TSTP Solution File: BOO001-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : BOO001-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 23:44:22 EDT 2022
% Result : Unsatisfiable 0.20s 0.52s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 28
% Syntax : Number of clauses : 100 ( 57 unt; 0 nHn; 47 RR)
% Number of literals : 163 ( 162 equ; 65 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-3 aty)
% Number of variables : 293 ( 40 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(V,W,X),Y,multiply(V,W,Z)) = multiply(V,W,multiply(X,Y,Z)) ).
cnf(ternary_multiply_1,axiom,
multiply(Y,X,X) = X ).
cnf(ternary_multiply_2,axiom,
multiply(X,X,Y) = X ).
cnf(right_inverse,axiom,
multiply(X,Y,inverse(Y)) = X ).
cnf(prove_inverse_is_self_cancelling,negated_conjecture,
inverse(inverse(a)) != a ).
cnf(refute_0_0,plain,
multiply(multiply(Z,W,X),Y,multiply(Z,W,Z)) = multiply(Z,W,multiply(X,Y,Z)),
inference(subst,[],[associativity:[bind(V,$fot(Z))]]) ).
cnf(refute_0_1,plain,
multiply(multiply(X_9,X_9,X_10),X_11,multiply(X_9,X_9,X_12)) = multiply(X_9,X_9,multiply(X_10,X_11,X_12)),
inference(subst,[],[associativity:[bind(V,$fot(X_9)),bind(W,$fot(X_9)),bind(X,$fot(X_10)),bind(Y,$fot(X_11)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_2,plain,
multiply(X_9,X_9,X_12) = X_9,
inference(subst,[],[ternary_multiply_2:[bind(X,$fot(X_9)),bind(Y,$fot(X_12))]]) ).
cnf(refute_0_3,plain,
( multiply(X_9,X_9,X_12) != X_9
| multiply(multiply(X_9,X_9,X_10),X_11,multiply(X_9,X_9,X_12)) != multiply(X_9,X_9,multiply(X_10,X_11,X_12))
| multiply(multiply(X_9,X_9,X_10),X_11,X_9) = multiply(X_9,X_9,multiply(X_10,X_11,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_9,X_9,X_10),X_11,multiply(X_9,X_9,X_12)),multiply(X_9,X_9,multiply(X_10,X_11,X_12))) ),[0,2],$fot(X_9)]]) ).
cnf(refute_0_4,plain,
( multiply(multiply(X_9,X_9,X_10),X_11,multiply(X_9,X_9,X_12)) != multiply(X_9,X_9,multiply(X_10,X_11,X_12))
| multiply(multiply(X_9,X_9,X_10),X_11,X_9) = multiply(X_9,X_9,multiply(X_10,X_11,X_12)) ),
inference(resolve,[$cnf( $equal(multiply(X_9,X_9,X_12),X_9) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(multiply(X_9,X_9,X_10),X_11,X_9) = multiply(X_9,X_9,multiply(X_10,X_11,X_12)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_9,X_9,X_10),X_11,multiply(X_9,X_9,X_12)),multiply(X_9,X_9,multiply(X_10,X_11,X_12))) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
multiply(X_9,X_9,X_10) = X_9,
inference(subst,[],[ternary_multiply_2:[bind(X,$fot(X_9)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_7,plain,
multiply(multiply(X_9,X_9,X_10),X_11,X_9) = multiply(multiply(X_9,X_9,X_10),X_11,X_9),
introduced(tautology,[refl,[$fot(multiply(multiply(X_9,X_9,X_10),X_11,X_9))]]) ).
cnf(refute_0_8,plain,
( multiply(X_9,X_9,X_10) != X_9
| multiply(multiply(X_9,X_9,X_10),X_11,X_9) != multiply(multiply(X_9,X_9,X_10),X_11,X_9)
| multiply(multiply(X_9,X_9,X_10),X_11,X_9) = multiply(X_9,X_11,X_9) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_9,X_9,X_10),X_11,X_9),multiply(multiply(X_9,X_9,X_10),X_11,X_9)) ),[1,0],$fot(X_9)]]) ).
