TSTP Solution File: GRP001-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP001-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 10:32:07 EDT 2022
% Result : Unsatisfiable 0.19s 0.35s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 28
% Syntax : Number of clauses : 90 ( 49 unt; 0 nHn; 67 RR)
% Number of literals : 150 ( 149 equ; 61 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X ).
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity ).
cnf(associativity,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ).
cnf(right_identity,axiom,
multiply(X,identity) = 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(a,c),Z) = multiply(a,multiply(c,Z)),
inference(subst,[],[associativity:[bind(X,$fot(a)),bind(Y,$fot(c))]]) ).
cnf(refute_0_1,plain,
multiply(multiply(inverse(X_6),X_6),X_7) = multiply(inverse(X_6),multiply(X_6,X_7)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_6))),bind(Y,$fot(X_6)),bind(Z,$fot(X_7))]]) ).
cnf(refute_0_2,plain,
multiply(inverse(X_6),X_6) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_3,plain,
( multiply(multiply(inverse(X_6),X_6),X_7) != multiply(inverse(X_6),multiply(X_6,X_7))
| multiply(inverse(X_6),X_6) != identity
| multiply(identity,X_7) = multiply(inverse(X_6),multiply(X_6,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_6),X_6),X_7),multiply(inverse(X_6),multiply(X_6,X_7))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_4,plain,
( multiply(multiply(inverse(X_6),X_6),X_7) != multiply(inverse(X_6),multiply(X_6,X_7))
| multiply(identity,X_7) = multiply(inverse(X_6),multiply(X_6,X_7)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_6),X_6),identity) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(identity,X_7) = multiply(inverse(X_6),multiply(X_6,X_7)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_6),X_6),X_7),multiply(inverse(X_6),multiply(X_6,X_7))) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
multiply(identity,X_7) = X_7,
inference(subst,[],[left_identity:[bind(X,$fot(X_7))]]) ).
cnf(refute_0_7,plain,
( multiply(identity,X_7) != X_7
| multiply(identity,X_7) != multiply(inverse(X_6),multiply(X_6,X_7))
| X_7 = multiply(inverse(X_6),multiply(X_6,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_7),multiply(inverse(X_6),multiply(X_6,X_7))) ),[0],$fot(X_7)]]) ).
cnf(refute_0_8,plain,
( multiply(identity,X_7) != multiply(inverse(X_6),multiply(X_6,X_7))
| X_7 = multiply(inverse(X_6),multiply(X_6,X_7)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_7),X_7) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
X_7 = multiply(inverse(X_6),multiply(X_6,X_7)),
inference(resolve,[$cnf( $equal(multiply(identity,X_7),multiply(inverse(X_6),multiply(X_6,X_7))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
b = multiply(inverse(a),multiply(a,b)),
inference(subst,[],[refute_0_9:[bind(X_6,$fot(a)),bind(X_7,$fot(b))]]) ).
cnf(refute_0_11,plain,
( multiply(a,b) != c
| b != multiply(inverse(a),multiply(a,b))
| b = multiply(inverse(a),c) ),
introduced(tautology,[equality,[$cnf( $equal(b,multiply(inverse(a),multiply(a,b))) ),[1,1],$fot(c)]]) ).
cnf(refute_0_12,plain,
( b != multiply(inverse(a),multiply(a,b))
| b = multiply(inverse(a),c) ),
inference(resolve,[$cnf( $equal(multiply(a,b),c) )],[a_times_b_is_c,refute_0_11]) ).
cnf(refute_0_13,plain,
b = multiply(inverse(a),c),
inference(resolve,[$cnf( $equal(b,multiply(inverse(a),multiply(a,b))) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,plain,
X_9 = multiply(inverse(X_9),multiply(X_9,X_9)),
inference(subst,[],[refute_0_9:[bind(X_6,$fot(X_9)),bind(X_7,$fot(X_9))]]) ).
cnf(refute_0_15,plain,
multiply(X_9,X_9) = identity,
inference(subst,[],[squareness:[bind(X,$fot(X_9))]]) ).
