%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP129-2.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 10:36:49 EDT 2022
% Result : Unsatisfiable 38.49s 38.66s
% Output : CNFRefutation 38.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 89
% Number of leaves : 27
% Syntax : Number of clauses : 308 ( 25 unt; 233 nHn; 308 RR)
% Number of literals : 1395 ( 0 equ; 227 neg)
% Maximal clause size : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 103 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(e_1_then_e_2,axiom,
next(e_1,e_2) ).
cnf(e_2_then_e_3,axiom,
next(e_2,e_3) ).
cnf(e_3_greater_e_2,axiom,
greater(e_3,e_2) ).
cnf(e_4_greater_e_2,axiom,
greater(e_4,e_2) ).
cnf(e_4_greater_e_3,axiom,
greater(e_4,e_3) ).
cnf(no_redundancy,axiom,
( ~ product(X,e_1,Y)
| ~ next(X,X1)
| ~ greater(Y,X1) ) ).
cnf(element_1,axiom,
group_element(e_1) ).
cnf(element_2,axiom,
group_element(e_2) ).
cnf(element_3,axiom,
group_element(e_3) ).
cnf(element_4,axiom,
group_element(e_4) ).
cnf(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3) ).
cnf(e_1_is_not_e_4,axiom,
~ equalish(e_1,e_4) ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1) ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3) ).
cnf(e_2_is_not_e_4,axiom,
~ equalish(e_2,e_4) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2) ).
cnf(e_3_is_not_e_4,axiom,
~ equalish(e_3,e_4) ).
cnf(e_4_is_not_e_1,axiom,
~ equalish(e_4,e_1) ).
cnf(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2) ).
cnf(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3) ).
cnf(product_total_function1,axiom,
( ~ group_element(X)
| ~ group_element(Y)
| product(X,Y,e_1)
| product(X,Y,e_2)
| product(X,Y,e_3)
| product(X,Y,e_4) ) ).
cnf(product_total_function2,axiom,
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ) ).
cnf(product_right_cancellation,axiom,
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ) ).
cnf(product_left_cancellation,axiom,
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ) ).
cnf(qg3,negated_conjecture,
( ~ product(Y,X,Z1)
| ~ product(X,Z1,Z2)
| product(Z1,Y,Z2) ) ).
cnf(refute_0_0,plain,
( ~ product(e_1,Z,e_1)
| ~ product(e_1,e_1,e_1)
| equalish(e_1,Z) ),
inference(subst,[],[product_right_cancellation:[bind(W,$fot(e_1)),bind(X,$fot(e_1)),bind(Y,$fot(e_1))]]) ).
cnf(refute_0_1,plain,
( ~ product(e_1,e_1,Z)
| ~ product(e_1,e_1,e_2)
| equalish(e_2,Z) ),
inference(subst,[],[product_total_function2:[bind(W,$fot(e_2)),bind(X,$fot(e_1)),bind(Y,$fot(e_1))]]) ).
cnf(refute_0_2,plain,
( ~ greater(e_3,X1)
| ~ next(e_1,X1)
| ~ product(e_1,e_1,e_3) ),
inference(subst,[],[no_redundancy:[bind(X,$fot(e_1)),bind(Y,$fot(e_3))]]) ).
cnf(refute_0_3,plain,
( ~ greater(e_4,X1)
| ~ next(e_1,X1)
| ~ product(e_1,e_1,e_4) ),
inference(subst,[],[no_redundancy:[bind(X,$fot(e_1)),bind(Y,$fot(e_4))]]) ).
cnf(refute_0_4,plain,
( ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_4) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(e_1)),bind(Y,$fot(e_1))]]) ).
cnf(refute_0_5,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_4) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ greater(e_4,X1)
| ~ next(e_1,X1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3) ),
inference(resolve,[$cnf( product(e_1,e_1,e_4) )],[refute_0_5,refute_0_3]) ).
cnf(refute_0_7,plain,
( ~ greater(e_4,e_2)
| ~ next(e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3) ),
inference(subst,[],[refute_0_6:[bind(X1,$fot(e_2))]]) ).
cnf(refute_0_8,plain,
( ~ greater(e_4,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3) ),
inference(resolve,[$cnf( next(e_1,e_2) )],[e_1_then_e_2,refute_0_7]) ).
cnf(refute_0_9,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3) ),
inference(resolve,[$cnf( greater(e_4,e_2) )],[e_4_greater_e_2,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ greater(e_3,X1)
| ~ next(e_1,X1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(resolve,[$cnf( product(e_1,e_1,e_3) )],[refute_0_9,refute_0_2]) ).
cnf(refute_0_11,plain,
( ~ greater(e_3,e_2)
| ~ next(e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(subst,[],[refute_0_10:[bind(X1,$fot(e_2))]]) ).
cnf(refute_0_12,plain,
( ~ greater(e_3,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(resolve,[$cnf( next(e_1,e_2) )],[e_1_then_e_2,refute_0_11]) ).
cnf(refute_0_13,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(resolve,[$cnf( greater(e_3,e_2) )],[e_3_greater_e_2,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ product(e_1,e_1,Z)
| equalish(e_2,Z)
| product(e_1,e_1,e_1) ),
inference(resolve,[$cnf( product(e_1,e_1,e_2) )],[refute_0_13,refute_0_1]) ).
cnf(refute_0_15,plain,
( ~ product(e_1,e_1,e_3)
| equalish(e_2,e_3)
| product(e_1,e_1,e_1) ),
inference(subst,[],[refute_0_14:[bind(Z,$fot(e_3))]]) ).
cnf(refute_0_16,plain,
( ~ product(e_1,Z,e_2)
| ~ product(e_1,e_1,e_2)
| equalish(e_1,Z) ),
inference(subst,[],[product_right_cancellation:[bind(W,$fot(e_1)),bind(X,$fot(e_1)),bind(Y,$fot(e_2))]]) ).
cnf(refute_0_17,plain,
( ~ product(e_1,Z,e_2)
| equalish(e_1,Z)
| product(e_1,e_1,e_1) ),
inference(resolve,[$cnf( product(e_1,e_1,e_2) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ product(e_1,e_2,e_2)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(subst,[],[refute_0_17:[bind(Z,$fot(e_2))]]) ).
cnf(refute_0_19,plain,
( ~ product(Y,e_1,e_1)
| ~ product(e_1,e_1,e_2)
| product(e_1,Y,e_2) ),
inference(subst,[],[qg3:[bind(X,$fot(e_1)),bind(Z1,$fot(e_1)),bind(Z2,$fot(e_2))]]) ).
cnf(refute_0_20,plain,
( ~ product(Y,e_1,e_1)
| product(e_1,Y,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[$cnf( product(e_1,e_1,e_2) )],[refute_0_13,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ product(e_2,e_1,e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_2,e_2) ),
inference(subst,[],[refute_0_20:[bind(Y,$fot(e_2))]]) ).
cnf(refute_0_22,plain,
( ~ product(Z,e_1,e_2)
| ~ product(e_1,e_1,e_2)
| equalish(e_1,Z) ),
inference(subst,[],[product_left_cancellation:[bind(W,$fot(e_1)),bind(X,$fot(e_2)),bind(Y,$fot(e_1))]]) ).
cnf(refute_0_23,plain,
( ~ product(Z,e_1,e_2)
| equalish(e_1,Z)
| product(e_1,e_1,e_1) ),
inference(resolve,[$cnf( product(e_1,e_1,e_2) )],[refute_0_13,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ product(e_2,e_1,e_2)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(subst,[],[refute_0_23:[bind(Z,$fot(e_2))]]) ).
