%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP702-10 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 10:50:19 EDT 2022
% Result : Unsatisfiable 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 21
% Syntax : Number of clauses : 52 ( 27 unt; 0 nHn; 45 RR)
% Number of literals : 89 ( 88 equ; 39 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 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 : 22 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(f01,axiom,
mult(A,ld(A,B)) = B ).
cnf(f05,axiom,
mult(A,unit) = A ).
cnf(f06,axiom,
mult(unit,A) = A ).
cnf(f08,axiom,
mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ).
cnf(f11,axiom,
op_d = ld(A,mult(op_c,A)) ).
cnf(goal,negated_conjecture,
mult(op_d,mult(x0,x1)) != mult(mult(op_d,x0),x1) ).
cnf(refute_0_0,plain,
mult(unit,ld(unit,op_c)) = op_c,
inference(subst,[],[f01:[bind(A,$fot(unit)),bind(B,$fot(op_c))]]) ).
cnf(refute_0_1,plain,
op_d = ld(unit,mult(op_c,unit)),
inference(subst,[],[f11:[bind(A,$fot(unit))]]) ).
cnf(refute_0_2,plain,
mult(op_c,unit) = op_c,
inference(subst,[],[f05:[bind(A,$fot(op_c))]]) ).
cnf(refute_0_3,plain,
( mult(op_c,unit) != op_c
| op_d != ld(unit,mult(op_c,unit))
| op_d = ld(unit,op_c) ),
introduced(tautology,[equality,[$cnf( $equal(op_d,ld(unit,mult(op_c,unit))) ),[1,1],$fot(op_c)]]) ).
cnf(refute_0_4,plain,
( op_d != ld(unit,mult(op_c,unit))
| op_d = ld(unit,op_c) ),
inference(resolve,[$cnf( $equal(mult(op_c,unit),op_c) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
op_d = ld(unit,op_c),
inference(resolve,[$cnf( $equal(op_d,ld(unit,mult(op_c,unit))) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_7,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_8,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( op_d != ld(unit,op_c)
| ld(unit,op_c) = op_d ),
inference(subst,[],[refute_0_8:[bind(X,$fot(op_d)),bind(Y,$fot(ld(unit,op_c)))]]) ).
cnf(refute_0_10,plain,
ld(unit,op_c) = op_d,
inference(resolve,[$cnf( $equal(op_d,ld(unit,op_c)) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
( ld(unit,op_c) != op_d
| mult(unit,ld(unit,op_c)) != op_c
| mult(unit,op_d) = op_c ),
introduced(tautology,[equality,[$cnf( $equal(mult(unit,ld(unit,op_c)),op_c) ),[0,1],$fot(op_d)]]) ).
cnf(refute_0_12,plain,
( mult(unit,ld(unit,op_c)) != op_c
| mult(unit,op_d) = op_c ),
inference(resolve,[$cnf( $equal(ld(unit,op_c),op_d) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
mult(unit,op_d) = op_c,
inference(resolve,[$cnf( $equal(mult(unit,ld(unit,op_c)),op_c) )],[refute_0_0,refute_0_12]) ).
cnf(refute_0_14,plain,
mult(unit,op_d) = op_d,
inference(subst,[],[f06:[bind(A,$fot(op_d))]]) ).
cnf(refute_0_15,plain,
( mult(unit,op_d) != op_c
| mult(unit,op_d) != op_d
| op_d = op_c ),
introduced(tautology,[equality,[$cnf( $equal(mult(unit,op_d),op_c) ),[0],$fot(op_d)]]) ).
cnf(refute_0_16,plain,
( mult(unit,op_d) != op_c
| op_d = op_c ),
inference(resolve,[$cnf( $equal(mult(unit,op_d),op_d) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
op_d = op_c,
inference(resolve,[$cnf( $equal(mult(unit,op_d),op_c) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
mult(op_d,mult(x0,x1)) = mult(op_d,mult(x0,x1)),
introduced(tautology,[refl,[$fot(mult(op_d,mult(x0,x1)))]]) ).
cnf(refute_0_19,plain,
( mult(op_d,mult(x0,x1)) != mult(op_d,mult(x0,x1))
| op_d != op_c
| mult(op_d,mult(x0,x1)) = mult(op_c,mult(x0,x1)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_d,mult(x0,x1)),mult(op_d,mult(x0,x1))) ),[1,0],$fot(op_c)]]) ).
cnf(refute_0_20,plain,
( op_d != op_c
| mult(op_d,mult(x0,x1)) = mult(op_c,mult(x0,x1)) ),
inference(resolve,[$cnf( $equal(mult(op_d,mult(x0,x1)),mult(op_d,mult(x0,x1))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
mult(op_d,mult(x0,x1)) = mult(op_c,mult(x0,x1)),
inference(resolve,[$cnf( $equal(op_d,op_c) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
( mult(op_c,mult(x0,x1)) != mult(mult(op_d,x0),x1)
| mult(op_d,mult(x0,x1)) != mult(op_c,mult(x0,x1))
| mult(op_d,mult(x0,x1)) = mult(mult(op_d,x0),x1) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_d,mult(x0,x1)),mult(op_c,mult(x0,x1))) ),[1],$fot(mult(mult(op_d,x0),x1))]]) ).
cnf(refute_0_23,plain,
( mult(op_c,mult(x0,x1)) != mult(mult(op_d,x0),x1)
| mult(op_d,mult(x0,x1)) = mult(mult(op_d,x0),x1) ),
inference(resolve,[$cnf( $equal(mult(op_d,mult(x0,x1)),mult(op_c,mult(x0,x1))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( mult(op_c,mult(A,B)) != mult(mult(op_c,A),B)
| mult(mult(op_c,A),B) = mult(op_c,mult(A,B)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(mult(op_c,mult(A,B)))),bind(Y,$fot(mult(mult(op_c,A),B)))]]) ).
