54)),bind(B,$fot(mult(X_53,X_54)))]]) ).
cnf(refute_0_6,plain,
mult(op_c,mult(X_54,ld(X_54,mult(X_53,X_54)))) = mult(op_c,mult(X_54,ld(X_54,mult(X_53,X_54)))),
introduced(tautology,[refl,[$fot(mult(op_c,mult(X_54,ld(X_54,mult(X_53,X_54)))))]]) ).
cnf(refute_0_7,plain,
( mult(X_54,ld(X_54,mult(X_53,X_54))) != mult(X_53,X_54)
| mult(op_c,mult(X_54,ld(X_54,mult(X_53,X_54)))) != mult(op_c,mult(X_54,ld(X_54,mult(X_53,X_54))))
| mult(op_c,mult(X_54,ld(X_54,mult(X_53,X_54)))) = mult(op_c,mult(X_53,X_54)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_c,mult(X_54,ld(X_54,mult(X_53,X_54)))),mult(op_c,mult(X_54,ld(X_54,mult(X_53,X_54))))) ),[1,1],$fot(mult(X_53,X_54))]]) ).
cnf(refute_0_8,plain,
( mult(X_54,ld(X_54,mult(X_53,X_54))) != mult(X_53,X_54)
| mult(op_c,mult(X_54,ld(X_54,mult(X_53,X_54)))) = mult(op_c,mult(X_53,X_54)) ),
inference(resolve,[$cnf( $equal(mult(op_c,mult(X_54,ld(X_54,mult(X_53,X_54)))),mult(op_c,mult(X_54,ld(X_54,mult(X_53,X_54))))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
mult(op_c,mult(X_54,ld(X_54,mult(X_53,X_54)))) = mult(op_c,mult(X_53,X_54)),
inference(resolve,[$cnf( $equal(mult(X_54,ld(X_54,mult(X_53,X_54))),mult(X_53,X_54)) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
mult(mult(X_52,op_c),X_54) = mult(mult(X_52,X_54),ld(X_54,mult(op_c,X_54))),
inference(subst,[],[f08:[bind(A,$fot(X_52)),bind(B,$fot(op_c)),bind(C,$fot(X_54))]]) ).
cnf(refute_0_11,plain,
( mult(mult(X_52,op_c),X_54) != mult(mult(X_52,X_54),ld(X_54,mult(op_c,X_54)))
| mult(op_c,X_54) != mult(X_54,op_c)
| mult(mult(X_52,op_c),X_54) = mult(mult(X_52,X_54),ld(X_54,mult(X_54,op_c))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(X_52,op_c),X_54),mult(mult(X_52,X_54),ld(X_54,mult(op_c,X_54)))) ),[1,1,1],$fot(mult(X_54,op_c))]]) ).
cnf(refute_0_12,plain,
( mult(mult(X_52,op_c),X_54) != mult(mult(X_52,X_54),ld(X_54,mult(op_c,X_54)))
| mult(mult(X_52,op_c),X_54) = mult(mult(X_52,X_54),ld(X_54,mult(X_54,op_c))) ),
inference(resolve,[$cnf( $equal(mult(op_c,X_54),mult(X_54,op_c)) )],[refute_0_1,refute_0_11]) ).
cnf(refute_0_13,plain,
mult(mult(X_52,op_c),X_54) = mult(mult(X_52,X_54),ld(X_54,mult(X_54,op_c))),
inference(resolve,[$cnf( $equal(mult(mult(X_52,op_c),X_54),mult(mult(X_52,X_54),ld(X_54,mult(op_c,X_54)))) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_15,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_16,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( mult(op_c,A) != mult(A,op_c)
| mult(A,op_c) = mult(op_c,A) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(mult(op_c,A))),bind(Y,$fot(mult(A,op_c)))]]) ).
cnf(refute_0_18,plain,
mult(A,op_c) = mult(op_c,A),
inference(resolve,[$cnf( $equal(mult(op_c,A),mult(A,op_c)) )],[f09,refute_0_17]) ).
cnf(refute_0_19,plain,
mult(mult(X_52,X_54),op_c) = mult(op_c,mult(X_52,X_54)),
inference(subst,[],[refute_0_18:[bind(A,$fot(mult(X_52,X_54)))]]) ).
cnf(refute_0_20,plain,
ld(X_54,mult(X_54,op_c)) = op_c,
inference(subst,[],[f02:[bind(A,$fot(X_54)),bind(B,$fot(op_c))]]) ).
cnf(refute_0_21,plain,
mult(mult(X_52,X_54),ld(X_54,mult(X_54,op_c))) = mult(mult(X_52,X_54),ld(X_54,mult(X_54,op_c))),
introduced(tautology,[refl,[$fot(mult(mult(X_52,X_54),ld(X_54,mult(X_54,op_c))))]]) ).
