TSTP Solution File: GRP126-2.004 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP126-2.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 10:36:41 EDT 2022
% Result : Unsatisfiable 0.44s 0.62s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 24
% Syntax : Number of clauses : 146 ( 24 unt; 88 nHn; 142 RR)
% Number of literals : 460 ( 0 equ; 111 neg)
% Maximal clause size : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 67 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(e_2_then_e_3,axiom,
next(e_2,e_3) ).
cnf(e_4_greater_e_3,axiom,
greater(e_4,e_3) ).
cnf(no_redundancy,axiom,
( ~ product(X,e_1,Y)
| ~ next(X,X1)
| ~ greater(Y,X1) ) ).
cnf(element_1,axiom,
group_element(e_1) ).
cnf(element_2,axiom,
group_element(e_2) ).
cnf(element_3,axiom,
group_element(e_3) ).
cnf(element_4,axiom,
group_element(e_4) ).
cnf(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2) ).
cnf(e_1_is_not_e_4,axiom,
~ equalish(e_1,e_4) ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1) ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3) ).
cnf(e_2_is_not_e_4,axiom,
~ equalish(e_2,e_4) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2) ).
cnf(e_3_is_not_e_4,axiom,
~ equalish(e_3,e_4) ).
cnf(e_4_is_not_e_1,axiom,
~ equalish(e_4,e_1) ).
cnf(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2) ).
cnf(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3) ).
cnf(product_total_function1,axiom,
( ~ group_element(X)
| ~ group_element(Y)
| product(X,Y,e_1)
| product(X,Y,e_2)
| product(X,Y,e_3)
| product(X,Y,e_4) ) ).
cnf(product_total_function2,axiom,
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ) ).
cnf(product_right_cancellation,axiom,
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ) ).
cnf(product_left_cancellation,axiom,
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ) ).
cnf(product_idempotence,axiom,
product(X,X,X) ).
cnf(qg4,negated_conjecture,
( ~ product(X,Y,Z1)
| ~ product(Y,X,Z2)
| product(Z1,Z2,Y) ) ).
cnf(refute_0_0,plain,
product(X_21,X_21,X_21),
inference(subst,[],[product_idempotence:[bind(X,$fot(X_21))]]) ).
cnf(refute_0_1,plain,
( ~ product(X_21,X_21,X_21)
| ~ product(X_21,X_22,X_21)
| equalish(X_21,X_22) ),
inference(subst,[],[product_right_cancellation:[bind(W,$fot(X_21)),bind(X,$fot(X_21)),bind(Y,$fot(X_21)),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_2,plain,
( ~ product(X_21,X_22,X_21)
| equalish(X_21,X_22) ),
inference(resolve,[$cnf( product(X_21,X_21,X_21) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ product(e_1,e_4,e_1)
| equalish(e_1,e_4) ),
inference(subst,[],[refute_0_2:[bind(X_21,$fot(e_1)),bind(X_22,$fot(e_4))]]) ).
cnf(refute_0_4,plain,
product(X_28,X_28,X_28),
inference(subst,[],[product_idempotence:[bind(X,$fot(X_28))]]) ).
cnf(refute_0_5,plain,
( ~ product(X_27,X_28,X_28)
| ~ product(X_28,X_28,X_28)
| equalish(X_27,X_28) ),
inference(subst,[],[product_left_cancellation:[bind(W,$fot(X_27)),bind(X,$fot(X_28)),bind(Y,$fot(X_28)),bind(Z,$fot(X_28))]]) ).
cnf(refute_0_6,plain,
( ~ product(X_27,X_28,X_28)
| equalish(X_27,X_28) ),
inference(resolve,[$cnf( product(X_28,X_28,X_28) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ product(e_2,e_1,e_1)
| equalish(e_2,e_1) ),
inference(subst,[],[refute_0_6:[bind(X_27,$fot(e_2)),bind(X_28,$fot(e_1))]]) ).
cnf(refute_0_8,plain,
( ~ product(e_2,e_1,e_2)
| equalish(e_2,e_1) ),
inference(subst,[],[refute_0_2:[bind(X_21,$fot(e_2)),bind(X_22,$fot(e_1))]]) ).
cnf(refute_0_9,plain,
( ~ product(Z,e_4,e_1)
| ~ product(e_3,e_4,e_1)
| equalish(e_3,Z) ),
inference(subst,[],[product_left_cancellation:[bind(W,$fot(e_3)),bind(X,$fot(e_1)),bind(Y,$fot(e_4))]]) ).
cnf(refute_0_10,plain,
( ~ product(Z,e_4,e_2)
| ~ product(e_3,e_4,e_2)
| equalish(e_3,Z) ),
inference(subst,[],[product_left_cancellation:[bind(W,$fot(e_3)),bind(X,$fot(e_2)),bind(Y,$fot(e_4))]]) ).
cnf(refute_0_11,plain,
( ~ product(e_3,e_4,e_3)
| equalish(e_3,e_4) ),
inference(subst,[],[refute_0_2:[bind(X_21,$fot(e_3)),bind(X_22,$fot(e_4))]]) ).
cnf(refute_0_12,plain,
( ~ product(e_3,e_4,e_4)
| equalish(e_3,e_4) ),
inference(subst,[],[refute_0_6:[bind(X_27,$fot(e_3)),bind(X_28,$fot(e_4))]]) ).
cnf(refute_0_13,plain,
( ~ group_element(X_45)
| ~ group_element(e_3)
| product(e_3,X_45,e_1)
| product(e_3,X_45,e_2)
| product(e_3,X_45,e_3)
| product(e_3,X_45,e_4) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(e_3)),bind(Y,$fot(X_45))]]) ).
