%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP124-3.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:36:34 EDT 2022
% Result : Unsatisfiable 0.18s 0.49s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 18
% Syntax : Number of clauses : 119 ( 20 unt; 69 nHn; 115 RR)
% Number of literals : 364 ( 0 equ; 92 neg)
% Maximal clause size : 6 ( 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 : 50 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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_1,axiom,
~ equalish(e_3,e_1) ).
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_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(qg2_2,negated_conjecture,
( ~ product(X1,Y1,Z1)
| ~ product(X2,Y2,Z1)
| ~ product(Z2,X1,Y1)
| ~ product(Z2,X2,Y2)
| equalish(Y1,Y2) ) ).
cnf(refute_0_0,plain,
product(X_33,X_33,X_33),
inference(subst,[],[product_idempotence:[bind(X,$fot(X_33))]]) ).
cnf(refute_0_1,plain,
( ~ product(X_33,X_33,X_33)
| ~ product(X_33,X_34,X_33)
| equalish(X_33,X_34) ),
inference(subst,[],[product_right_cancellation:[bind(W,$fot(X_33)),bind(X,$fot(X_33)),bind(Y,$fot(X_33)),bind(Z,$fot(X_34))]]) ).
cnf(refute_0_2,plain,
( ~ product(X_33,X_34,X_33)
| equalish(X_33,X_34) ),
inference(resolve,[$cnf( product(X_33,X_33,X_33) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ product(e_1,e_3,e_1)
| equalish(e_1,e_3) ),
inference(subst,[],[refute_0_2:[bind(X_33,$fot(e_1)),bind(X_34,$fot(e_3))]]) ).
cnf(refute_0_4,plain,
( ~ product(e_1,e_4,e_1)
| equalish(e_1,e_4) ),
inference(subst,[],[refute_0_2:[bind(X_33,$fot(e_1)),bind(X_34,$fot(e_4))]]) ).
cnf(refute_0_5,plain,
( ~ product(e_1,Z,e_2)
| ~ product(e_1,e_3,e_2)
| equalish(e_3,Z) ),
inference(subst,[],[product_right_cancellation:[bind(W,$fot(e_3)),bind(X,$fot(e_1)),bind(Y,$fot(e_2))]]) ).
cnf(refute_0_6,plain,
product(X_40,X_40,X_40),
inference(subst,[],[product_idempotence:[bind(X,$fot(X_40))]]) ).
cnf(refute_0_7,plain,
( ~ product(X_40,X_40,X_40)
| ~ product(X_42,X_40,X_40)
| equalish(X_40,X_42) ),
inference(subst,[],[product_left_cancellation:[bind(W,$fot(X_40)),bind(X,$fot(X_40)),bind(Y,$fot(X_40)),bind(Z,$fot(X_42))]]) ).
cnf(refute_0_8,plain,
( ~ product(X_42,X_40,X_40)
| equalish(X_40,X_42) ),
inference(resolve,[$cnf( product(X_40,X_40,X_40) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ product(e_1,e_3,e_3)
| equalish(e_3,e_1) ),
inference(subst,[],[refute_0_8:[bind(X_40,$fot(e_3)),bind(X_42,$fot(e_1))]]) ).
cnf(refute_0_10,plain,
( ~ group_element(X_82)
| ~ group_element(e_3)
| product(X_82,e_3,e_1)
| product(X_82,e_3,e_2)
| product(X_82,e_3,e_3)
| product(X_82,e_3,e_4) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(X_82)),bind(Y,$fot(e_3))]]) ).
cnf(refute_0_11,plain,
( ~ group_element(X_82)
| product(X_82,e_3,e_1)
| product(X_82,e_3,e_2)
| product(X_82,e_3,e_3)
| product(X_82,e_3,e_4) ),
inference(resolve,[$cnf( group_element(e_3) )],[element_3,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ group_element(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_1,e_3,e_4) ),
inference(subst,[],[refute_0_11:[bind(X_82,$fot(e_1))]]) ).
cnf(refute_0_13,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ product(X1,Y1,Z2)
| ~ product(Z2,X1,Y1)
| ~ product(Z2,Z2,Z2)
| equalish(Y1,Z2) ),
inference(subst,[],[qg2_2:[bind(X2,$fot(Z2)),bind(Y2,$fot(Z2)),bind(Z1,$fot(Z2))]]) ).