cnf(refute_0_25,plain,
( ~ product(Y,e_2,e_1)
| ~ product(e_2,e_1,e_3)
| product(e_1,Y,e_3) ),
inference(subst,[],[qg3:[bind(X,$fot(e_2)),bind(Z1,$fot(e_1)),bind(Z2,$fot(e_3))]]) ).
cnf(refute_0_26,plain,
( ~ greater(e_4,X1)
| ~ next(e_2,X1)
| ~ product(e_2,e_1,e_4) ),
inference(subst,[],[no_redundancy:[bind(X,$fot(e_2)),bind(Y,$fot(e_4))]]) ).
cnf(refute_0_27,plain,
( ~ group_element(X_34)
| ~ group_element(e_2)
| product(e_2,X_34,e_1)
| product(e_2,X_34,e_2)
| product(e_2,X_34,e_3)
| product(e_2,X_34,e_4) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(e_2)),bind(Y,$fot(X_34))]]) ).
cnf(refute_0_28,plain,
( ~ group_element(X_34)
| product(e_2,X_34,e_1)
| product(e_2,X_34,e_2)
| product(e_2,X_34,e_3)
| product(e_2,X_34,e_4) ),
inference(resolve,[$cnf( group_element(e_2) )],[element_2,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ group_element(e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_4) ),
inference(subst,[],[refute_0_28:[bind(X_34,$fot(e_1))]]) ).
cnf(refute_0_30,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_4) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_29]) ).
cnf(refute_0_31,plain,
( ~ greater(e_4,X1)
| ~ next(e_2,X1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(resolve,[$cnf( product(e_2,e_1,e_4) )],[refute_0_30,refute_0_26]) ).
cnf(refute_0_32,plain,
( ~ greater(e_4,e_3)
| ~ next(e_2,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(subst,[],[refute_0_31:[bind(X1,$fot(e_3))]]) ).
cnf(refute_0_33,plain,
( ~ greater(e_4,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(resolve,[$cnf( next(e_2,e_3) )],[e_2_then_e_3,refute_0_32]) ).
cnf(refute_0_34,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(resolve,[$cnf( greater(e_4,e_3) )],[e_4_greater_e_3,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ product(Y,e_2,e_1)
| product(e_1,Y,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolve,[$cnf( product(e_2,e_1,e_3) )],[refute_0_34,refute_0_25]) ).
cnf(refute_0_36,plain,
( ~ product(e_1,e_2,e_1)
| product(e_1,e_1,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(subst,[],[refute_0_35:[bind(Y,$fot(e_1))]]) ).
cnf(refute_0_37,plain,
( ~ product(e_1,W,e_3)
| ~ product(e_1,e_2,e_3)
| equalish(W,e_2) ),
inference(subst,[],[product_right_cancellation:[bind(X,$fot(e_1)),bind(Y,$fot(e_3)),bind(Z,$fot(e_2))]]) ).
cnf(refute_0_38,plain,
( ~ product(e_2,e_1,Z)
| ~ product(e_2,e_1,e_3)
| equalish(e_3,Z) ),
inference(subst,[],[product_total_function2:[bind(W,$fot(e_3)),bind(X,$fot(e_2)),bind(Y,$fot(e_1))]]) ).
cnf(refute_0_39,plain,
( ~ product(e_2,e_1,Z)
| equalish(e_3,Z)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolve,[$cnf( product(e_2,e_1,e_3) )],[refute_0_34,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ product(e_2,e_1,e_4)
| equalish(e_3,e_4)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(subst,[],[refute_0_39:[bind(Z,$fot(e_4))]]) ).
cnf(refute_0_41,plain,
( ~ product(Y,e_1,e_2)
| ~ product(e_1,e_2,e_4)
| product(e_2,Y,e_4) ),
inference(subst,[],[qg3:[bind(X,$fot(e_1)),bind(Z1,$fot(e_2)),bind(Z2,$fot(e_4))]]) ).
cnf(refute_0_42,plain,
( ~ group_element(X_34)
| ~ group_element(e_1)
| product(e_1,X_34,e_1)
| product(e_1,X_34,e_2)
| product(e_1,X_34,e_3)
| product(e_1,X_34,e_4) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(e_1)),bind(Y,$fot(X_34))]]) ).
cnf(refute_0_43,plain,
( ~ group_element(X_34)
| product(e_1,X_34,e_1)
| product(e_1,X_34,e_2)
| product(e_1,X_34,e_3)
| product(e_1,X_34,e_4) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ group_element(e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(subst,[],[refute_0_43:[bind(X_34,$fot(e_2))]]) ).
cnf(refute_0_45,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(resolve,[$cnf( group_element(e_2) )],[element_2,refute_0_44]) ).
cnf(refute_0_46,plain,
( ~ product(Y,e_1,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,Y,e_4) ),
inference(resolve,[$cnf( product(e_1,e_2,e_4) )],[refute_0_45,refute_0_41]) ).
cnf(refute_0_47,plain,
( ~ product(e_1,e_1,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_1,e_4) ),
inference(subst,[],[refute_0_46:[bind(Y,$fot(e_1))]]) ).
cnf(refute_0_48,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_1,e_4) ),
inference(resolve,[$cnf( product(e_1,e_1,e_2) )],[refute_0_13,refute_0_47]) ).
cnf(refute_0_49,plain,
( equalish(e_3,e_4)
| product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolve,[$cnf( product(e_2,e_1,e_4) )],[refute_0_48,refute_0_40]) ).
cnf(refute_0_50,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolve,[$cnf( equalish(e_3,e_4) )],[refute_0_49,e_3_is_not_e_4]) ).
cnf(refute_0_51,plain,
( equalish(e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( product(e_2,e_1,e_2) )],[refute_0_50,refute_0_24]) ).
cnf(refute_0_52,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_51,e_1_is_not_e_2]) ).
cnf(refute_0_53,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(resolve,[$cnf( product(e_2,e_1,e_1) )],[refute_0_52,refute_0_21]) ).
cnf(refute_0_54,plain,
( ~ product(e_1,W,e_3)
| equalish(W,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(resolve,[$cnf( product(e_1,e_2,e_3) )],[refute_0_53,refute_0_37]) ).
cnf(refute_0_55,plain,
( ~ product(e_1,e_3,e_3)
| equalish(e_3,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(subst,[],[refute_0_54:[bind(W,$fot(e_3))]]) ).
cnf(refute_0_56,plain,
( ~ product(e_3,e_2,e_1)
| product(e_1,e_3,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(subst,[],[refute_0_35:[bind(Y,$fot(e_3))]]) ).
cnf(refute_0_57,plain,
( ~ product(e_1,e_3,Z2)
| ~ product(e_2,e_1,e_3)
| product(e_3,e_2,Z2) ),
inference(subst,[],[qg3:[bind(X,$fot(e_1)),bind(Y,$fot(e_2)),bind(Z1,$fot(e_3))]]) ).
cnf(refute_0_58,plain,
( ~ product(e_1,e_3,Z2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_2,Z2) ),
inference(resolve,[$cnf( product(e_2,e_1,e_3) )],[refute_0_34,refute_0_57]) ).
cnf(refute_0_59,plain,
( ~ product(e_1,e_3,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_2,e_1) ),
inference(subst,[],[refute_0_58:[bind(Z2,$fot(e_1))]]) ).
cnf(refute_0_60,plain,
( ~ product(e_1,e_3,e_2)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(subst,[],[refute_0_17:[bind(Z,$fot(e_3))]]) ).
