TSTP Solution File: GRP129-4.004 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP129-4.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 10:36:50 EDT 2022
% Result : Unsatisfiable 39.10s 39.27s
% Output : CNFRefutation 39.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 23
% Syntax : Number of clauses : 281 ( 18 unt; 210 nHn; 281 RR)
% Number of literals : 1104 ( 0 equ; 194 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 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(row_surjectivity,axiom,
( ~ group_element(X)
| ~ group_element(Y)
| product(e_1,X,Y)
| product(e_2,X,Y)
| product(e_3,X,Y)
| product(e_4,X,Y) ) ).
cnf(column_surjectivity,axiom,
( ~ group_element(X)
| ~ group_element(Y)
| product(X,e_1,Y)
| product(X,e_2,Y)
| product(X,e_3,Y)
| product(X,e_4,Y) ) ).
cnf(qg3_1,negated_conjecture,
( product(Y,X,Z1)
| ~ product(Z1,Y,Z2)
| ~ product(X,Z1,Z2) ) ).
cnf(qg3_2,negated_conjecture,
( product(X,Z1,Z2)
| ~ product(Z1,Y,Z2)
| ~ product(Y,X,Z1) ) ).
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_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,e_1,Z)
| ~ product(e_1,e_1,e_1)
| equalish(e_1,Z) ),
inference(subst,[],[product_total_function2:[bind(W,$fot(e_1)),bind(X,$fot(e_1)),bind(Y,$fot(e_1))]]) ).
cnf(refute_0_1,plain,
( ~ product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(subst,[],[qg3_1:[bind(X,$fot(e_1)),bind(Y,$fot(e_1)),bind(Z1,$fot(e_1)),bind(Z2,$fot(e_2))]]) ).
cnf(refute_0_2,plain,
( ~ product(e_1,e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(subst,[],[qg3_1:[bind(X,$fot(e_1)),bind(Y,$fot(e_1)),bind(Z1,$fot(e_1)),bind(Z2,$fot(e_3))]]) ).
cnf(refute_0_3,plain,
( ~ product(e_1,e_1,e_4)
| product(e_1,e_1,e_1) ),
inference(subst,[],[qg3_1:[bind(X,$fot(e_1)),bind(Y,$fot(e_1)),bind(Z1,$fot(e_1)),bind(Z2,$fot(e_4))]]) ).
cnf(refute_0_4,plain,
( ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_4) ),
inference(subst,[],[product_total_function1:[bind(X,$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,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3) ),
inference(resolve,[$cnf( product(e_1,e_1,e_4) )],[refute_0_5,refute_0_3]) ).
cnf(refute_0_7,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(resolve,[$cnf( product(e_1,e_1,e_3) )],[refute_0_6,refute_0_2]) ).
cnf(refute_0_8,plain,
product(e_1,e_1,e_1),
inference(resolve,[$cnf( product(e_1,e_1,e_2) )],[refute_0_7,refute_0_1]) ).
cnf(refute_0_9,plain,
( ~ product(e_1,e_1,Z)
| equalish(e_1,Z) ),
inference(resolve,[$cnf( product(e_1,e_1,e_1) )],[refute_0_8,refute_0_0]) ).
cnf(refute_0_10,plain,
( ~ product(e_1,e_1,e_4)
| equalish(e_1,e_4) ),
inference(subst,[],[refute_0_9:[bind(Z,$fot(e_4))]]) ).
cnf(refute_0_11,plain,
( ~ product(e_2,Z,e_4)
| ~ product(e_2,e_3,e_4)
| equalish(e_3,Z) ),
inference(subst,[],[product_right_cancellation:[bind(W,$fot(e_3)),bind(X,$fot(e_2)),bind(Y,$fot(e_4))]]) ).
cnf(refute_0_12,plain,
( ~ product(e_3,e_3,e_4)
| product(e_3,e_3,e_3) ),
inference(subst,[],[qg3_1:[bind(X,$fot(e_3)),bind(Y,$fot(e_3)),bind(Z1,$fot(e_3)),bind(Z2,$fot(e_4))]]) ).
cnf(refute_0_13,plain,
( ~ product(e_4,W,e_4)
| ~ product(e_4,e_3,e_4)
| equalish(W,e_3) ),
inference(subst,[],[product_right_cancellation:[bind(X,$fot(e_4)),bind(Y,$fot(e_4)),bind(Z,$fot(e_3))]]) ).
cnf(refute_0_14,plain,
( ~ group_element(X_76)
| ~ group_element(e_4)
| product(e_1,X_76,e_4)
| product(e_2,X_76,e_4)
| product(e_3,X_76,e_4)
| product(e_4,X_76,e_4) ),
inference(subst,[],[row_surjectivity:[bind(X,$fot(X_76)),bind(Y,$fot(e_4))]]) ).
cnf(refute_0_15,plain,
( ~ group_element(X_76)
| product(e_1,X_76,e_4)
| product(e_2,X_76,e_4)
| product(e_3,X_76,e_4)
| product(e_4,X_76,e_4) ),
inference(resolve,[$cnf( group_element(e_4) )],[element_4,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ group_element(e_3)
| product(e_1,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_3,e_3,e_4)
| product(e_4,e_3,e_4) ),
inference(subst,[],[refute_0_15:[bind(X_76,$fot(e_3))]]) ).
cnf(refute_0_17,plain,
( product(e_1,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_3,e_3,e_4)
| product(e_4,e_3,e_4) ),
inference(resolve,[$cnf( group_element(e_3) )],[element_3,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ product(e_4,W,e_4)
| equalish(W,e_3)
| product(e_1,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_3,e_3,e_4) ),
inference(resolve,[$cnf( product(e_4,e_3,e_4) )],[refute_0_17,refute_0_13]) ).
cnf(refute_0_19,plain,
( ~ product(e_4,e_4,e_4)
| equalish(e_4,e_3)
| product(e_1,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_3,e_3,e_4) ),
inference(subst,[],[refute_0_18:[bind(W,$fot(e_4))]]) ).
cnf(refute_0_20,plain,
( ~ product(e_4,e_4,e_1)
| product(e_4,e_4,e_4) ),
inference(subst,[],[qg3_1:[bind(X,$fot(e_4)),bind(Y,$fot(e_4)),bind(Z1,$fot(e_4)),bind(Z2,$fot(e_1))]]) ).
cnf(refute_0_21,plain,
( ~ product(e_4,e_4,e_2)
| product(e_4,e_4,e_4) ),
inference(subst,[],[qg3_1:[bind(X,$fot(e_4)),bind(Y,$fot(e_4)),bind(Z1,$fot(e_4)),bind(Z2,$fot(e_2))]]) ).
cnf(refute_0_22,plain,
( ~ product(e_4,e_4,e_3)
| product(e_4,e_4,e_4) ),
inference(subst,[],[qg3_1:[bind(X,$fot(e_4)),bind(Y,$fot(e_4)),bind(Z1,$fot(e_4)),bind(Z2,$fot(e_3))]]) ).
cnf(refute_0_23,plain,
( ~ product(e_4,W,e_4)
| ~ product(e_4,e_4,e_4)
| equalish(W,e_4) ),
inference(subst,[],[product_right_cancellation:[bind(X,$fot(e_4)),bind(Y,$fot(e_4)),bind(Z,$fot(e_4))]]) ).
cnf(refute_0_24,plain,
( ~ group_element(e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_4) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(e_4)),bind(Y,$fot(e_4))]]) ).
cnf(refute_0_25,plain,
( product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_4) ),
inference(resolve,[$cnf( group_element(e_4) )],[element_4,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ product(e_4,W,e_4)
| equalish(W,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3) ),
inference(resolve,[$cnf( product(e_4,e_4,e_4) )],[refute_0_25,refute_0_23]) ).
cnf(refute_0_27,plain,
( ~ product(e_4,e_3,e_4)
| equalish(e_3,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3) ),
inference(subst,[],[refute_0_26:[bind(W,$fot(e_3))]]) ).
cnf(refute_0_28,plain,
( equalish(e_3,e_4)
| product(e_1,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_3,e_3,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3) ),
inference(resolve,[$cnf( product(e_4,e_3,e_4) )],[refute_0_17,refute_0_27]) ).
cnf(refute_0_29,plain,
( product(e_1,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_3,e_3,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3) ),
inference(resolve,[$cnf( equalish(e_3,e_4) )],[refute_0_28,e_3_is_not_e_4]) ).
cnf(refute_0_30,plain,
( product(e_1,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_3,e_3,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_4) ),
inference(resolve,[$cnf( product(e_4,e_4,e_3) )],[refute_0_29,refute_0_22]) ).