cnf(refute_0_15,plain,
product(Z2,Z2,Z2),
inference(subst,[],[product_idempotence:[bind(X,$fot(Z2))]]) ).
cnf(refute_0_16,plain,
( ~ product(X1,Y1,Z2)
| ~ product(Z2,X1,Y1)
| equalish(Y1,Z2) ),
inference(resolve,[$cnf( product(Z2,Z2,Z2) )],[refute_0_15,refute_0_14]) ).
cnf(refute_0_17,plain,
( ~ product(e_1,e_3,e_4)
| ~ product(e_3,e_4,e_1)
| equalish(e_4,e_1) ),
inference(subst,[],[refute_0_16:[bind(X1,$fot(e_3)),bind(Y1,$fot(e_4)),bind(Z2,$fot(e_1))]]) ).
cnf(refute_0_18,plain,
( ~ product(e_4,e_1,e_1)
| equalish(e_1,e_4) ),
inference(subst,[],[refute_0_8:[bind(X_40,$fot(e_1)),bind(X_42,$fot(e_4))]]) ).
cnf(refute_0_19,plain,
( ~ product(e_4,Z,e_2)
| ~ product(e_4,e_3,e_2)
| equalish(e_3,Z) ),
inference(subst,[],[product_right_cancellation:[bind(W,$fot(e_3)),bind(X,$fot(e_4)),bind(Y,$fot(e_2))]]) ).
cnf(refute_0_20,plain,
( ~ product(e_4,e_3,e_3)
| equalish(e_3,e_4) ),
inference(subst,[],[refute_0_8:[bind(X_40,$fot(e_3)),bind(X_42,$fot(e_4))]]) ).
cnf(refute_0_21,plain,
( ~ product(e_4,e_3,e_4)
| equalish(e_4,e_3) ),
inference(subst,[],[refute_0_2:[bind(X_33,$fot(e_4)),bind(X_34,$fot(e_3))]]) ).
cnf(refute_0_22,plain,
( ~ group_element(X_83)
| ~ group_element(e_4)
| product(e_4,X_83,e_1)
| product(e_4,X_83,e_2)
| product(e_4,X_83,e_3)
| product(e_4,X_83,e_4) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(e_4)),bind(Y,$fot(X_83))]]) ).
cnf(refute_0_23,plain,
( ~ group_element(X_83)
| product(e_4,X_83,e_1)
| product(e_4,X_83,e_2)
| product(e_4,X_83,e_3)
| product(e_4,X_83,e_4) ),
inference(resolve,[$cnf( group_element(e_4) )],[element_4,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ group_element(e_3)
| product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_4) ),
inference(subst,[],[refute_0_23:[bind(X_83,$fot(e_3))]]) ).
cnf(refute_0_25,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_4) ),
inference(resolve,[$cnf( group_element(e_3) )],[element_3,refute_0_24]) ).
cnf(refute_0_26,plain,
( equalish(e_4,e_3)
| product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3) ),
inference(resolve,[$cnf( product(e_4,e_3,e_4) )],[refute_0_25,refute_0_21]) ).
cnf(refute_0_27,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3) ),
inference(resolve,[$cnf( equalish(e_4,e_3) )],[refute_0_26,e_4_is_not_e_3]) ).
cnf(refute_0_28,plain,
( equalish(e_3,e_4)
| product(e_4,e_3,e_1)
| product(e_4,e_3,e_2) ),
inference(resolve,[$cnf( product(e_4,e_3,e_3) )],[refute_0_27,refute_0_20]) ).
cnf(refute_0_29,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2) ),
inference(resolve,[$cnf( equalish(e_3,e_4) )],[refute_0_28,e_3_is_not_e_4]) ).
cnf(refute_0_30,plain,
( ~ product(e_4,Z,e_2)
| equalish(e_3,Z)
| product(e_4,e_3,e_1) ),
inference(resolve,[$cnf( product(e_4,e_3,e_2) )],[refute_0_29,refute_0_19]) ).
cnf(refute_0_31,plain,
( ~ product(e_4,e_1,e_2)
| equalish(e_3,e_1)
| product(e_4,e_3,e_1) ),
inference(subst,[],[refute_0_30:[bind(Z,$fot(e_1))]]) ).