cnf(refute_0_9,plain,
( multiply(X_9,X_9,X_10) != X_9
| multiply(multiply(X_9,X_9,X_10),X_11,X_9) = multiply(X_9,X_11,X_9) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_9,X_9,X_10),X_11,X_9),multiply(multiply(X_9,X_9,X_10),X_11,X_9)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
multiply(multiply(X_9,X_9,X_10),X_11,X_9) = multiply(X_9,X_11,X_9),
inference(resolve,[$cnf( $equal(multiply(X_9,X_9,X_10),X_9) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
( multiply(multiply(X_9,X_9,X_10),X_11,X_9) != multiply(X_9,X_11,X_9)
| multiply(multiply(X_9,X_9,X_10),X_11,X_9) != multiply(X_9,X_9,multiply(X_10,X_11,X_12))
| multiply(X_9,X_11,X_9) = multiply(X_9,X_9,multiply(X_10,X_11,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_9,X_9,X_10),X_11,X_9),multiply(X_9,X_9,multiply(X_10,X_11,X_12))) ),[0],$fot(multiply(X_9,X_11,X_9))]]) ).
cnf(refute_0_12,plain,
( multiply(multiply(X_9,X_9,X_10),X_11,X_9) != multiply(X_9,X_9,multiply(X_10,X_11,X_12))
| multiply(X_9,X_11,X_9) = multiply(X_9,X_9,multiply(X_10,X_11,X_12)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_9,X_9,X_10),X_11,X_9),multiply(X_9,X_11,X_9)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
multiply(X_9,X_9,multiply(X_10,X_11,X_12)) = X_9,
inference(subst,[],[ternary_multiply_2:[bind(X,$fot(X_9)),bind(Y,$fot(multiply(X_10,X_11,X_12)))]]) ).
cnf(refute_0_14,plain,
( multiply(X_9,X_11,X_9) != multiply(X_9,X_9,multiply(X_10,X_11,X_12))
| multiply(X_9,X_9,multiply(X_10,X_11,X_12)) != X_9
| multiply(X_9,X_11,X_9) = X_9 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_9,X_11,X_9),X_9) ),[0],$fot(multiply(X_9,X_9,multiply(X_10,X_11,X_12)))]]) ).
cnf(refute_0_15,plain,
( multiply(X_9,X_11,X_9) != multiply(X_9,X_9,multiply(X_10,X_11,X_12))
| multiply(X_9,X_11,X_9) = X_9 ),
inference(resolve,[$cnf( $equal(multiply(X_9,X_9,multiply(X_10,X_11,X_12)),X_9) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( multiply(multiply(X_9,X_9,X_10),X_11,X_9) != multiply(X_9,X_9,multiply(X_10,X_11,X_12))
| multiply(X_9,X_11,X_9) = X_9 ),
inference(resolve,[$cnf( $equal(multiply(X_9,X_11,X_9),multiply(X_9,X_9,multiply(X_10,X_11,X_12))) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
multiply(X_9,X_11,X_9) = X_9,
inference(resolve,[$cnf( $equal(multiply(multiply(X_9,X_9,X_10),X_11,X_9),multiply(X_9,X_9,multiply(X_10,X_11,X_12))) )],[refute_0_5,refute_0_16]) ).
cnf(refute_0_18,plain,
multiply(Z,W,Z) = Z,
inference(subst,[],[refute_0_17:[bind(X_11,$fot(W)),bind(X_9,$fot(Z))]]) ).
cnf(refute_0_19,plain,
( multiply(Z,W,Z) != Z
| multiply(multiply(Z,W,X),Y,multiply(Z,W,Z)) != multiply(Z,W,multiply(X,Y,Z))
| multiply(multiply(Z,W,X),Y,Z) = multiply(Z,W,multiply(X,Y,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(Z,W,X),Y,multiply(Z,W,Z)),multiply(Z,W,multiply(X,Y,Z))) ),[0,2],$fot(Z)]]) ).
cnf(refute_0_20,plain,
( multiply(multiply(Z,W,X),Y,multiply(Z,W,Z)) != multiply(Z,W,multiply(X,Y,Z))
| multiply(multiply(Z,W,X),Y,Z) = multiply(Z,W,multiply(X,Y,Z)) ),
inference(resolve,[$cnf( $equal(multiply(Z,W,Z),Z) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
multiply(multiply(Z,W,X),Y,Z) = multiply(Z,W,multiply(X,Y,Z)),
inference(resolve,[$cnf( $equal(multiply(multiply(Z,W,X),Y,multiply(Z,W,Z)),multiply(Z,W,multiply(X,Y,Z))) )],[refute_0_0,refute_0_20]) ).
cnf(refute_0_22,plain,
multiply(multiply(X_49,X_47,X_47),X_48,X_49) = multiply(X_49,X_47,multiply(X_47,X_48,X_49)),
inference(subst,[],[refute_0_21:[bind(W,$fot(X_47)),bind(X,$fot(X_47)),bind(Y,$fot(X_48)),bind(Z,$fot(X_49))]]) ).
