TSTP Solution File: GRP127-4.004 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP127-4.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n004.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 10:36:45 EDT 2022
% Result : Unsatisfiable 0.22s 0.56s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 20
% Syntax : Number of clauses : 137 ( 20 unt; 82 nHn; 133 RR)
% Number of literals : 404 ( 0 equ; 97 neg)
% Maximal clause size : 6 ( 2 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 : 62 ( 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(qg3_1,negated_conjecture,
( product(Y,X,Z1)
| ~ product(Z2,Y,X)
| ~ product(Z1,Y,Z2) ) ).
cnf(qg3_2,negated_conjecture,
( product(Z1,Y,Z2)
| ~ product(Z2,Y,X)
| ~ 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_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_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_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_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(product_idempotence,axiom,
product(X,X,X) ).
cnf(refute_0_0,plain,
product(X_10,X_10,X_10),
inference(subst,[],[product_idempotence:[bind(X,$fot(X_10))]]) ).
cnf(refute_0_1,plain,
( ~ product(X_10,X_10,X_10)
| ~ product(X_10,X_10,X_7)
| equalish(X_7,X_10) ),
inference(subst,[],[product_total_function2:[bind(W,$fot(X_7)),bind(X,$fot(X_10)),bind(Y,$fot(X_10)),bind(Z,$fot(X_10))]]) ).
cnf(refute_0_2,plain,
( ~ product(X_10,X_10,X_7)
| equalish(X_7,X_10) ),
inference(resolve,[$cnf( product(X_10,X_10,X_10) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ product(e_1,e_1,e_4)
| equalish(e_4,e_1) ),
inference(subst,[],[refute_0_2:[bind(X_10,$fot(e_1)),bind(X_7,$fot(e_4))]]) ).
cnf(refute_0_4,plain,
( ~ product(e_1,Z,e_4)
| ~ product(e_1,e_3,e_4)
| equalish(e_3,Z) ),
inference(subst,[],[product_right_cancellation:[bind(W,$fot(e_3)),bind(X,$fot(e_1)),bind(Y,$fot(e_4))]]) ).
cnf(refute_0_5,plain,
product(X_17,X_17,X_17),
inference(subst,[],[product_idempotence:[bind(X,$fot(X_17))]]) ).
cnf(refute_0_6,plain,
( ~ product(X_17,X_15,X_17)
| ~ product(X_17,X_17,X_17)
| equalish(X_15,X_17) ),
inference(subst,[],[product_right_cancellation:[bind(W,$fot(X_15)),bind(X,$fot(X_17)),bind(Y,$fot(X_17)),bind(Z,$fot(X_17))]]) ).
cnf(refute_0_7,plain,
( ~ product(X_17,X_15,X_17)
| equalish(X_15,X_17) ),
inference(resolve,[$cnf( product(X_17,X_17,X_17) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ product(e_2,e_3,e_2)
| equalish(e_3,e_2) ),
inference(subst,[],[refute_0_7:[bind(X_15,$fot(e_3)),bind(X_17,$fot(e_2))]]) ).
cnf(refute_0_9,plain,
( ~ product(e_3,e_3,e_2)
| equalish(e_2,e_3) ),
inference(subst,[],[refute_0_2:[bind(X_10,$fot(e_3)),bind(X_7,$fot(e_2))]]) ).
cnf(refute_0_10,plain,
product(X_24,X_24,X_24),
inference(subst,[],[product_idempotence:[bind(X,$fot(X_24))]]) ).
cnf(refute_0_11,plain,
( ~ product(X_24,X_24,X_24)
| ~ product(X_26,X_24,X_24)
| equalish(X_24,X_26) ),
inference(subst,[],[product_left_cancellation:[bind(W,$fot(X_24)),bind(X,$fot(X_24)),bind(Y,$fot(X_24)),bind(Z,$fot(X_26))]]) ).
cnf(refute_0_12,plain,
( ~ product(X_26,X_24,X_24)
| equalish(X_24,X_26) ),
inference(resolve,[$cnf( product(X_24,X_24,X_24) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ product(e_3,e_4,e_4)
| equalish(e_4,e_3) ),
inference(subst,[],[refute_0_12:[bind(X_24,$fot(e_4)),bind(X_26,$fot(e_3))]]) ).