cnf(refute_0_32,plain,
( ~ product(e_1,e_3,e_4)
| ~ product(e_4,e_1,e_3)
| equalish(e_3,e_4) ),
inference(subst,[],[refute_0_16:[bind(X1,$fot(e_1)),bind(Y1,$fot(e_3)),bind(Z2,$fot(e_4))]]) ).
cnf(refute_0_33,plain,
( ~ product(e_4,e_1,e_4)
| equalish(e_4,e_1) ),
inference(subst,[],[refute_0_2:[bind(X_33,$fot(e_4)),bind(X_34,$fot(e_1))]]) ).
cnf(refute_0_34,plain,
( ~ group_element(e_1)
| product(e_4,e_1,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4) ),
inference(subst,[],[refute_0_23:[bind(X_83,$fot(e_1))]]) ).
cnf(refute_0_35,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,[$cnf( group_element(e_1) )],[element_1,refute_0_34]) ).
cnf(refute_0_36,plain,
( equalish(e_4,e_1)
| product(e_4,e_1,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3) ),
inference(resolve,[$cnf( product(e_4,e_1,e_4) )],[refute_0_35,refute_0_33]) ).
cnf(refute_0_37,plain,
( product(e_4,e_1,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3) ),
inference(resolve,[$cnf( equalish(e_4,e_1) )],[refute_0_36,e_4_is_not_e_1]) ).
cnf(refute_0_38,plain,
( ~ product(e_1,e_3,e_4)
| equalish(e_3,e_4)
| product(e_4,e_1,e_1)
| product(e_4,e_1,e_2) ),
inference(resolve,[$cnf( product(e_4,e_1,e_3) )],[refute_0_37,refute_0_32]) ).
cnf(refute_0_39,plain,
( ~ product(e_1,e_3,e_4)
| product(e_4,e_1,e_1)
| product(e_4,e_1,e_2) ),
inference(resolve,[$cnf( equalish(e_3,e_4) )],[refute_0_38,e_3_is_not_e_4]) ).
cnf(refute_0_40,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_4,e_1,e_1)
| product(e_4,e_1,e_2) ),
inference(resolve,[$cnf( product(e_1,e_3,e_4) )],[refute_0_13,refute_0_39]) ).
cnf(refute_0_41,plain,
( equalish(e_3,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_4,e_1,e_1)
| product(e_4,e_3,e_1) ),
inference(resolve,[$cnf( product(e_4,e_1,e_2) )],[refute_0_40,refute_0_31]) ).
cnf(refute_0_42,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_4,e_1,e_1)
| product(e_4,e_3,e_1) ),
inference(resolve,[$cnf( equalish(e_3,e_1) )],[refute_0_41,e_3_is_not_e_1]) ).
cnf(refute_0_43,plain,
( ~ product(e_4,Z,e_1)
| ~ product(e_4,e_2,e_1)
| equalish(e_2,Z) ),
inference(subst,[],[product_right_cancellation:[bind(W,$fot(e_2)),bind(X,$fot(e_4)),bind(Y,$fot(e_1))]]) ).
cnf(refute_0_44,plain,
( ~ product(e_4,e_2,e_2)
| equalish(e_2,e_4) ),
inference(subst,[],[refute_0_8:[bind(X_40,$fot(e_2)),bind(X_42,$fot(e_4))]]) ).
cnf(refute_0_45,plain,
( ~ product(e_3,e_4,e_2)
| ~ product(e_4,e_2,e_3)
| equalish(e_2,e_3) ),
inference(subst,[],[refute_0_16:[bind(X1,$fot(e_4)),bind(Y1,$fot(e_2)),bind(Z2,$fot(e_3))]]) ).
cnf(refute_0_46,plain,
( ~ product(e_4,e_2,e_4)
| equalish(e_4,e_2) ),
inference(subst,[],[refute_0_2:[bind(X_33,$fot(e_4)),bind(X_34,$fot(e_2))]]) ).
cnf(refute_0_47,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_23:[bind(X_83,$fot(e_2))]]) ).
cnf(refute_0_48,plain,
( product(e_4,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_4) ),
inference(resolve,[$cnf( group_element(e_2) )],[element_2,refute_0_47]) ).