cnf(refute_0_61,plain,
( ~ product(e_3,e_1,e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_3,e_2) ),
inference(subst,[],[refute_0_20:[bind(Y,$fot(e_3))]]) ).
cnf(refute_0_62,plain,
( ~ product(e_3,e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(subst,[],[refute_0_23:[bind(Z,$fot(e_3))]]) ).
cnf(refute_0_63,plain,
( ~ product(Z,e_1,e_3)
| ~ product(e_2,e_1,e_3)
| equalish(e_2,Z) ),
inference(subst,[],[product_left_cancellation:[bind(W,$fot(e_2)),bind(X,$fot(e_3)),bind(Y,$fot(e_1))]]) ).
cnf(refute_0_64,plain,
( ~ product(Z,e_1,e_3)
| equalish(e_2,Z)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolve,[$cnf( product(e_2,e_1,e_3) )],[refute_0_34,refute_0_63]) ).
cnf(refute_0_65,plain,
( ~ product(e_3,e_1,e_3)
| equalish(e_2,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(subst,[],[refute_0_64:[bind(Z,$fot(e_3))]]) ).
cnf(refute_0_66,plain,
( ~ group_element(e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4) ),
inference(subst,[],[refute_0_43:[bind(X_34,$fot(e_3))]]) ).
cnf(refute_0_67,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4) ),
inference(resolve,[$cnf( group_element(e_3) )],[element_3,refute_0_66]) ).
cnf(refute_0_68,plain,
( ~ product(e_1,e_3,e_4)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_2,e_4) ),
inference(subst,[],[refute_0_58:[bind(Z2,$fot(e_4))]]) ).
cnf(refute_0_69,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_2,e_4) ),
inference(resolve,[$cnf( product(e_1,e_3,e_4) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
( ~ product(e_3,W,e_4)
| ~ product(e_3,e_1,e_4)
| equalish(W,e_1) ),
inference(subst,[],[product_right_cancellation:[bind(X,$fot(e_3)),bind(Y,$fot(e_4)),bind(Z,$fot(e_1))]]) ).
cnf(refute_0_71,plain,
( ~ group_element(X_34)
| ~ group_element(e_3)
| product(e_3,X_34,e_1)
| product(e_3,X_34,e_2)
| product(e_3,X_34,e_3)
| product(e_3,X_34,e_4) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(e_3)),bind(Y,$fot(X_34))]]) ).
cnf(refute_0_72,plain,
( ~ group_element(X_34)
| product(e_3,X_34,e_1)
| product(e_3,X_34,e_2)
| product(e_3,X_34,e_3)
| product(e_3,X_34,e_4) ),
inference(resolve,[$cnf( group_element(e_3) )],[element_3,refute_0_71]) ).
cnf(refute_0_73,plain,
( ~ group_element(e_1)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_4) ),
inference(subst,[],[refute_0_72:[bind(X_34,$fot(e_1))]]) ).
cnf(refute_0_74,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_4) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_73]) ).
cnf(refute_0_75,plain,
( ~ product(e_3,W,e_4)
| equalish(W,e_1)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(resolve,[$cnf( product(e_3,e_1,e_4) )],[refute_0_74,refute_0_70]) ).
cnf(refute_0_76,plain,
( ~ product(e_3,e_2,e_4)
| equalish(e_2,e_1)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(subst,[],[refute_0_75:[bind(W,$fot(e_2))]]) ).
cnf(refute_0_77,plain,
( equalish(e_2,e_1)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(resolve,[$cnf( product(e_3,e_2,e_4) )],[refute_0_69,refute_0_76]) ).
cnf(refute_0_78,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(resolve,[$cnf( equalish(e_2,e_1) )],[refute_0_77,e_2_is_not_e_1]) ).
cnf(refute_0_79,plain,
( equalish(e_2,e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2) ),
inference(resolve,[$cnf( product(e_3,e_1,e_3) )],[refute_0_78,refute_0_65]) ).
cnf(refute_0_80,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2) ),
inference(resolve,[$cnf( equalish(e_2,e_3) )],[refute_0_79,e_2_is_not_e_3]) ).
cnf(refute_0_81,plain,
( equalish(e_1,e_3)
| product(e_1,e_1,e_1)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolve,[$cnf( product(e_3,e_1,e_2) )],[refute_0_80,refute_0_62]) ).
cnf(refute_0_82,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolve,[$cnf( equalish(e_1,e_3) )],[refute_0_81,e_1_is_not_e_3]) ).
cnf(refute_0_83,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolve,[$cnf( product(e_3,e_1,e_1) )],[refute_0_82,refute_0_61]) ).
cnf(refute_0_84,plain,
( equalish(e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( product(e_2,e_1,e_2) )],[refute_0_83,refute_0_24]) ).
cnf(refute_0_85,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_84,e_1_is_not_e_2]) ).
cnf(refute_0_86,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(resolve,[$cnf( product(e_2,e_1,e_1) )],[refute_0_85,refute_0_21]) ).
cnf(refute_0_87,plain,
( equalish(e_3,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(resolve,[$cnf( product(e_1,e_3,e_3) )],[refute_0_86,refute_0_55]) ).
cnf(refute_0_88,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(resolve,[$cnf( equalish(e_3,e_2) )],[refute_0_87,e_3_is_not_e_2]) ).
cnf(refute_0_89,plain,
( equalish(e_1,e_3)
| product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[$cnf( product(e_1,e_3,e_2) )],[refute_0_88,refute_0_60]) ).
cnf(refute_0_90,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[$cnf( equalish(e_1,e_3) )],[refute_0_89,e_1_is_not_e_3]) ).
cnf(refute_0_91,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_2,e_1) ),
inference(resolve,[$cnf( product(e_1,e_3,e_1) )],[refute_0_90,refute_0_59]) ).
cnf(refute_0_92,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_3,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolve,[$cnf( product(e_3,e_2,e_1) )],[refute_0_91,refute_0_56]) ).
cnf(refute_0_93,plain,
( equalish(e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_3,e_3)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( product(e_2,e_1,e_2) )],[refute_0_92,refute_0_24]) ).
cnf(refute_0_94,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_3,e_3)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_93,e_1_is_not_e_2]) ).
cnf(refute_0_95,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_3,e_3) ),
inference(resolve,[$cnf( product(e_2,e_1,e_1) )],[refute_0_94,refute_0_21]) ).
cnf(refute_0_96,plain,
( equalish(e_3,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(resolve,[$cnf( product(e_1,e_3,e_3) )],[refute_0_95,refute_0_55]) ).
cnf(refute_0_97,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(resolve,[$cnf( equalish(e_3,e_2) )],[refute_0_96,e_3_is_not_e_2]) ).
cnf(refute_0_98,plain,
( equalish(e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_2,e_1) ),
inference(resolve,[$cnf( product(e_1,e_2,e_2) )],[refute_0_97,refute_0_18]) ).
cnf(refute_0_99,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_2,e_1) ),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_98,e_1_is_not_e_2]) ).
cnf(refute_0_100,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolve,[$cnf( product(e_1,e_2,e_1) )],[refute_0_99,refute_0_36]) ).
cnf(refute_0_101,plain,
( equalish(e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( product(e_2,e_1,e_2) )],[refute_0_100,refute_0_24]) ).
cnf(refute_0_102,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_101,e_1_is_not_e_2]) ).
cnf(refute_0_103,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| product(e_1,e_2,e_2) ),
inference(resolve,[$cnf( product(e_2,e_1,e_1) )],[refute_0_102,refute_0_21]) ).
