TSTP Solution File: GRP206-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP206-1 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.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 10:38:02 EDT 2022
% Result : Unsatisfiable 0.14s 0.36s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of clauses : 38 ( 22 unt; 0 nHn; 22 RR)
% Number of literals : 61 ( 60 equ; 26 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 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 : 52 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X ).
cnf(right_identity,axiom,
multiply(X,identity) = X ).
cnf(moufang4,axiom,
multiply(X,multiply(multiply(Y,Z),X)) = multiply(multiply(X,Y),multiply(Z,X)) ).
cnf(prove_moufang1,negated_conjecture,
multiply(multiply(a,multiply(b,c)),a) != multiply(multiply(a,b),multiply(c,a)) ).
cnf(refute_0_0,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_1,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_2,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( multiply(X,multiply(multiply(Y,Z),X)) != multiply(multiply(X,Y),multiply(Z,X))
| multiply(multiply(X,Y),multiply(Z,X)) = multiply(X,multiply(multiply(Y,Z),X)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X,multiply(multiply(Y,Z),X)))),bind(Y0,$fot(multiply(multiply(X,Y),multiply(Z,X))))]]) ).
cnf(refute_0_4,plain,
multiply(multiply(X,Y),multiply(Z,X)) = multiply(X,multiply(multiply(Y,Z),X)),
inference(resolve,[$cnf( $equal(multiply(X,multiply(multiply(Y,Z),X)),multiply(multiply(X,Y),multiply(Z,X))) )],[moufang4,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(multiply(a,b),multiply(c,a)) = multiply(a,multiply(multiply(b,c),a)),
inference(subst,[],[refute_0_4:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(c))]]) ).
cnf(refute_0_6,plain,
( multiply(multiply(a,multiply(b,c)),a) != multiply(a,multiply(multiply(b,c),a))
| multiply(multiply(a,b),multiply(c,a)) != multiply(a,multiply(multiply(b,c),a))
| multiply(multiply(a,multiply(b,c)),a) = multiply(multiply(a,b),multiply(c,a)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(a,b),multiply(c,a))) ),[1],$fot(multiply(a,multiply(multiply(b,c),a)))]]) ).
cnf(refute_0_7,plain,
( multiply(multiply(a,multiply(b,c)),a) != multiply(a,multiply(multiply(b,c),a))
| multiply(multiply(a,multiply(b,c)),a) = multiply(multiply(a,b),multiply(c,a)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(a,b),multiply(c,a)),multiply(a,multiply(multiply(b,c),a))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
multiply(multiply(a,multiply(b,c)),a) != multiply(a,multiply(multiply(b,c),a)),
inference(resolve,[$cnf( $equal(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(a,b),multiply(c,a))) )],[refute_0_7,prove_moufang1]) ).
cnf(refute_0_9,plain,
multiply(X_25,multiply(multiply(X_26,identity),X_25)) = multiply(multiply(X_25,X_26),multiply(identity,X_25)),
inference(subst,[],[moufang4:[bind(X,$fot(X_25)),bind(Y,$fot(X_26)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_10,plain,
multiply(identity,X_25) = X_25,
inference(subst,[],[left_identity:[bind(X,$fot(X_25))]]) ).
cnf(refute_0_11,plain,
( multiply(X_25,multiply(multiply(X_26,identity),X_25)) != multiply(multiply(X_25,X_26),multiply(identity,X_25))
| multiply(identity,X_25) != X_25
| multiply(X_25,multiply(multiply(X_26,identity),X_25)) = multiply(multiply(X_25,X_26),X_25) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_25,multiply(multiply(X_26,identity),X_25)),multiply(multiply(X_25,X_26),multiply(identity,X_25))) ),[1,1],$fot(X_25)]]) ).
cnf(refute_0_12,plain,
( multiply(X_25,multiply(multiply(X_26,identity),X_25)) != multiply(multiply(X_25,X_26),multiply(identity,X_25))
| multiply(X_25,multiply(multiply(X_26,identity),X_25)) = multiply(multiply(X_25,X_26),X_25) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_25),X_25) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
multiply(X_25,multiply(multiply(X_26,identity),X_25)) = multiply(multiply(X_25,X_26),X_25),
inference(resolve,[$cnf( $equal(multiply(X_25,multiply(multiply(X_26,identity),X_25)),multiply(multiply(X_25,X_26),multiply(identity,X_25))) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
multiply(X_26,identity) = X_26,
inference(subst,[],[right_identity:[bind(X,$fot(X_26))]]) ).
cnf(refute_0_15,plain,
multiply(multiply(X_26,identity),X_25) = multiply(multiply(X_26,identity),X_25),
introduced(tautology,[refl,[$fot(multiply(multiply(X_26,identity),X_25))]]) ).
cnf(refute_0_16,plain,
( multiply(X_26,identity) != X_26
| multiply(multiply(X_26,identity),X_25) != multiply(multiply(X_26,identity),X_25)
| multiply(multiply(X_26,identity),X_25) = multiply(X_26,X_25) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_26,identity),X_25),multiply(multiply(X_26,identity),X_25)) ),[1,0],$fot(X_26)]]) ).
cnf(refute_0_17,plain,
( multiply(X_26,identity) != X_26
| multiply(multiply(X_26,identity),X_25) = multiply(X_26,X_25) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_26,identity),X_25),multiply(multiply(X_26,identity),X_25)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
multiply(multiply(X_26,identity),X_25) = multiply(X_26,X_25),
inference(resolve,[$cnf( $equal(multiply(X_26,identity),X_26) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
multiply(X_25,multiply(multiply(X_26,identity),X_25)) = multiply(X_25,multiply(multiply(X_26,identity),X_25)),
introduced(tautology,[refl,[$fot(multiply(X_25,multiply(multiply(X_26,identity),X_25)))]]) ).