cnf(refute_0_23,plain,
multiply(X_49,X_47,X_47) = X_47,
inference(subst,[],[ternary_multiply_1:[bind(X,$fot(X_47)),bind(Y,$fot(X_49))]]) ).
cnf(refute_0_24,plain,
( multiply(X_49,X_47,X_47) != X_47
| multiply(multiply(X_49,X_47,X_47),X_48,X_49) != multiply(X_49,X_47,multiply(X_47,X_48,X_49))
| multiply(X_47,X_48,X_49) = multiply(X_49,X_47,multiply(X_47,X_48,X_49)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_49,X_47,X_47),X_48,X_49),multiply(X_49,X_47,multiply(X_47,X_48,X_49))) ),[0,0],$fot(X_47)]]) ).
cnf(refute_0_25,plain,
( multiply(multiply(X_49,X_47,X_47),X_48,X_49) != multiply(X_49,X_47,multiply(X_47,X_48,X_49))
| multiply(X_47,X_48,X_49) = multiply(X_49,X_47,multiply(X_47,X_48,X_49)) ),
inference(resolve,[$cnf( $equal(multiply(X_49,X_47,X_47),X_47) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
multiply(X_47,X_48,X_49) = multiply(X_49,X_47,multiply(X_47,X_48,X_49)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_49,X_47,X_47),X_48,X_49),multiply(X_49,X_47,multiply(X_47,X_48,X_49))) )],[refute_0_22,refute_0_25]) ).
cnf(refute_0_27,plain,
multiply(X_47,X_48,inverse(inverse(X_47))) = multiply(inverse(inverse(X_47)),X_47,multiply(X_47,X_48,inverse(inverse(X_47)))),
inference(subst,[],[refute_0_26:[bind(X_49,$fot(inverse(inverse(X_47))))]]) ).
cnf(refute_0_28,plain,
multiply(multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_12),multiply(X_8,X_9,X_12)) = multiply(X_8,X_9,X_12),
inference(subst,[],[ternary_multiply_1:[bind(X,$fot(multiply(X_8,X_9,X_12))),bind(Y,$fot(multiply(X_8,X_9,X_10)))]]) ).
cnf(refute_0_29,plain,
multiply(multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_12),multiply(X_8,X_9,X_12)) = multiply(X_8,X_9,multiply(X_10,multiply(X_8,X_9,X_12),X_12)),
inference(subst,[],[associativity:[bind(V,$fot(X_8)),bind(W,$fot(X_9)),bind(X,$fot(X_10)),bind(Y,$fot(multiply(X_8,X_9,X_12))),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_30,plain,
( multiply(multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_12),multiply(X_8,X_9,X_12)) != multiply(X_8,X_9,X_12)
| multiply(multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_12),multiply(X_8,X_9,X_12)) != multiply(X_8,X_9,multiply(X_10,multiply(X_8,X_9,X_12),X_12))
| multiply(X_8,X_9,multiply(X_10,multiply(X_8,X_9,X_12),X_12)) = multiply(X_8,X_9,X_12) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_12),multiply(X_8,X_9,X_12)),multiply(X_8,X_9,X_12)) ),[0],$fot(multiply(X_8,X_9,multiply(X_10,multiply(X_8,X_9,X_12),X_12)))]]) ).
cnf(refute_0_31,plain,
( multiply(multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_12),multiply(X_8,X_9,X_12)) != multiply(X_8,X_9,X_12)
| multiply(X_8,X_9,multiply(X_10,multiply(X_8,X_9,X_12),X_12)) = multiply(X_8,X_9,X_12) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_12),multiply(X_8,X_9,X_12)),multiply(X_8,X_9,multiply(X_10,multiply(X_8,X_9,X_12),X_12))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
multiply(X_8,X_9,multiply(X_10,multiply(X_8,X_9,X_12),X_12)) = multiply(X_8,X_9,X_12),
inference(resolve,[$cnf( $equal(multiply(multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_12),multiply(X_8,X_9,X_12)),multiply(X_8,X_9,X_12)) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
multiply(X_27,X_28,multiply(X_25,multiply(X_27,X_28,inverse(X_28)),inverse(X_28))) = multiply(X_27,X_28,inverse(X_28)),
inference(subst,[],[refute_0_32:[bind(X_10,$fot(X_25)),bind(X_12,$fot(inverse(X_28))),bind(X_8,$fot(X_27)),bind(X_9,$fot(X_28))]]) ).
