TSTP Solution File: GRP001-4 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP001-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 10:32:08 EDT 2022
% Result : Unsatisfiable 0.14s 0.37s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 17
% Syntax : Number of clauses : 57 ( 32 unt; 0 nHn; 39 RR)
% Number of literals : 93 ( 92 equ; 37 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ).
cnf(left_identity,axiom,
multiply(identity,X) = X ).
cnf(squareness,hypothesis,
multiply(X,X) = identity ).
cnf(a_times_b_is_c,hypothesis,
multiply(a,b) = c ).
cnf(prove_b_times_a_is_c,negated_conjecture,
multiply(b,a) != c ).
cnf(refute_0_0,plain,
multiply(multiply(X_3,X_3),X_4) = multiply(X_3,multiply(X_3,X_4)),
inference(subst,[],[associativity:[bind(X,$fot(X_3)),bind(Y,$fot(X_3)),bind(Z,$fot(X_4))]]) ).
cnf(refute_0_1,plain,
multiply(X_3,X_3) = identity,
inference(subst,[],[squareness:[bind(X,$fot(X_3))]]) ).
cnf(refute_0_2,plain,
( multiply(X_3,X_3) != identity
| multiply(multiply(X_3,X_3),X_4) != multiply(X_3,multiply(X_3,X_4))
| multiply(identity,X_4) = multiply(X_3,multiply(X_3,X_4)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_3,X_3),X_4),multiply(X_3,multiply(X_3,X_4))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_3,plain,
( multiply(multiply(X_3,X_3),X_4) != multiply(X_3,multiply(X_3,X_4))
| multiply(identity,X_4) = multiply(X_3,multiply(X_3,X_4)) ),
inference(resolve,[$cnf( $equal(multiply(X_3,X_3),identity) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(identity,X_4) = multiply(X_3,multiply(X_3,X_4)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_3,X_3),X_4),multiply(X_3,multiply(X_3,X_4))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(identity,X_4) = X_4,
inference(subst,[],[left_identity:[bind(X,$fot(X_4))]]) ).
cnf(refute_0_6,plain,
( multiply(identity,X_4) != X_4
| multiply(identity,X_4) != multiply(X_3,multiply(X_3,X_4))
| X_4 = multiply(X_3,multiply(X_3,X_4)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_4),multiply(X_3,multiply(X_3,X_4))) ),[0],$fot(X_4)]]) ).
cnf(refute_0_7,plain,
( multiply(identity,X_4) != multiply(X_3,multiply(X_3,X_4))
| X_4 = multiply(X_3,multiply(X_3,X_4)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_4),X_4) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
X_4 = multiply(X_3,multiply(X_3,X_4)),
inference(resolve,[$cnf( $equal(multiply(identity,X_4),multiply(X_3,multiply(X_3,X_4))) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
multiply(b,X_4) = multiply(a,multiply(a,multiply(b,X_4))),
inference(subst,[],[refute_0_8:[bind(X_3,$fot(a)),bind(X_4,$fot(multiply(b,X_4)))]]) ).
cnf(refute_0_10,plain,
multiply(multiply(a,b),X_4) = multiply(a,multiply(b,X_4)),
inference(subst,[],[associativity:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(X_4))]]) ).
cnf(refute_0_11,plain,
( multiply(multiply(a,b),X_4) != multiply(a,multiply(b,X_4))
| multiply(a,b) != c
| multiply(c,X_4) = multiply(a,multiply(b,X_4)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(a,b),X_4),multiply(a,multiply(b,X_4))) ),[0,0],$fot(c)]]) ).
cnf(refute_0_12,plain,
( multiply(multiply(a,b),X_4) != multiply(a,multiply(b,X_4))
| multiply(c,X_4) = multiply(a,multiply(b,X_4)) ),
inference(resolve,[$cnf( $equal(multiply(a,b),c) )],[a_times_b_is_c,refute_0_11]) ).
