TSTP Solution File: GRP702-12 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP702-12 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n005.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 10:50:20 EDT 2022
% Result : Unsatisfiable 0.14s 0.36s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of clauses : 44 ( 22 unt; 0 nHn; 39 RR)
% Number of literals : 77 ( 76 equ; 35 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(f02,axiom,
ld(A,mult(A,B)) = B ).
cnf(f10,axiom,
mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ).
cnf(f11,axiom,
op_d = ld(A,mult(op_c,A)) ).
cnf(goal,negated_conjecture,
mult(x0,mult(op_d,x1)) != mult(mult(x0,op_d),x1) ).
cnf(refute_0_0,plain,
op_d = ld(op_c,mult(op_c,op_c)),
inference(subst,[],[f11:[bind(A,$fot(op_c))]]) ).
cnf(refute_0_1,plain,
ld(op_c,mult(op_c,op_c)) = op_c,
inference(subst,[],[f02:[bind(A,$fot(op_c)),bind(B,$fot(op_c))]]) ).
cnf(refute_0_2,plain,
( ld(op_c,mult(op_c,op_c)) != op_c
| op_d != ld(op_c,mult(op_c,op_c))
| op_d = op_c ),
introduced(tautology,[equality,[$cnf( $equal(op_d,ld(op_c,mult(op_c,op_c))) ),[1],$fot(op_c)]]) ).
cnf(refute_0_3,plain,
( op_d != ld(op_c,mult(op_c,op_c))
| op_d = op_c ),
inference(resolve,[$cnf( $equal(ld(op_c,mult(op_c,op_c)),op_c) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
op_d = op_c,
inference(resolve,[$cnf( $equal(op_d,ld(op_c,mult(op_c,op_c))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
mult(op_d,x1) = mult(op_d,x1),
introduced(tautology,[refl,[$fot(mult(op_d,x1))]]) ).
cnf(refute_0_6,plain,
( mult(op_d,x1) != mult(op_d,x1)
| op_d != op_c
| mult(op_d,x1) = mult(op_c,x1) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_d,x1),mult(op_d,x1)) ),[1,0],$fot(op_c)]]) ).
cnf(refute_0_7,plain,
( op_d != op_c
| mult(op_d,x1) = mult(op_c,x1) ),
inference(resolve,[$cnf( $equal(mult(op_d,x1),mult(op_d,x1)) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
mult(op_d,x1) = mult(op_c,x1),
inference(resolve,[$cnf( $equal(op_d,op_c) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
mult(x0,mult(op_d,x1)) = mult(x0,mult(op_d,x1)),
introduced(tautology,[refl,[$fot(mult(x0,mult(op_d,x1)))]]) ).
cnf(refute_0_10,plain,
( mult(op_d,x1) != mult(op_c,x1)
| mult(x0,mult(op_d,x1)) != mult(x0,mult(op_d,x1))
| mult(x0,mult(op_d,x1)) = mult(x0,mult(op_c,x1)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(x0,mult(op_d,x1)),mult(x0,mult(op_d,x1))) ),[1,1],$fot(mult(op_c,x1))]]) ).
cnf(refute_0_11,plain,
( mult(op_d,x1) != mult(op_c,x1)
| mult(x0,mult(op_d,x1)) = mult(x0,mult(op_c,x1)) ),
inference(resolve,[$cnf( $equal(mult(x0,mult(op_d,x1)),mult(x0,mult(op_d,x1))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
mult(x0,mult(op_d,x1)) = mult(x0,mult(op_c,x1)),
inference(resolve,[$cnf( $equal(mult(op_d,x1),mult(op_c,x1)) )],[refute_0_8,refute_0_11]) ).
cnf(refute_0_13,plain,
( mult(x0,mult(op_c,x1)) != mult(mult(x0,op_d),x1)
| mult(x0,mult(op_d,x1)) != mult(x0,mult(op_c,x1))
| mult(x0,mult(op_d,x1)) = mult(mult(x0,op_d),x1) ),
introduced(tautology,[equality,[$cnf( $equal(mult(x0,mult(op_d,x1)),mult(x0,mult(op_c,x1))) ),[1],$fot(mult(mult(x0,op_d),x1))]]) ).
cnf(refute_0_14,plain,
( mult(x0,mult(op_c,x1)) != mult(mult(x0,op_d),x1)
| mult(x0,mult(op_d,x1)) = mult(mult(x0,op_d),x1) ),
inference(resolve,[$cnf( $equal(mult(x0,mult(op_d,x1)),mult(x0,mult(op_c,x1))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_16,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_17,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( mult(A,mult(op_c,B)) != mult(mult(A,op_c),B)
| mult(mult(A,op_c),B) = mult(A,mult(op_c,B)) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(mult(A,mult(op_c,B)))),bind(Y,$fot(mult(mult(A,op_c),B)))]]) ).
cnf(refute_0_19,plain,
mult(mult(A,op_c),B) = mult(A,mult(op_c,B)),
inference(resolve,[$cnf( $equal(mult(A,mult(op_c,B)),mult(mult(A,op_c),B)) )],[f10,refute_0_18]) ).
cnf(refute_0_20,plain,
mult(mult(x0,op_c),x1) = mult(x0,mult(op_c,x1)),
inference(subst,[],[refute_0_19:[bind(A,$fot(x0)),bind(B,$fot(x1))]]) ).