cnf(refute_0_34,plain,
multiply(X_27,X_28,inverse(X_28)) = X_27,
inference(subst,[],[right_inverse:[bind(X,$fot(X_27)),bind(Y,$fot(X_28))]]) ).
cnf(refute_0_35,plain,
( multiply(X_27,X_28,inverse(X_28)) != X_27
| multiply(X_27,X_28,multiply(X_25,multiply(X_27,X_28,inverse(X_28)),inverse(X_28))) != multiply(X_27,X_28,inverse(X_28))
| multiply(X_27,X_28,multiply(X_25,X_27,inverse(X_28))) = multiply(X_27,X_28,inverse(X_28)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_27,X_28,multiply(X_25,multiply(X_27,X_28,inverse(X_28)),inverse(X_28))),multiply(X_27,X_28,inverse(X_28))) ),[0,2,1],$fot(X_27)]]) ).
cnf(refute_0_36,plain,
( multiply(X_27,X_28,multiply(X_25,multiply(X_27,X_28,inverse(X_28)),inverse(X_28))) != multiply(X_27,X_28,inverse(X_28))
| multiply(X_27,X_28,multiply(X_25,X_27,inverse(X_28))) = multiply(X_27,X_28,inverse(X_28)) ),
inference(resolve,[$cnf( $equal(multiply(X_27,X_28,inverse(X_28)),X_27) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
multiply(X_27,X_28,multiply(X_25,X_27,inverse(X_28))) = multiply(X_27,X_28,inverse(X_28)),
inference(resolve,[$cnf( $equal(multiply(X_27,X_28,multiply(X_25,multiply(X_27,X_28,inverse(X_28)),inverse(X_28))),multiply(X_27,X_28,inverse(X_28))) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
( multiply(X_27,X_28,inverse(X_28)) != X_27
| multiply(X_27,X_28,multiply(X_25,X_27,inverse(X_28))) != multiply(X_27,X_28,inverse(X_28))
| multiply(X_27,X_28,multiply(X_25,X_27,inverse(X_28))) = X_27 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_27,X_28,multiply(X_25,X_27,inverse(X_28))),multiply(X_27,X_28,inverse(X_28))) ),[1],$fot(X_27)]]) ).
cnf(refute_0_39,plain,
( multiply(X_27,X_28,multiply(X_25,X_27,inverse(X_28))) != multiply(X_27,X_28,inverse(X_28))
| multiply(X_27,X_28,multiply(X_25,X_27,inverse(X_28))) = X_27 ),
inference(resolve,[$cnf( $equal(multiply(X_27,X_28,inverse(X_28)),X_27) )],[refute_0_34,refute_0_38]) ).
cnf(refute_0_40,plain,
multiply(X_27,X_28,multiply(X_25,X_27,inverse(X_28))) = X_27,
inference(resolve,[$cnf( $equal(multiply(X_27,X_28,multiply(X_25,X_27,inverse(X_28))),multiply(X_27,X_28,inverse(X_28))) )],[refute_0_37,refute_0_39]) ).
cnf(refute_0_41,plain,
multiply(X_27,X_28,multiply(multiply(X_35,inverse(X_28),X_32),X_27,inverse(X_28))) = X_27,
inference(subst,[],[refute_0_40:[bind(X_25,$fot(multiply(X_35,inverse(X_28),X_32)))]]) ).
cnf(refute_0_42,plain,
multiply(multiply(X_8,X_12,X_10),X_11,multiply(X_8,X_12,X_12)) = multiply(X_8,X_12,multiply(X_10,X_11,X_12)),
inference(subst,[],[associativity:[bind(V,$fot(X_8)),bind(W,$fot(X_12)),bind(X,$fot(X_10)),bind(Y,$fot(X_11)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_43,plain,
multiply(X_8,X_12,X_12) = X_12,
inference(subst,[],[ternary_multiply_1:[bind(X,$fot(X_12)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_44,plain,
( multiply(X_8,X_12,X_12) != X_12
| multiply(multiply(X_8,X_12,X_10),X_11,multiply(X_8,X_12,X_12)) != multiply(X_8,X_12,multiply(X_10,X_11,X_12))
| multiply(multiply(X_8,X_12,X_10),X_11,X_12) = multiply(X_8,X_12,multiply(X_10,X_11,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_8,X_12,X_10),X_11,multiply(X_8,X_12,X_12)),multiply(X_8,X_12,multiply(X_10,X_11,X_12))) ),[0,2],$fot(X_12)]]) ).