cnf(refute_0_49,plain,
( equalish(e_4,e_2)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3) ),
inference(resolve,[$cnf( product(e_4,e_2,e_4) )],[refute_0_48,refute_0_46]) ).
cnf(refute_0_50,plain,
( product(e_4,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3) ),
inference(resolve,[$cnf( equalish(e_4,e_2) )],[refute_0_49,e_4_is_not_e_2]) ).
cnf(refute_0_51,plain,
( ~ product(e_3,e_4,e_2)
| equalish(e_2,e_3)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2) ),
inference(resolve,[$cnf( product(e_4,e_2,e_3) )],[refute_0_50,refute_0_45]) ).
cnf(refute_0_52,plain,
( ~ product(e_3,e_4,e_2)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2) ),
inference(resolve,[$cnf( equalish(e_2,e_3) )],[refute_0_51,e_2_is_not_e_3]) ).
cnf(refute_0_53,plain,
( ~ product(e_3,e_4,e_3)
| equalish(e_3,e_4) ),
inference(subst,[],[refute_0_2:[bind(X_33,$fot(e_3)),bind(X_34,$fot(e_4))]]) ).
cnf(refute_0_54,plain,
( ~ product(e_3,e_4,e_4)
| equalish(e_4,e_3) ),
inference(subst,[],[refute_0_8:[bind(X_40,$fot(e_4)),bind(X_42,$fot(e_3))]]) ).
cnf(refute_0_55,plain,
( ~ group_element(X_83)
| ~ group_element(e_3)
| product(e_3,X_83,e_1)
| product(e_3,X_83,e_2)
| product(e_3,X_83,e_3)
| product(e_3,X_83,e_4) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(e_3)),bind(Y,$fot(X_83))]]) ).
cnf(refute_0_56,plain,
( ~ group_element(X_83)
| product(e_3,X_83,e_1)
| product(e_3,X_83,e_2)
| product(e_3,X_83,e_3)
| product(e_3,X_83,e_4) ),
inference(resolve,[$cnf( group_element(e_3) )],[element_3,refute_0_55]) ).
cnf(refute_0_57,plain,
( ~ group_element(e_4)
| product(e_3,e_4,e_1)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_4) ),
inference(subst,[],[refute_0_56:[bind(X_83,$fot(e_4))]]) ).
cnf(refute_0_58,plain,
( product(e_3,e_4,e_1)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_4) ),
inference(resolve,[$cnf( group_element(e_4) )],[element_4,refute_0_57]) ).
cnf(refute_0_59,plain,
( equalish(e_4,e_3)
| product(e_3,e_4,e_1)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_3) ),
inference(resolve,[$cnf( product(e_3,e_4,e_4) )],[refute_0_58,refute_0_54]) ).
cnf(refute_0_60,plain,
( product(e_3,e_4,e_1)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_3) ),
inference(resolve,[$cnf( equalish(e_4,e_3) )],[refute_0_59,e_4_is_not_e_3]) ).
cnf(refute_0_61,plain,
( equalish(e_3,e_4)
| product(e_3,e_4,e_1)
| product(e_3,e_4,e_2) ),
inference(resolve,[$cnf( product(e_3,e_4,e_3) )],[refute_0_60,refute_0_53]) ).
cnf(refute_0_62,plain,
( product(e_3,e_4,e_1)
| product(e_3,e_4,e_2) ),
inference(resolve,[$cnf( equalish(e_3,e_4) )],[refute_0_61,e_3_is_not_e_4]) ).
cnf(refute_0_63,plain,
( product(e_3,e_4,e_1)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2) ),
inference(resolve,[$cnf( product(e_3,e_4,e_2) )],[refute_0_62,refute_0_52]) ).
cnf(refute_0_64,plain,
( equalish(e_2,e_4)
| product(e_3,e_4,e_1)
| product(e_4,e_2,e_1) ),
inference(resolve,[$cnf( product(e_4,e_2,e_2) )],[refute_0_63,refute_0_44]) ).
cnf(refute_0_65,plain,
( product(e_3,e_4,e_1)
| product(e_4,e_2,e_1) ),
inference(resolve,[$cnf( equalish(e_2,e_4) )],[refute_0_64,e_2_is_not_e_4]) ).