cnf(refute_0_16,plain,
( X_9 != multiply(inverse(X_9),multiply(X_9,X_9))
| multiply(X_9,X_9) != identity
| X_9 = multiply(inverse(X_9),identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_9,multiply(inverse(X_9),multiply(X_9,X_9))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_17,plain,
( X_9 != multiply(inverse(X_9),multiply(X_9,X_9))
| X_9 = multiply(inverse(X_9),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_9,X_9),identity) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
X_9 = multiply(inverse(X_9),identity),
inference(resolve,[$cnf( $equal(X_9,multiply(inverse(X_9),multiply(X_9,X_9))) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
multiply(inverse(X_9),identity) = inverse(X_9),
inference(subst,[],[right_identity:[bind(X,$fot(inverse(X_9)))]]) ).
cnf(refute_0_20,plain,
( X_9 != multiply(inverse(X_9),identity)
| multiply(inverse(X_9),identity) != inverse(X_9)
| X_9 = inverse(X_9) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_9,inverse(X_9)) ),[0],$fot(multiply(inverse(X_9),identity))]]) ).
cnf(refute_0_21,plain,
( X_9 != multiply(inverse(X_9),identity)
| X_9 = inverse(X_9) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_9),identity),inverse(X_9)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
X_9 = inverse(X_9),
inference(resolve,[$cnf( $equal(X_9,multiply(inverse(X_9),identity)) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_24,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_25,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( X_9 != inverse(X_9)
| inverse(X_9) = X_9 ),
inference(subst,[],[refute_0_25:[bind(X0,$fot(X_9)),bind(Y0,$fot(inverse(X_9)))]]) ).
cnf(refute_0_27,plain,
inverse(X_9) = X_9,
inference(resolve,[$cnf( $equal(X_9,inverse(X_9)) )],[refute_0_22,refute_0_26]) ).
cnf(refute_0_28,plain,
inverse(a) = a,
inference(subst,[],[refute_0_27:[bind(X_9,$fot(a))]]) ).
cnf(refute_0_29,plain,
multiply(inverse(a),c) = multiply(inverse(a),c),
introduced(tautology,[refl,[$fot(multiply(inverse(a),c))]]) ).
cnf(refute_0_30,plain,
( multiply(inverse(a),c) != multiply(inverse(a),c)
| inverse(a) != a
| multiply(inverse(a),c) = multiply(a,c) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),c),multiply(inverse(a),c)) ),[1,0],$fot(a)]]) ).
cnf(refute_0_31,plain,
( inverse(a) != a
| multiply(inverse(a),c) = multiply(a,c) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),c),multiply(inverse(a),c)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
multiply(inverse(a),c) = multiply(a,c),
inference(resolve,[$cnf( $equal(inverse(a),a) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
( multiply(inverse(a),c) != multiply(a,c)
| b != multiply(inverse(a),c)
| b = multiply(a,c) ),
introduced(tautology,[equality,[$cnf( $equal(b,multiply(inverse(a),c)) ),[1],$fot(multiply(a,c))]]) ).
cnf(refute_0_34,plain,
( b != multiply(inverse(a),c)
| b = multiply(a,c) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),c),multiply(a,c)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
b = multiply(a,c),
inference(resolve,[$cnf( $equal(b,multiply(inverse(a),c)) )],[refute_0_13,refute_0_34]) ).
cnf(refute_0_36,plain,
( b != multiply(a,c)
| multiply(a,c) = b ),
inference(subst,[],[refute_0_25:[bind(X0,$fot(b)),bind(Y0,$fot(multiply(a,c)))]]) ).
cnf(refute_0_37,plain,
multiply(a,c) = b,
inference(resolve,[$cnf( $equal(b,multiply(a,c)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( multiply(multiply(a,c),Z) != multiply(a,multiply(c,Z))
| multiply(a,c) != b
| multiply(b,Z) = multiply(a,multiply(c,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(a,c),Z),multiply(a,multiply(c,Z))) ),[0,0],$fot(b)]]) ).
cnf(refute_0_39,plain,
( multiply(multiply(a,c),Z) != multiply(a,multiply(c,Z))
| multiply(b,Z) = multiply(a,multiply(c,Z)) ),
inference(resolve,[$cnf( $equal(multiply(a,c),b) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
multiply(b,Z) = multiply(a,multiply(c,Z)),
inference(resolve,[$cnf( $equal(multiply(multiply(a,c),Z),multiply(a,multiply(c,Z))) )],[refute_0_0,refute_0_39]) ).
cnf(refute_0_41,plain,
multiply(b,a) = multiply(a,multiply(c,a)),
inference(subst,[],[refute_0_40:[bind(Z,$fot(a))]]) ).
cnf(refute_0_42,plain,
multiply(multiply(c,b),Z) = multiply(c,multiply(b,Z)),
inference(subst,[],[associativity:[bind(X,$fot(c)),bind(Y,$fot(b))]]) ).