cnf(refute_0_31,plain,
( equalish(e_4,e_3)
| product(e_1,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_3,e_3,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2) ),
inference(resolve,[$cnf( product(e_4,e_4,e_4) )],[refute_0_30,refute_0_19]) ).
cnf(refute_0_32,plain,
( product(e_1,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_3,e_3,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2) ),
inference(resolve,[$cnf( equalish(e_4,e_3) )],[refute_0_31,e_4_is_not_e_3]) ).
cnf(refute_0_33,plain,
( product(e_1,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_3,e_3,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_4) ),
inference(resolve,[$cnf( product(e_4,e_4,e_2) )],[refute_0_32,refute_0_21]) ).
cnf(refute_0_34,plain,
( equalish(e_4,e_3)
| product(e_1,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_3,e_3,e_4)
| product(e_4,e_4,e_1) ),
inference(resolve,[$cnf( product(e_4,e_4,e_4) )],[refute_0_33,refute_0_19]) ).
cnf(refute_0_35,plain,
( product(e_1,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_3,e_3,e_4)
| product(e_4,e_4,e_1) ),
inference(resolve,[$cnf( equalish(e_4,e_3) )],[refute_0_34,e_4_is_not_e_3]) ).
cnf(refute_0_36,plain,
( product(e_1,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_3,e_3,e_4)
| product(e_4,e_4,e_4) ),
inference(resolve,[$cnf( product(e_4,e_4,e_1) )],[refute_0_35,refute_0_20]) ).
cnf(refute_0_37,plain,
( equalish(e_4,e_3)
| product(e_1,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_3,e_3,e_4) ),
inference(resolve,[$cnf( product(e_4,e_4,e_4) )],[refute_0_36,refute_0_19]) ).
cnf(refute_0_38,plain,
( product(e_1,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_3,e_3,e_4) ),
inference(resolve,[$cnf( equalish(e_4,e_3) )],[refute_0_37,e_4_is_not_e_3]) ).
cnf(refute_0_39,plain,
( product(e_1,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_3,e_3,e_3) ),
inference(resolve,[$cnf( product(e_3,e_3,e_4) )],[refute_0_38,refute_0_12]) ).
cnf(refute_0_40,plain,
( ~ product(e_3,e_3,W)
| ~ product(e_3,e_3,e_4)
| equalish(W,e_4) ),
inference(subst,[],[product_total_function2:[bind(X,$fot(e_3)),bind(Y,$fot(e_3)),bind(Z,$fot(e_4))]]) ).
cnf(refute_0_41,plain,
( ~ product(e_3,e_3,W)
| equalish(W,e_4)
| product(e_1,e_3,e_4)
| product(e_2,e_3,e_4) ),
inference(resolve,[$cnf( product(e_3,e_3,e_4) )],[refute_0_38,refute_0_40]) ).
cnf(refute_0_42,plain,
( ~ product(e_3,e_3,e_3)
| equalish(e_3,e_4)
| product(e_1,e_3,e_4)
| product(e_2,e_3,e_4) ),
inference(subst,[],[refute_0_41:[bind(W,$fot(e_3))]]) ).
cnf(refute_0_43,plain,
( equalish(e_3,e_4)
| product(e_1,e_3,e_4)
| product(e_2,e_3,e_4) ),
inference(resolve,[$cnf( product(e_3,e_3,e_3) )],[refute_0_39,refute_0_42]) ).
cnf(refute_0_44,plain,
( product(e_1,e_3,e_4)
| product(e_2,e_3,e_4) ),
inference(resolve,[$cnf( equalish(e_3,e_4) )],[refute_0_43,e_3_is_not_e_4]) ).
cnf(refute_0_45,plain,
( ~ product(e_2,Z,e_4)
| equalish(e_3,Z)
| product(e_1,e_3,e_4) ),
inference(resolve,[$cnf( product(e_2,e_3,e_4) )],[refute_0_44,refute_0_11]) ).
cnf(refute_0_46,plain,
( ~ product(e_2,e_1,e_4)
| equalish(e_3,e_1)
| product(e_1,e_3,e_4) ),
inference(subst,[],[refute_0_45:[bind(Z,$fot(e_1))]]) ).
cnf(refute_0_47,plain,
( ~ product(e_3,e_1,Z)
| ~ product(e_3,e_1,e_4)
| equalish(e_4,Z) ),
inference(subst,[],[product_total_function2:[bind(W,$fot(e_4)),bind(X,$fot(e_3)),bind(Y,$fot(e_1))]]) ).
cnf(refute_0_48,plain,
( ~ product(e_4,Z,e_4)
| ~ product(e_4,e_1,e_4)
| equalish(e_1,Z) ),
inference(subst,[],[product_right_cancellation:[bind(W,$fot(e_1)),bind(X,$fot(e_4)),bind(Y,$fot(e_4))]]) ).
cnf(refute_0_49,plain,
( ~ group_element(e_1)
| product(e_1,e_1,e_4)
| product(e_2,e_1,e_4)
| product(e_3,e_1,e_4)
| product(e_4,e_1,e_4) ),
inference(subst,[],[refute_0_15:[bind(X_76,$fot(e_1))]]) ).
cnf(refute_0_50,plain,
( product(e_1,e_1,e_4)
| product(e_2,e_1,e_4)
| product(e_3,e_1,e_4)
| product(e_4,e_1,e_4) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_49]) ).
cnf(refute_0_51,plain,
( ~ product(e_4,Z,e_4)
| equalish(e_1,Z)
| product(e_1,e_1,e_4)
| product(e_2,e_1,e_4)
| product(e_3,e_1,e_4) ),
inference(resolve,[$cnf( product(e_4,e_1,e_4) )],[refute_0_50,refute_0_48]) ).
cnf(refute_0_52,plain,
( ~ product(e_4,e_4,e_4)
| equalish(e_1,e_4)
| product(e_1,e_1,e_4)
| product(e_2,e_1,e_4)
| product(e_3,e_1,e_4) ),
inference(subst,[],[refute_0_51:[bind(Z,$fot(e_4))]]) ).
cnf(refute_0_53,plain,
( ~ product(e_4,e_1,e_4)
| equalish(e_1,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3) ),
inference(subst,[],[refute_0_26:[bind(W,$fot(e_1))]]) ).
cnf(refute_0_54,plain,
( equalish(e_1,e_4)
| product(e_1,e_1,e_4)
| product(e_2,e_1,e_4)
| product(e_3,e_1,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3) ),
inference(resolve,[$cnf( product(e_4,e_1,e_4) )],[refute_0_50,refute_0_53]) ).
cnf(refute_0_55,plain,
( product(e_1,e_1,e_4)
| product(e_2,e_1,e_4)
| product(e_3,e_1,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3) ),
inference(resolve,[$cnf( equalish(e_1,e_4) )],[refute_0_54,e_1_is_not_e_4]) ).
cnf(refute_0_56,plain,
( product(e_1,e_1,e_4)
| product(e_2,e_1,e_4)
| product(e_3,e_1,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_4) ),
inference(resolve,[$cnf( product(e_4,e_4,e_3) )],[refute_0_55,refute_0_22]) ).
cnf(refute_0_57,plain,
( equalish(e_1,e_4)
| product(e_1,e_1,e_4)
| product(e_2,e_1,e_4)
| product(e_3,e_1,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2) ),
inference(resolve,[$cnf( product(e_4,e_4,e_4) )],[refute_0_56,refute_0_52]) ).
cnf(refute_0_58,plain,
( product(e_1,e_1,e_4)
| product(e_2,e_1,e_4)
| product(e_3,e_1,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2) ),
inference(resolve,[$cnf( equalish(e_1,e_4) )],[refute_0_57,e_1_is_not_e_4]) ).
cnf(refute_0_59,plain,
( product(e_1,e_1,e_4)
| product(e_2,e_1,e_4)
| product(e_3,e_1,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_4) ),
inference(resolve,[$cnf( product(e_4,e_4,e_2) )],[refute_0_58,refute_0_21]) ).
cnf(refute_0_60,plain,
( equalish(e_1,e_4)
| product(e_1,e_1,e_4)
| product(e_2,e_1,e_4)
| product(e_3,e_1,e_4)
| product(e_4,e_4,e_1) ),
inference(resolve,[$cnf( product(e_4,e_4,e_4) )],[refute_0_59,refute_0_52]) ).
cnf(refute_0_61,plain,
( product(e_1,e_1,e_4)
| product(e_2,e_1,e_4)
| product(e_3,e_1,e_4)
| product(e_4,e_4,e_1) ),
inference(resolve,[$cnf( equalish(e_1,e_4) )],[refute_0_60,e_1_is_not_e_4]) ).
