%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : BOO021-1 : TPTP v8.1.0. Released v2.2.0.
% 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 : Thu Jul 14 23:45:13 EDT 2022
% Result : Unsatisfiable 0.19s 0.40s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of clauses : 35 ( 21 unt; 0 nHn; 18 RR)
% Number of literals : 55 ( 54 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 54 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(multiply_add,axiom,
multiply(add(X,Y),Y) = Y ).
cnf(multiply_add_property,axiom,
multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) ).
cnf(add_multiply,axiom,
add(multiply(X,Y),Y) = Y ).
cnf(prove_commutativity_of_multiply,negated_conjecture,
multiply(b,a) != multiply(a,b) ).
cnf(refute_0_0,plain,
add(multiply(add(X,X_6),X_6),X_6) = X_6,
inference(subst,[],[add_multiply:[bind(X,$fot(add(X,X_6))),bind(Y,$fot(X_6))]]) ).
cnf(refute_0_1,plain,
multiply(add(X,X_6),X_6) = X_6,
inference(subst,[],[multiply_add:[bind(Y,$fot(X_6))]]) ).
cnf(refute_0_2,plain,
( multiply(add(X,X_6),X_6) != X_6
| add(multiply(add(X,X_6),X_6),X_6) != X_6
| add(X_6,X_6) = X_6 ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(add(X,X_6),X_6),X_6),X_6) ),[0,0],$fot(X_6)]]) ).
cnf(refute_0_3,plain,
( add(multiply(add(X,X_6),X_6),X_6) != X_6
| add(X_6,X_6) = X_6 ),
inference(resolve,[$cnf( $equal(multiply(add(X,X_6),X_6),X_6) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
add(X_6,X_6) = X_6,
inference(resolve,[$cnf( $equal(add(multiply(add(X,X_6),X_6),X_6),X_6) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
add(multiply(X_28,X_27),multiply(X_28,X_27)) = multiply(X_28,X_27),
inference(subst,[],[refute_0_4:[bind(X_6,$fot(multiply(X_28,X_27)))]]) ).
cnf(refute_0_6,plain,
multiply(X_27,add(X_28,X_28)) = add(multiply(X_28,X_27),multiply(X_28,X_27)),
inference(subst,[],[multiply_add_property:[bind(X,$fot(X_27)),bind(Y,$fot(X_28)),bind(Z,$fot(X_28))]]) ).
cnf(refute_0_7,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_8,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_9,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( multiply(X_27,add(X_28,X_28)) != add(multiply(X_28,X_27),multiply(X_28,X_27))
| add(multiply(X_28,X_27),multiply(X_28,X_27)) = multiply(X_27,add(X_28,X_28)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(multiply(X_27,add(X_28,X_28)))),bind(Y0,$fot(add(multiply(X_28,X_27),multiply(X_28,X_27))))]]) ).
cnf(refute_0_11,plain,
add(multiply(X_28,X_27),multiply(X_28,X_27)) = multiply(X_27,add(X_28,X_28)),
inference(resolve,[$cnf( $equal(multiply(X_27,add(X_28,X_28)),add(multiply(X_28,X_27),multiply(X_28,X_27))) )],[refute_0_6,refute_0_10]) ).
cnf(refute_0_12,plain,
( add(multiply(X_28,X_27),multiply(X_28,X_27)) != multiply(X_27,add(X_28,X_28))
| add(multiply(X_28,X_27),multiply(X_28,X_27)) != multiply(X_28,X_27)
| multiply(X_27,add(X_28,X_28)) = multiply(X_28,X_27) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_28,X_27),multiply(X_28,X_27)),multiply(X_28,X_27)) ),[0],$fot(multiply(X_27,add(X_28,X_28)))]]) ).
cnf(refute_0_13,plain,
( add(multiply(X_28,X_27),multiply(X_28,X_27)) != multiply(X_28,X_27)
| multiply(X_27,add(X_28,X_28)) = multiply(X_28,X_27) ),
inference(resolve,[$cnf( $equal(add(multiply(X_28,X_27),multiply(X_28,X_27)),multiply(X_27,add(X_28,X_28))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
multiply(X_27,add(X_28,X_28)) = multiply(X_28,X_27),
inference(resolve,[$cnf( $equal(add(multiply(X_28,X_27),multiply(X_28,X_27)),multiply(X_28,X_27)) )],[refute_0_5,refute_0_13]) ).