cnf(refute_0_45,plain,
( multiply(multiply(X_8,X_12,X_10),X_11,multiply(X_8,X_12,X_12)) != multiply(X_8,X_12,multiply(X_10,X_11,X_12))
| multiply(multiply(X_8,X_12,X_10),X_11,X_12) = multiply(X_8,X_12,multiply(X_10,X_11,X_12)) ),
inference(resolve,[$cnf( $equal(multiply(X_8,X_12,X_12),X_12) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
multiply(multiply(X_8,X_12,X_10),X_11,X_12) = multiply(X_8,X_12,multiply(X_10,X_11,X_12)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_8,X_12,X_10),X_11,multiply(X_8,X_12,X_12)),multiply(X_8,X_12,multiply(X_10,X_11,X_12))) )],[refute_0_42,refute_0_45]) ).
cnf(refute_0_47,plain,
multiply(multiply(X_35,inverse(X_28),X_32),X_27,inverse(X_28)) = multiply(X_35,inverse(X_28),multiply(X_32,X_27,inverse(X_28))),
inference(subst,[],[refute_0_46:[bind(X_10,$fot(X_32)),bind(X_11,$fot(X_27)),bind(X_12,$fot(inverse(X_28))),bind(X_8,$fot(X_35))]]) ).
cnf(refute_0_48,plain,
( multiply(X_27,X_28,multiply(multiply(X_35,inverse(X_28),X_32),X_27,inverse(X_28))) != X_27
| multiply(multiply(X_35,inverse(X_28),X_32),X_27,inverse(X_28)) != multiply(X_35,inverse(X_28),multiply(X_32,X_27,inverse(X_28)))
| multiply(X_27,X_28,multiply(X_35,inverse(X_28),multiply(X_32,X_27,inverse(X_28)))) = X_27 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_27,X_28,multiply(multiply(X_35,inverse(X_28),X_32),X_27,inverse(X_28))),X_27) ),[0,2],$fot(multiply(X_35,inverse(X_28),multiply(X_32,X_27,inverse(X_28))))]]) ).
cnf(refute_0_49,plain,
( multiply(X_27,X_28,multiply(multiply(X_35,inverse(X_28),X_32),X_27,inverse(X_28))) != X_27
| multiply(X_27,X_28,multiply(X_35,inverse(X_28),multiply(X_32,X_27,inverse(X_28)))) = X_27 ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_35,inverse(X_28),X_32),X_27,inverse(X_28)),multiply(X_35,inverse(X_28),multiply(X_32,X_27,inverse(X_28)))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
multiply(X_27,X_28,multiply(X_35,inverse(X_28),multiply(X_32,X_27,inverse(X_28)))) = X_27,
inference(resolve,[$cnf( $equal(multiply(X_27,X_28,multiply(multiply(X_35,inverse(X_28),X_32),X_27,inverse(X_28))),X_27) )],[refute_0_41,refute_0_49]) ).
cnf(refute_0_51,plain,
multiply(multiply(V,W,X),Y,multiply(V,W,multiply(X_29,V,inverse(W)))) = multiply(V,W,multiply(X,Y,multiply(X_29,V,inverse(W)))),
inference(subst,[],[associativity:[bind(Z,$fot(multiply(X_29,V,inverse(W))))]]) ).
cnf(refute_0_52,plain,
multiply(V,W,multiply(X_29,V,inverse(W))) = V,
inference(subst,[],[refute_0_40:[bind(X_25,$fot(X_29)),bind(X_27,$fot(V)),bind(X_28,$fot(W))]]) ).
cnf(refute_0_53,plain,
( multiply(V,W,multiply(X_29,V,inverse(W))) != V
| multiply(multiply(V,W,X),Y,multiply(V,W,multiply(X_29,V,inverse(W)))) != multiply(V,W,multiply(X,Y,multiply(X_29,V,inverse(W))))
| multiply(multiply(V,W,X),Y,V) = multiply(V,W,multiply(X,Y,multiply(X_29,V,inverse(W)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(V,W,X),Y,multiply(V,W,multiply(X_29,V,inverse(W)))),multiply(V,W,multiply(X,Y,multiply(X_29,V,inverse(W))))) ),[0,2],$fot(V)]]) ).