cnf(refute_0_62,plain,
( product(e_1,e_1,e_4)
| product(e_2,e_1,e_4)
| product(e_3,e_1,e_4)
| product(e_4,e_4,e_4) ),
inference(resolve,[$cnf( product(e_4,e_4,e_1) )],[refute_0_61,refute_0_20]) ).
cnf(refute_0_63,plain,
( equalish(e_1,e_4)
| product(e_1,e_1,e_4)
| product(e_2,e_1,e_4)
| product(e_3,e_1,e_4) ),
inference(resolve,[$cnf( product(e_4,e_4,e_4) )],[refute_0_62,refute_0_52]) ).
cnf(refute_0_64,plain,
( product(e_1,e_1,e_4)
| product(e_2,e_1,e_4)
| product(e_3,e_1,e_4) ),
inference(resolve,[$cnf( equalish(e_1,e_4) )],[refute_0_63,e_1_is_not_e_4]) ).
cnf(refute_0_65,plain,
( ~ product(e_3,e_1,Z)
| equalish(e_4,Z)
| product(e_1,e_1,e_4)
| product(e_2,e_1,e_4) ),
inference(resolve,[$cnf( product(e_3,e_1,e_4) )],[refute_0_64,refute_0_47]) ).
cnf(refute_0_66,plain,
( ~ product(e_3,e_1,e_2)
| equalish(e_4,e_2)
| product(e_1,e_1,e_4)
| product(e_2,e_1,e_4) ),
inference(subst,[],[refute_0_65:[bind(Z,$fot(e_2))]]) ).
cnf(refute_0_67,plain,
( ~ product(X,e_2,e_4)
| ~ product(e_2,e_3,e_4)
| product(e_3,X,e_2) ),
inference(subst,[],[qg3_1:[bind(Y,$fot(e_3)),bind(Z1,$fot(e_2)),bind(Z2,$fot(e_4))]]) ).
cnf(refute_0_68,plain,
( ~ product(X,e_2,e_4)
| product(e_1,e_3,e_4)
| product(e_3,X,e_2) ),
inference(resolve,[$cnf( product(e_2,e_3,e_4) )],[refute_0_44,refute_0_67]) ).
cnf(refute_0_69,plain,
( ~ product(e_1,e_2,e_4)
| product(e_1,e_3,e_4)
| product(e_3,e_1,e_2) ),
inference(subst,[],[refute_0_68:[bind(X,$fot(e_1))]]) ).
cnf(refute_0_70,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,$fot(e_1))]]) ).
cnf(refute_0_71,plain,
( ~ product(e_1,Z,e_1)
| equalish(e_1,Z) ),
inference(resolve,[$cnf( product(e_1,e_1,e_1) )],[refute_0_8,refute_0_70]) ).
cnf(refute_0_72,plain,
( ~ product(e_1,e_4,e_1)
| equalish(e_1,e_4) ),
inference(subst,[],[refute_0_71:[bind(Z,$fot(e_4))]]) ).
cnf(refute_0_73,plain,
( ~ product(e_2,Z,e_4)
| ~ product(e_2,e_1,e_4)
| equalish(e_1,Z) ),
inference(subst,[],[product_right_cancellation:[bind(W,$fot(e_1)),bind(X,$fot(e_2)),bind(Y,$fot(e_4))]]) ).
cnf(refute_0_74,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,$fot(e_1))]]) ).
cnf(refute_0_75,plain,
( ~ product(Z,e_1,e_1)
| equalish(e_1,Z) ),
inference(resolve,[$cnf( product(e_1,e_1,e_1) )],[refute_0_8,refute_0_74]) ).
cnf(refute_0_76,plain,
( ~ product(e_3,e_1,e_1)
| equalish(e_1,e_3) ),
inference(subst,[],[refute_0_75:[bind(Z,$fot(e_3))]]) ).
cnf(refute_0_77,plain,
( ~ product(e_3,e_1,e_3)
| equalish(e_4,e_3)
| product(e_1,e_1,e_4)
| product(e_2,e_1,e_4) ),
inference(subst,[],[refute_0_65:[bind(Z,$fot(e_3))]]) ).
cnf(refute_0_78,plain,
( ~ product(Z,e_3,e_4)
| ~ product(e_1,e_3,e_4)
| equalish(e_1,Z) ),
inference(subst,[],[product_left_cancellation:[bind(W,$fot(e_1)),bind(X,$fot(e_4)),bind(Y,$fot(e_3))]]) ).
cnf(refute_0_79,plain,
( ~ product(Z,e_4,e_4)
| ~ product(e_1,e_4,e_4)
| equalish(e_1,Z) ),
inference(subst,[],[product_left_cancellation:[bind(W,$fot(e_1)),bind(X,$fot(e_4)),bind(Y,$fot(e_4))]]) ).
cnf(refute_0_80,plain,
( ~ group_element(X_89)
| ~ group_element(e_1)
| product(e_1,e_1,X_89)
| product(e_1,e_2,X_89)
| product(e_1,e_3,X_89)
| product(e_1,e_4,X_89) ),
inference(subst,[],[column_surjectivity:[bind(X,$fot(e_1)),bind(Y,$fot(X_89))]]) ).
cnf(refute_0_81,plain,
( ~ group_element(X_89)
| product(e_1,e_1,X_89)
| product(e_1,e_2,X_89)
| product(e_1,e_3,X_89)
| product(e_1,e_4,X_89) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_80]) ).
cnf(refute_0_82,plain,
( ~ group_element(e_4)
| product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_3,e_4)
| product(e_1,e_4,e_4) ),
inference(subst,[],[refute_0_81:[bind(X_89,$fot(e_4))]]) ).
cnf(refute_0_83,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_3,e_4)
| product(e_1,e_4,e_4) ),
inference(resolve,[$cnf( group_element(e_4) )],[element_4,refute_0_82]) ).
cnf(refute_0_84,plain,
( ~ product(Z,e_4,e_4)
| equalish(e_1,Z)
| product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_3,e_4) ),
inference(resolve,[$cnf( product(e_1,e_4,e_4) )],[refute_0_83,refute_0_79]) ).
cnf(refute_0_85,plain,
( ~ product(e_4,e_4,e_4)
| equalish(e_1,e_4)
| product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_3,e_4) ),
inference(subst,[],[refute_0_84:[bind(Z,$fot(e_4))]]) ).
cnf(refute_0_86,plain,
( ~ product(W,e_4,e_4)
| ~ product(e_4,e_4,e_4)
| equalish(W,e_4) ),
inference(subst,[],[product_left_cancellation:[bind(X,$fot(e_4)),bind(Y,$fot(e_4)),bind(Z,$fot(e_4))]]) ).
cnf(refute_0_87,plain,
( ~ product(W,e_4,e_4)
| equalish(W,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3) ),
inference(resolve,[$cnf( product(e_4,e_4,e_4) )],[refute_0_25,refute_0_86]) ).
cnf(refute_0_88,plain,
( ~ product(e_1,e_4,e_4)
| equalish(e_1,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3) ),
inference(subst,[],[refute_0_87:[bind(W,$fot(e_1))]]) ).
cnf(refute_0_89,plain,
( equalish(e_1,e_4)
| product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_3,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3) ),
inference(resolve,[$cnf( product(e_1,e_4,e_4) )],[refute_0_83,refute_0_88]) ).
cnf(refute_0_90,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_3,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3) ),
inference(resolve,[$cnf( equalish(e_1,e_4) )],[refute_0_89,e_1_is_not_e_4]) ).
cnf(refute_0_91,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_3,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_4) ),
inference(resolve,[$cnf( product(e_4,e_4,e_3) )],[refute_0_90,refute_0_22]) ).
cnf(refute_0_92,plain,
( equalish(e_1,e_4)
| product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_3,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2) ),
inference(resolve,[$cnf( product(e_4,e_4,e_4) )],[refute_0_91,refute_0_85]) ).
cnf(refute_0_93,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_3,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2) ),
inference(resolve,[$cnf( equalish(e_1,e_4) )],[refute_0_92,e_1_is_not_e_4]) ).
cnf(refute_0_94,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_3,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_4) ),
inference(resolve,[$cnf( product(e_4,e_4,e_2) )],[refute_0_93,refute_0_21]) ).
cnf(refute_0_95,plain,
( equalish(e_1,e_4)
| product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_3,e_4)
| product(e_4,e_4,e_1) ),
inference(resolve,[$cnf( product(e_4,e_4,e_4) )],[refute_0_94,refute_0_85]) ).