cnf(refute_0_14,plain,
( ~ group_element(X_55)
| ~ group_element(e_3)
| product(e_1,e_3,X_55)
| product(e_2,e_3,X_55)
| product(e_3,e_3,X_55)
| product(e_4,e_3,X_55) ),
inference(subst,[],[row_surjectivity:[bind(X,$fot(e_3)),bind(Y,$fot(X_55))]]) ).
cnf(refute_0_15,plain,
( ~ group_element(X_55)
| product(e_1,e_3,X_55)
| product(e_2,e_3,X_55)
| product(e_3,e_3,X_55)
| product(e_4,e_3,X_55) ),
inference(resolve,[$cnf( group_element(e_3) )],[element_3,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ group_element(e_2)
| product(e_1,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_3,e_3,e_2)
| product(e_4,e_3,e_2) ),
inference(subst,[],[refute_0_15:[bind(X_55,$fot(e_2))]]) ).
cnf(refute_0_17,plain,
( product(e_1,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_3,e_3,e_2)
| product(e_4,e_3,e_2) ),
inference(resolve,[$cnf( group_element(e_2) )],[element_2,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ product(Z1,e_3,e_2)
| ~ product(e_2,e_3,e_4)
| product(e_3,e_4,Z1) ),
inference(subst,[],[qg3_1:[bind(X,$fot(e_4)),bind(Y,$fot(e_3)),bind(Z2,$fot(e_2))]]) ).
cnf(refute_0_19,plain,
( ~ product(e_3,e_3,e_4)
| equalish(e_4,e_3) ),
inference(subst,[],[refute_0_2:[bind(X_10,$fot(e_3)),bind(X_7,$fot(e_4))]]) ).
cnf(refute_0_20,plain,
( ~ product(e_4,e_3,e_4)
| equalish(e_3,e_4) ),
inference(subst,[],[refute_0_7:[bind(X_15,$fot(e_3)),bind(X_17,$fot(e_4))]]) ).
cnf(refute_0_21,plain,
( ~ group_element(e_4)
| product(e_1,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_3,e_3,e_4)
| product(e_4,e_3,e_4) ),
inference(subst,[],[refute_0_15:[bind(X_55,$fot(e_4))]]) ).
cnf(refute_0_22,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,[$cnf( group_element(e_4) )],[element_4,refute_0_21]) ).
cnf(refute_0_23,plain,
( equalish(e_3,e_4)
| product(e_1,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_3,e_3,e_4) ),
inference(resolve,[$cnf( product(e_4,e_3,e_4) )],[refute_0_22,refute_0_20]) ).
cnf(refute_0_24,plain,
( product(e_1,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_3,e_3,e_4) ),
inference(resolve,[$cnf( equalish(e_3,e_4) )],[refute_0_23,e_3_is_not_e_4]) ).
cnf(refute_0_25,plain,
( equalish(e_4,e_3)
| product(e_1,e_3,e_4)
| product(e_2,e_3,e_4) ),
inference(resolve,[$cnf( product(e_3,e_3,e_4) )],[refute_0_24,refute_0_19]) ).
cnf(refute_0_26,plain,
( product(e_1,e_3,e_4)
| product(e_2,e_3,e_4) ),
inference(resolve,[$cnf( equalish(e_4,e_3) )],[refute_0_25,e_4_is_not_e_3]) ).
cnf(refute_0_27,plain,
( ~ product(Z1,e_3,e_2)
| product(e_1,e_3,e_4)
| product(e_3,e_4,Z1) ),
inference(resolve,[$cnf( product(e_2,e_3,e_4) )],[refute_0_26,refute_0_18]) ).
cnf(refute_0_28,plain,
( ~ product(e_4,e_3,e_2)
| product(e_1,e_3,e_4)
| product(e_3,e_4,e_4) ),
inference(subst,[],[refute_0_27:[bind(Z1,$fot(e_4))]]) ).
cnf(refute_0_29,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_4)
| product(e_2,e_3,e_2)
| product(e_3,e_3,e_2)
| product(e_3,e_4,e_4) ),
inference(resolve,[$cnf( product(e_4,e_3,e_2) )],[refute_0_17,refute_0_28]) ).
cnf(refute_0_30,plain,
( equalish(e_4,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_4)
| product(e_2,e_3,e_2)
| product(e_3,e_3,e_2) ),
inference(resolve,[$cnf( product(e_3,e_4,e_4) )],[refute_0_29,refute_0_13]) ).