cnf(refute_0_54,plain,
( multiply(multiply(V,W,X),Y,multiply(V,W,multiply(X_29,V,inverse(W)))) != multiply(V,W,multiply(X,Y,multiply(X_29,V,inverse(W))))
| multiply(multiply(V,W,X),Y,V) = multiply(V,W,multiply(X,Y,multiply(X_29,V,inverse(W)))) ),
inference(resolve,[$cnf( $equal(multiply(V,W,multiply(X_29,V,inverse(W))),V) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
multiply(multiply(V,W,X),Y,V) = multiply(V,W,multiply(X,Y,multiply(X_29,V,inverse(W)))),
inference(resolve,[$cnf( $equal(multiply(multiply(V,W,X),Y,multiply(V,W,multiply(X_29,V,inverse(W)))),multiply(V,W,multiply(X,Y,multiply(X_29,V,inverse(W))))) )],[refute_0_51,refute_0_54]) ).
cnf(refute_0_56,plain,
multiply(multiply(V,W,X),Y,V) = multiply(V,W,multiply(X,Y,V)),
inference(subst,[],[refute_0_21:[bind(Z,$fot(V))]]) ).
cnf(refute_0_57,plain,
( multiply(multiply(V,W,X),Y,V) != multiply(V,W,multiply(X,Y,V))
| multiply(multiply(V,W,X),Y,V) != multiply(V,W,multiply(X,Y,multiply(X_29,V,inverse(W))))
| multiply(V,W,multiply(X,Y,V)) = multiply(V,W,multiply(X,Y,multiply(X_29,V,inverse(W)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(V,W,X),Y,V),multiply(V,W,multiply(X,Y,multiply(X_29,V,inverse(W))))) ),[0],$fot(multiply(V,W,multiply(X,Y,V)))]]) ).
cnf(refute_0_58,plain,
( multiply(multiply(V,W,X),Y,V) != multiply(V,W,multiply(X,Y,multiply(X_29,V,inverse(W))))
| multiply(V,W,multiply(X,Y,V)) = multiply(V,W,multiply(X,Y,multiply(X_29,V,inverse(W)))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(V,W,X),Y,V),multiply(V,W,multiply(X,Y,V))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
multiply(V,W,multiply(X,Y,V)) = multiply(V,W,multiply(X,Y,multiply(X_29,V,inverse(W)))),
inference(resolve,[$cnf( $equal(multiply(multiply(V,W,X),Y,V),multiply(V,W,multiply(X,Y,multiply(X_29,V,inverse(W))))) )],[refute_0_55,refute_0_58]) ).
cnf(refute_0_60,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_61,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_62,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
( multiply(V,W,multiply(X,Y,V)) != multiply(V,W,multiply(X,Y,multiply(X_29,V,inverse(W))))
| multiply(V,W,multiply(X,Y,multiply(X_29,V,inverse(W)))) = multiply(V,W,multiply(X,Y,V)) ),
inference(subst,[],[refute_0_62:[bind(X0,$fot(multiply(V,W,multiply(X,Y,V)))),bind(Y0,$fot(multiply(V,W,multiply(X,Y,multiply(X_29,V,inverse(W))))))]]) ).
cnf(refute_0_64,plain,
multiply(V,W,multiply(X,Y,multiply(X_29,V,inverse(W)))) = multiply(V,W,multiply(X,Y,V)),
inference(resolve,[$cnf( $equal(multiply(V,W,multiply(X,Y,V)),multiply(V,W,multiply(X,Y,multiply(X_29,V,inverse(W))))) )],[refute_0_59,refute_0_63]) ).
cnf(refute_0_65,plain,
multiply(X_27,X_28,multiply(X_35,inverse(X_28),multiply(X_32,X_27,inverse(X_28)))) = multiply(X_27,X_28,multiply(X_35,inverse(X_28),X_27)),
inference(subst,[],[refute_0_64:[bind(V,$fot(X_27)),bind(W,$fot(X_28)),bind(X,$fot(X_35)),bind(Y,$fot(inverse(X_28))),bind(X_29,$fot(X_32))]]) ).
cnf(refute_0_66,plain,
( multiply(X_27,X_28,multiply(X_35,inverse(X_28),multiply(X_32,X_27,inverse(X_28)))) != X_27
| multiply(X_27,X_28,multiply(X_35,inverse(X_28),multiply(X_32,X_27,inverse(X_28)))) != multiply(X_27,X_28,multiply(X_35,inverse(X_28),X_27))
| multiply(X_27,X_28,multiply(X_35,inverse(X_28),X_27)) = X_27 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_27,X_28,multiply(X_35,inverse(X_28),multiply(X_32,X_27,inverse(X_28)))),X_27) ),[0],$fot(multiply(X_27,X_28,multiply(X_35,inverse(X_28),X_27)))]]) ).