cnf(refute_0_66,plain,
( ~ product(e_4,Z,e_1)
| equalish(e_2,Z)
| product(e_3,e_4,e_1) ),
inference(resolve,[$cnf( product(e_4,e_2,e_1) )],[refute_0_65,refute_0_43]) ).
cnf(refute_0_67,plain,
( ~ product(e_4,e_3,e_1)
| equalish(e_2,e_3)
| product(e_3,e_4,e_1) ),
inference(subst,[],[refute_0_66:[bind(Z,$fot(e_3))]]) ).
cnf(refute_0_68,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_3,e_4,e_1)
| product(e_4,e_1,e_1) ),
inference(resolve,[$cnf( product(e_4,e_3,e_1) )],[refute_0_42,refute_0_67]) ).
cnf(refute_0_69,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_3,e_4,e_1)
| product(e_4,e_1,e_1) ),
inference(resolve,[$cnf( equalish(e_2,e_3) )],[refute_0_68,e_2_is_not_e_3]) ).
cnf(refute_0_70,plain,
( equalish(e_1,e_4)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_3,e_4,e_1) ),
inference(resolve,[$cnf( product(e_4,e_1,e_1) )],[refute_0_69,refute_0_18]) ).
cnf(refute_0_71,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_3,e_4,e_1) ),
inference(resolve,[$cnf( equalish(e_1,e_4) )],[refute_0_70,e_1_is_not_e_4]) ).
cnf(refute_0_72,plain,
( ~ product(e_1,e_3,e_4)
| equalish(e_4,e_1)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(resolve,[$cnf( product(e_3,e_4,e_1) )],[refute_0_71,refute_0_17]) ).
cnf(refute_0_73,plain,
( ~ product(e_1,e_3,e_4)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(resolve,[$cnf( equalish(e_4,e_1) )],[refute_0_72,e_4_is_not_e_1]) ).
cnf(refute_0_74,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(resolve,[$cnf( product(e_1,e_3,e_4) )],[refute_0_13,refute_0_73]) ).
cnf(refute_0_75,plain,
( equalish(e_3,e_1)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(resolve,[$cnf( product(e_1,e_3,e_3) )],[refute_0_74,refute_0_9]) ).
cnf(refute_0_76,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(resolve,[$cnf( equalish(e_3,e_1) )],[refute_0_75,e_3_is_not_e_1]) ).
cnf(refute_0_77,plain,
( ~ product(e_1,Z,e_2)
| equalish(e_3,Z)
| product(e_1,e_3,e_1) ),
inference(resolve,[$cnf( product(e_1,e_3,e_2) )],[refute_0_76,refute_0_5]) ).
cnf(refute_0_78,plain,
( ~ product(e_1,e_4,e_2)
| equalish(e_3,e_4)
| product(e_1,e_3,e_1) ),
inference(subst,[],[refute_0_77:[bind(Z,$fot(e_4))]]) ).
cnf(refute_0_79,plain,
( ~ product(e_1,e_4,e_4)
| equalish(e_4,e_1) ),
inference(subst,[],[refute_0_8:[bind(X_40,$fot(e_4)),bind(X_42,$fot(e_1))]]) ).
cnf(refute_0_80,plain,
( ~ group_element(X_83)
| ~ group_element(e_1)
| product(e_1,X_83,e_1)
| product(e_1,X_83,e_2)
| product(e_1,X_83,e_3)
| product(e_1,X_83,e_4) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(e_1)),bind(Y,$fot(X_83))]]) ).
cnf(refute_0_81,plain,
( ~ group_element(X_83)
| product(e_1,X_83,e_1)
| product(e_1,X_83,e_2)
| product(e_1,X_83,e_3)
| product(e_1,X_83,e_4) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_80]) ).
cnf(refute_0_82,plain,
( ~ group_element(e_4)
| product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4) ),
inference(subst,[],[refute_0_81:[bind(X_83,$fot(e_4))]]) ).
cnf(refute_0_83,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4) ),
inference(resolve,[$cnf( group_element(e_4) )],[element_4,refute_0_82]) ).
cnf(refute_0_84,plain,
( equalish(e_4,e_1)
| product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3) ),
inference(resolve,[$cnf( product(e_1,e_4,e_4) )],[refute_0_83,refute_0_79]) ).