cnf(refute_0_31,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_4)
| product(e_2,e_3,e_2)
| product(e_3,e_3,e_2) ),
inference(resolve,[$cnf( equalish(e_4,e_3) )],[refute_0_30,e_4_is_not_e_3]) ).
cnf(refute_0_32,plain,
( equalish(e_2,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_4)
| product(e_2,e_3,e_2) ),
inference(resolve,[$cnf( product(e_3,e_3,e_2) )],[refute_0_31,refute_0_9]) ).
cnf(refute_0_33,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_4)
| product(e_2,e_3,e_2) ),
inference(resolve,[$cnf( equalish(e_2,e_3) )],[refute_0_32,e_2_is_not_e_3]) ).
cnf(refute_0_34,plain,
( equalish(e_3,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_4) ),
inference(resolve,[$cnf( product(e_2,e_3,e_2) )],[refute_0_33,refute_0_8]) ).
cnf(refute_0_35,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_4) ),
inference(resolve,[$cnf( equalish(e_3,e_2) )],[refute_0_34,e_3_is_not_e_2]) ).
cnf(refute_0_36,plain,
( ~ product(e_1,Z,e_4)
| equalish(e_3,Z)
| product(e_1,e_3,e_2) ),
inference(resolve,[$cnf( product(e_1,e_3,e_4) )],[refute_0_35,refute_0_4]) ).
cnf(refute_0_37,plain,
( ~ product(e_1,e_2,e_4)
| equalish(e_3,e_2)
| product(e_1,e_3,e_2) ),
inference(subst,[],[refute_0_36:[bind(Z,$fot(e_2))]]) ).
cnf(refute_0_38,plain,
( ~ product(e_1,e_4,Z)
| ~ product(e_1,e_4,e_3)
| equalish(e_3,Z) ),
inference(subst,[],[product_total_function2:[bind(W,$fot(e_3)),bind(X,$fot(e_1)),bind(Y,$fot(e_4))]]) ).
cnf(refute_0_39,plain,
( ~ product(e_2,e_2,e_4)
| equalish(e_4,e_2) ),
inference(subst,[],[refute_0_2:[bind(X_10,$fot(e_2)),bind(X_7,$fot(e_4))]]) ).
cnf(refute_0_40,plain,
( ~ product(e_3,e_2,e_3)
| equalish(e_2,e_3) ),
inference(subst,[],[refute_0_7:[bind(X_15,$fot(e_2)),bind(X_17,$fot(e_3))]]) ).
cnf(refute_0_41,plain,
( ~ product(e_4,e_2,e_4)
| equalish(e_2,e_4) ),
inference(subst,[],[refute_0_7:[bind(X_15,$fot(e_2)),bind(X_17,$fot(e_4))]]) ).
cnf(refute_0_42,plain,
( ~ group_element(X_55)
| ~ group_element(e_2)
| product(e_1,e_2,X_55)
| product(e_2,e_2,X_55)
| product(e_3,e_2,X_55)
| product(e_4,e_2,X_55) ),
inference(subst,[],[row_surjectivity:[bind(X,$fot(e_2)),bind(Y,$fot(X_55))]]) ).
cnf(refute_0_43,plain,
( ~ group_element(X_55)
| product(e_1,e_2,X_55)
| product(e_2,e_2,X_55)
| product(e_3,e_2,X_55)
| product(e_4,e_2,X_55) ),
inference(resolve,[$cnf( group_element(e_2) )],[element_2,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ group_element(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_2,e_4) ),
inference(subst,[],[refute_0_43:[bind(X_55,$fot(e_4))]]) ).
cnf(refute_0_45,plain,
( product(e_1,e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_3,e_2,e_4)
| product(e_4,e_2,e_4) ),
inference(resolve,[$cnf( group_element(e_4) )],[element_4,refute_0_44]) ).
cnf(refute_0_46,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) ),
inference(resolve,[$cnf( product(e_4,e_2,e_4) )],[refute_0_45,refute_0_41]) ).
cnf(refute_0_47,plain,
( product(e_1,e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_3,e_2,e_4) ),
inference(resolve,[$cnf( equalish(e_2,e_4) )],[refute_0_46,e_2_is_not_e_4]) ).
cnf(refute_0_48,plain,
( ~ product(Z2,e_2,e_4)
| ~ product(e_2,e_4,e_3)
| product(e_3,e_2,Z2) ),
inference(subst,[],[qg3_2:[bind(X,$fot(e_4)),bind(Y,$fot(e_2)),bind(Z1,$fot(e_3))]]) ).