cnf(refute_0_67,plain,
( multiply(X_27,X_28,multiply(X_35,inverse(X_28),multiply(X_32,X_27,inverse(X_28)))) != X_27
| multiply(X_27,X_28,multiply(X_35,inverse(X_28),X_27)) = X_27 ),
inference(resolve,[$cnf( $equal(multiply(X_27,X_28,multiply(X_35,inverse(X_28),multiply(X_32,X_27,inverse(X_28)))),multiply(X_27,X_28,multiply(X_35,inverse(X_28),X_27))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
multiply(X_27,X_28,multiply(X_35,inverse(X_28),X_27)) = X_27,
inference(resolve,[$cnf( $equal(multiply(X_27,X_28,multiply(X_35,inverse(X_28),multiply(X_32,X_27,inverse(X_28)))),X_27) )],[refute_0_50,refute_0_67]) ).
cnf(refute_0_69,plain,
multiply(inverse(inverse(X_37)),X_37,multiply(X_38,inverse(X_37),inverse(inverse(X_37)))) = inverse(inverse(X_37)),
inference(subst,[],[refute_0_68:[bind(X_27,$fot(inverse(inverse(X_37)))),bind(X_28,$fot(X_37)),bind(X_35,$fot(X_38))]]) ).
cnf(refute_0_70,plain,
multiply(X_38,inverse(X_37),inverse(inverse(X_37))) = X_38,
inference(subst,[],[right_inverse:[bind(X,$fot(X_38)),bind(Y,$fot(inverse(X_37)))]]) ).
cnf(refute_0_71,plain,
( multiply(X_38,inverse(X_37),inverse(inverse(X_37))) != X_38
| multiply(inverse(inverse(X_37)),X_37,multiply(X_38,inverse(X_37),inverse(inverse(X_37)))) != inverse(inverse(X_37))
| multiply(inverse(inverse(X_37)),X_37,X_38) = inverse(inverse(X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_37)),X_37,multiply(X_38,inverse(X_37),inverse(inverse(X_37)))),inverse(inverse(X_37))) ),[0,2],$fot(X_38)]]) ).
cnf(refute_0_72,plain,
( multiply(inverse(inverse(X_37)),X_37,multiply(X_38,inverse(X_37),inverse(inverse(X_37)))) != inverse(inverse(X_37))
| multiply(inverse(inverse(X_37)),X_37,X_38) = inverse(inverse(X_37)) ),
inference(resolve,[$cnf( $equal(multiply(X_38,inverse(X_37),inverse(inverse(X_37))),X_38) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
multiply(inverse(inverse(X_37)),X_37,X_38) = inverse(inverse(X_37)),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_37)),X_37,multiply(X_38,inverse(X_37),inverse(inverse(X_37)))),inverse(inverse(X_37))) )],[refute_0_69,refute_0_72]) ).
cnf(refute_0_74,plain,
multiply(inverse(inverse(X_47)),X_47,multiply(X_47,X_48,inverse(inverse(X_47)))) = inverse(inverse(X_47)),
inference(subst,[],[refute_0_73:[bind(X_37,$fot(X_47)),bind(X_38,$fot(multiply(X_47,X_48,inverse(inverse(X_47)))))]]) ).
cnf(refute_0_75,plain,
( multiply(X_47,X_48,inverse(inverse(X_47))) != multiply(inverse(inverse(X_47)),X_47,multiply(X_47,X_48,inverse(inverse(X_47))))
| multiply(inverse(inverse(X_47)),X_47,multiply(X_47,X_48,inverse(inverse(X_47)))) != inverse(inverse(X_47))
| multiply(X_47,X_48,inverse(inverse(X_47))) = inverse(inverse(X_47)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_47,X_48,inverse(inverse(X_47))),inverse(inverse(X_47))) ),[0],$fot(multiply(inverse(inverse(X_47)),X_47,multiply(X_47,X_48,inverse(inverse(X_47)))))]]) ).
cnf(refute_0_76,plain,
( multiply(X_47,X_48,inverse(inverse(X_47))) != multiply(inverse(inverse(X_47)),X_47,multiply(X_47,X_48,inverse(inverse(X_47))))
| multiply(X_47,X_48,inverse(inverse(X_47))) = inverse(inverse(X_47)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_47)),X_47,multiply(X_47,X_48,inverse(inverse(X_47)))),inverse(inverse(X_47))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
multiply(X_47,X_48,inverse(inverse(X_47))) = inverse(inverse(X_47)),
inference(resolve,[$cnf( $equal(multiply(X_47,X_48,inverse(inverse(X_47))),multiply(inverse(inverse(X_47)),X_47,multiply(X_47,X_48,inverse(inverse(X_47))))) )],[refute_0_27,refute_0_76]) ).