cnf(refute_0_96,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_3,e_4)
| product(e_4,e_4,e_1) ),
inference(resolve,[$cnf( equalish(e_1,e_4) )],[refute_0_95,e_1_is_not_e_4]) ).
cnf(refute_0_97,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_3,e_4)
| product(e_4,e_4,e_4) ),
inference(resolve,[$cnf( product(e_4,e_4,e_1) )],[refute_0_96,refute_0_20]) ).
cnf(refute_0_98,plain,
( equalish(e_1,e_4)
| product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_3,e_4) ),
inference(resolve,[$cnf( product(e_4,e_4,e_4) )],[refute_0_97,refute_0_85]) ).
cnf(refute_0_99,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_3,e_4) ),
inference(resolve,[$cnf( equalish(e_1,e_4) )],[refute_0_98,e_1_is_not_e_4]) ).
cnf(refute_0_100,plain,
( ~ product(Z,e_3,e_4)
| equalish(e_1,Z)
| product(e_1,e_1,e_4)
| product(e_1,e_2,e_4) ),
inference(resolve,[$cnf( product(e_1,e_3,e_4) )],[refute_0_99,refute_0_78]) ).
cnf(refute_0_101,plain,
( ~ product(e_4,e_3,e_4)
| equalish(e_1,e_4)
| product(e_1,e_1,e_4)
| product(e_1,e_2,e_4) ),
inference(subst,[],[refute_0_100:[bind(Z,$fot(e_4))]]) ).
cnf(refute_0_102,plain,
( ~ product(X_38,e_1,e_1)
| ~ product(e_1,e_1,e_1)
| product(e_1,X_38,e_1) ),
inference(subst,[],[qg3_1:[bind(X,$fot(X_38)),bind(Y,$fot(e_1)),bind(Z1,$fot(e_1)),bind(Z2,$fot(e_1))]]) ).
cnf(refute_0_103,plain,
( ~ product(X_38,e_1,e_1)
| product(e_1,X_38,e_1) ),
inference(resolve,[$cnf( product(e_1,e_1,e_1) )],[refute_0_8,refute_0_102]) ).
cnf(refute_0_104,plain,
( ~ product(e_4,e_1,e_1)
| product(e_1,e_4,e_1) ),
inference(subst,[],[refute_0_103:[bind(X_38,$fot(e_4))]]) ).
cnf(refute_0_105,plain,
( ~ product(Y,e_3,e_4)
| ~ product(e_3,e_4,e_1)
| product(e_4,Y,e_1) ),
inference(subst,[],[qg3:[bind(X,$fot(e_3)),bind(Z1,$fot(e_4)),bind(Z2,$fot(e_1))]]) ).
cnf(refute_0_106,plain,
( ~ group_element(X_77)
| ~ group_element(e_4)
| product(e_1,e_4,X_77)
| product(e_2,e_4,X_77)
| product(e_3,e_4,X_77)
| product(e_4,e_4,X_77) ),
inference(subst,[],[row_surjectivity:[bind(X,$fot(e_4)),bind(Y,$fot(X_77))]]) ).
cnf(refute_0_107,plain,
( ~ group_element(X_77)
| product(e_1,e_4,X_77)
| product(e_2,e_4,X_77)
| product(e_3,e_4,X_77)
| product(e_4,e_4,X_77) ),
inference(resolve,[$cnf( group_element(e_4) )],[element_4,refute_0_106]) ).
cnf(refute_0_108,plain,
( ~ group_element(e_1)
| product(e_1,e_4,e_1)
| product(e_2,e_4,e_1)
| product(e_3,e_4,e_1)
| product(e_4,e_4,e_1) ),
inference(subst,[],[refute_0_107:[bind(X_77,$fot(e_1))]]) ).
cnf(refute_0_109,plain,
( product(e_1,e_4,e_1)
| product(e_2,e_4,e_1)
| product(e_3,e_4,e_1)
| product(e_4,e_4,e_1) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_108]) ).
cnf(refute_0_110,plain,
( product(e_1,e_4,e_1)
| product(e_2,e_4,e_1)
| product(e_3,e_4,e_1)
| product(e_4,e_4,e_4) ),
inference(resolve,[$cnf( product(e_4,e_4,e_1) )],[refute_0_109,refute_0_20]) ).
cnf(refute_0_111,plain,
( ~ product(e_4,e_4,W)
| ~ product(e_4,e_4,e_1)
| equalish(W,e_1) ),
inference(subst,[],[product_total_function2:[bind(X,$fot(e_4)),bind(Y,$fot(e_4)),bind(Z,$fot(e_1))]]) ).
cnf(refute_0_112,plain,
( ~ product(e_4,e_4,W)
| equalish(W,e_1)
| product(e_1,e_4,e_1)
| product(e_2,e_4,e_1)
| product(e_3,e_4,e_1) ),
inference(resolve,[$cnf( product(e_4,e_4,e_1) )],[refute_0_109,refute_0_111]) ).
cnf(refute_0_113,plain,
( ~ product(e_4,e_4,e_4)
| equalish(e_4,e_1)
| product(e_1,e_4,e_1)
| product(e_2,e_4,e_1)
| product(e_3,e_4,e_1) ),
inference(subst,[],[refute_0_112:[bind(W,$fot(e_4))]]) ).
cnf(refute_0_114,plain,
( equalish(e_4,e_1)
| product(e_1,e_4,e_1)
| product(e_2,e_4,e_1)
| product(e_3,e_4,e_1) ),
inference(resolve,[$cnf( product(e_4,e_4,e_4) )],[refute_0_110,refute_0_113]) ).
cnf(refute_0_115,plain,
( product(e_1,e_4,e_1)
| product(e_2,e_4,e_1)
| product(e_3,e_4,e_1) ),
inference(resolve,[$cnf( equalish(e_4,e_1) )],[refute_0_114,e_4_is_not_e_1]) ).
cnf(refute_0_116,plain,
( ~ product(Y,e_3,e_4)
| product(e_1,e_4,e_1)
| product(e_2,e_4,e_1)
| product(e_4,Y,e_1) ),
inference(resolve,[$cnf( product(e_3,e_4,e_1) )],[refute_0_115,refute_0_105]) ).
cnf(refute_0_117,plain,
( ~ product(e_1,e_3,e_4)
| product(e_1,e_4,e_1)
| product(e_2,e_4,e_1)
| product(e_4,e_1,e_1) ),
inference(subst,[],[refute_0_116:[bind(Y,$fot(e_1))]]) ).
cnf(refute_0_118,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_4,e_1)
| product(e_2,e_4,e_1)
| product(e_4,e_1,e_1) ),
inference(resolve,[$cnf( product(e_1,e_3,e_4) )],[refute_0_99,refute_0_117]) ).
cnf(refute_0_119,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_4,e_1)
| product(e_2,e_4,e_1) ),
inference(resolve,[$cnf( product(e_4,e_1,e_1) )],[refute_0_118,refute_0_104]) ).
cnf(refute_0_120,plain,
( ~ product(e_2,e_4,W)
| ~ product(e_2,e_4,e_3)
| equalish(W,e_3) ),
inference(subst,[],[product_total_function2:[bind(X,$fot(e_2)),bind(Y,$fot(e_4)),bind(Z,$fot(e_3))]]) ).
cnf(refute_0_121,plain,
( ~ product(e_3,W,e_3)
| ~ product(e_3,e_4,e_3)
| equalish(W,e_4) ),
inference(subst,[],[product_right_cancellation:[bind(X,$fot(e_3)),bind(Y,$fot(e_3)),bind(Z,$fot(e_4))]]) ).
cnf(refute_0_122,plain,
( ~ product(e_4,W,e_3)
| ~ product(e_4,e_4,e_3)
| equalish(W,e_4) ),
inference(subst,[],[product_right_cancellation:[bind(X,$fot(e_4)),bind(Y,$fot(e_3)),bind(Z,$fot(e_4))]]) ).
cnf(refute_0_123,plain,
( ~ group_element(e_3)
| product(e_1,e_4,e_3)
| product(e_2,e_4,e_3)
| product(e_3,e_4,e_3)
| product(e_4,e_4,e_3) ),
inference(subst,[],[refute_0_107:[bind(X_77,$fot(e_3))]]) ).
cnf(refute_0_124,plain,
( product(e_1,e_4,e_3)
| product(e_2,e_4,e_3)
| product(e_3,e_4,e_3)
| product(e_4,e_4,e_3) ),
inference(resolve,[$cnf( group_element(e_3) )],[element_3,refute_0_123]) ).