cnf(refute_0_49,plain,
( ~ product(e_3,e_4,e_3)
| equalish(e_4,e_3) ),
inference(subst,[],[refute_0_7:[bind(X_15,$fot(e_4)),bind(X_17,$fot(e_3))]]) ).
cnf(refute_0_50,plain,
( ~ product(e_4,e_4,e_3)
| equalish(e_3,e_4) ),
inference(subst,[],[refute_0_2:[bind(X_10,$fot(e_4)),bind(X_7,$fot(e_3))]]) ).
cnf(refute_0_51,plain,
( ~ group_element(X_55)
| ~ group_element(e_4)
| product(e_1,e_4,X_55)
| product(e_2,e_4,X_55)
| product(e_3,e_4,X_55)
| product(e_4,e_4,X_55) ),
inference(subst,[],[row_surjectivity:[bind(X,$fot(e_4)),bind(Y,$fot(X_55))]]) ).
cnf(refute_0_52,plain,
( ~ group_element(X_55)
| product(e_1,e_4,X_55)
| product(e_2,e_4,X_55)
| product(e_3,e_4,X_55)
| product(e_4,e_4,X_55) ),
inference(resolve,[$cnf( group_element(e_4) )],[element_4,refute_0_51]) ).
cnf(refute_0_53,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_52:[bind(X_55,$fot(e_3))]]) ).
cnf(refute_0_54,plain,
( product(e_1,e_4,e_3)
| product(e_2,e_4,e_3)
| product(e_3,e_4,e_3)
| product(e_4,e_4,e_3) ),
inference(resolve,[$cnf( group_element(e_3) )],[element_3,refute_0_53]) ).
cnf(refute_0_55,plain,
( equalish(e_3,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,[$cnf( product(e_4,e_4,e_3) )],[refute_0_54,refute_0_50]) ).
cnf(refute_0_56,plain,
( product(e_1,e_4,e_3)
| product(e_2,e_4,e_3)
| product(e_3,e_4,e_3) ),
inference(resolve,[$cnf( equalish(e_3,e_4) )],[refute_0_55,e_3_is_not_e_4]) ).
cnf(refute_0_57,plain,
( equalish(e_4,e_3)
| product(e_1,e_4,e_3)
| product(e_2,e_4,e_3) ),
inference(resolve,[$cnf( product(e_3,e_4,e_3) )],[refute_0_56,refute_0_49]) ).
cnf(refute_0_58,plain,
( product(e_1,e_4,e_3)
| product(e_2,e_4,e_3) ),
inference(resolve,[$cnf( equalish(e_4,e_3) )],[refute_0_57,e_4_is_not_e_3]) ).
cnf(refute_0_59,plain,
( ~ product(Z2,e_2,e_4)
| product(e_1,e_4,e_3)
| product(e_3,e_2,Z2) ),
inference(resolve,[$cnf( product(e_2,e_4,e_3) )],[refute_0_58,refute_0_48]) ).
cnf(refute_0_60,plain,
( ~ product(e_3,e_2,e_4)
| product(e_1,e_4,e_3)
| product(e_3,e_2,e_3) ),
inference(subst,[],[refute_0_59:[bind(Z2,$fot(e_3))]]) ).
cnf(refute_0_61,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_4,e_3)
| product(e_2,e_2,e_4)
| product(e_3,e_2,e_3) ),
inference(resolve,[$cnf( product(e_3,e_2,e_4) )],[refute_0_47,refute_0_60]) ).
cnf(refute_0_62,plain,
( equalish(e_2,e_3)
| product(e_1,e_2,e_4)
| product(e_1,e_4,e_3)
| product(e_2,e_2,e_4) ),
inference(resolve,[$cnf( product(e_3,e_2,e_3) )],[refute_0_61,refute_0_40]) ).
cnf(refute_0_63,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_4,e_3)
| product(e_2,e_2,e_4) ),
inference(resolve,[$cnf( equalish(e_2,e_3) )],[refute_0_62,e_2_is_not_e_3]) ).
cnf(refute_0_64,plain,
( equalish(e_4,e_2)
| product(e_1,e_2,e_4)
| product(e_1,e_4,e_3) ),
inference(resolve,[$cnf( product(e_2,e_2,e_4) )],[refute_0_63,refute_0_39]) ).
cnf(refute_0_65,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_4,e_3) ),
inference(resolve,[$cnf( equalish(e_4,e_2) )],[refute_0_64,e_4_is_not_e_2]) ).
