%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP010-4 : TPTP v8.1.0. Released v1.0.0.
% 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 10:32:14 EDT 2022
% Result : Unsatisfiable 0.13s 0.34s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of clauses : 38 ( 22 unt; 0 nHn; 23 RR)
% Number of literals : 61 ( 60 equ; 24 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; 3 con; 0-2 aty)
% Number of variables : 39 ( 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(left_inverse,axiom,
multiply(inverse(X),X) = identity ).
cnf(c_times_b_is_e,hypothesis,
multiply(c,b) = identity ).
cnf(prove_b_times_c_is_e,negated_conjecture,
multiply(b,c) != identity ).
cnf(refute_0_0,plain,
multiply(inverse(c),c) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(c))]]) ).
cnf(refute_0_1,plain,
multiply(multiply(inverse(X_3),X_3),X_4) = multiply(inverse(X_3),multiply(X_3,X_4)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_3))),bind(Y,$fot(X_3)),bind(Z,$fot(X_4))]]) ).
cnf(refute_0_2,plain,
multiply(inverse(X_3),X_3) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_3))]]) ).
cnf(refute_0_3,plain,
( multiply(multiply(inverse(X_3),X_3),X_4) != multiply(inverse(X_3),multiply(X_3,X_4))
| multiply(inverse(X_3),X_3) != identity
| multiply(identity,X_4) = multiply(inverse(X_3),multiply(X_3,X_4)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_3),X_3),X_4),multiply(inverse(X_3),multiply(X_3,X_4))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_4,plain,
( multiply(multiply(inverse(X_3),X_3),X_4) != multiply(inverse(X_3),multiply(X_3,X_4))
| multiply(identity,X_4) = multiply(inverse(X_3),multiply(X_3,X_4)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_3),X_3),identity) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(identity,X_4) = multiply(inverse(X_3),multiply(X_3,X_4)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_3),X_3),X_4),multiply(inverse(X_3),multiply(X_3,X_4))) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
multiply(identity,X_4) = X_4,
inference(subst,[],[left_identity:[bind(X,$fot(X_4))]]) ).
cnf(refute_0_7,plain,
( multiply(identity,X_4) != X_4
| multiply(identity,X_4) != multiply(inverse(X_3),multiply(X_3,X_4))
| X_4 = multiply(inverse(X_3),multiply(X_3,X_4)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_4),multiply(inverse(X_3),multiply(X_3,X_4))) ),[0],$fot(X_4)]]) ).
cnf(refute_0_8,plain,
( multiply(identity,X_4) != multiply(inverse(X_3),multiply(X_3,X_4))
| X_4 = multiply(inverse(X_3),multiply(X_3,X_4)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_4),X_4) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
X_4 = multiply(inverse(X_3),multiply(X_3,X_4)),
inference(resolve,[$cnf( $equal(multiply(identity,X_4),multiply(inverse(X_3),multiply(X_3,X_4))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
multiply(b,X_4) = multiply(inverse(c),multiply(c,multiply(b,X_4))),
inference(subst,[],[refute_0_9:[bind(X_3,$fot(c)),bind(X_4,$fot(multiply(b,X_4)))]]) ).
cnf(refute_0_11,plain,
multiply(multiply(c,b),X_4) = multiply(c,multiply(b,X_4)),
inference(subst,[],[associativity:[bind(X,$fot(c)),bind(Y,$fot(b)),bind(Z,$fot(X_4))]]) ).
cnf(refute_0_12,plain,
( multiply(multiply(c,b),X_4) != multiply(c,multiply(b,X_4))
| multiply(c,b) != identity
| multiply(identity,X_4) = multiply(c,multiply(b,X_4)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(c,b),X_4),multiply(c,multiply(b,X_4))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_13,plain,
( multiply(multiply(c,b),X_4) != multiply(c,multiply(b,X_4))
| multiply(identity,X_4) = multiply(c,multiply(b,X_4)) ),
inference(resolve,[$cnf( $equal(multiply(c,b),identity) )],[c_times_b_is_e,refute_0_12]) ).
