TSTP Solution File: GRP679-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP679-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n003.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 10:44:52 EDT 2022
% Result : Unsatisfiable 0.21s 0.42s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 20
% Syntax : Number of clauses : 60 ( 34 unt; 0 nHn; 37 RR)
% Number of literals : 99 ( 98 equ; 42 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 : 71 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c02,axiom,
ld(A,mult(A,B)) = B ).
cnf(c06,axiom,
mult(unit,A) = A ).
cnf(c07,axiom,
mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ).
cnf(c08,axiom,
mult(op_c,A) = mult(A,op_c) ).
cnf(goals,negated_conjecture,
mult(mult(op_c,op_c),a) != mult(a,mult(op_c,op_c)) ).
cnf(refute_0_0,plain,
mult(op_c,a) = mult(a,op_c),
inference(subst,[],[c08:[bind(A,$fot(a))]]) ).
cnf(refute_0_1,plain,
mult(op_c,mult(op_c,a)) = mult(op_c,mult(op_c,a)),
introduced(tautology,[refl,[$fot(mult(op_c,mult(op_c,a)))]]) ).
cnf(refute_0_2,plain,
( mult(op_c,a) != mult(a,op_c)
| mult(op_c,mult(op_c,a)) != mult(op_c,mult(op_c,a))
| mult(op_c,mult(op_c,a)) = mult(op_c,mult(a,op_c)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_c,mult(op_c,a)),mult(op_c,mult(op_c,a))) ),[1,1],$fot(mult(a,op_c))]]) ).
cnf(refute_0_3,plain,
( mult(op_c,a) != mult(a,op_c)
| mult(op_c,mult(op_c,a)) = mult(op_c,mult(a,op_c)) ),
inference(resolve,[$cnf( $equal(mult(op_c,mult(op_c,a)),mult(op_c,mult(op_c,a))) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
mult(op_c,mult(op_c,a)) = mult(op_c,mult(a,op_c)),
inference(resolve,[$cnf( $equal(mult(op_c,a),mult(a,op_c)) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
mult(X_25,mult(unit,mult(X_25,X_27))) = mult(mult(X_25,mult(unit,X_25)),X_27),
inference(subst,[],[c07:[bind(A,$fot(X_25)),bind(B,$fot(unit)),bind(C,$fot(X_27))]]) ).
cnf(refute_0_6,plain,
mult(unit,X_25) = X_25,
inference(subst,[],[c06:[bind(A,$fot(X_25))]]) ).
cnf(refute_0_7,plain,
( mult(X_25,mult(unit,mult(X_25,X_27))) != mult(mult(X_25,mult(unit,X_25)),X_27)
| mult(unit,X_25) != X_25
| mult(X_25,mult(unit,mult(X_25,X_27))) = mult(mult(X_25,X_25),X_27) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_25,mult(unit,mult(X_25,X_27))),mult(mult(X_25,mult(unit,X_25)),X_27)) ),[1,0,1],$fot(X_25)]]) ).
cnf(refute_0_8,plain,
( mult(X_25,mult(unit,mult(X_25,X_27))) != mult(mult(X_25,mult(unit,X_25)),X_27)
| mult(X_25,mult(unit,mult(X_25,X_27))) = mult(mult(X_25,X_25),X_27) ),
inference(resolve,[$cnf( $equal(mult(unit,X_25),X_25) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
mult(X_25,mult(unit,mult(X_25,X_27))) = mult(mult(X_25,X_25),X_27),
inference(resolve,[$cnf( $equal(mult(X_25,mult(unit,mult(X_25,X_27))),mult(mult(X_25,mult(unit,X_25)),X_27)) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
mult(unit,mult(X_25,X_27)) = mult(X_25,X_27),
inference(subst,[],[c06:[bind(A,$fot(mult(X_25,X_27)))]]) ).
cnf(refute_0_11,plain,
mult(X_25,mult(unit,mult(X_25,X_27))) = mult(X_25,mult(unit,mult(X_25,X_27))),
introduced(tautology,[refl,[$fot(mult(X_25,mult(unit,mult(X_25,X_27))))]]) ).
cnf(refute_0_12,plain,
( mult(X_25,mult(unit,mult(X_25,X_27))) != mult(X_25,mult(unit,mult(X_25,X_27)))
| mult(unit,mult(X_25,X_27)) != mult(X_25,X_27)
| mult(X_25,mult(unit,mult(X_25,X_27))) = mult(X_25,mult(X_25,X_27)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_25,mult(unit,mult(X_25,X_27))),mult(X_25,mult(unit,mult(X_25,X_27)))) ),[1,1],$fot(mult(X_25,X_27))]]) ).