cnf(refute_0_66,plain,
( ~ product(e_1,e_4,Z)
| equalish(e_3,Z)
| product(e_1,e_2,e_4) ),
inference(resolve,[$cnf( product(e_1,e_4,e_3) )],[refute_0_65,refute_0_38]) ).
cnf(refute_0_67,plain,
( ~ product(e_1,e_4,e_2)
| equalish(e_3,e_2)
| product(e_1,e_2,e_4) ),
inference(subst,[],[refute_0_66:[bind(Z,$fot(e_2))]]) ).
cnf(refute_0_68,plain,
( ~ product(e_2,e_4,e_2)
| equalish(e_4,e_2) ),
inference(subst,[],[refute_0_7:[bind(X_15,$fot(e_4)),bind(X_17,$fot(e_2))]]) ).
cnf(refute_0_69,plain,
( ~ product(Z2,e_1,e_4)
| ~ product(e_1,e_4,e_3)
| product(e_3,e_1,Z2) ),
inference(subst,[],[qg3_2:[bind(X,$fot(e_4)),bind(Y,$fot(e_1)),bind(Z1,$fot(e_3))]]) ).
cnf(refute_0_70,plain,
( ~ product(e_4,e_3,e_3)
| equalish(e_3,e_4) ),
inference(subst,[],[refute_0_12:[bind(X_24,$fot(e_3)),bind(X_26,$fot(e_4))]]) ).
cnf(refute_0_71,plain,
( ~ product(e_4,e_4,e_2)
| equalish(e_2,e_4) ),
inference(subst,[],[refute_0_2:[bind(X_10,$fot(e_4)),bind(X_7,$fot(e_2))]]) ).
cnf(refute_0_72,plain,
( ~ group_element(e_2)
| product(e_1,e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_3,e_4,e_2)
| product(e_4,e_4,e_2) ),
inference(subst,[],[refute_0_52:[bind(X_55,$fot(e_2))]]) ).
cnf(refute_0_73,plain,
( product(e_1,e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_3,e_4,e_2)
| product(e_4,e_4,e_2) ),
inference(resolve,[$cnf( group_element(e_2) )],[element_2,refute_0_72]) ).
cnf(refute_0_74,plain,
( equalish(e_2,e_4)
| product(e_1,e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_3,e_4,e_2) ),
inference(resolve,[$cnf( product(e_4,e_4,e_2) )],[refute_0_73,refute_0_71]) ).
cnf(refute_0_75,plain,
( product(e_1,e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_3,e_4,e_2) ),
inference(resolve,[$cnf( equalish(e_2,e_4) )],[refute_0_74,e_2_is_not_e_4]) ).
cnf(refute_0_76,plain,
( ~ product(Z1,e_4,e_2)
| ~ product(e_2,e_4,e_3)
| product(e_4,e_3,Z1) ),
inference(subst,[],[qg3_1:[bind(X,$fot(e_3)),bind(Y,$fot(e_4)),bind(Z2,$fot(e_2))]]) ).
cnf(refute_0_77,plain,
( ~ product(Z1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_4,e_3,Z1) ),
inference(resolve,[$cnf( product(e_2,e_4,e_3) )],[refute_0_58,refute_0_76]) ).
cnf(refute_0_78,plain,
( ~ product(e_3,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_4,e_3,e_3) ),
inference(subst,[],[refute_0_77:[bind(Z1,$fot(e_3))]]) ).
cnf(refute_0_79,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_2,e_4,e_2)
| product(e_4,e_3,e_3) ),
inference(resolve,[$cnf( product(e_3,e_4,e_2) )],[refute_0_75,refute_0_78]) ).
cnf(refute_0_80,plain,
( equalish(e_3,e_4)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_2,e_4,e_2) ),
inference(resolve,[$cnf( product(e_4,e_3,e_3) )],[refute_0_79,refute_0_70]) ).
cnf(refute_0_81,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_2,e_4,e_2) ),
inference(resolve,[$cnf( equalish(e_3,e_4) )],[refute_0_80,e_3_is_not_e_4]) ).
cnf(refute_0_82,plain,
( equalish(e_4,e_2)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3) ),
inference(resolve,[$cnf( product(e_2,e_4,e_2) )],[refute_0_81,refute_0_68]) ).