cnf(refute_0_22,plain,
( ld(X_54,mult(X_54,op_c)) != op_c
| mult(mult(X_52,X_54),ld(X_54,mult(X_54,op_c))) != mult(mult(X_52,X_54),ld(X_54,mult(X_54,op_c)))
| mult(mult(X_52,X_54),ld(X_54,mult(X_54,op_c))) = mult(mult(X_52,X_54),op_c) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(X_52,X_54),ld(X_54,mult(X_54,op_c))),mult(mult(X_52,X_54),ld(X_54,mult(X_54,op_c)))) ),[1,1],$fot(op_c)]]) ).
cnf(refute_0_23,plain,
( ld(X_54,mult(X_54,op_c)) != op_c
| mult(mult(X_52,X_54),ld(X_54,mult(X_54,op_c))) = mult(mult(X_52,X_54),op_c) ),
inference(resolve,[$cnf( $equal(mult(mult(X_52,X_54),ld(X_54,mult(X_54,op_c))),mult(mult(X_52,X_54),ld(X_54,mult(X_54,op_c)))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
mult(mult(X_52,X_54),ld(X_54,mult(X_54,op_c))) = mult(mult(X_52,X_54),op_c),
inference(resolve,[$cnf( $equal(ld(X_54,mult(X_54,op_c)),op_c) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_26,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_16,refute_0_25]) ).
cnf(refute_0_27,plain,
( mult(mult(X_52,X_54),ld(X_54,mult(X_54,op_c))) != mult(mult(X_52,X_54),op_c)
| mult(mult(X_52,X_54),op_c) != mult(op_c,mult(X_52,X_54))
| mult(mult(X_52,X_54),ld(X_54,mult(X_54,op_c))) = mult(op_c,mult(X_52,X_54)) ),
inference(subst,[],[refute_0_26:[bind(X,$fot(mult(mult(X_52,X_54),ld(X_54,mult(X_54,op_c))))),bind(Y,$fot(mult(mult(X_52,X_54),op_c))),bind(Z,$fot(mult(op_c,mult(X_52,X_54))))]]) ).
cnf(refute_0_28,plain,
( mult(mult(X_52,X_54),op_c) != mult(op_c,mult(X_52,X_54))
| mult(mult(X_52,X_54),ld(X_54,mult(X_54,op_c))) = mult(op_c,mult(X_52,X_54)) ),
inference(resolve,[$cnf( $equal(mult(mult(X_52,X_54),ld(X_54,mult(X_54,op_c))),mult(mult(X_52,X_54),op_c)) )],[refute_0_24,refute_0_27]) ).
cnf(refute_0_29,plain,
mult(mult(X_52,X_54),ld(X_54,mult(X_54,op_c))) = mult(op_c,mult(X_52,X_54)),
inference(resolve,[$cnf( $equal(mult(mult(X_52,X_54),op_c),mult(op_c,mult(X_52,X_54))) )],[refute_0_19,refute_0_28]) ).
cnf(refute_0_30,plain,
( mult(mult(X_52,X_54),ld(X_54,mult(X_54,op_c))) != mult(op_c,mult(X_52,X_54))
| mult(mult(X_52,op_c),X_54) != mult(mult(X_52,X_54),ld(X_54,mult(X_54,op_c)))
| mult(mult(X_52,op_c),X_54) = mult(op_c,mult(X_52,X_54)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(X_52,op_c),X_54),mult(mult(X_52,X_54),ld(X_54,mult(X_54,op_c)))) ),[1],$fot(mult(op_c,mult(X_52,X_54)))]]) ).
cnf(refute_0_31,plain,
( mult(mult(X_52,op_c),X_54) != mult(mult(X_52,X_54),ld(X_54,mult(X_54,op_c)))
| mult(mult(X_52,op_c),X_54) = mult(op_c,mult(X_52,X_54)) ),
inference(resolve,[$cnf( $equal(mult(mult(X_52,X_54),ld(X_54,mult(X_54,op_c))),mult(op_c,mult(X_52,X_54))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
mult(mult(X_52,op_c),X_54) = mult(op_c,mult(X_52,X_54)),
inference(resolve,[$cnf( $equal(mult(mult(X_52,op_c),X_54),mult(mult(X_52,X_54),ld(X_54,mult(X_54,op_c)))) )],[refute_0_13,refute_0_31]) ).
cnf(refute_0_33,plain,
mult(mult(X_54,op_c),ld(X_54,mult(X_53,X_54))) = mult(op_c,mult(X_54,ld(X_54,mult(X_53,X_54)))),
inference(subst,[],[refute_0_32:[bind(X_52,$fot(X_54)),bind(X_54,$fot(ld(X_54,mult(X_53,X_54))))]]) ).