cnf(refute_0_125,plain,
( ~ product(e_4,W,e_3)
| equalish(W,e_4)
| product(e_1,e_4,e_3)
| product(e_2,e_4,e_3)
| product(e_3,e_4,e_3) ),
inference(resolve,[$cnf( product(e_4,e_4,e_3) )],[refute_0_124,refute_0_122]) ).
cnf(refute_0_126,plain,
( ~ product(e_4,e_1,e_3)
| equalish(e_1,e_4)
| product(e_1,e_4,e_3)
| product(e_2,e_4,e_3)
| product(e_3,e_4,e_3) ),
inference(subst,[],[refute_0_125:[bind(W,$fot(e_1))]]) ).
cnf(refute_0_127,plain,
( ~ product(e_4,W,e_3)
| ~ product(e_4,e_3,e_3)
| equalish(W,e_3) ),
inference(subst,[],[product_right_cancellation:[bind(X,$fot(e_4)),bind(Y,$fot(e_3)),bind(Z,$fot(e_3))]]) ).
cnf(refute_0_128,plain,
( ~ group_element(X_89)
| ~ group_element(e_4)
| product(e_4,e_1,X_89)
| product(e_4,e_2,X_89)
| product(e_4,e_3,X_89)
| product(e_4,e_4,X_89) ),
inference(subst,[],[column_surjectivity:[bind(X,$fot(e_4)),bind(Y,$fot(X_89))]]) ).
cnf(refute_0_129,plain,
( ~ group_element(X_89)
| product(e_4,e_1,X_89)
| product(e_4,e_2,X_89)
| product(e_4,e_3,X_89)
| product(e_4,e_4,X_89) ),
inference(resolve,[$cnf( group_element(e_4) )],[element_4,refute_0_128]) ).
cnf(refute_0_130,plain,
( ~ group_element(e_3)
| product(e_4,e_1,e_3)
| product(e_4,e_2,e_3)
| product(e_4,e_3,e_3)
| product(e_4,e_4,e_3) ),
inference(subst,[],[refute_0_129:[bind(X_89,$fot(e_3))]]) ).
cnf(refute_0_131,plain,
( product(e_4,e_1,e_3)
| product(e_4,e_2,e_3)
| product(e_4,e_3,e_3)
| product(e_4,e_4,e_3) ),
inference(resolve,[$cnf( group_element(e_3) )],[element_3,refute_0_130]) ).
cnf(refute_0_132,plain,
( product(e_4,e_1,e_3)
| product(e_4,e_2,e_3)
| product(e_4,e_3,e_3)
| product(e_4,e_4,e_4) ),
inference(resolve,[$cnf( product(e_4,e_4,e_3) )],[refute_0_131,refute_0_22]) ).
cnf(refute_0_133,plain,
( ~ product(e_4,e_4,W)
| ~ product(e_4,e_4,e_3)
| equalish(W,e_3) ),
inference(subst,[],[product_total_function2:[bind(X,$fot(e_4)),bind(Y,$fot(e_4)),bind(Z,$fot(e_3))]]) ).
cnf(refute_0_134,plain,
( ~ product(e_4,e_4,W)
| equalish(W,e_3)
| product(e_4,e_1,e_3)
| product(e_4,e_2,e_3)
| product(e_4,e_3,e_3) ),
inference(resolve,[$cnf( product(e_4,e_4,e_3) )],[refute_0_131,refute_0_133]) ).
cnf(refute_0_135,plain,
( ~ product(e_4,e_4,e_4)
| equalish(e_4,e_3)
| product(e_4,e_1,e_3)
| product(e_4,e_2,e_3)
| product(e_4,e_3,e_3) ),
inference(subst,[],[refute_0_134:[bind(W,$fot(e_4))]]) ).
cnf(refute_0_136,plain,
( equalish(e_4,e_3)
| product(e_4,e_1,e_3)
| product(e_4,e_2,e_3)
| product(e_4,e_3,e_3) ),
inference(resolve,[$cnf( product(e_4,e_4,e_4) )],[refute_0_132,refute_0_135]) ).
cnf(refute_0_137,plain,
( product(e_4,e_1,e_3)
| product(e_4,e_2,e_3)
| product(e_4,e_3,e_3) ),
inference(resolve,[$cnf( equalish(e_4,e_3) )],[refute_0_136,e_4_is_not_e_3]) ).
cnf(refute_0_138,plain,
( ~ product(e_4,W,e_3)
| equalish(W,e_3)
| product(e_4,e_1,e_3)
| product(e_4,e_2,e_3) ),
inference(resolve,[$cnf( product(e_4,e_3,e_3) )],[refute_0_137,refute_0_127]) ).
cnf(refute_0_139,plain,
( ~ product(e_4,e_4,e_3)
| equalish(e_4,e_3)
| product(e_4,e_1,e_3)
| product(e_4,e_2,e_3) ),
inference(subst,[],[refute_0_138:[bind(W,$fot(e_4))]]) ).
cnf(refute_0_140,plain,
( equalish(e_4,e_3)
| product(e_1,e_4,e_3)
| product(e_2,e_4,e_3)
| product(e_3,e_4,e_3)
| product(e_4,e_1,e_3)
| product(e_4,e_2,e_3) ),
inference(resolve,[$cnf( product(e_4,e_4,e_3) )],[refute_0_124,refute_0_139]) ).
cnf(refute_0_141,plain,
( product(e_1,e_4,e_3)
| product(e_2,e_4,e_3)
| product(e_3,e_4,e_3)
| product(e_4,e_1,e_3)
| product(e_4,e_2,e_3) ),
inference(resolve,[$cnf( equalish(e_4,e_3) )],[refute_0_140,e_4_is_not_e_3]) ).
cnf(refute_0_142,plain,
( ~ product(e_4,e_2,e_3)
| equalish(e_2,e_4)
| product(e_1,e_4,e_3)
| product(e_2,e_4,e_3)
| product(e_3,e_4,e_3) ),
inference(subst,[],[refute_0_125:[bind(W,$fot(e_2))]]) ).
cnf(refute_0_143,plain,
( equalish(e_2,e_4)
| product(e_1,e_4,e_3)
| product(e_2,e_4,e_3)
| product(e_3,e_4,e_3)
| product(e_4,e_1,e_3) ),
inference(resolve,[$cnf( product(e_4,e_2,e_3) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
( product(e_1,e_4,e_3)
| product(e_2,e_4,e_3)
| product(e_3,e_4,e_3)
| product(e_4,e_1,e_3) ),
inference(resolve,[$cnf( equalish(e_2,e_4) )],[refute_0_143,e_2_is_not_e_4]) ).
cnf(refute_0_145,plain,
( equalish(e_1,e_4)
| product(e_1,e_4,e_3)
| product(e_2,e_4,e_3)
| product(e_3,e_4,e_3) ),
inference(resolve,[$cnf( product(e_4,e_1,e_3) )],[refute_0_144,refute_0_126]) ).
cnf(refute_0_146,plain,
( product(e_1,e_4,e_3)
| product(e_2,e_4,e_3)
| product(e_3,e_4,e_3) ),
inference(resolve,[$cnf( equalish(e_1,e_4) )],[refute_0_145,e_1_is_not_e_4]) ).
cnf(refute_0_147,plain,
( ~ product(e_3,W,e_3)
| equalish(W,e_4)
| product(e_1,e_4,e_3)
| product(e_2,e_4,e_3) ),
inference(resolve,[$cnf( product(e_3,e_4,e_3) )],[refute_0_146,refute_0_121]) ).
cnf(refute_0_148,plain,
( ~ product(e_3,e_3,e_3)
| equalish(e_3,e_4)
| product(e_1,e_4,e_3)
| product(e_2,e_4,e_3) ),
inference(subst,[],[refute_0_147:[bind(W,$fot(e_3))]]) ).
cnf(refute_0_149,plain,
( ~ product(e_3,e_3,e_1)
| product(e_3,e_3,e_3) ),
inference(subst,[],[qg3_1:[bind(X,$fot(e_3)),bind(Y,$fot(e_3)),bind(Z1,$fot(e_3)),bind(Z2,$fot(e_1))]]) ).
cnf(refute_0_150,plain,
( ~ product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(subst,[],[qg3_1:[bind(X,$fot(e_3)),bind(Y,$fot(e_3)),bind(Z1,$fot(e_3)),bind(Z2,$fot(e_2))]]) ).