cnf(refute_0_13,plain,
( mult(unit,mult(X_25,X_27)) != mult(X_25,X_27)
| mult(X_25,mult(unit,mult(X_25,X_27))) = mult(X_25,mult(X_25,X_27)) ),
inference(resolve,[$cnf( $equal(mult(X_25,mult(unit,mult(X_25,X_27))),mult(X_25,mult(unit,mult(X_25,X_27)))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
mult(X_25,mult(unit,mult(X_25,X_27))) = mult(X_25,mult(X_25,X_27)),
inference(resolve,[$cnf( $equal(mult(unit,mult(X_25,X_27)),mult(X_25,X_27)) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
( mult(X_25,mult(unit,mult(X_25,X_27))) != mult(X_25,mult(X_25,X_27))
| mult(X_25,mult(unit,mult(X_25,X_27))) != mult(mult(X_25,X_25),X_27)
| mult(X_25,mult(X_25,X_27)) = mult(mult(X_25,X_25),X_27) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_25,mult(unit,mult(X_25,X_27))),mult(mult(X_25,X_25),X_27)) ),[0],$fot(mult(X_25,mult(X_25,X_27)))]]) ).
cnf(refute_0_16,plain,
( mult(X_25,mult(unit,mult(X_25,X_27))) != mult(mult(X_25,X_25),X_27)
| mult(X_25,mult(X_25,X_27)) = mult(mult(X_25,X_25),X_27) ),
inference(resolve,[$cnf( $equal(mult(X_25,mult(unit,mult(X_25,X_27))),mult(X_25,mult(X_25,X_27))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
mult(X_25,mult(X_25,X_27)) = mult(mult(X_25,X_25),X_27),
inference(resolve,[$cnf( $equal(mult(X_25,mult(unit,mult(X_25,X_27))),mult(mult(X_25,X_25),X_27)) )],[refute_0_9,refute_0_16]) ).
cnf(refute_0_18,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_19,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_20,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( mult(X_25,mult(X_25,X_27)) != mult(mult(X_25,X_25),X_27)
| mult(mult(X_25,X_25),X_27) = mult(X_25,mult(X_25,X_27)) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(mult(X_25,mult(X_25,X_27)))),bind(Y,$fot(mult(mult(X_25,X_25),X_27)))]]) ).
cnf(refute_0_22,plain,
mult(mult(X_25,X_25),X_27) = mult(X_25,mult(X_25,X_27)),
inference(resolve,[$cnf( $equal(mult(X_25,mult(X_25,X_27)),mult(mult(X_25,X_25),X_27)) )],[refute_0_17,refute_0_21]) ).
cnf(refute_0_23,plain,
mult(mult(op_c,op_c),a) = mult(op_c,mult(op_c,a)),
inference(subst,[],[refute_0_22:[bind(X_25,$fot(op_c)),bind(X_27,$fot(a))]]) ).
cnf(refute_0_24,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_25,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_20,refute_0_24]) ).
cnf(refute_0_26,plain,
( mult(mult(op_c,op_c),a) != mult(op_c,mult(op_c,a))
| mult(op_c,mult(op_c,a)) != mult(op_c,mult(a,op_c))
| mult(mult(op_c,op_c),a) = mult(op_c,mult(a,op_c)) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(mult(mult(op_c,op_c),a))),bind(Y,$fot(mult(op_c,mult(op_c,a)))),bind(Z,$fot(mult(op_c,mult(a,op_c))))]]) ).
cnf(refute_0_27,plain,
( mult(op_c,mult(op_c,a)) != mult(op_c,mult(a,op_c))
| mult(mult(op_c,op_c),a) = mult(op_c,mult(a,op_c)) ),
inference(resolve,[$cnf( $equal(mult(mult(op_c,op_c),a),mult(op_c,mult(op_c,a))) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
mult(mult(op_c,op_c),a) = mult(op_c,mult(a,op_c)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(op_c,a)),mult(op_c,mult(a,op_c))) )],[refute_0_4,refute_0_27]) ).
cnf(refute_0_29,plain,
( mult(mult(op_c,op_c),a) != mult(op_c,mult(a,op_c))
| mult(op_c,mult(a,op_c)) != mult(a,mult(op_c,op_c))
| mult(mult(op_c,op_c),a) = mult(a,mult(op_c,op_c)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(mult(op_c,op_c),a),mult(a,mult(op_c,op_c))) ),[0],$fot(mult(op_c,mult(a,op_c)))]]) ).