cnf(refute_0_43,plain,
multiply(multiply(a,b),X_7) = multiply(a,multiply(b,X_7)),
inference(subst,[],[associativity:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(X_7))]]) ).
cnf(refute_0_44,plain,
( multiply(multiply(a,b),X_7) != multiply(a,multiply(b,X_7))
| multiply(a,b) != c
| multiply(c,X_7) = multiply(a,multiply(b,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(a,b),X_7),multiply(a,multiply(b,X_7))) ),[0,0],$fot(c)]]) ).
cnf(refute_0_45,plain,
( multiply(multiply(a,b),X_7) != multiply(a,multiply(b,X_7))
| multiply(c,X_7) = multiply(a,multiply(b,X_7)) ),
inference(resolve,[$cnf( $equal(multiply(a,b),c) )],[a_times_b_is_c,refute_0_44]) ).
cnf(refute_0_46,plain,
multiply(c,X_7) = multiply(a,multiply(b,X_7)),
inference(resolve,[$cnf( $equal(multiply(multiply(a,b),X_7),multiply(a,multiply(b,X_7))) )],[refute_0_43,refute_0_45]) ).
cnf(refute_0_47,plain,
multiply(c,b) = multiply(a,multiply(b,b)),
inference(subst,[],[refute_0_46:[bind(X_7,$fot(b))]]) ).
cnf(refute_0_48,plain,
multiply(b,b) = identity,
inference(subst,[],[squareness:[bind(X,$fot(b))]]) ).
cnf(refute_0_49,plain,
( multiply(b,b) != identity
| multiply(c,b) != multiply(a,multiply(b,b))
| multiply(c,b) = multiply(a,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,b),multiply(a,multiply(b,b))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_50,plain,
( multiply(c,b) != multiply(a,multiply(b,b))
| multiply(c,b) = multiply(a,identity) ),
inference(resolve,[$cnf( $equal(multiply(b,b),identity) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
multiply(c,b) = multiply(a,identity),
inference(resolve,[$cnf( $equal(multiply(c,b),multiply(a,multiply(b,b))) )],[refute_0_47,refute_0_50]) ).
cnf(refute_0_52,plain,
multiply(a,identity) = a,
inference(subst,[],[right_identity:[bind(X,$fot(a))]]) ).
cnf(refute_0_53,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_54,plain,
( multiply(c,b) != multiply(a,identity)
| multiply(c,b) = a ),
inference(resolve,[$cnf( $equal(multiply(a,identity),a) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
multiply(c,b) = a,
inference(resolve,[$cnf( $equal(multiply(c,b),multiply(a,identity)) )],[refute_0_51,refute_0_54]) ).
cnf(refute_0_56,plain,
( multiply(multiply(c,b),Z) != multiply(c,multiply(b,Z))
| multiply(c,b) != a
| multiply(a,Z) = multiply(c,multiply(b,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(c,b),Z),multiply(c,multiply(b,Z))) ),[0,0],$fot(a)]]) ).
cnf(refute_0_57,plain,
( multiply(multiply(c,b),Z) != multiply(c,multiply(b,Z))
| multiply(a,Z) = multiply(c,multiply(b,Z)) ),
inference(resolve,[$cnf( $equal(multiply(c,b),a) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
multiply(a,Z) = multiply(c,multiply(b,Z)),
inference(resolve,[$cnf( $equal(multiply(multiply(c,b),Z),multiply(c,multiply(b,Z))) )],[refute_0_42,refute_0_57]) ).
cnf(refute_0_59,plain,
multiply(a,c) = multiply(c,multiply(b,c)),
inference(subst,[],[refute_0_58:[bind(Z,$fot(c))]]) ).
cnf(refute_0_60,plain,
multiply(b,c) = multiply(a,multiply(c,c)),
inference(subst,[],[refute_0_40:[bind(Z,$fot(c))]]) ).
cnf(refute_0_61,plain,
multiply(c,c) = identity,
inference(subst,[],[squareness:[bind(X,$fot(c))]]) ).