cnf(refute_0_151,plain,
( ~ product(e_3,Z,e_3)
| ~ product(e_3,e_3,e_3)
| equalish(e_3,Z) ),
inference(subst,[],[product_right_cancellation:[bind(W,$fot(e_3)),bind(X,$fot(e_3)),bind(Y,$fot(e_3))]]) ).
cnf(refute_0_152,plain,
( ~ group_element(e_3)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_4) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(e_3)),bind(Y,$fot(e_3))]]) ).
cnf(refute_0_153,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_4) ),
inference(resolve,[$cnf( group_element(e_3) )],[element_3,refute_0_152]) ).
cnf(refute_0_154,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(resolve,[$cnf( product(e_3,e_3,e_4) )],[refute_0_153,refute_0_12]) ).
cnf(refute_0_155,plain,
( ~ product(e_3,Z,e_3)
| equalish(e_3,Z)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_2) ),
inference(resolve,[$cnf( product(e_3,e_3,e_3) )],[refute_0_154,refute_0_151]) ).
cnf(refute_0_156,plain,
( ~ product(e_3,e_4,e_3)
| equalish(e_3,e_4)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_2) ),
inference(subst,[],[refute_0_155:[bind(Z,$fot(e_4))]]) ).
cnf(refute_0_157,plain,
( equalish(e_3,e_4)
| product(e_1,e_4,e_3)
| product(e_2,e_4,e_3)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_2) ),
inference(resolve,[$cnf( product(e_3,e_4,e_3) )],[refute_0_146,refute_0_156]) ).
cnf(refute_0_158,plain,
( product(e_1,e_4,e_3)
| product(e_2,e_4,e_3)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_2) ),
inference(resolve,[$cnf( equalish(e_3,e_4) )],[refute_0_157,e_3_is_not_e_4]) ).
cnf(refute_0_159,plain,
( product(e_1,e_4,e_3)
| product(e_2,e_4,e_3)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_3) ),
inference(resolve,[$cnf( product(e_3,e_3,e_2) )],[refute_0_158,refute_0_150]) ).
cnf(refute_0_160,plain,
( equalish(e_3,e_4)
| product(e_1,e_4,e_3)
| product(e_2,e_4,e_3)
| product(e_3,e_3,e_1) ),
inference(resolve,[$cnf( product(e_3,e_3,e_3) )],[refute_0_159,refute_0_148]) ).
cnf(refute_0_161,plain,
( product(e_1,e_4,e_3)
| product(e_2,e_4,e_3)
| product(e_3,e_3,e_1) ),
inference(resolve,[$cnf( equalish(e_3,e_4) )],[refute_0_160,e_3_is_not_e_4]) ).
cnf(refute_0_162,plain,
( product(e_1,e_4,e_3)
| product(e_2,e_4,e_3)
| product(e_3,e_3,e_3) ),
inference(resolve,[$cnf( product(e_3,e_3,e_1) )],[refute_0_161,refute_0_149]) ).
cnf(refute_0_163,plain,
( equalish(e_3,e_4)
| product(e_1,e_4,e_3)
| product(e_2,e_4,e_3) ),
inference(resolve,[$cnf( product(e_3,e_3,e_3) )],[refute_0_162,refute_0_148]) ).
cnf(refute_0_164,plain,
( product(e_1,e_4,e_3)
| product(e_2,e_4,e_3) ),
inference(resolve,[$cnf( equalish(e_3,e_4) )],[refute_0_163,e_3_is_not_e_4]) ).
cnf(refute_0_165,plain,
( ~ product(e_2,e_4,W)
| equalish(W,e_3)
| product(e_1,e_4,e_3) ),
inference(resolve,[$cnf( product(e_2,e_4,e_3) )],[refute_0_164,refute_0_120]) ).
cnf(refute_0_166,plain,
( ~ product(e_2,e_4,e_1)
| equalish(e_1,e_3)
| product(e_1,e_4,e_3) ),
inference(subst,[],[refute_0_165:[bind(W,$fot(e_1))]]) ).
cnf(refute_0_167,plain,
( equalish(e_1,e_3)
| product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_4,e_1)
| product(e_1,e_4,e_3) ),
inference(resolve,[$cnf( product(e_2,e_4,e_1) )],[refute_0_119,refute_0_166]) ).
cnf(refute_0_168,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_4,e_1)
| product(e_1,e_4,e_3) ),
inference(resolve,[$cnf( equalish(e_1,e_3) )],[refute_0_167,e_1_is_not_e_3]) ).
cnf(refute_0_169,plain,
( ~ product(e_1,X,e_3)
| ~ product(e_3,e_1,e_4)
| product(X,e_3,e_4) ),
inference(subst,[],[qg3_2:[bind(Y,$fot(e_1)),bind(Z1,$fot(e_3)),bind(Z2,$fot(e_4))]]) ).
cnf(refute_0_170,plain,
( ~ group_element(X_99)
| ~ group_element(e_3)
| product(e_3,X_99,e_1)
| product(e_3,X_99,e_2)
| product(e_3,X_99,e_3)
| product(e_3,X_99,e_4) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(e_3)),bind(Y,$fot(X_99))]]) ).
cnf(refute_0_171,plain,
( ~ group_element(X_99)
| product(e_3,X_99,e_1)
| product(e_3,X_99,e_2)
| product(e_3,X_99,e_3)
| product(e_3,X_99,e_4) ),
inference(resolve,[$cnf( group_element(e_3) )],[element_3,refute_0_170]) ).
cnf(refute_0_172,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_171:[bind(X_99,$fot(e_1))]]) ).
cnf(refute_0_173,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_4) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_172]) ).
cnf(refute_0_174,plain,
( ~ product(e_1,X,e_3)
| product(X,e_3,e_4)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(resolve,[$cnf( product(e_3,e_1,e_4) )],[refute_0_173,refute_0_169]) ).
cnf(refute_0_175,plain,
( ~ product(e_1,e_4,e_3)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_4,e_3,e_4) ),
inference(subst,[],[refute_0_174:[bind(X,$fot(e_4))]]) ).
cnf(refute_0_176,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_4,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_4,e_3,e_4) ),
inference(resolve,[$cnf( product(e_1,e_4,e_3) )],[refute_0_168,refute_0_175]) ).
cnf(refute_0_177,plain,
( equalish(e_1,e_4)
| product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_4,e_1)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(resolve,[$cnf( product(e_4,e_3,e_4) )],[refute_0_176,refute_0_101]) ).
cnf(refute_0_178,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_4,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,[$cnf( equalish(e_1,e_4) )],[refute_0_177,e_1_is_not_e_4]) ).
cnf(refute_0_179,plain,
( equalish(e_4,e_3)
| product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_4,e_1)
| product(e_2,e_1,e_4)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2) ),
inference(resolve,[$cnf( product(e_3,e_1,e_3) )],[refute_0_178,refute_0_77]) ).
cnf(refute_0_180,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_4,e_1)
| product(e_2,e_1,e_4)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2) ),
inference(resolve,[$cnf( equalish(e_4,e_3) )],[refute_0_179,e_4_is_not_e_3]) ).
cnf(refute_0_181,plain,
( equalish(e_4,e_2)
| product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_4,e_1)
| product(e_2,e_1,e_4)
| product(e_3,e_1,e_1) ),
inference(resolve,[$cnf( product(e_3,e_1,e_2) )],[refute_0_180,refute_0_66]) ).
cnf(refute_0_182,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_4,e_1)
| product(e_2,e_1,e_4)
| product(e_3,e_1,e_1) ),
inference(resolve,[$cnf( equalish(e_4,e_2) )],[refute_0_181,e_4_is_not_e_2]) ).
cnf(refute_0_183,plain,
( equalish(e_1,e_3)
| product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_4,e_1)
| product(e_2,e_1,e_4) ),
inference(resolve,[$cnf( product(e_3,e_1,e_1) )],[refute_0_182,refute_0_76]) ).
cnf(refute_0_184,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_4,e_1)
| product(e_2,e_1,e_4) ),
inference(resolve,[$cnf( equalish(e_1,e_3) )],[refute_0_183,e_1_is_not_e_3]) ).
cnf(refute_0_185,plain,
( ~ product(e_2,Z,e_4)
| equalish(e_1,Z)
| product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_4,e_1) ),
inference(resolve,[$cnf( product(e_2,e_1,e_4) )],[refute_0_184,refute_0_73]) ).
cnf(refute_0_186,plain,
( ~ product(e_2,e_2,e_4)
| equalish(e_1,e_2)
| product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_4,e_1) ),
inference(subst,[],[refute_0_185:[bind(Z,$fot(e_2))]]) ).