cnf(refute_0_83,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3) ),
inference(resolve,[$cnf( equalish(e_4,e_2) )],[refute_0_82,e_4_is_not_e_2]) ).
cnf(refute_0_84,plain,
( ~ product(Z2,e_1,e_4)
| product(e_1,e_4,e_2)
| product(e_3,e_1,Z2) ),
inference(resolve,[$cnf( product(e_1,e_4,e_3) )],[refute_0_83,refute_0_69]) ).
cnf(refute_0_85,plain,
( ~ product(e_2,e_1,e_4)
| product(e_1,e_4,e_2)
| product(e_3,e_1,e_2) ),
inference(subst,[],[refute_0_84:[bind(Z2,$fot(e_2))]]) ).
cnf(refute_0_86,plain,
( ~ product(e_3,e_1,e_3)
| equalish(e_1,e_3) ),
inference(subst,[],[refute_0_7:[bind(X_15,$fot(e_1)),bind(X_17,$fot(e_3))]]) ).
cnf(refute_0_87,plain,
( ~ product(e_4,e_1,e_4)
| equalish(e_1,e_4) ),
inference(subst,[],[refute_0_7:[bind(X_15,$fot(e_1)),bind(X_17,$fot(e_4))]]) ).
cnf(refute_0_88,plain,
( ~ group_element(X_55)
| ~ group_element(e_1)
| product(e_1,e_1,X_55)
| product(e_2,e_1,X_55)
| product(e_3,e_1,X_55)
| product(e_4,e_1,X_55) ),
inference(subst,[],[row_surjectivity:[bind(X,$fot(e_1)),bind(Y,$fot(X_55))]]) ).
cnf(refute_0_89,plain,
( ~ group_element(X_55)
| product(e_1,e_1,X_55)
| product(e_2,e_1,X_55)
| product(e_3,e_1,X_55)
| product(e_4,e_1,X_55) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_88]) ).
cnf(refute_0_90,plain,
( ~ group_element(e_4)
| product(e_1,e_1,e_4)
| product(e_2,e_1,e_4)
| product(e_3,e_1,e_4)
| product(e_4,e_1,e_4) ),
inference(subst,[],[refute_0_89:[bind(X_55,$fot(e_4))]]) ).
cnf(refute_0_91,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,[$cnf( group_element(e_4) )],[element_4,refute_0_90]) ).
cnf(refute_0_92,plain,
( equalish(e_1,e_4)
| product(e_1,e_1,e_4)
| product(e_2,e_1,e_4)
| product(e_3,e_1,e_4) ),
inference(resolve,[$cnf( product(e_4,e_1,e_4) )],[refute_0_91,refute_0_87]) ).
cnf(refute_0_93,plain,
( product(e_1,e_1,e_4)
| product(e_2,e_1,e_4)
| product(e_3,e_1,e_4) ),
inference(resolve,[$cnf( equalish(e_1,e_4) )],[refute_0_92,e_1_is_not_e_4]) ).
cnf(refute_0_94,plain,
( ~ product(e_3,e_1,e_4)
| product(e_1,e_4,e_2)
| product(e_3,e_1,e_3) ),
inference(subst,[],[refute_0_84:[bind(Z2,$fot(e_3))]]) ).
cnf(refute_0_95,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_4,e_2)
| product(e_2,e_1,e_4)
| product(e_3,e_1,e_3) ),
inference(resolve,[$cnf( product(e_3,e_1,e_4) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
( equalish(e_1,e_3)
| product(e_1,e_1,e_4)
| product(e_1,e_4,e_2)
| product(e_2,e_1,e_4) ),
inference(resolve,[$cnf( product(e_3,e_1,e_3) )],[refute_0_95,refute_0_86]) ).
cnf(refute_0_97,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_4,e_2)
| product(e_2,e_1,e_4) ),
inference(resolve,[$cnf( equalish(e_1,e_3) )],[refute_0_96,e_1_is_not_e_3]) ).
cnf(refute_0_98,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_4,e_2)
| product(e_3,e_1,e_2) ),
inference(resolve,[$cnf( product(e_2,e_1,e_4) )],[refute_0_97,refute_0_85]) ).
cnf(refute_0_99,plain,
( ~ product(e_3,W,e_2)
| ~ product(e_3,e_4,e_2)
| equalish(W,e_4) ),
inference(subst,[],[product_right_cancellation:[bind(X,$fot(e_3)),bind(Y,$fot(e_2)),bind(Z,$fot(e_4))]]) ).