cnf(refute_0_104,plain,
( equalish(e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_3) ),
inference(resolve,[$cnf( product(e_1,e_2,e_2) )],[refute_0_103,refute_0_18]) ).
cnf(refute_0_105,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_3) ),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_104,e_1_is_not_e_2]) ).
cnf(refute_0_106,plain,
( equalish(e_2,e_3)
| product(e_1,e_1,e_1) ),
inference(resolve,[$cnf( product(e_1,e_1,e_3) )],[refute_0_105,refute_0_15]) ).
cnf(refute_0_107,plain,
product(e_1,e_1,e_1),
inference(resolve,[$cnf( equalish(e_2,e_3) )],[refute_0_106,e_2_is_not_e_3]) ).
cnf(refute_0_108,plain,
( ~ product(e_1,Z,e_1)
| equalish(e_1,Z) ),
inference(resolve,[$cnf( product(e_1,e_1,e_1) )],[refute_0_107,refute_0_0]) ).
cnf(refute_0_109,plain,
( ~ product(e_1,e_2,e_1)
| equalish(e_1,e_2) ),
inference(subst,[],[refute_0_108:[bind(Z,$fot(e_2))]]) ).
cnf(refute_0_110,plain,
( ~ product(e_1,e_2,Z)
| ~ product(e_1,e_2,e_2)
| equalish(e_2,Z) ),
inference(subst,[],[product_total_function2:[bind(W,$fot(e_2)),bind(X,$fot(e_1)),bind(Y,$fot(e_2))]]) ).
cnf(refute_0_111,plain,
( ~ product(Y,e_1,e_1)
| ~ product(e_1,e_1,e_1)
| product(e_1,Y,e_1) ),
inference(subst,[],[qg3:[bind(X,$fot(e_1)),bind(Z1,$fot(e_1)),bind(Z2,$fot(e_1))]]) ).
cnf(refute_0_112,plain,
( ~ product(Y,e_1,e_1)
| product(e_1,Y,e_1) ),
inference(resolve,[$cnf( product(e_1,e_1,e_1) )],[refute_0_107,refute_0_111]) ).
cnf(refute_0_113,plain,
( ~ product(e_2,e_1,e_1)
| product(e_1,e_2,e_1) ),
inference(subst,[],[refute_0_112:[bind(Y,$fot(e_2))]]) ).
cnf(refute_0_114,plain,
( ~ product(Z,e_2,e_3)
| ~ product(e_1,e_2,e_3)
| equalish(e_1,Z) ),
inference(subst,[],[product_left_cancellation:[bind(W,$fot(e_1)),bind(X,$fot(e_3)),bind(Y,$fot(e_2))]]) ).
cnf(refute_0_115,plain,
( ~ product(e_1,e_3,e_1)
| equalish(e_1,e_3) ),
inference(subst,[],[refute_0_108:[bind(Z,$fot(e_3))]]) ).
cnf(refute_0_116,plain,
( ~ product(Z,e_2,e_4)
| ~ product(e_1,e_2,e_4)
| equalish(e_1,Z) ),
inference(subst,[],[product_left_cancellation:[bind(W,$fot(e_1)),bind(X,$fot(e_4)),bind(Y,$fot(e_2))]]) ).
cnf(refute_0_117,plain,
( ~ product(Z,e_2,e_4)
| equalish(e_1,Z)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(resolve,[$cnf( product(e_1,e_2,e_4) )],[refute_0_45,refute_0_116]) ).
cnf(refute_0_118,plain,
( ~ product(e_2,e_2,e_4)
| equalish(e_1,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(subst,[],[refute_0_117:[bind(Z,$fot(e_2))]]) ).
cnf(refute_0_119,plain,
( ~ product(e_2,e_1,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_4) ),
inference(subst,[],[refute_0_46:[bind(Y,$fot(e_2))]]) ).
cnf(refute_0_120,plain,
( ~ product(e_2,e_2,e_1)
| product(e_1,e_2,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(subst,[],[refute_0_35:[bind(Y,$fot(e_2))]]) ).
cnf(refute_0_121,plain,
( ~ product(Z,e_2,e_2)
| ~ product(e_2,e_2,e_2)
| equalish(e_2,Z) ),
inference(subst,[],[product_left_cancellation:[bind(W,$fot(e_2)),bind(X,$fot(e_2)),bind(Y,$fot(e_2))]]) ).
cnf(refute_0_122,plain,
( ~ product(e_2,Z,e_3)
| ~ product(e_2,e_2,e_3)
| equalish(e_2,Z) ),
inference(subst,[],[product_right_cancellation:[bind(W,$fot(e_2)),bind(X,$fot(e_2)),bind(Y,$fot(e_3))]]) ).
cnf(refute_0_123,plain,
( ~ product(W,e_2,e_4)
| ~ product(e_2,e_2,e_4)
| equalish(W,e_2) ),
inference(subst,[],[product_left_cancellation:[bind(X,$fot(e_4)),bind(Y,$fot(e_2)),bind(Z,$fot(e_2))]]) ).
cnf(refute_0_124,plain,
( ~ group_element(e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_4) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(e_2)),bind(Y,$fot(e_2))]]) ).
cnf(refute_0_125,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_4) ),
inference(resolve,[$cnf( group_element(e_2) )],[element_2,refute_0_124]) ).
cnf(refute_0_126,plain,
( ~ product(W,e_2,e_4)
| equalish(W,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(resolve,[$cnf( product(e_2,e_2,e_4) )],[refute_0_125,refute_0_123]) ).
cnf(refute_0_127,plain,
( ~ product(e_1,e_2,e_4)
| equalish(e_1,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(subst,[],[refute_0_126:[bind(W,$fot(e_1))]]) ).
cnf(refute_0_128,plain,
( equalish(e_1,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(resolve,[$cnf( product(e_1,e_2,e_4) )],[refute_0_45,refute_0_127]) ).
cnf(refute_0_129,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_128,e_1_is_not_e_2]) ).
cnf(refute_0_130,plain,
( ~ product(e_2,Z,e_3)
| equalish(e_2,Z)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(resolve,[$cnf( product(e_2,e_2,e_3) )],[refute_0_129,refute_0_122]) ).
cnf(refute_0_131,plain,
( ~ product(e_2,e_3,e_3)
| equalish(e_2,e_3)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(subst,[],[refute_0_130:[bind(Z,$fot(e_3))]]) ).
cnf(refute_0_132,plain,
( ~ product(e_2,e_4,e_3)
| equalish(e_2,e_4)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(subst,[],[refute_0_130:[bind(Z,$fot(e_4))]]) ).
cnf(refute_0_133,plain,
( ~ group_element(X_34)
| ~ group_element(e_4)
| product(e_4,X_34,e_1)
| product(e_4,X_34,e_2)
| product(e_4,X_34,e_3)
| product(e_4,X_34,e_4) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(e_4)),bind(Y,$fot(X_34))]]) ).
cnf(refute_0_134,plain,
( ~ group_element(X_34)
| product(e_4,X_34,e_1)
| product(e_4,X_34,e_2)
| product(e_4,X_34,e_3)
| product(e_4,X_34,e_4) ),
inference(resolve,[$cnf( group_element(e_4) )],[element_4,refute_0_133]) ).
cnf(refute_0_135,plain,
( ~ group_element(e_2)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_4) ),
inference(subst,[],[refute_0_134:[bind(X_34,$fot(e_2))]]) ).
cnf(refute_0_136,plain,
( product(e_4,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_4) ),
inference(resolve,[$cnf( group_element(e_2) )],[element_2,refute_0_135]) ).