cnf(refute_0_85,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3) ),
inference(resolve,[$cnf( equalish(e_4,e_1) )],[refute_0_84,e_4_is_not_e_1]) ).
cnf(refute_0_86,plain,
( ~ product(e_1,e_4,e_3)
| ~ product(e_4,e_3,e_1)
| equalish(e_3,e_1) ),
inference(subst,[],[refute_0_16:[bind(X1,$fot(e_4)),bind(Y1,$fot(e_3)),bind(Z2,$fot(e_1))]]) ).
cnf(refute_0_87,plain,
( ~ product(Z,e_3,e_2)
| ~ product(e_4,e_3,e_2)
| equalish(e_4,Z) ),
inference(subst,[],[product_left_cancellation:[bind(W,$fot(e_4)),bind(X,$fot(e_2)),bind(Y,$fot(e_3))]]) ).
cnf(refute_0_88,plain,
( ~ product(Z,e_3,e_2)
| equalish(e_4,Z)
| product(e_4,e_3,e_1) ),
inference(resolve,[$cnf( product(e_4,e_3,e_2) )],[refute_0_29,refute_0_87]) ).
cnf(refute_0_89,plain,
( ~ product(e_1,e_3,e_2)
| equalish(e_4,e_1)
| product(e_4,e_3,e_1) ),
inference(subst,[],[refute_0_88:[bind(Z,$fot(e_1))]]) ).
cnf(refute_0_90,plain,
( equalish(e_4,e_1)
| product(e_1,e_3,e_1)
| product(e_4,e_3,e_1) ),
inference(resolve,[$cnf( product(e_1,e_3,e_2) )],[refute_0_76,refute_0_89]) ).
cnf(refute_0_91,plain,
( product(e_1,e_3,e_1)
| product(e_4,e_3,e_1) ),
inference(resolve,[$cnf( equalish(e_4,e_1) )],[refute_0_90,e_4_is_not_e_1]) ).
cnf(refute_0_92,plain,
( ~ product(e_1,e_4,e_3)
| equalish(e_3,e_1)
| product(e_1,e_3,e_1) ),
inference(resolve,[$cnf( product(e_4,e_3,e_1) )],[refute_0_91,refute_0_86]) ).
cnf(refute_0_93,plain,
( ~ product(e_1,e_4,e_3)
| product(e_1,e_3,e_1) ),
inference(resolve,[$cnf( equalish(e_3,e_1) )],[refute_0_92,e_3_is_not_e_1]) ).
cnf(refute_0_94,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_4,e_1)
| product(e_1,e_4,e_2) ),
inference(resolve,[$cnf( product(e_1,e_4,e_3) )],[refute_0_85,refute_0_93]) ).
cnf(refute_0_95,plain,
( equalish(e_3,e_4)
| product(e_1,e_3,e_1)
| product(e_1,e_4,e_1) ),
inference(resolve,[$cnf( product(e_1,e_4,e_2) )],[refute_0_94,refute_0_78]) ).
cnf(refute_0_96,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_4,e_1) ),
inference(resolve,[$cnf( equalish(e_3,e_4) )],[refute_0_95,e_3_is_not_e_4]) ).
cnf(refute_0_97,plain,
( equalish(e_1,e_4)
| product(e_1,e_3,e_1) ),
inference(resolve,[$cnf( product(e_1,e_4,e_1) )],[refute_0_96,refute_0_4]) ).
cnf(refute_0_98,plain,
product(e_1,e_3,e_1),
inference(resolve,[$cnf( equalish(e_1,e_4) )],[refute_0_97,e_1_is_not_e_4]) ).
cnf(refute_0_99,plain,
equalish(e_1,e_3),
inference(resolve,[$cnf( product(e_1,e_3,e_1) )],[refute_0_98,refute_0_3]) ).
cnf(refute_0_100,plain,
$false,
inference(resolve,[$cnf( equalish(e_1,e_3) )],[refute_0_99,e_1_is_not_e_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP124-3.004 : TPTP v8.1.0. Released v1.2.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 10:04:59 EDT 2022
% 0.18/0.33 % CPUTime :
% 0.18/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.49 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.49
% 0.18/0.49 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.50
%------------------------------------------------------------------------------