cnf(refute_0_13,plain,
multiply(c,X_4) = multiply(a,multiply(b,X_4)),
inference(resolve,[$cnf( $equal(multiply(multiply(a,b),X_4),multiply(a,multiply(b,X_4))) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_15,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_16,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( multiply(c,X_4) != multiply(a,multiply(b,X_4))
| multiply(a,multiply(b,X_4)) = multiply(c,X_4) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(c,X_4))),bind(Y0,$fot(multiply(a,multiply(b,X_4))))]]) ).
cnf(refute_0_18,plain,
multiply(a,multiply(b,X_4)) = multiply(c,X_4),
inference(resolve,[$cnf( $equal(multiply(c,X_4),multiply(a,multiply(b,X_4))) )],[refute_0_13,refute_0_17]) ).
cnf(refute_0_19,plain,
( multiply(a,multiply(b,X_4)) != multiply(c,X_4)
| multiply(b,X_4) != multiply(a,multiply(a,multiply(b,X_4)))
| multiply(b,X_4) = multiply(a,multiply(c,X_4)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(b,X_4),multiply(a,multiply(a,multiply(b,X_4)))) ),[1,1],$fot(multiply(c,X_4))]]) ).
cnf(refute_0_20,plain,
( multiply(b,X_4) != multiply(a,multiply(a,multiply(b,X_4)))
| multiply(b,X_4) = multiply(a,multiply(c,X_4)) ),
inference(resolve,[$cnf( $equal(multiply(a,multiply(b,X_4)),multiply(c,X_4)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
multiply(b,X_4) = multiply(a,multiply(c,X_4)),
inference(resolve,[$cnf( $equal(multiply(b,X_4),multiply(a,multiply(a,multiply(b,X_4)))) )],[refute_0_9,refute_0_20]) ).
cnf(refute_0_22,plain,
multiply(b,a) = multiply(a,multiply(c,a)),
inference(subst,[],[refute_0_21:[bind(X_4,$fot(a))]]) ).
cnf(refute_0_23,plain,
b = multiply(c,multiply(c,b)),
inference(subst,[],[refute_0_8:[bind(X_3,$fot(c)),bind(X_4,$fot(b))]]) ).
cnf(refute_0_24,plain,
multiply(c,b) = multiply(a,multiply(b,b)),
inference(subst,[],[refute_0_13:[bind(X_4,$fot(b))]]) ).
cnf(refute_0_25,plain,
multiply(b,b) = identity,
inference(subst,[],[squareness:[bind(X,$fot(b))]]) ).
cnf(refute_0_26,plain,
( multiply(b,b) != identity
| multiply(c,b) != multiply(a,multiply(b,b))
| multiply(c,b) = multiply(a,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,b),multiply(a,multiply(b,b))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_27,plain,
( multiply(c,b) != multiply(a,multiply(b,b))
| multiply(c,b) = multiply(a,identity) ),
inference(resolve,[$cnf( $equal(multiply(b,b),identity) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
multiply(c,b) = multiply(a,identity),
inference(resolve,[$cnf( $equal(multiply(c,b),multiply(a,multiply(b,b))) )],[refute_0_24,refute_0_27]) ).
cnf(refute_0_29,plain,
X_8 = multiply(X_8,multiply(X_8,X_8)),
inference(subst,[],[refute_0_8:[bind(X_3,$fot(X_8)),bind(X_4,$fot(X_8))]]) ).
cnf(refute_0_30,plain,
multiply(X_8,X_8) = identity,
inference(subst,[],[squareness:[bind(X,$fot(X_8))]]) ).