cnf(refute_0_78,plain,
multiply(X_27,X_28,multiply(inverse(inverse(X_27)),X_27,inverse(X_28))) = X_27,
inference(subst,[],[refute_0_40:[bind(X_25,$fot(inverse(inverse(X_27))))]]) ).
cnf(refute_0_79,plain,
multiply(inverse(inverse(X_27)),X_27,inverse(X_28)) = inverse(inverse(X_27)),
inference(subst,[],[refute_0_73:[bind(X_37,$fot(X_27)),bind(X_38,$fot(inverse(X_28)))]]) ).
cnf(refute_0_80,plain,
( multiply(X_27,X_28,multiply(inverse(inverse(X_27)),X_27,inverse(X_28))) != X_27
| multiply(inverse(inverse(X_27)),X_27,inverse(X_28)) != inverse(inverse(X_27))
| multiply(X_27,X_28,inverse(inverse(X_27))) = X_27 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_27,X_28,multiply(inverse(inverse(X_27)),X_27,inverse(X_28))),X_27) ),[0,2],$fot(inverse(inverse(X_27)))]]) ).
cnf(refute_0_81,plain,
( multiply(X_27,X_28,multiply(inverse(inverse(X_27)),X_27,inverse(X_28))) != X_27
| multiply(X_27,X_28,inverse(inverse(X_27))) = X_27 ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_27)),X_27,inverse(X_28)),inverse(inverse(X_27))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
multiply(X_27,X_28,inverse(inverse(X_27))) = X_27,
inference(resolve,[$cnf( $equal(multiply(X_27,X_28,multiply(inverse(inverse(X_27)),X_27,inverse(X_28))),X_27) )],[refute_0_78,refute_0_81]) ).
cnf(refute_0_83,plain,
multiply(X_47,X_48,inverse(inverse(X_47))) = X_47,
inference(subst,[],[refute_0_82:[bind(X_27,$fot(X_47)),bind(X_28,$fot(X_48))]]) ).
cnf(refute_0_84,plain,
( multiply(X_47,X_48,inverse(inverse(X_47))) != X_47
| multiply(X_47,X_48,inverse(inverse(X_47))) != inverse(inverse(X_47))
| X_47 = inverse(inverse(X_47)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_47,X_48,inverse(inverse(X_47))),inverse(inverse(X_47))) ),[0],$fot(X_47)]]) ).
cnf(refute_0_85,plain,
( multiply(X_47,X_48,inverse(inverse(X_47))) != inverse(inverse(X_47))
| X_47 = inverse(inverse(X_47)) ),
inference(resolve,[$cnf( $equal(multiply(X_47,X_48,inverse(inverse(X_47))),X_47) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
X_47 = inverse(inverse(X_47)),
inference(resolve,[$cnf( $equal(multiply(X_47,X_48,inverse(inverse(X_47))),inverse(inverse(X_47))) )],[refute_0_77,refute_0_85]) ).
cnf(refute_0_87,plain,
( X_47 != inverse(inverse(X_47))
| inverse(inverse(X_47)) = X_47 ),
inference(subst,[],[refute_0_62:[bind(X0,$fot(X_47)),bind(Y0,$fot(inverse(inverse(X_47))))]]) ).
cnf(refute_0_88,plain,
inverse(inverse(X_47)) = X_47,
inference(resolve,[$cnf( $equal(X_47,inverse(inverse(X_47))) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
inverse(inverse(a)) = a,
inference(subst,[],[refute_0_88:[bind(X_47,$fot(a))]]) ).
cnf(refute_0_90,plain,
( a != a
| inverse(inverse(a)) != a
| inverse(inverse(a)) = a ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(a)),a) ),[0,0,0],$fot(a)]]) ).
cnf(refute_0_91,plain,
( a != a
| inverse(inverse(a)) = a ),
inference(resolve,[$cnf( $equal(inverse(inverse(a)),a) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
a != a,
inference(resolve,[$cnf( $equal(inverse(inverse(a)),a) )],[refute_0_91,prove_inverse_is_self_cancelling]) ).
cnf(refute_0_93,plain,
a = a,
introduced(tautology,[refl,[$fot(a)]]) ).
cnf(refute_0_94,plain,
$false,
inference(resolve,[$cnf( $equal(a,a) )],[refute_0_93,refute_0_92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n024.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 20:09:21 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.52 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.52
% 0.20/0.52 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.53
%------------------------------------------------------------------------------