cnf(refute_0_21,plain,
mult(x0,op_d) = mult(x0,op_d),
introduced(tautology,[refl,[$fot(mult(x0,op_d))]]) ).
cnf(refute_0_22,plain,
( mult(x0,op_d) != mult(x0,op_d)
| op_d != op_c
| mult(x0,op_d) = mult(x0,op_c) ),
introduced(tautology,[equality,[$cnf( $equal(mult(x0,op_d),mult(x0,op_d)) ),[1,1],$fot(op_c)]]) ).
cnf(refute_0_23,plain,
( op_d != op_c
| mult(x0,op_d) = mult(x0,op_c) ),
inference(resolve,[$cnf( $equal(mult(x0,op_d),mult(x0,op_d)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
mult(x0,op_d) = mult(x0,op_c),
inference(resolve,[$cnf( $equal(op_d,op_c) )],[refute_0_4,refute_0_23]) ).
cnf(refute_0_25,plain,
mult(mult(x0,op_d),x1) = mult(mult(x0,op_d),x1),
introduced(tautology,[refl,[$fot(mult(mult(x0,op_d),x1))]]) ).
cnf(refute_0_26,plain,
( mult(mult(x0,op_d),x1) != mult(mult(x0,op_d),x1)
| mult(x0,op_d) != mult(x0,op_c)
| mult(mult(x0,op_d),x1) = mult(mult(x0,op_c),x1) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(x0,op_d),x1),mult(mult(x0,op_d),x1)) ),[1,0],$fot(mult(x0,op_c))]]) ).
cnf(refute_0_27,plain,
( mult(x0,op_d) != mult(x0,op_c)
| mult(mult(x0,op_d),x1) = mult(mult(x0,op_c),x1) ),
inference(resolve,[$cnf( $equal(mult(mult(x0,op_d),x1),mult(mult(x0,op_d),x1)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
mult(mult(x0,op_d),x1) = mult(mult(x0,op_c),x1),
inference(resolve,[$cnf( $equal(mult(x0,op_d),mult(x0,op_c)) )],[refute_0_24,refute_0_27]) ).
cnf(refute_0_29,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_30,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_17,refute_0_29]) ).
cnf(refute_0_31,plain,
( mult(mult(x0,op_c),x1) != mult(x0,mult(op_c,x1))
| mult(mult(x0,op_d),x1) != mult(mult(x0,op_c),x1)
| mult(mult(x0,op_d),x1) = mult(x0,mult(op_c,x1)) ),
inference(subst,[],[refute_0_30:[bind(X,$fot(mult(mult(x0,op_d),x1))),bind(Y,$fot(mult(mult(x0,op_c),x1))),bind(Z,$fot(mult(x0,mult(op_c,x1))))]]) ).
cnf(refute_0_32,plain,
( mult(mult(x0,op_c),x1) != mult(x0,mult(op_c,x1))
| mult(mult(x0,op_d),x1) = mult(x0,mult(op_c,x1)) ),
inference(resolve,[$cnf( $equal(mult(mult(x0,op_d),x1),mult(mult(x0,op_c),x1)) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
mult(mult(x0,op_d),x1) = mult(x0,mult(op_c,x1)),
inference(resolve,[$cnf( $equal(mult(mult(x0,op_c),x1),mult(x0,mult(op_c,x1))) )],[refute_0_20,refute_0_32]) ).
cnf(refute_0_34,plain,
( mult(mult(x0,op_d),x1) != mult(x0,mult(op_c,x1))
| mult(x0,mult(op_c,x1)) != mult(x0,mult(op_c,x1))
| mult(x0,mult(op_c,x1)) = mult(mult(x0,op_d),x1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(x0,mult(op_c,x1)),mult(mult(x0,op_d),x1)) ),[1],$fot(mult(x0,mult(op_c,x1)))]]) ).
cnf(refute_0_35,plain,
( mult(x0,mult(op_c,x1)) != mult(x0,mult(op_c,x1))
| mult(x0,mult(op_c,x1)) = mult(mult(x0,op_d),x1) ),
inference(resolve,[$cnf( $equal(mult(mult(x0,op_d),x1),mult(x0,mult(op_c,x1))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( mult(x0,mult(op_c,x1)) != mult(x0,mult(op_c,x1))
| mult(x0,mult(op_d,x1)) = mult(mult(x0,op_d),x1) ),
inference(resolve,[$cnf( $equal(mult(x0,mult(op_c,x1)),mult(mult(x0,op_d),x1)) )],[refute_0_35,refute_0_14]) ).
cnf(refute_0_37,plain,
mult(x0,mult(op_c,x1)) != mult(x0,mult(op_c,x1)),
inference(resolve,[$cnf( $equal(mult(x0,mult(op_d,x1)),mult(mult(x0,op_d),x1)) )],[refute_0_36,goal]) ).
cnf(refute_0_38,plain,
mult(x0,mult(op_c,x1)) = mult(x0,mult(op_c,x1)),
introduced(tautology,[refl,[$fot(mult(x0,mult(op_c,x1)))]]) ).
cnf(refute_0_39,plain,
$false,
inference(resolve,[$cnf( $equal(mult(x0,mult(op_c,x1)),mult(x0,mult(op_c,x1))) )],[refute_0_38,refute_0_37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP702-12 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n005.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
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 08:25:09 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36
% 0.14/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.14/0.37
%------------------------------------------------------------------------------