cnf(refute_0_14,plain,
multiply(identity,X_4) = multiply(c,multiply(b,X_4)),
inference(resolve,[$cnf( $equal(multiply(multiply(c,b),X_4),multiply(c,multiply(b,X_4))) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
( multiply(identity,X_4) != X_4
| multiply(identity,X_4) != multiply(c,multiply(b,X_4))
| X_4 = multiply(c,multiply(b,X_4)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_4),multiply(c,multiply(b,X_4))) ),[0],$fot(X_4)]]) ).
cnf(refute_0_16,plain,
( multiply(identity,X_4) != multiply(c,multiply(b,X_4))
| X_4 = multiply(c,multiply(b,X_4)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_4),X_4) )],[refute_0_6,refute_0_15]) ).
cnf(refute_0_17,plain,
X_4 = multiply(c,multiply(b,X_4)),
inference(resolve,[$cnf( $equal(multiply(identity,X_4),multiply(c,multiply(b,X_4))) )],[refute_0_14,refute_0_16]) ).
cnf(refute_0_18,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_19,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_20,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( X_4 != multiply(c,multiply(b,X_4))
| multiply(c,multiply(b,X_4)) = X_4 ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(X_4)),bind(Y0,$fot(multiply(c,multiply(b,X_4))))]]) ).
cnf(refute_0_22,plain,
multiply(c,multiply(b,X_4)) = X_4,
inference(resolve,[$cnf( $equal(X_4,multiply(c,multiply(b,X_4))) )],[refute_0_17,refute_0_21]) ).
cnf(refute_0_23,plain,
( multiply(b,X_4) != multiply(inverse(c),multiply(c,multiply(b,X_4)))
| multiply(c,multiply(b,X_4)) != X_4
| multiply(b,X_4) = multiply(inverse(c),X_4) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(b,X_4),multiply(inverse(c),multiply(c,multiply(b,X_4)))) ),[1,1],$fot(X_4)]]) ).
cnf(refute_0_24,plain,
( multiply(b,X_4) != multiply(inverse(c),multiply(c,multiply(b,X_4)))
| multiply(b,X_4) = multiply(inverse(c),X_4) ),
inference(resolve,[$cnf( $equal(multiply(c,multiply(b,X_4)),X_4) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
multiply(b,X_4) = multiply(inverse(c),X_4),
inference(resolve,[$cnf( $equal(multiply(b,X_4),multiply(inverse(c),multiply(c,multiply(b,X_4)))) )],[refute_0_10,refute_0_24]) ).
cnf(refute_0_26,plain,
multiply(b,c) = multiply(inverse(c),c),
inference(subst,[],[refute_0_25:[bind(X_4,$fot(c))]]) ).
cnf(refute_0_27,plain,
( multiply(b,c) != multiply(inverse(c),c)
| multiply(inverse(c),c) = multiply(b,c) ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(multiply(b,c))),bind(Y0,$fot(multiply(inverse(c),c)))]]) ).
cnf(refute_0_28,plain,
multiply(inverse(c),c) = multiply(b,c),
inference(resolve,[$cnf( $equal(multiply(b,c),multiply(inverse(c),c)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( multiply(inverse(c),c) != multiply(b,c)
| multiply(inverse(c),c) != identity
| multiply(b,c) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(c),c),identity) ),[0],$fot(multiply(b,c))]]) ).
cnf(refute_0_30,plain,
( multiply(inverse(c),c) != identity
| multiply(b,c) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(c),c),multiply(b,c)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
multiply(b,c) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(c),c),identity) )],[refute_0_0,refute_0_30]) ).
cnf(refute_0_32,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(b,c),identity) )],[refute_0_31,prove_b_times_c_is_e]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP010-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 06:33:40 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.34 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34
% 0.13/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.35
%------------------------------------------------------------------------------