cnf(refute_0_25,plain,
mult(mult(op_c,A),B) = mult(op_c,mult(A,B)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(A,B)),mult(mult(op_c,A),B)) )],[f08,refute_0_24]) ).
cnf(refute_0_26,plain,
mult(mult(op_c,x0),x1) = mult(op_c,mult(x0,x1)),
inference(subst,[],[refute_0_25:[bind(A,$fot(x0)),bind(B,$fot(x1))]]) ).
cnf(refute_0_27,plain,
mult(op_d,x0) = mult(op_d,x0),
introduced(tautology,[refl,[$fot(mult(op_d,x0))]]) ).
cnf(refute_0_28,plain,
( mult(op_d,x0) != mult(op_d,x0)
| op_d != op_c
| mult(op_d,x0) = mult(op_c,x0) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_d,x0),mult(op_d,x0)) ),[1,0],$fot(op_c)]]) ).
cnf(refute_0_29,plain,
( op_d != op_c
| mult(op_d,x0) = mult(op_c,x0) ),
inference(resolve,[$cnf( $equal(mult(op_d,x0),mult(op_d,x0)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
mult(op_d,x0) = mult(op_c,x0),
inference(resolve,[$cnf( $equal(op_d,op_c) )],[refute_0_17,refute_0_29]) ).
cnf(refute_0_31,plain,
mult(mult(op_d,x0),x1) = mult(mult(op_d,x0),x1),
introduced(tautology,[refl,[$fot(mult(mult(op_d,x0),x1))]]) ).
cnf(refute_0_32,plain,
( mult(mult(op_d,x0),x1) != mult(mult(op_d,x0),x1)
| mult(op_d,x0) != mult(op_c,x0)
| mult(mult(op_d,x0),x1) = mult(mult(op_c,x0),x1) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(op_d,x0),x1),mult(mult(op_d,x0),x1)) ),[1,0],$fot(mult(op_c,x0))]]) ).
cnf(refute_0_33,plain,
( mult(op_d,x0) != mult(op_c,x0)
| mult(mult(op_d,x0),x1) = mult(mult(op_c,x0),x1) ),
inference(resolve,[$cnf( $equal(mult(mult(op_d,x0),x1),mult(mult(op_d,x0),x1)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
mult(mult(op_d,x0),x1) = mult(mult(op_c,x0),x1),
inference(resolve,[$cnf( $equal(mult(op_d,x0),mult(op_c,x0)) )],[refute_0_30,refute_0_33]) ).
cnf(refute_0_35,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_36,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_8,refute_0_35]) ).
cnf(refute_0_37,plain,
( mult(mult(op_c,x0),x1) != mult(op_c,mult(x0,x1))
| mult(mult(op_d,x0),x1) != mult(mult(op_c,x0),x1)
| mult(mult(op_d,x0),x1) = mult(op_c,mult(x0,x1)) ),
inference(subst,[],[refute_0_36:[bind(X,$fot(mult(mult(op_d,x0),x1))),bind(Y,$fot(mult(mult(op_c,x0),x1))),bind(Z,$fot(mult(op_c,mult(x0,x1))))]]) ).
cnf(refute_0_38,plain,
( mult(mult(op_c,x0),x1) != mult(op_c,mult(x0,x1))
| mult(mult(op_d,x0),x1) = mult(op_c,mult(x0,x1)) ),
inference(resolve,[$cnf( $equal(mult(mult(op_d,x0),x1),mult(mult(op_c,x0),x1)) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
mult(mult(op_d,x0),x1) = mult(op_c,mult(x0,x1)),
inference(resolve,[$cnf( $equal(mult(mult(op_c,x0),x1),mult(op_c,mult(x0,x1))) )],[refute_0_26,refute_0_38]) ).
cnf(refute_0_40,plain,
( mult(mult(op_d,x0),x1) != mult(op_c,mult(x0,x1))
| mult(op_c,mult(x0,x1)) != mult(op_c,mult(x0,x1))
| mult(op_c,mult(x0,x1)) = mult(mult(op_d,x0),x1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(op_c,mult(x0,x1)),mult(mult(op_d,x0),x1)) ),[1],$fot(mult(op_c,mult(x0,x1)))]]) ).
cnf(refute_0_41,plain,
( mult(op_c,mult(x0,x1)) != mult(op_c,mult(x0,x1))
| mult(op_c,mult(x0,x1)) = mult(mult(op_d,x0),x1) ),
inference(resolve,[$cnf( $equal(mult(mult(op_d,x0),x1),mult(op_c,mult(x0,x1))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( mult(op_c,mult(x0,x1)) != mult(op_c,mult(x0,x1))
| mult(op_d,mult(x0,x1)) = mult(mult(op_d,x0),x1) ),
inference(resolve,[$cnf( $equal(mult(op_c,mult(x0,x1)),mult(mult(op_d,x0),x1)) )],[refute_0_41,refute_0_23]) ).
cnf(refute_0_43,plain,
mult(op_c,mult(x0,x1)) != mult(op_c,mult(x0,x1)),
inference(resolve,[$cnf( $equal(mult(op_d,mult(x0,x1)),mult(mult(op_d,x0),x1)) )],[refute_0_42,goal]) ).
cnf(refute_0_44,plain,
mult(op_c,mult(x0,x1)) = mult(op_c,mult(x0,x1)),
introduced(tautology,[refl,[$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
% 0.08/0.13 % Problem : GRP702-10 : TPTP v8.1.0. Released v8.1.0.
% 0.08/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 18:44:25 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.38
% 0.14/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.14/0.38
%------------------------------------------------------------------------------