cnf(refute_0_30,plain,
( mult(op_c,mult(a,op_c)) != mult(a,mult(op_c,op_c))
| mult(mult(op_c,op_c),a) = mult(a,mult(op_c,op_c)) ),
inference(resolve,[$cnf( $equal(mult(mult(op_c,op_c),a),mult(op_c,mult(a,op_c))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
mult(op_c,mult(a,op_c)) != mult(a,mult(op_c,op_c)),
inference(resolve,[$cnf( $equal(mult(mult(op_c,op_c),a),mult(a,mult(op_c,op_c))) )],[refute_0_30,goals]) ).
cnf(refute_0_32,plain,
ld(op_c,mult(op_c,mult(X_37,mult(op_c,op_c)))) = mult(X_37,mult(op_c,op_c)),
inference(subst,[],[c02:[bind(A,$fot(op_c)),bind(B,$fot(mult(X_37,mult(op_c,op_c))))]]) ).
cnf(refute_0_33,plain,
ld(op_c,mult(op_c,X_11)) = X_11,
inference(subst,[],[c02:[bind(A,$fot(op_c)),bind(B,$fot(X_11))]]) ).
cnf(refute_0_34,plain,
mult(op_c,X_11) = mult(X_11,op_c),
inference(subst,[],[c08:[bind(A,$fot(X_11))]]) ).
cnf(refute_0_35,plain,
( ld(op_c,mult(op_c,X_11)) != X_11
| mult(op_c,X_11) != mult(X_11,op_c)
| ld(op_c,mult(X_11,op_c)) = X_11 ),
introduced(tautology,[equality,[$cnf( $equal(ld(op_c,mult(op_c,X_11)),X_11) ),[0,1],$fot(mult(X_11,op_c))]]) ).
cnf(refute_0_36,plain,
( ld(op_c,mult(op_c,X_11)) != X_11
| ld(op_c,mult(X_11,op_c)) = X_11 ),
inference(resolve,[$cnf( $equal(mult(op_c,X_11),mult(X_11,op_c)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
ld(op_c,mult(X_11,op_c)) = X_11,
inference(resolve,[$cnf( $equal(ld(op_c,mult(op_c,X_11)),X_11) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
ld(op_c,mult(mult(X_25,mult(X_26,X_25)),op_c)) = mult(X_25,mult(X_26,X_25)),
inference(subst,[],[refute_0_37:[bind(X_11,$fot(mult(X_25,mult(X_26,X_25))))]]) ).
cnf(refute_0_39,plain,
mult(X_25,mult(X_26,mult(X_25,op_c))) = mult(mult(X_25,mult(X_26,X_25)),op_c),
inference(subst,[],[c07:[bind(A,$fot(X_25)),bind(B,$fot(X_26)),bind(C,$fot(op_c))]]) ).
cnf(refute_0_40,plain,
( mult(X_25,mult(X_26,mult(X_25,op_c))) != mult(mult(X_25,mult(X_26,X_25)),op_c)
| mult(mult(X_25,mult(X_26,X_25)),op_c) = mult(X_25,mult(X_26,mult(X_25,op_c))) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(mult(X_25,mult(X_26,mult(X_25,op_c))))),bind(Y,$fot(mult(mult(X_25,mult(X_26,X_25)),op_c)))]]) ).
cnf(refute_0_41,plain,
mult(mult(X_25,mult(X_26,X_25)),op_c) = mult(X_25,mult(X_26,mult(X_25,op_c))),
inference(resolve,[$cnf( $equal(mult(X_25,mult(X_26,mult(X_25,op_c))),mult(mult(X_25,mult(X_26,X_25)),op_c)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( ld(op_c,mult(mult(X_25,mult(X_26,X_25)),op_c)) != mult(X_25,mult(X_26,X_25))
| mult(mult(X_25,mult(X_26,X_25)),op_c) != mult(X_25,mult(X_26,mult(X_25,op_c)))
| ld(op_c,mult(X_25,mult(X_26,mult(X_25,op_c)))) = mult(X_25,mult(X_26,X_25)) ),
introduced(tautology,[equality,[$cnf( $equal(ld(op_c,mult(mult(X_25,mult(X_26,X_25)),op_c)),mult(X_25,mult(X_26,X_25))) ),[0,1],$fot(mult(X_25,mult(X_26,mult(X_25,op_c))))]]) ).