cnf(refute_0_187,plain,
( ~ product(e_3,e_2,Z)
| ~ product(e_3,e_2,e_4)
| equalish(e_4,Z) ),
inference(subst,[],[product_total_function2:[bind(W,$fot(e_4)),bind(X,$fot(e_3)),bind(Y,$fot(e_2))]]) ).
cnf(refute_0_188,plain,
( ~ product(W,e_4,e_4)
| ~ product(e_3,e_4,e_4)
| equalish(W,e_3) ),
inference(subst,[],[product_left_cancellation:[bind(X,$fot(e_4)),bind(Y,$fot(e_4)),bind(Z,$fot(e_3))]]) ).
cnf(refute_0_189,plain,
( ~ group_element(X_88)
| ~ group_element(e_4)
| product(X_88,e_1,e_4)
| product(X_88,e_2,e_4)
| product(X_88,e_3,e_4)
| product(X_88,e_4,e_4) ),
inference(subst,[],[column_surjectivity:[bind(X,$fot(X_88)),bind(Y,$fot(e_4))]]) ).
cnf(refute_0_190,plain,
( ~ group_element(X_88)
| product(X_88,e_1,e_4)
| product(X_88,e_2,e_4)
| product(X_88,e_3,e_4)
| product(X_88,e_4,e_4) ),
inference(resolve,[$cnf( group_element(e_4) )],[element_4,refute_0_189]) ).
cnf(refute_0_191,plain,
( ~ group_element(e_3)
| product(e_3,e_1,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_3,e_4)
| product(e_3,e_4,e_4) ),
inference(subst,[],[refute_0_190:[bind(X_88,$fot(e_3))]]) ).
cnf(refute_0_192,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_3,e_4)
| product(e_3,e_4,e_4) ),
inference(resolve,[$cnf( group_element(e_3) )],[element_3,refute_0_191]) ).
cnf(refute_0_193,plain,
( ~ product(W,e_4,e_4)
| equalish(W,e_3)
| product(e_3,e_1,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_3,e_4) ),
inference(resolve,[$cnf( product(e_3,e_4,e_4) )],[refute_0_192,refute_0_188]) ).
cnf(refute_0_194,plain,
( ~ product(e_4,e_4,e_4)
| equalish(e_4,e_3)
| product(e_3,e_1,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_3,e_4) ),
inference(subst,[],[refute_0_193:[bind(W,$fot(e_4))]]) ).
cnf(refute_0_195,plain,
( ~ product(e_3,e_4,e_4)
| equalish(e_3,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3) ),
inference(subst,[],[refute_0_87:[bind(W,$fot(e_3))]]) ).
cnf(refute_0_196,plain,
( equalish(e_3,e_4)
| product(e_3,e_1,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_3,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3) ),
inference(resolve,[$cnf( product(e_3,e_4,e_4) )],[refute_0_192,refute_0_195]) ).
cnf(refute_0_197,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_3,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3) ),
inference(resolve,[$cnf( equalish(e_3,e_4) )],[refute_0_196,e_3_is_not_e_4]) ).
cnf(refute_0_198,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_3,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_4) ),
inference(resolve,[$cnf( product(e_4,e_4,e_3) )],[refute_0_197,refute_0_22]) ).
cnf(refute_0_199,plain,
( equalish(e_4,e_3)
| product(e_3,e_1,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_3,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2) ),
inference(resolve,[$cnf( product(e_4,e_4,e_4) )],[refute_0_198,refute_0_194]) ).
cnf(refute_0_200,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_3,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2) ),
inference(resolve,[$cnf( equalish(e_4,e_3) )],[refute_0_199,e_4_is_not_e_3]) ).
cnf(refute_0_201,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_3,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_4) ),
inference(resolve,[$cnf( product(e_4,e_4,e_2) )],[refute_0_200,refute_0_21]) ).
cnf(refute_0_202,plain,
( equalish(e_4,e_3)
| product(e_3,e_1,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_3,e_4)
| product(e_4,e_4,e_1) ),
inference(resolve,[$cnf( product(e_4,e_4,e_4) )],[refute_0_201,refute_0_194]) ).
cnf(refute_0_203,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_3,e_4)
| product(e_4,e_4,e_1) ),
inference(resolve,[$cnf( equalish(e_4,e_3) )],[refute_0_202,e_4_is_not_e_3]) ).
cnf(refute_0_204,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_3,e_4)
| product(e_4,e_4,e_4) ),
inference(resolve,[$cnf( product(e_4,e_4,e_1) )],[refute_0_203,refute_0_20]) ).
cnf(refute_0_205,plain,
( equalish(e_4,e_3)
| product(e_3,e_1,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_3,e_4) ),
inference(resolve,[$cnf( product(e_4,e_4,e_4) )],[refute_0_204,refute_0_194]) ).
cnf(refute_0_206,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_3,e_4) ),
inference(resolve,[$cnf( equalish(e_4,e_3) )],[refute_0_205,e_4_is_not_e_3]) ).
cnf(refute_0_207,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_3,e_3) ),
inference(resolve,[$cnf( product(e_3,e_3,e_4) )],[refute_0_206,refute_0_12]) ).
cnf(refute_0_208,plain,
( ~ product(e_3,e_3,W)
| equalish(W,e_4)
| product(e_3,e_1,e_4)
| product(e_3,e_2,e_4) ),
inference(resolve,[$cnf( product(e_3,e_3,e_4) )],[refute_0_206,refute_0_40]) ).
cnf(refute_0_209,plain,
( ~ product(e_3,e_3,e_3)
| equalish(e_3,e_4)
| product(e_3,e_1,e_4)
| product(e_3,e_2,e_4) ),
inference(subst,[],[refute_0_208:[bind(W,$fot(e_3))]]) ).
cnf(refute_0_210,plain,
( equalish(e_3,e_4)
| product(e_3,e_1,e_4)
| product(e_3,e_2,e_4) ),
inference(resolve,[$cnf( product(e_3,e_3,e_3) )],[refute_0_207,refute_0_209]) ).
cnf(refute_0_211,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_2,e_4) ),
inference(resolve,[$cnf( equalish(e_3,e_4) )],[refute_0_210,e_3_is_not_e_4]) ).
cnf(refute_0_212,plain,
( ~ product(e_3,e_2,Z)
| equalish(e_4,Z)
| product(e_3,e_1,e_4) ),
inference(resolve,[$cnf( product(e_3,e_2,e_4) )],[refute_0_211,refute_0_187]) ).
cnf(refute_0_213,plain,
( ~ product(e_3,e_2,e_1)
| equalish(e_4,e_1)
| product(e_3,e_1,e_4) ),
inference(subst,[],[refute_0_212:[bind(Z,$fot(e_1))]]) ).
cnf(refute_0_214,plain,
( ~ product(X,e_1,e_4)
| ~ product(e_1,e_3,e_4)
| product(e_3,X,e_1) ),
inference(subst,[],[qg3_1:[bind(Y,$fot(e_3)),bind(Z1,$fot(e_1)),bind(Z2,$fot(e_4))]]) ).
cnf(refute_0_215,plain,
( ~ product(X,e_1,e_4)
| product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_3,X,e_1) ),
inference(resolve,[$cnf( product(e_1,e_3,e_4) )],[refute_0_99,refute_0_214]) ).
cnf(refute_0_216,plain,
( ~ product(e_2,e_1,e_4)
| product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_3,e_2,e_1) ),
inference(subst,[],[refute_0_215:[bind(X,$fot(e_2))]]) ).
cnf(refute_0_217,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_4,e_1)
| product(e_3,e_2,e_1) ),
inference(resolve,[$cnf( product(e_2,e_1,e_4) )],[refute_0_184,refute_0_216]) ).
cnf(refute_0_218,plain,
( equalish(e_4,e_1)
| product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_4,e_1)
| product(e_3,e_1,e_4) ),
inference(resolve,[$cnf( product(e_3,e_2,e_1) )],[refute_0_217,refute_0_213]) ).
cnf(refute_0_219,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_4,e_1)
| product(e_3,e_1,e_4) ),
inference(resolve,[$cnf( equalish(e_4,e_1) )],[refute_0_218,e_4_is_not_e_1]) ).
cnf(refute_0_220,plain,
( ~ product(e_3,W,e_4)
| ~ product(e_3,e_2,e_4)
| equalish(W,e_2) ),
inference(subst,[],[product_right_cancellation:[bind(X,$fot(e_3)),bind(Y,$fot(e_4)),bind(Z,$fot(e_2))]]) ).
cnf(refute_0_221,plain,
( ~ product(e_4,W,e_4)
| ~ product(e_4,e_2,e_4)
| equalish(W,e_2) ),
inference(subst,[],[product_right_cancellation:[bind(X,$fot(e_4)),bind(Y,$fot(e_4)),bind(Z,$fot(e_2))]]) ).