cnf(refute_0_20,plain,
( multiply(X_25,multiply(multiply(X_26,identity),X_25)) != multiply(X_25,multiply(multiply(X_26,identity),X_25))
| multiply(multiply(X_26,identity),X_25) != multiply(X_26,X_25)
| multiply(X_25,multiply(multiply(X_26,identity),X_25)) = multiply(X_25,multiply(X_26,X_25)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_25,multiply(multiply(X_26,identity),X_25)),multiply(X_25,multiply(multiply(X_26,identity),X_25))) ),[1,1],$fot(multiply(X_26,X_25))]]) ).
cnf(refute_0_21,plain,
( multiply(multiply(X_26,identity),X_25) != multiply(X_26,X_25)
| multiply(X_25,multiply(multiply(X_26,identity),X_25)) = multiply(X_25,multiply(X_26,X_25)) ),
inference(resolve,[$cnf( $equal(multiply(X_25,multiply(multiply(X_26,identity),X_25)),multiply(X_25,multiply(multiply(X_26,identity),X_25))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
multiply(X_25,multiply(multiply(X_26,identity),X_25)) = multiply(X_25,multiply(X_26,X_25)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_26,identity),X_25),multiply(X_26,X_25)) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
( multiply(X_25,multiply(multiply(X_26,identity),X_25)) != multiply(X_25,multiply(X_26,X_25))
| multiply(X_25,multiply(multiply(X_26,identity),X_25)) != multiply(multiply(X_25,X_26),X_25)
| multiply(X_25,multiply(X_26,X_25)) = multiply(multiply(X_25,X_26),X_25) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_25,multiply(multiply(X_26,identity),X_25)),multiply(multiply(X_25,X_26),X_25)) ),[0],$fot(multiply(X_25,multiply(X_26,X_25)))]]) ).
cnf(refute_0_24,plain,
( multiply(X_25,multiply(multiply(X_26,identity),X_25)) != multiply(multiply(X_25,X_26),X_25)
| multiply(X_25,multiply(X_26,X_25)) = multiply(multiply(X_25,X_26),X_25) ),
inference(resolve,[$cnf( $equal(multiply(X_25,multiply(multiply(X_26,identity),X_25)),multiply(X_25,multiply(X_26,X_25))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
multiply(X_25,multiply(X_26,X_25)) = multiply(multiply(X_25,X_26),X_25),
inference(resolve,[$cnf( $equal(multiply(X_25,multiply(multiply(X_26,identity),X_25)),multiply(multiply(X_25,X_26),X_25)) )],[refute_0_13,refute_0_24]) ).
cnf(refute_0_26,plain,
( multiply(X_25,multiply(X_26,X_25)) != multiply(multiply(X_25,X_26),X_25)
| multiply(multiply(X_25,X_26),X_25) = multiply(X_25,multiply(X_26,X_25)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_25,multiply(X_26,X_25)))),bind(Y0,$fot(multiply(multiply(X_25,X_26),X_25)))]]) ).
cnf(refute_0_27,plain,
multiply(multiply(X_25,X_26),X_25) = multiply(X_25,multiply(X_26,X_25)),
inference(resolve,[$cnf( $equal(multiply(X_25,multiply(X_26,X_25)),multiply(multiply(X_25,X_26),X_25)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
multiply(multiply(a,multiply(b,c)),a) = multiply(a,multiply(multiply(b,c),a)),
inference(subst,[],[refute_0_27:[bind(X_25,$fot(a)),bind(X_26,$fot(multiply(b,c)))]]) ).
cnf(refute_0_29,plain,
( multiply(multiply(a,multiply(b,c)),a) != multiply(a,multiply(multiply(b,c),a))
| multiply(a,multiply(multiply(b,c),a)) != multiply(a,multiply(multiply(b,c),a))
| multiply(multiply(a,multiply(b,c)),a) = multiply(a,multiply(multiply(b,c),a)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(a,multiply(b,c)),a),multiply(a,multiply(multiply(b,c),a))) ),[0],$fot(multiply(a,multiply(multiply(b,c),a)))]]) ).
cnf(refute_0_30,plain,
( multiply(a,multiply(multiply(b,c),a)) != multiply(a,multiply(multiply(b,c),a))
| multiply(multiply(a,multiply(b,c)),a) = multiply(a,multiply(multiply(b,c),a)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(a,multiply(b,c)),a),multiply(a,multiply(multiply(b,c),a))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
multiply(a,multiply(multiply(b,c),a)) != multiply(a,multiply(multiply(b,c),a)),
inference(resolve,[$cnf( $equal(multiply(multiply(a,multiply(b,c)),a),multiply(a,multiply(multiply(b,c),a))) )],[refute_0_30,refute_0_8]) ).
cnf(refute_0_32,plain,
multiply(a,multiply(multiply(b,c),a)) = multiply(a,multiply(multiply(b,c),a)),
introduced(tautology,[refl,[$fot(multiply(a,multiply(multiply(b,c),a)))]]) ).
cnf(refute_0_33,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(a,multiply(multiply(b,c),a)),multiply(a,multiply(multiply(b,c),a))) )],[refute_0_32,refute_0_31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP206-1 : TPTP v8.1.0. Released v2.3.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.14/0.33 % Computer : n006.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Mon Jun 13 15:08:11 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.14/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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
% 0.14/0.36
%------------------------------------------------------------------------------