cnf(refute_0_137,plain,
( ~ product(W,e_2,e_4)
| ~ product(e_1,e_2,e_4)
| equalish(W,e_1) ),
inference(subst,[],[product_left_cancellation:[bind(X,$fot(e_4)),bind(Y,$fot(e_2)),bind(Z,$fot(e_1))]]) ).
cnf(refute_0_138,plain,
( ~ product(W,e_2,e_4)
| equalish(W,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(resolve,[$cnf( product(e_1,e_2,e_4) )],[refute_0_45,refute_0_137]) ).
cnf(refute_0_139,plain,
( ~ product(e_4,e_2,e_4)
| equalish(e_4,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(subst,[],[refute_0_138:[bind(W,$fot(e_4))]]) ).
cnf(refute_0_140,plain,
( equalish(e_4,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3) ),
inference(resolve,[$cnf( product(e_4,e_2,e_4) )],[refute_0_136,refute_0_139]) ).
cnf(refute_0_141,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3) ),
inference(resolve,[$cnf( equalish(e_4,e_1) )],[refute_0_140,e_4_is_not_e_1]) ).
cnf(refute_0_142,plain,
( ~ product(W,e_2,e_3)
| ~ product(e_2,e_2,e_3)
| equalish(W,e_2) ),
inference(subst,[],[product_left_cancellation:[bind(X,$fot(e_3)),bind(Y,$fot(e_2)),bind(Z,$fot(e_2))]]) ).
cnf(refute_0_143,plain,
( ~ product(W,e_2,e_3)
| equalish(W,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(resolve,[$cnf( product(e_2,e_2,e_3) )],[refute_0_129,refute_0_142]) ).
cnf(refute_0_144,plain,
( ~ product(e_4,e_2,e_3)
| equalish(e_4,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(subst,[],[refute_0_143:[bind(W,$fot(e_4))]]) ).
cnf(refute_0_145,plain,
( equalish(e_4,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2) ),
inference(resolve,[$cnf( product(e_4,e_2,e_3) )],[refute_0_141,refute_0_144]) ).
cnf(refute_0_146,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2) ),
inference(resolve,[$cnf( equalish(e_4,e_2) )],[refute_0_145,e_4_is_not_e_2]) ).
cnf(refute_0_147,plain,
( ~ product(Y,e_2,e_2)
| ~ product(e_2,e_2,e_3)
| product(e_2,Y,e_3) ),
inference(subst,[],[qg3:[bind(X,$fot(e_2)),bind(Z1,$fot(e_2)),bind(Z2,$fot(e_3))]]) ).
cnf(refute_0_148,plain,
( ~ product(Y,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,Y,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(resolve,[$cnf( product(e_2,e_2,e_3) )],[refute_0_129,refute_0_147]) ).
cnf(refute_0_149,plain,
( ~ product(e_4,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_4,e_3) ),
inference(subst,[],[refute_0_148:[bind(Y,$fot(e_4))]]) ).
cnf(refute_0_150,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_4,e_3)
| product(e_4,e_2,e_1) ),
inference(resolve,[$cnf( product(e_4,e_2,e_2) )],[refute_0_146,refute_0_149]) ).
cnf(refute_0_151,plain,
( ~ product(W,e_2,e_1)
| ~ product(e_3,e_2,e_1)
| equalish(W,e_3) ),
inference(subst,[],[product_left_cancellation:[bind(X,$fot(e_1)),bind(Y,$fot(e_2)),bind(Z,$fot(e_3))]]) ).
cnf(refute_0_152,plain,
( ~ group_element(e_2)
| product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_4) ),
inference(subst,[],[refute_0_72:[bind(X_34,$fot(e_2))]]) ).
cnf(refute_0_153,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_4) ),
inference(resolve,[$cnf( group_element(e_2) )],[element_2,refute_0_152]) ).
cnf(refute_0_154,plain,
( ~ product(e_3,e_2,e_4)
| equalish(e_3,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(subst,[],[refute_0_138:[bind(W,$fot(e_3))]]) ).
cnf(refute_0_155,plain,
( equalish(e_3,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3) ),
inference(resolve,[$cnf( product(e_3,e_2,e_4) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3) ),
inference(resolve,[$cnf( equalish(e_3,e_1) )],[refute_0_155,e_3_is_not_e_1]) ).
cnf(refute_0_157,plain,
( ~ product(e_3,e_2,e_3)
| equalish(e_3,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(subst,[],[refute_0_143:[bind(W,$fot(e_3))]]) ).
cnf(refute_0_158,plain,
( equalish(e_3,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_3,e_2,e_1)
| product(e_3,e_2,e_2) ),
inference(resolve,[$cnf( product(e_3,e_2,e_3) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_3,e_2,e_1)
| product(e_3,e_2,e_2) ),
inference(resolve,[$cnf( equalish(e_3,e_2) )],[refute_0_158,e_3_is_not_e_2]) ).
cnf(refute_0_160,plain,
( ~ product(e_3,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_3,e_3) ),
inference(subst,[],[refute_0_148:[bind(Y,$fot(e_3))]]) ).
cnf(refute_0_161,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_3,e_3)
| product(e_3,e_2,e_1) ),
inference(resolve,[$cnf( product(e_3,e_2,e_2) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
( ~ product(W,e_2,e_1)
| equalish(W,e_3)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_3,e_3) ),
inference(resolve,[$cnf( product(e_3,e_2,e_1) )],[refute_0_161,refute_0_151]) ).
cnf(refute_0_163,plain,
( ~ product(e_4,e_2,e_1)
| equalish(e_4,e_3)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_3,e_3) ),
inference(subst,[],[refute_0_162:[bind(W,$fot(e_4))]]) ).
cnf(refute_0_164,plain,
( equalish(e_4,e_3)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_3,e_3)
| product(e_2,e_4,e_3) ),
inference(resolve,[$cnf( product(e_4,e_2,e_1) )],[refute_0_150,refute_0_163]) ).
cnf(refute_0_165,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_3,e_3)
| product(e_2,e_4,e_3) ),
inference(resolve,[$cnf( equalish(e_4,e_3) )],[refute_0_164,e_4_is_not_e_3]) ).
cnf(refute_0_166,plain,
( equalish(e_2,e_4)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_3,e_3) ),
inference(resolve,[$cnf( product(e_2,e_4,e_3) )],[refute_0_165,refute_0_132]) ).
cnf(refute_0_167,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_3,e_3) ),
inference(resolve,[$cnf( equalish(e_2,e_4) )],[refute_0_166,e_2_is_not_e_4]) ).
cnf(refute_0_168,plain,
( equalish(e_2,e_3)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(resolve,[$cnf( product(e_2,e_3,e_3) )],[refute_0_167,refute_0_131]) ).
cnf(refute_0_169,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(resolve,[$cnf( equalish(e_2,e_3) )],[refute_0_168,e_2_is_not_e_3]) ).
cnf(refute_0_170,plain,
( ~ product(Z,e_2,e_2)
| equalish(e_2,Z)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1) ),
inference(resolve,[$cnf( product(e_2,e_2,e_2) )],[refute_0_169,refute_0_121]) ).
cnf(refute_0_171,plain,
( ~ product(e_3,e_2,e_2)
| equalish(e_2,e_3)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1) ),
inference(subst,[],[refute_0_170:[bind(Z,$fot(e_3))]]) ).
cnf(refute_0_172,plain,
( ~ product(e_1,e_3,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_2,e_2) ),
inference(subst,[],[refute_0_58:[bind(Z2,$fot(e_2))]]) ).