cnf(refute_0_31,plain,
( X_8 != multiply(X_8,multiply(X_8,X_8))
| multiply(X_8,X_8) != identity
| X_8 = multiply(X_8,identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_8,multiply(X_8,multiply(X_8,X_8))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_32,plain,
( X_8 != multiply(X_8,multiply(X_8,X_8))
| X_8 = multiply(X_8,identity) ),
inference(resolve,[$cnf( $equal(multiply(X_8,X_8),identity) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
X_8 = multiply(X_8,identity),
inference(resolve,[$cnf( $equal(X_8,multiply(X_8,multiply(X_8,X_8))) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
( X_8 != multiply(X_8,identity)
| multiply(X_8,identity) = X_8 ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(X_8)),bind(Y0,$fot(multiply(X_8,identity)))]]) ).
cnf(refute_0_35,plain,
multiply(X_8,identity) = X_8,
inference(resolve,[$cnf( $equal(X_8,multiply(X_8,identity)) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
multiply(a,identity) = a,
inference(subst,[],[refute_0_35:[bind(X_8,$fot(a))]]) ).
cnf(refute_0_37,plain,
( multiply(a,identity) != a
| multiply(c,b) != multiply(a,identity)
| multiply(c,b) = a ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,b),multiply(a,identity)) ),[1],$fot(a)]]) ).
cnf(refute_0_38,plain,
( multiply(c,b) != multiply(a,identity)
| multiply(c,b) = a ),
inference(resolve,[$cnf( $equal(multiply(a,identity),a) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
multiply(c,b) = a,
inference(resolve,[$cnf( $equal(multiply(c,b),multiply(a,identity)) )],[refute_0_28,refute_0_38]) ).
cnf(refute_0_40,plain,
( multiply(c,b) != a
| b != multiply(c,multiply(c,b))
| b = multiply(c,a) ),
introduced(tautology,[equality,[$cnf( $equal(b,multiply(c,multiply(c,b))) ),[1,1],$fot(a)]]) ).
cnf(refute_0_41,plain,
( b != multiply(c,multiply(c,b))
| b = multiply(c,a) ),
inference(resolve,[$cnf( $equal(multiply(c,b),a) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
b = multiply(c,a),
inference(resolve,[$cnf( $equal(b,multiply(c,multiply(c,b))) )],[refute_0_23,refute_0_41]) ).
cnf(refute_0_43,plain,
( b != multiply(c,a)
| multiply(c,a) = b ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(b)),bind(Y0,$fot(multiply(c,a)))]]) ).
cnf(refute_0_44,plain,
multiply(c,a) = b,
inference(resolve,[$cnf( $equal(b,multiply(c,a)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
( multiply(b,a) != multiply(a,multiply(c,a))
| multiply(c,a) != b
| multiply(b,a) = multiply(a,b) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(b,a),multiply(a,multiply(c,a))) ),[1,1],$fot(b)]]) ).
cnf(refute_0_46,plain,
( multiply(b,a) != multiply(a,multiply(c,a))
| multiply(b,a) = multiply(a,b) ),
inference(resolve,[$cnf( $equal(multiply(c,a),b) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
multiply(b,a) = multiply(a,b),
inference(resolve,[$cnf( $equal(multiply(b,a),multiply(a,multiply(c,a))) )],[refute_0_22,refute_0_46]) ).
cnf(refute_0_48,plain,
( multiply(a,b) != c
| multiply(b,a) != multiply(a,b)
| multiply(b,a) = c ),
introduced(tautology,[equality,[$cnf( $equal(multiply(b,a),multiply(a,b)) ),[1],$fot(c)]]) ).
cnf(refute_0_49,plain,
( multiply(b,a) != multiply(a,b)
| multiply(b,a) = c ),
inference(resolve,[$cnf( $equal(multiply(a,b),c) )],[a_times_b_is_c,refute_0_48]) ).
cnf(refute_0_50,plain,
multiply(b,a) = c,
inference(resolve,[$cnf( $equal(multiply(b,a),multiply(a,b)) )],[refute_0_47,refute_0_49]) ).
cnf(refute_0_51,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(b,a),c) )],[refute_0_50,prove_b_times_a_is_c]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : GRP001-4 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n029.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue Jun 14 06:20:40 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.37
% 0.14/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.14/0.38
%------------------------------------------------------------------------------