cnf(refute_0_15,plain,
add(X_28,X_28) = X_28,
inference(subst,[],[refute_0_4:[bind(X_6,$fot(X_28))]]) ).
cnf(refute_0_16,plain,
multiply(X_27,add(X_28,X_28)) = multiply(X_27,add(X_28,X_28)),
introduced(tautology,[refl,[$fot(multiply(X_27,add(X_28,X_28)))]]) ).
cnf(refute_0_17,plain,
( multiply(X_27,add(X_28,X_28)) != multiply(X_27,add(X_28,X_28))
| add(X_28,X_28) != X_28
| multiply(X_27,add(X_28,X_28)) = multiply(X_27,X_28) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_27,add(X_28,X_28)),multiply(X_27,add(X_28,X_28))) ),[1,1],$fot(X_28)]]) ).
cnf(refute_0_18,plain,
( add(X_28,X_28) != X_28
| multiply(X_27,add(X_28,X_28)) = multiply(X_27,X_28) ),
inference(resolve,[$cnf( $equal(multiply(X_27,add(X_28,X_28)),multiply(X_27,add(X_28,X_28))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
multiply(X_27,add(X_28,X_28)) = multiply(X_27,X_28),
inference(resolve,[$cnf( $equal(add(X_28,X_28),X_28) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
( multiply(X_27,add(X_28,X_28)) != multiply(X_27,X_28)
| multiply(X_27,add(X_28,X_28)) != multiply(X_28,X_27)
| multiply(X_27,X_28) = multiply(X_28,X_27) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_27,add(X_28,X_28)),multiply(X_28,X_27)) ),[0],$fot(multiply(X_27,X_28))]]) ).
cnf(refute_0_21,plain,
( multiply(X_27,add(X_28,X_28)) != multiply(X_28,X_27)
| multiply(X_27,X_28) = multiply(X_28,X_27) ),
inference(resolve,[$cnf( $equal(multiply(X_27,add(X_28,X_28)),multiply(X_27,X_28)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
multiply(X_27,X_28) = multiply(X_28,X_27),
inference(resolve,[$cnf( $equal(multiply(X_27,add(X_28,X_28)),multiply(X_28,X_27)) )],[refute_0_14,refute_0_21]) ).
cnf(refute_0_23,plain,
( multiply(X_27,X_28) != multiply(X_28,X_27)
| multiply(X_28,X_27) = multiply(X_27,X_28) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(multiply(X_27,X_28))),bind(Y0,$fot(multiply(X_28,X_27)))]]) ).
cnf(refute_0_24,plain,
multiply(X_28,X_27) = multiply(X_27,X_28),
inference(resolve,[$cnf( $equal(multiply(X_27,X_28),multiply(X_28,X_27)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
multiply(b,a) = multiply(a,b),
inference(subst,[],[refute_0_24:[bind(X_27,$fot(a)),bind(X_28,$fot(b))]]) ).
cnf(refute_0_26,plain,
( multiply(a,b) != multiply(a,b)
| multiply(b,a) != multiply(a,b)
| multiply(b,a) = multiply(a,b) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(b,a),multiply(a,b)) ),[1],$fot(multiply(a,b))]]) ).
cnf(refute_0_27,plain,
( multiply(a,b) != multiply(a,b)
| multiply(b,a) = multiply(a,b) ),
inference(resolve,[$cnf( $equal(multiply(b,a),multiply(a,b)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
multiply(a,b) != multiply(a,b),
inference(resolve,[$cnf( $equal(multiply(b,a),multiply(a,b)) )],[refute_0_27,prove_commutativity_of_multiply]) ).
cnf(refute_0_29,plain,
multiply(a,b) = multiply(a,b),
introduced(tautology,[refl,[$fot(multiply(a,b))]]) ).
cnf(refute_0_30,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(a,b),multiply(a,b)) )],[refute_0_29,refute_0_28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO021-1 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 1 22:15:42 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.40
% 0.19/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.41
%------------------------------------------------------------------------------