cnf(refute_0_173,plain,
( ~ product(e_1,Z,e_3)
| ~ product(e_1,e_3,e_3)
| equalish(e_3,Z) ),
inference(subst,[],[product_right_cancellation:[bind(W,$fot(e_3)),bind(X,$fot(e_1)),bind(Y,$fot(e_3))]]) ).
cnf(refute_0_174,plain,
( ~ product(e_1,W,e_4)
| ~ product(e_1,e_2,e_4)
| equalish(W,e_2) ),
inference(subst,[],[product_right_cancellation:[bind(X,$fot(e_1)),bind(Y,$fot(e_4)),bind(Z,$fot(e_2))]]) ).
cnf(refute_0_175,plain,
( ~ product(e_1,W,e_4)
| equalish(W,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(resolve,[$cnf( product(e_1,e_2,e_4) )],[refute_0_45,refute_0_174]) ).
cnf(refute_0_176,plain,
( ~ product(e_1,e_3,e_4)
| equalish(e_3,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(subst,[],[refute_0_175:[bind(W,$fot(e_3))]]) ).
cnf(refute_0_177,plain,
( equalish(e_3,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(resolve,[$cnf( product(e_1,e_3,e_4) )],[refute_0_67,refute_0_176]) ).
cnf(refute_0_178,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(resolve,[$cnf( equalish(e_3,e_2) )],[refute_0_177,e_3_is_not_e_2]) ).
cnf(refute_0_179,plain,
( ~ product(e_1,Z,e_3)
| equalish(e_3,Z)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(resolve,[$cnf( product(e_1,e_3,e_3) )],[refute_0_178,refute_0_173]) ).
cnf(refute_0_180,plain,
( ~ product(e_1,e_4,e_3)
| equalish(e_3,e_4)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(subst,[],[refute_0_179:[bind(Z,$fot(e_4))]]) ).
cnf(refute_0_181,plain,
( ~ product(e_4,e_2,e_1)
| product(e_1,e_4,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(subst,[],[refute_0_35:[bind(Y,$fot(e_4))]]) ).
cnf(refute_0_182,plain,
( ~ product(e_1,e_3,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_2,e_3) ),
inference(subst,[],[refute_0_58:[bind(Z2,$fot(e_3))]]) ).
cnf(refute_0_183,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_2,e_3) ),
inference(resolve,[$cnf( product(e_1,e_3,e_3) )],[refute_0_178,refute_0_182]) ).
cnf(refute_0_184,plain,
( ~ product(Z,e_2,e_3)
| ~ product(e_4,e_2,e_3)
| equalish(e_4,Z) ),
inference(subst,[],[product_left_cancellation:[bind(W,$fot(e_4)),bind(X,$fot(e_3)),bind(Y,$fot(e_2))]]) ).
cnf(refute_0_185,plain,
( ~ product(Z,e_2,e_3)
| equalish(e_4,Z)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2) ),
inference(resolve,[$cnf( product(e_4,e_2,e_3) )],[refute_0_141,refute_0_184]) ).
cnf(refute_0_186,plain,
( ~ product(e_3,e_2,e_3)
| equalish(e_4,e_3)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2) ),
inference(subst,[],[refute_0_185:[bind(Z,$fot(e_3))]]) ).
cnf(refute_0_187,plain,
( equalish(e_4,e_3)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2) ),
inference(resolve,[$cnf( product(e_3,e_2,e_3) )],[refute_0_183,refute_0_186]) ).
cnf(refute_0_188,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2) ),
inference(resolve,[$cnf( equalish(e_4,e_3) )],[refute_0_187,e_4_is_not_e_3]) ).
cnf(refute_0_189,plain,
( ~ product(e_4,e_2,e_2)
| equalish(e_2,e_4)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1) ),
inference(subst,[],[refute_0_170:[bind(Z,$fot(e_4))]]) ).
cnf(refute_0_190,plain,
( equalish(e_2,e_4)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_2,e_1)
| product(e_4,e_2,e_1) ),
inference(resolve,[$cnf( product(e_4,e_2,e_2) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_2,e_1)
| product(e_4,e_2,e_1) ),
inference(resolve,[$cnf( equalish(e_2,e_4) )],[refute_0_190,e_2_is_not_e_4]) ).
cnf(refute_0_192,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_4,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[$cnf( product(e_4,e_2,e_1) )],[refute_0_191,refute_0_181]) ).
cnf(refute_0_193,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_4,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolve,[$cnf( product(e_2,e_2,e_1) )],[refute_0_192,refute_0_120]) ).
cnf(refute_0_194,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_4,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_2,e_4) ),
inference(resolve,[$cnf( product(e_2,e_1,e_2) )],[refute_0_193,refute_0_119]) ).
cnf(refute_0_195,plain,
( equalish(e_1,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_4,e_3)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( product(e_2,e_2,e_4) )],[refute_0_194,refute_0_118]) ).
cnf(refute_0_196,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_4,e_3)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_195,e_1_is_not_e_2]) ).
cnf(refute_0_197,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_4,e_3) ),
inference(resolve,[$cnf( product(e_2,e_1,e_1) )],[refute_0_196,refute_0_113]) ).
cnf(refute_0_198,plain,
( equalish(e_3,e_4)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(resolve,[$cnf( product(e_1,e_4,e_3) )],[refute_0_197,refute_0_180]) ).
cnf(refute_0_199,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(resolve,[$cnf( equalish(e_3,e_4) )],[refute_0_198,e_3_is_not_e_4]) ).
cnf(refute_0_200,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_2,e_2) ),
inference(resolve,[$cnf( product(e_1,e_3,e_2) )],[refute_0_199,refute_0_172]) ).
cnf(refute_0_201,plain,
( equalish(e_2,e_3)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[$cnf( product(e_3,e_2,e_2) )],[refute_0_200,refute_0_171]) ).
cnf(refute_0_202,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[$cnf( equalish(e_2,e_3) )],[refute_0_201,e_2_is_not_e_3]) ).
cnf(refute_0_203,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolve,[$cnf( product(e_2,e_2,e_1) )],[refute_0_202,refute_0_120]) ).
cnf(refute_0_204,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_2,e_4) ),
inference(resolve,[$cnf( product(e_2,e_1,e_2) )],[refute_0_203,refute_0_119]) ).
cnf(refute_0_205,plain,
( equalish(e_1,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_1)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( product(e_2,e_2,e_4) )],[refute_0_204,refute_0_118]) ).
cnf(refute_0_206,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_1)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_205,e_1_is_not_e_2]) ).
cnf(refute_0_207,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_1) ),
inference(resolve,[$cnf( product(e_2,e_1,e_1) )],[refute_0_206,refute_0_113]) ).
cnf(refute_0_208,plain,
( equalish(e_1,e_3)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(resolve,[$cnf( product(e_1,e_3,e_1) )],[refute_0_207,refute_0_115]) ).
cnf(refute_0_209,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(resolve,[$cnf( equalish(e_1,e_3) )],[refute_0_208,e_1_is_not_e_3]) ).
cnf(refute_0_210,plain,
( ~ product(Z,e_2,e_3)
| equalish(e_1,Z)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(resolve,[$cnf( product(e_1,e_2,e_3) )],[refute_0_209,refute_0_114]) ).
cnf(refute_0_211,plain,
( ~ product(e_2,e_2,e_3)
| equalish(e_1,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(subst,[],[refute_0_210:[bind(Z,$fot(e_2))]]) ).