cnf(refute_0_34,plain,
( mult(mult(X_54,op_c),ld(X_54,mult(X_53,X_54))) != mult(op_c,mult(X_54,ld(X_54,mult(X_53,X_54))))
| mult(op_c,mult(X_54,ld(X_54,mult(X_53,X_54)))) != mult(op_c,mult(X_53,X_54))
| mult(mult(X_54,op_c),ld(X_54,mult(X_53,X_54))) = mult(op_c,mult(X_53,X_54)) ),
inference(subst,[],[refute_0_26:[bind(X,$fot(mult(mult(X_54,op_c),ld(X_54,mult(X_53,X_54))))),bind(Y,$fot(mult(op_c,mult(X_54,ld(X_54,mult(X_53,X_54)))))),bind(Z,$fot(mult(op_c,mult(X_53,X_54))))]]) ).
cnf(refute_0_35,plain,
( mult(op_c,mult(X_54,ld(X_54,mult(X_53,X_54)))) != mult(op_c,mult(X_53,X_54))
| mult(mult(X_54,op_c),ld(X_54,mult(X_53,X_54))) = mult(op_c,mult(X_53,X_54)) ),
inference(resolve,[$cnf( $equal(mult(mult(X_54,op_c),ld(X_54,mult(X_53,X_54))),mult(op_c,mult(X_54,ld(X_54,mult(X_53,X_54))))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
mult(mult(X_54,op_c),ld(X_54,mult(X_53,X_54))) = mult(op_c,mult(X_53,X_54)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(X_54,ld(X_54,mult(X_53,X_54)))),mult(op_c,mult(X_53,X_54))) )],[refute_0_9,refute_0_35]) ).
cnf(refute_0_37,plain,
( mult(mult(X_54,op_c),ld(X_54,mult(X_53,X_54))) != mult(op_c,mult(X_53,X_54))
| mult(mult(op_c,X_53),X_54) != mult(mult(X_54,op_c),ld(X_54,mult(X_53,X_54)))
| mult(mult(op_c,X_53),X_54) = mult(op_c,mult(X_53,X_54)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(op_c,X_53),X_54),mult(mult(X_54,op_c),ld(X_54,mult(X_53,X_54)))) ),[1],$fot(mult(op_c,mult(X_53,X_54)))]]) ).
cnf(refute_0_38,plain,
( mult(mult(op_c,X_53),X_54) != mult(mult(X_54,op_c),ld(X_54,mult(X_53,X_54)))
| mult(mult(op_c,X_53),X_54) = mult(op_c,mult(X_53,X_54)) ),
inference(resolve,[$cnf( $equal(mult(mult(X_54,op_c),ld(X_54,mult(X_53,X_54))),mult(op_c,mult(X_53,X_54))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
mult(mult(op_c,X_53),X_54) = mult(op_c,mult(X_53,X_54)),
inference(resolve,[$cnf( $equal(mult(mult(op_c,X_53),X_54),mult(mult(X_54,op_c),ld(X_54,mult(X_53,X_54)))) )],[refute_0_4,refute_0_38]) ).
cnf(refute_0_40,plain,
mult(mult(op_c,x0),x1) = mult(op_c,mult(x0,x1)),
inference(subst,[],[refute_0_39:[bind(X_53,$fot(x0)),bind(X_54,$fot(x1))]]) ).
cnf(refute_0_41,plain,
( mult(mult(op_c,x0),x1) != mult(op_c,mult(x0,x1))
| mult(op_c,mult(x0,x1)) != mult(op_c,mult(x0,x1))
| mult(op_c,mult(x0,x1)) = mult(mult(op_c,x0),x1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(op_c,mult(x0,x1)),mult(mult(op_c,x0),x1)) ),[1],$fot(mult(op_c,mult(x0,x1)))]]) ).
cnf(refute_0_42,plain,
( mult(op_c,mult(x0,x1)) != mult(op_c,mult(x0,x1))
| mult(op_c,mult(x0,x1)) = mult(mult(op_c,x0),x1) ),
inference(resolve,[$cnf( $equal(mult(mult(op_c,x0),x1),mult(op_c,mult(x0,x1))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
mult(op_c,mult(x0,x1)) != mult(op_c,mult(x0,x1)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(x0,x1)),mult(mult(op_c,x0),x1)) )],[refute_0_42,goal]) ).
cnf(refute_0_44,plain,
mult(op_c,mult(x0,x1)) = mult(op_c,mult(x0,x1)),
introduced(tautology,[refl,[$fot(mult(op_c,mult(x0,x1)))]]) ).
cnf(refute_0_45,plain,
$false,
inference(resolve,[$cnf( $equal(mult(op_c,mult(x0,x1)),mult(op_c,mult(x0,x1))) )],[refute_0_44,refute_0_43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP665-10 : TPTP v8.1.0. Released v8.1.0.
% 0.00/0.09 % Command : metis --show proof --show saturation %s
% 0.09/0.28 % Computer : n017.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Mon Jun 13 14:02:53 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.09/0.29 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.44 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.44
% 0.13/0.44 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.44
%------------------------------------------------------------------------------