cnf(refute_0_62,plain,
( multiply(b,c) != multiply(a,multiply(c,c))
| multiply(c,c) != identity
| multiply(b,c) = multiply(a,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(b,c),multiply(a,multiply(c,c))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_63,plain,
( multiply(b,c) != multiply(a,multiply(c,c))
| multiply(b,c) = multiply(a,identity) ),
inference(resolve,[$cnf( $equal(multiply(c,c),identity) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
multiply(b,c) = multiply(a,identity),
inference(resolve,[$cnf( $equal(multiply(b,c),multiply(a,multiply(c,c))) )],[refute_0_60,refute_0_63]) ).
cnf(refute_0_65,plain,
( multiply(a,identity) != a
| multiply(b,c) != multiply(a,identity)
| multiply(b,c) = a ),
introduced(tautology,[equality,[$cnf( $equal(multiply(b,c),multiply(a,identity)) ),[1],$fot(a)]]) ).
cnf(refute_0_66,plain,
( multiply(b,c) != multiply(a,identity)
| multiply(b,c) = a ),
inference(resolve,[$cnf( $equal(multiply(a,identity),a) )],[refute_0_52,refute_0_65]) ).
cnf(refute_0_67,plain,
multiply(b,c) = a,
inference(resolve,[$cnf( $equal(multiply(b,c),multiply(a,identity)) )],[refute_0_64,refute_0_66]) ).
cnf(refute_0_68,plain,
( multiply(a,c) != multiply(c,multiply(b,c))
| multiply(b,c) != a
| multiply(a,c) = multiply(c,a) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(a,c),multiply(c,multiply(b,c))) ),[1,1],$fot(a)]]) ).
cnf(refute_0_69,plain,
( multiply(a,c) != multiply(c,multiply(b,c))
| multiply(a,c) = multiply(c,a) ),
inference(resolve,[$cnf( $equal(multiply(b,c),a) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
multiply(a,c) = multiply(c,a),
inference(resolve,[$cnf( $equal(multiply(a,c),multiply(c,multiply(b,c))) )],[refute_0_59,refute_0_69]) ).
cnf(refute_0_71,plain,
( multiply(a,c) != multiply(c,a)
| multiply(a,c) != b
| b = multiply(c,a) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(a,c),multiply(c,a)) ),[0],$fot(b)]]) ).
cnf(refute_0_72,plain,
( multiply(a,c) != multiply(c,a)
| b = multiply(c,a) ),
inference(resolve,[$cnf( $equal(multiply(a,c),b) )],[refute_0_37,refute_0_71]) ).
cnf(refute_0_73,plain,
b = multiply(c,a),
inference(resolve,[$cnf( $equal(multiply(a,c),multiply(c,a)) )],[refute_0_70,refute_0_72]) ).
cnf(refute_0_74,plain,
( b != multiply(c,a)
| multiply(c,a) = b ),
inference(subst,[],[refute_0_25:[bind(X0,$fot(b)),bind(Y0,$fot(multiply(c,a)))]]) ).
cnf(refute_0_75,plain,
multiply(c,a) = b,
inference(resolve,[$cnf( $equal(b,multiply(c,a)) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
( multiply(b,a) != multiply(a,multiply(c,a))
| multiply(c,a) != b
| multiply(b,a) = multiply(a,b) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(b,a),multiply(a,multiply(c,a))) ),[1,1],$fot(b)]]) ).
cnf(refute_0_77,plain,
( multiply(b,a) != multiply(a,multiply(c,a))
| multiply(b,a) = multiply(a,b) ),
inference(resolve,[$cnf( $equal(multiply(c,a),b) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
multiply(b,a) = multiply(a,b),
inference(resolve,[$cnf( $equal(multiply(b,a),multiply(a,multiply(c,a))) )],[refute_0_41,refute_0_77]) ).
cnf(refute_0_79,plain,
( multiply(a,b) != c
| multiply(b,a) != multiply(a,b)
| multiply(b,a) = c ),
introduced(tautology,[equality,[$cnf( $equal(multiply(b,a),multiply(a,b)) ),[1],$fot(c)]]) ).
cnf(refute_0_80,plain,
( multiply(b,a) != multiply(a,b)
| multiply(b,a) = c ),
inference(resolve,[$cnf( $equal(multiply(a,b),c) )],[a_times_b_is_c,refute_0_79]) ).
cnf(refute_0_81,plain,
multiply(b,a) = c,
inference(resolve,[$cnf( $equal(multiply(b,a),multiply(a,b)) )],[refute_0_78,refute_0_80]) ).
cnf(refute_0_82,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(b,a),c) )],[refute_0_81,prove_b_times_a_is_c]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP001-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 18:55:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.35 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.35
% 0.19/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.36
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