cnf(refute_0_212,plain,
( ~ product(Y,e_1,e_2)
| ~ product(e_1,e_2,e_3)
| product(e_2,Y,e_3) ),
inference(subst,[],[qg3:[bind(X,$fot(e_1)),bind(Z1,$fot(e_2)),bind(Z2,$fot(e_3))]]) ).
cnf(refute_0_213,plain,
( ~ product(Y,e_1,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_2,Y,e_3) ),
inference(resolve,[$cnf( product(e_1,e_2,e_3) )],[refute_0_209,refute_0_212]) ).
cnf(refute_0_214,plain,
( ~ product(e_2,e_1,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(subst,[],[refute_0_213:[bind(Y,$fot(e_2))]]) ).
cnf(refute_0_215,plain,
( ~ product(e_2,Z,e_3)
| ~ product(e_2,e_1,e_3)
| equalish(e_1,Z) ),
inference(subst,[],[product_right_cancellation:[bind(W,$fot(e_1)),bind(X,$fot(e_2)),bind(Y,$fot(e_3))]]) ).
cnf(refute_0_216,plain,
( ~ product(e_2,Z,e_3)
| equalish(e_1,Z)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolve,[$cnf( product(e_2,e_1,e_3) )],[refute_0_34,refute_0_215]) ).
cnf(refute_0_217,plain,
( ~ product(e_2,e_3,e_3)
| equalish(e_1,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(subst,[],[refute_0_216:[bind(Z,$fot(e_3))]]) ).
cnf(refute_0_218,plain,
( ~ product(e_2,e_4,e_3)
| equalish(e_1,e_4)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(subst,[],[refute_0_216:[bind(Z,$fot(e_4))]]) ).
cnf(refute_0_219,plain,
( ~ product(Z,e_1,e_1)
| ~ product(e_1,e_1,e_1)
| equalish(e_1,Z) ),
inference(subst,[],[product_left_cancellation:[bind(W,$fot(e_1)),bind(X,$fot(e_1)),bind(Y,$fot(e_1))]]) ).
cnf(refute_0_220,plain,
( ~ product(Z,e_1,e_1)
| equalish(e_1,Z) ),
inference(resolve,[$cnf( product(e_1,e_1,e_1) )],[refute_0_107,refute_0_219]) ).
cnf(refute_0_221,plain,
( ~ product(e_3,e_1,e_1)
| equalish(e_1,e_3) ),
inference(subst,[],[refute_0_220:[bind(Z,$fot(e_3))]]) ).
cnf(refute_0_222,plain,
( ~ product(e_3,e_1,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_2,e_3,e_3) ),
inference(subst,[],[refute_0_213:[bind(Y,$fot(e_3))]]) ).
cnf(refute_0_223,plain,
( ~ product(e_4,e_1,e_1)
| equalish(e_1,e_4) ),
inference(subst,[],[refute_0_220:[bind(Z,$fot(e_4))]]) ).
cnf(refute_0_224,plain,
( ~ product(e_1,e_2,Z2)
| ~ product(e_4,e_1,e_2)
| product(e_2,e_4,Z2) ),
inference(subst,[],[qg3:[bind(X,$fot(e_1)),bind(Y,$fot(e_4)),bind(Z1,$fot(e_2))]]) ).
cnf(refute_0_225,plain,
( ~ product(e_4,e_1,e_3)
| equalish(e_2,e_4)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(subst,[],[refute_0_64:[bind(Z,$fot(e_4))]]) ).
cnf(refute_0_226,plain,
( ~ group_element(e_1)
| product(e_4,e_1,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4) ),
inference(subst,[],[refute_0_134:[bind(X_34,$fot(e_1))]]) ).
cnf(refute_0_227,plain,
( product(e_4,e_1,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_226]) ).
cnf(refute_0_228,plain,
( ~ product(W,e_1,e_4)
| ~ product(e_3,e_1,e_4)
| equalish(W,e_3) ),
inference(subst,[],[product_left_cancellation:[bind(X,$fot(e_4)),bind(Y,$fot(e_1)),bind(Z,$fot(e_3))]]) ).
cnf(refute_0_229,plain,
( ~ product(W,e_1,e_4)
| equalish(W,e_3)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(resolve,[$cnf( product(e_3,e_1,e_4) )],[refute_0_74,refute_0_228]) ).
cnf(refute_0_230,plain,
( ~ product(e_4,e_1,e_4)
| equalish(e_4,e_3)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(subst,[],[refute_0_229:[bind(W,$fot(e_4))]]) ).
cnf(refute_0_231,plain,
( equalish(e_4,e_3)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_4,e_1,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3) ),
inference(resolve,[$cnf( product(e_4,e_1,e_4) )],[refute_0_227,refute_0_230]) ).
cnf(refute_0_232,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_4,e_1,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3) ),
inference(resolve,[$cnf( equalish(e_4,e_3) )],[refute_0_231,e_4_is_not_e_3]) ).
cnf(refute_0_233,plain,
( equalish(e_2,e_4)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_4,e_1,e_1)
| product(e_4,e_1,e_2) ),
inference(resolve,[$cnf( product(e_4,e_1,e_3) )],[refute_0_232,refute_0_225]) ).
cnf(refute_0_234,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_4,e_1,e_1)
| product(e_4,e_1,e_2) ),
inference(resolve,[$cnf( equalish(e_2,e_4) )],[refute_0_233,e_2_is_not_e_4]) ).
cnf(refute_0_235,plain,
( ~ product(e_1,e_2,Z2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_4,Z2)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_4,e_1,e_1) ),
inference(resolve,[$cnf( product(e_4,e_1,e_2) )],[refute_0_234,refute_0_224]) ).
cnf(refute_0_236,plain,
( ~ product(e_1,e_2,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_4,e_3)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_4,e_1,e_1) ),
inference(subst,[],[refute_0_235:[bind(Z2,$fot(e_3))]]) ).
cnf(refute_0_237,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_4,e_3)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_4,e_1,e_1) ),
inference(resolve,[$cnf( product(e_1,e_2,e_3) )],[refute_0_209,refute_0_236]) ).
cnf(refute_0_238,plain,
( equalish(e_1,e_4)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_4,e_3)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(resolve,[$cnf( product(e_4,e_1,e_1) )],[refute_0_237,refute_0_223]) ).
cnf(refute_0_239,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_4,e_3)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(resolve,[$cnf( equalish(e_1,e_4) )],[refute_0_238,e_1_is_not_e_4]) ).
cnf(refute_0_240,plain,
( equalish(e_2,e_3)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_4,e_3)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2) ),
inference(resolve,[$cnf( product(e_3,e_1,e_3) )],[refute_0_239,refute_0_65]) ).
cnf(refute_0_241,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_4,e_3)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2) ),
inference(resolve,[$cnf( equalish(e_2,e_3) )],[refute_0_240,e_2_is_not_e_3]) ).
cnf(refute_0_242,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_3,e_3)
| product(e_2,e_4,e_3)
| product(e_3,e_1,e_1) ),
inference(resolve,[$cnf( product(e_3,e_1,e_2) )],[refute_0_241,refute_0_222]) ).
cnf(refute_0_243,plain,
( equalish(e_1,e_3)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_3,e_3)
| product(e_2,e_4,e_3) ),
inference(resolve,[$cnf( product(e_3,e_1,e_1) )],[refute_0_242,refute_0_221]) ).
cnf(refute_0_244,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_3,e_3)
| product(e_2,e_4,e_3) ),
inference(resolve,[$cnf( equalish(e_1,e_3) )],[refute_0_243,e_1_is_not_e_3]) ).