cnf(refute_0_43,plain,
( ld(op_c,mult(mult(X_25,mult(X_26,X_25)),op_c)) != mult(X_25,mult(X_26,X_25))
| ld(op_c,mult(X_25,mult(X_26,mult(X_25,op_c)))) = mult(X_25,mult(X_26,X_25)) ),
inference(resolve,[$cnf( $equal(mult(mult(X_25,mult(X_26,X_25)),op_c),mult(X_25,mult(X_26,mult(X_25,op_c)))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
ld(op_c,mult(X_25,mult(X_26,mult(X_25,op_c)))) = mult(X_25,mult(X_26,X_25)),
inference(resolve,[$cnf( $equal(ld(op_c,mult(mult(X_25,mult(X_26,X_25)),op_c)),mult(X_25,mult(X_26,X_25))) )],[refute_0_38,refute_0_43]) ).
cnf(refute_0_45,plain,
ld(op_c,mult(op_c,mult(X_37,mult(op_c,op_c)))) = mult(op_c,mult(X_37,op_c)),
inference(subst,[],[refute_0_44:[bind(X_25,$fot(op_c)),bind(X_26,$fot(X_37))]]) ).
cnf(refute_0_46,plain,
( ld(op_c,mult(op_c,mult(X_37,mult(op_c,op_c)))) != mult(X_37,mult(op_c,op_c))
| ld(op_c,mult(op_c,mult(X_37,mult(op_c,op_c)))) != mult(op_c,mult(X_37,op_c))
| mult(op_c,mult(X_37,op_c)) = mult(X_37,mult(op_c,op_c)) ),
introduced(tautology,[equality,[$cnf( $equal(ld(op_c,mult(op_c,mult(X_37,mult(op_c,op_c)))),mult(X_37,mult(op_c,op_c))) ),[0],$fot(mult(op_c,mult(X_37,op_c)))]]) ).
cnf(refute_0_47,plain,
( ld(op_c,mult(op_c,mult(X_37,mult(op_c,op_c)))) != mult(X_37,mult(op_c,op_c))
| mult(op_c,mult(X_37,op_c)) = mult(X_37,mult(op_c,op_c)) ),
inference(resolve,[$cnf( $equal(ld(op_c,mult(op_c,mult(X_37,mult(op_c,op_c)))),mult(op_c,mult(X_37,op_c))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
mult(op_c,mult(X_37,op_c)) = mult(X_37,mult(op_c,op_c)),
inference(resolve,[$cnf( $equal(ld(op_c,mult(op_c,mult(X_37,mult(op_c,op_c)))),mult(X_37,mult(op_c,op_c))) )],[refute_0_32,refute_0_47]) ).
cnf(refute_0_49,plain,
mult(op_c,mult(a,op_c)) = mult(a,mult(op_c,op_c)),
inference(subst,[],[refute_0_48:[bind(X_37,$fot(a))]]) ).
cnf(refute_0_50,plain,
( mult(a,mult(op_c,op_c)) != mult(a,mult(op_c,op_c))
| mult(op_c,mult(a,op_c)) != mult(a,mult(op_c,op_c))
| mult(op_c,mult(a,op_c)) = mult(a,mult(op_c,op_c)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_c,mult(a,op_c)),mult(a,mult(op_c,op_c))) ),[1],$fot(mult(a,mult(op_c,op_c)))]]) ).
cnf(refute_0_51,plain,
( mult(a,mult(op_c,op_c)) != mult(a,mult(op_c,op_c))
| mult(op_c,mult(a,op_c)) = mult(a,mult(op_c,op_c)) ),
inference(resolve,[$cnf( $equal(mult(op_c,mult(a,op_c)),mult(a,mult(op_c,op_c))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
mult(a,mult(op_c,op_c)) != mult(a,mult(op_c,op_c)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(a,op_c)),mult(a,mult(op_c,op_c))) )],[refute_0_51,refute_0_31]) ).
cnf(refute_0_53,plain,
mult(a,mult(op_c,op_c)) = mult(a,mult(op_c,op_c)),
introduced(tautology,[refl,[$fot(mult(a,mult(op_c,op_c)))]]) ).
cnf(refute_0_54,plain,
$false,
inference(resolve,[$cnf( $equal(mult(a,mult(op_c,op_c)),mult(a,mult(op_c,op_c))) )],[refute_0_53,refute_0_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP679-1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 13 21:47:09 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.42 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.42
% 0.21/0.42 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.21/0.43
%------------------------------------------------------------------------------