cnf(refute_0_222,plain,
( ~ group_element(e_2)
| product(e_1,e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_3,e_2,e_4)
| product(e_4,e_2,e_4) ),
inference(subst,[],[refute_0_15:[bind(X_76,$fot(e_2))]]) ).
cnf(refute_0_223,plain,
( product(e_1,e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_3,e_2,e_4)
| product(e_4,e_2,e_4) ),
inference(resolve,[$cnf( group_element(e_2) )],[element_2,refute_0_222]) ).
cnf(refute_0_224,plain,
( ~ product(e_4,W,e_4)
| equalish(W,e_2)
| product(e_1,e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_3,e_2,e_4) ),
inference(resolve,[$cnf( product(e_4,e_2,e_4) )],[refute_0_223,refute_0_221]) ).
cnf(refute_0_225,plain,
( ~ product(e_4,e_4,e_4)
| equalish(e_4,e_2)
| product(e_1,e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_3,e_2,e_4) ),
inference(subst,[],[refute_0_224:[bind(W,$fot(e_4))]]) ).
cnf(refute_0_226,plain,
( ~ product(e_4,e_2,e_4)
| equalish(e_2,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3) ),
inference(subst,[],[refute_0_26:[bind(W,$fot(e_2))]]) ).
cnf(refute_0_227,plain,
( equalish(e_2,e_4)
| product(e_1,e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_3,e_2,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3) ),
inference(resolve,[$cnf( product(e_4,e_2,e_4) )],[refute_0_223,refute_0_226]) ).
cnf(refute_0_228,plain,
( product(e_1,e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_3,e_2,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3) ),
inference(resolve,[$cnf( equalish(e_2,e_4) )],[refute_0_227,e_2_is_not_e_4]) ).
cnf(refute_0_229,plain,
( product(e_1,e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_3,e_2,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_4) ),
inference(resolve,[$cnf( product(e_4,e_4,e_3) )],[refute_0_228,refute_0_22]) ).
cnf(refute_0_230,plain,
( equalish(e_4,e_2)
| product(e_1,e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_3,e_2,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2) ),
inference(resolve,[$cnf( product(e_4,e_4,e_4) )],[refute_0_229,refute_0_225]) ).
cnf(refute_0_231,plain,
( product(e_1,e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_3,e_2,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2) ),
inference(resolve,[$cnf( equalish(e_4,e_2) )],[refute_0_230,e_4_is_not_e_2]) ).
cnf(refute_0_232,plain,
( product(e_1,e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_3,e_2,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_4) ),
inference(resolve,[$cnf( product(e_4,e_4,e_2) )],[refute_0_231,refute_0_21]) ).
cnf(refute_0_233,plain,
( equalish(e_4,e_2)
| product(e_1,e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_3,e_2,e_4)
| product(e_4,e_4,e_1) ),
inference(resolve,[$cnf( product(e_4,e_4,e_4) )],[refute_0_232,refute_0_225]) ).
cnf(refute_0_234,plain,
( product(e_1,e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_3,e_2,e_4)
| product(e_4,e_4,e_1) ),
inference(resolve,[$cnf( equalish(e_4,e_2) )],[refute_0_233,e_4_is_not_e_2]) ).
cnf(refute_0_235,plain,
( product(e_1,e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_3,e_2,e_4)
| product(e_4,e_4,e_4) ),
inference(resolve,[$cnf( product(e_4,e_4,e_1) )],[refute_0_234,refute_0_20]) ).
cnf(refute_0_236,plain,
( equalish(e_4,e_2)
| product(e_1,e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_3,e_2,e_4) ),
inference(resolve,[$cnf( product(e_4,e_4,e_4) )],[refute_0_235,refute_0_225]) ).
cnf(refute_0_237,plain,
( product(e_1,e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_3,e_2,e_4) ),
inference(resolve,[$cnf( equalish(e_4,e_2) )],[refute_0_236,e_4_is_not_e_2]) ).
cnf(refute_0_238,plain,
( ~ product(e_3,W,e_4)
| equalish(W,e_2)
| product(e_1,e_2,e_4)
| product(e_2,e_2,e_4) ),
inference(resolve,[$cnf( product(e_3,e_2,e_4) )],[refute_0_237,refute_0_220]) ).
cnf(refute_0_239,plain,
( ~ product(e_3,e_1,e_4)
| equalish(e_1,e_2)
| product(e_1,e_2,e_4)
| product(e_2,e_2,e_4) ),
inference(subst,[],[refute_0_238:[bind(W,$fot(e_1))]]) ).
cnf(refute_0_240,plain,
( equalish(e_1,e_2)
| product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_4,e_1)
| product(e_2,e_2,e_4) ),
inference(resolve,[$cnf( product(e_3,e_1,e_4) )],[refute_0_219,refute_0_239]) ).
cnf(refute_0_241,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_4,e_1)
| product(e_2,e_2,e_4) ),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_240,e_1_is_not_e_2]) ).
cnf(refute_0_242,plain,
( equalish(e_1,e_2)
| product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_4,e_1) ),
inference(resolve,[$cnf( product(e_2,e_2,e_4) )],[refute_0_241,refute_0_186]) ).
cnf(refute_0_243,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_4,e_1) ),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_242,e_1_is_not_e_2]) ).
cnf(refute_0_244,plain,
( equalish(e_1,e_4)
| product(e_1,e_1,e_4)
| product(e_1,e_2,e_4) ),
inference(resolve,[$cnf( product(e_1,e_4,e_1) )],[refute_0_243,refute_0_72]) ).
cnf(refute_0_245,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_2,e_4) ),
inference(resolve,[$cnf( equalish(e_1,e_4) )],[refute_0_244,e_1_is_not_e_4]) ).
cnf(refute_0_246,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_3,e_4)
| product(e_3,e_1,e_2) ),
inference(resolve,[$cnf( product(e_1,e_2,e_4) )],[refute_0_245,refute_0_69]) ).
cnf(refute_0_247,plain,
( equalish(e_4,e_2)
| product(e_1,e_1,e_4)
| product(e_1,e_3,e_4)
| product(e_2,e_1,e_4) ),
inference(resolve,[$cnf( product(e_3,e_1,e_2) )],[refute_0_246,refute_0_66]) ).
cnf(refute_0_248,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_3,e_4)
| product(e_2,e_1,e_4) ),
inference(resolve,[$cnf( equalish(e_4,e_2) )],[refute_0_247,e_4_is_not_e_2]) ).
cnf(refute_0_249,plain,
( equalish(e_3,e_1)
| product(e_1,e_1,e_4)
| product(e_1,e_3,e_4) ),
inference(resolve,[$cnf( product(e_2,e_1,e_4) )],[refute_0_248,refute_0_46]) ).
cnf(refute_0_250,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_3,e_4) ),
inference(resolve,[$cnf( equalish(e_3,e_1) )],[refute_0_249,e_3_is_not_e_1]) ).
cnf(refute_0_251,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,$fot(e_2))]]) ).
cnf(refute_0_252,plain,
( ~ product(e_1,W,e_4)
| equalish(W,e_2)
| product(e_1,e_1,e_4) ),
inference(resolve,[$cnf( product(e_1,e_2,e_4) )],[refute_0_245,refute_0_251]) ).
cnf(refute_0_253,plain,
( ~ product(e_1,e_3,e_4)
| equalish(e_3,e_2)
| product(e_1,e_1,e_4) ),
inference(subst,[],[refute_0_252:[bind(W,$fot(e_3))]]) ).
cnf(refute_0_254,plain,
( equalish(e_3,e_2)
| product(e_1,e_1,e_4) ),
inference(resolve,[$cnf( product(e_1,e_3,e_4) )],[refute_0_250,refute_0_253]) ).
cnf(refute_0_255,plain,
product(e_1,e_1,e_4),
inference(resolve,[$cnf( equalish(e_3,e_2) )],[refute_0_254,e_3_is_not_e_2]) ).
cnf(refute_0_256,plain,
equalish(e_1,e_4),
inference(resolve,[$cnf( product(e_1,e_1,e_4) )],[refute_0_255,refute_0_10]) ).
cnf(refute_0_257,plain,
$false,
inference(resolve,[$cnf( equalish(e_1,e_4) )],[refute_0_256,e_1_is_not_e_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP129-4.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 07:13:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 39.10/39.27 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 39.10/39.27
% 39.10/39.27 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 39.11/39.29
%------------------------------------------------------------------------------