cnf(refute_0_100,plain,
( ~ product(e_3,W,e_2)
| equalish(W,e_4)
| product(e_1,e_4,e_2)
| product(e_2,e_4,e_2) ),
inference(resolve,[$cnf( product(e_3,e_4,e_2) )],[refute_0_75,refute_0_99]) ).
cnf(refute_0_101,plain,
( ~ product(e_3,e_1,e_2)
| equalish(e_1,e_4)
| product(e_1,e_4,e_2)
| product(e_2,e_4,e_2) ),
inference(subst,[],[refute_0_100:[bind(W,$fot(e_1))]]) ).
cnf(refute_0_102,plain,
( equalish(e_1,e_4)
| product(e_1,e_1,e_4)
| product(e_1,e_4,e_2)
| product(e_2,e_4,e_2) ),
inference(resolve,[$cnf( product(e_3,e_1,e_2) )],[refute_0_98,refute_0_101]) ).
cnf(refute_0_103,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_4,e_2)
| product(e_2,e_4,e_2) ),
inference(resolve,[$cnf( equalish(e_1,e_4) )],[refute_0_102,e_1_is_not_e_4]) ).
cnf(refute_0_104,plain,
( equalish(e_4,e_2)
| product(e_1,e_1,e_4)
| product(e_1,e_4,e_2) ),
inference(resolve,[$cnf( product(e_2,e_4,e_2) )],[refute_0_103,refute_0_68]) ).
cnf(refute_0_105,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_4,e_2) ),
inference(resolve,[$cnf( equalish(e_4,e_2) )],[refute_0_104,e_4_is_not_e_2]) ).
cnf(refute_0_106,plain,
( equalish(e_3,e_2)
| product(e_1,e_1,e_4)
| product(e_1,e_2,e_4) ),
inference(resolve,[$cnf( product(e_1,e_4,e_2) )],[refute_0_105,refute_0_67]) ).
cnf(refute_0_107,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_2,e_4) ),
inference(resolve,[$cnf( equalish(e_3,e_2) )],[refute_0_106,e_3_is_not_e_2]) ).
cnf(refute_0_108,plain,
( equalish(e_3,e_2)
| product(e_1,e_1,e_4)
| product(e_1,e_3,e_2) ),
inference(resolve,[$cnf( product(e_1,e_2,e_4) )],[refute_0_107,refute_0_37]) ).
cnf(refute_0_109,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_3,e_2) ),
inference(resolve,[$cnf( equalish(e_3,e_2) )],[refute_0_108,e_3_is_not_e_2]) ).
cnf(refute_0_110,plain,
( ~ product(e_1,W,e_2)
| ~ product(e_1,e_4,e_2)
| equalish(W,e_4) ),
inference(subst,[],[product_right_cancellation:[bind(X,$fot(e_1)),bind(Y,$fot(e_2)),bind(Z,$fot(e_4))]]) ).
cnf(refute_0_111,plain,
( ~ product(e_1,W,e_2)
| equalish(W,e_4)
| product(e_1,e_1,e_4) ),
inference(resolve,[$cnf( product(e_1,e_4,e_2) )],[refute_0_105,refute_0_110]) ).
cnf(refute_0_112,plain,
( ~ product(e_1,e_3,e_2)
| equalish(e_3,e_4)
| product(e_1,e_1,e_4) ),
inference(subst,[],[refute_0_111:[bind(W,$fot(e_3))]]) ).
cnf(refute_0_113,plain,
( equalish(e_3,e_4)
| product(e_1,e_1,e_4) ),
inference(resolve,[$cnf( product(e_1,e_3,e_2) )],[refute_0_109,refute_0_112]) ).
cnf(refute_0_114,plain,
product(e_1,e_1,e_4),
inference(resolve,[$cnf( equalish(e_3,e_4) )],[refute_0_113,e_3_is_not_e_4]) ).
cnf(refute_0_115,plain,
equalish(e_4,e_1),
inference(resolve,[$cnf( product(e_1,e_1,e_4) )],[refute_0_114,refute_0_3]) ).
cnf(refute_0_116,plain,
$false,
inference(resolve,[$cnf( equalish(e_4,e_1) )],[refute_0_115,e_4_is_not_e_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP127-4.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.15/0.36 % Computer : n004.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Tue Jun 14 11:44:54 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.22/0.56 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.56
% 0.22/0.56 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.22/0.57
%------------------------------------------------------------------------------