cnf(refute_0_245,plain,
( equalish(e_1,e_4)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_3,e_3) ),
inference(resolve,[$cnf( product(e_2,e_4,e_3) )],[refute_0_244,refute_0_218]) ).
cnf(refute_0_246,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_3,e_3) ),
inference(resolve,[$cnf( equalish(e_1,e_4) )],[refute_0_245,e_1_is_not_e_4]) ).
cnf(refute_0_247,plain,
( equalish(e_1,e_3)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolve,[$cnf( product(e_2,e_3,e_3) )],[refute_0_246,refute_0_217]) ).
cnf(refute_0_248,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolve,[$cnf( equalish(e_1,e_3) )],[refute_0_247,e_1_is_not_e_3]) ).
cnf(refute_0_249,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_2,e_3) ),
inference(resolve,[$cnf( product(e_2,e_1,e_2) )],[refute_0_248,refute_0_214]) ).
cnf(refute_0_250,plain,
( equalish(e_1,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( product(e_2,e_2,e_3) )],[refute_0_249,refute_0_211]) ).
cnf(refute_0_251,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_250,e_1_is_not_e_2]) ).
cnf(refute_0_252,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(resolve,[$cnf( product(e_2,e_1,e_1) )],[refute_0_251,refute_0_113]) ).
cnf(refute_0_253,plain,
( ~ product(e_1,e_2,Z)
| equalish(e_2,Z)
| product(e_1,e_2,e_1) ),
inference(resolve,[$cnf( product(e_1,e_2,e_2) )],[refute_0_252,refute_0_110]) ).
cnf(refute_0_254,plain,
( ~ product(e_1,e_2,e_3)
| equalish(e_2,e_3)
| product(e_1,e_2,e_1) ),
inference(subst,[],[refute_0_253:[bind(Z,$fot(e_3))]]) ).
cnf(refute_0_255,plain,
( ~ product(Z,e_2,e_2)
| ~ product(e_1,e_2,e_2)
| equalish(e_1,Z) ),
inference(subst,[],[product_left_cancellation:[bind(W,$fot(e_1)),bind(X,$fot(e_2)),bind(Y,$fot(e_2))]]) ).
cnf(refute_0_256,plain,
( ~ product(Z,e_2,e_2)
| equalish(e_1,Z)
| product(e_1,e_2,e_1) ),
inference(resolve,[$cnf( product(e_1,e_2,e_2) )],[refute_0_252,refute_0_255]) ).
cnf(refute_0_257,plain,
( ~ product(e_2,e_2,e_2)
| equalish(e_1,e_2)
| product(e_1,e_2,e_1) ),
inference(subst,[],[refute_0_256:[bind(Z,$fot(e_2))]]) ).
cnf(refute_0_258,plain,
( ~ product(Y,e_1,e_2)
| ~ product(e_1,e_2,e_2)
| product(e_2,Y,e_2) ),
inference(subst,[],[qg3:[bind(X,$fot(e_1)),bind(Z1,$fot(e_2)),bind(Z2,$fot(e_2))]]) ).
cnf(refute_0_259,plain,
( ~ product(Y,e_1,e_2)
| product(e_1,e_2,e_1)
| product(e_2,Y,e_2) ),
inference(resolve,[$cnf( product(e_1,e_2,e_2) )],[refute_0_252,refute_0_258]) ).
cnf(refute_0_260,plain,
( ~ product(e_2,e_1,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(subst,[],[refute_0_259:[bind(Y,$fot(e_2))]]) ).
cnf(refute_0_261,plain,
( ~ product(e_2,e_2,e_3)
| equalish(e_1,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(subst,[],[refute_0_216:[bind(Z,$fot(e_2))]]) ).
cnf(refute_0_262,plain,
( ~ product(X_26,e_2,e_2)
| ~ product(e_2,e_2,e_4)
| product(e_2,X_26,e_4) ),
inference(subst,[],[qg3:[bind(X,$fot(e_2)),bind(Y,$fot(X_26)),bind(Z1,$fot(e_2)),bind(Z2,$fot(e_4))]]) ).
cnf(refute_0_263,plain,
( ~ product(X_26,e_2,e_2)
| product(e_2,X_26,e_4)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(resolve,[$cnf( product(e_2,e_2,e_4) )],[refute_0_125,refute_0_262]) ).
cnf(refute_0_264,plain,
( ~ product(e_1,e_2,e_2)
| product(e_2,e_1,e_4)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(subst,[],[refute_0_263:[bind(X_26,$fot(e_1))]]) ).
cnf(refute_0_265,plain,
( product(e_1,e_2,e_1)
| product(e_2,e_1,e_4)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(resolve,[$cnf( product(e_1,e_2,e_2) )],[refute_0_252,refute_0_264]) ).
cnf(refute_0_266,plain,
( equalish(e_1,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_4)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(resolve,[$cnf( product(e_2,e_2,e_3) )],[refute_0_265,refute_0_261]) ).
cnf(refute_0_267,plain,
( product(e_1,e_2,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_4)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_266,e_1_is_not_e_2]) ).
cnf(refute_0_268,plain,
( equalish(e_1,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_4)
| product(e_2,e_2,e_1) ),
inference(resolve,[$cnf( product(e_2,e_2,e_2) )],[refute_0_267,refute_0_257]) ).
cnf(refute_0_269,plain,
( product(e_1,e_2,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_4)
| product(e_2,e_2,e_1) ),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_268,e_1_is_not_e_2]) ).
cnf(refute_0_270,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_4) ),
inference(resolve,[$cnf( product(e_2,e_2,e_1) )],[refute_0_269,refute_0_120]) ).
cnf(refute_0_271,plain,
( equalish(e_3,e_4)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolve,[$cnf( product(e_2,e_1,e_4) )],[refute_0_270,refute_0_40]) ).
cnf(refute_0_272,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolve,[$cnf( equalish(e_3,e_4) )],[refute_0_271,e_3_is_not_e_4]) ).
cnf(refute_0_273,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_2,e_2) ),
inference(resolve,[$cnf( product(e_2,e_1,e_2) )],[refute_0_272,refute_0_260]) ).
cnf(refute_0_274,plain,
( equalish(e_1,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_3)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( product(e_2,e_2,e_2) )],[refute_0_273,refute_0_257]) ).
cnf(refute_0_275,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_3)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_274,e_1_is_not_e_2]) ).
cnf(refute_0_276,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_3) ),
inference(resolve,[$cnf( product(e_2,e_1,e_1) )],[refute_0_275,refute_0_113]) ).
cnf(refute_0_277,plain,
( equalish(e_2,e_3)
| product(e_1,e_2,e_1) ),
inference(resolve,[$cnf( product(e_1,e_2,e_3) )],[refute_0_276,refute_0_254]) ).
cnf(refute_0_278,plain,
product(e_1,e_2,e_1),
inference(resolve,[$cnf( equalish(e_2,e_3) )],[refute_0_277,e_2_is_not_e_3]) ).
cnf(refute_0_279,plain,
equalish(e_1,e_2),
inference(resolve,[$cnf( product(e_1,e_2,e_1) )],[refute_0_278,refute_0_109]) ).
cnf(refute_0_280,plain,
$false,
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_279,e_1_is_not_e_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP129-2.004 : TPTP v8.1.0. Released v1.2.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n025.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 : Tue Jun 14 08:42:54 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 38.49/38.66 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 38.49/38.66
% 38.49/38.66 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 38.49/38.68
%------------------------------------------------------------------------------