cnf(refute_0_14,plain,
( ~ group_element(X_45)
| product(e_3,X_45,e_1)
| product(e_3,X_45,e_2)
| product(e_3,X_45,e_3)
| product(e_3,X_45,e_4) ),
inference(resolve,[$cnf( group_element(e_3) )],[element_3,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ group_element(e_4)
| product(e_3,e_4,e_1)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_4) ),
inference(subst,[],[refute_0_14:[bind(X_45,$fot(e_4))]]) ).
cnf(refute_0_16,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,[$cnf( group_element(e_4) )],[element_4,refute_0_15]) ).
cnf(refute_0_17,plain,
( equalish(e_3,e_4)
| product(e_3,e_4,e_1)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_3) ),
inference(resolve,[$cnf( product(e_3,e_4,e_4) )],[refute_0_16,refute_0_12]) ).
cnf(refute_0_18,plain,
( product(e_3,e_4,e_1)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_3) ),
inference(resolve,[$cnf( equalish(e_3,e_4) )],[refute_0_17,e_3_is_not_e_4]) ).
cnf(refute_0_19,plain,
( equalish(e_3,e_4)
| product(e_3,e_4,e_1)
| product(e_3,e_4,e_2) ),
inference(resolve,[$cnf( product(e_3,e_4,e_3) )],[refute_0_18,refute_0_11]) ).
cnf(refute_0_20,plain,
( product(e_3,e_4,e_1)
| product(e_3,e_4,e_2) ),
inference(resolve,[$cnf( equalish(e_3,e_4) )],[refute_0_19,e_3_is_not_e_4]) ).
cnf(refute_0_21,plain,
( ~ product(Z,e_4,e_2)
| equalish(e_3,Z)
| product(e_3,e_4,e_1) ),
inference(resolve,[$cnf( product(e_3,e_4,e_2) )],[refute_0_20,refute_0_10]) ).
cnf(refute_0_22,plain,
( ~ product(e_1,e_4,e_2)
| equalish(e_3,e_1)
| product(e_3,e_4,e_1) ),
inference(subst,[],[refute_0_21:[bind(Z,$fot(e_1))]]) ).
cnf(refute_0_23,plain,
product(X_11,X_11,X_11),
inference(subst,[],[product_idempotence:[bind(X,$fot(X_11))]]) ).
cnf(refute_0_24,plain,
( ~ product(X_11,X_11,X_11)
| ~ product(X_11,X_11,X_14)
| equalish(X_11,X_14) ),
inference(subst,[],[product_total_function2:[bind(W,$fot(X_11)),bind(X,$fot(X_11)),bind(Y,$fot(X_11)),bind(Z,$fot(X_14))]]) ).
cnf(refute_0_25,plain,
( ~ product(X_11,X_11,X_14)
| equalish(X_11,X_14) ),
inference(resolve,[$cnf( product(X_11,X_11,X_11) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ product(e_2,e_2,e_3)
| equalish(e_2,e_3) ),
inference(subst,[],[refute_0_25:[bind(X_11,$fot(e_2)),bind(X_14,$fot(e_3))]]) ).
cnf(refute_0_27,plain,
( ~ product(Z,e_4,e_1)
| ~ product(e_2,e_4,e_1)
| equalish(e_2,Z) ),
inference(subst,[],[product_left_cancellation:[bind(W,$fot(e_2)),bind(X,$fot(e_1)),bind(Y,$fot(e_4))]]) ).
cnf(refute_0_28,plain,
( ~ product(e_2,e_4,e_2)
| equalish(e_2,e_4) ),
inference(subst,[],[refute_0_2:[bind(X_21,$fot(e_2)),bind(X_22,$fot(e_4))]]) ).
cnf(refute_0_29,plain,
( ~ product(e_1,e_4,e_4)
| equalish(e_1,e_4) ),
inference(subst,[],[refute_0_6:[bind(X_27,$fot(e_1)),bind(X_28,$fot(e_4))]]) ).
cnf(refute_0_30,plain,
( ~ group_element(X_45)
| ~ group_element(e_1)
| product(e_1,X_45,e_1)
| product(e_1,X_45,e_2)
| product(e_1,X_45,e_3)
| product(e_1,X_45,e_4) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(e_1)),bind(Y,$fot(X_45))]]) ).
cnf(refute_0_31,plain,
( ~ group_element(X_45)
| product(e_1,X_45,e_1)
| product(e_1,X_45,e_2)
| product(e_1,X_45,e_3)
| product(e_1,X_45,e_4) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ group_element(e_4)
| product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4) ),
inference(subst,[],[refute_0_31:[bind(X_45,$fot(e_4))]]) ).
cnf(refute_0_33,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,[$cnf( group_element(e_4) )],[element_4,refute_0_32]) ).
cnf(refute_0_34,plain,
( equalish(e_1,e_4)
| product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3) ),
inference(resolve,[$cnf( product(e_1,e_4,e_4) )],[refute_0_33,refute_0_29]) ).
cnf(refute_0_35,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3) ),
inference(resolve,[$cnf( equalish(e_1,e_4) )],[refute_0_34,e_1_is_not_e_4]) ).
cnf(refute_0_36,plain,
( ~ product(W,e_4,e_3)
| ~ product(e_2,e_4,e_3)
| equalish(W,e_2) ),
inference(subst,[],[product_left_cancellation:[bind(X,$fot(e_3)),bind(Y,$fot(e_4)),bind(Z,$fot(e_2))]]) ).
cnf(refute_0_37,plain,
( ~ product(e_2,e_4,e_4)
| equalish(e_2,e_4) ),
inference(subst,[],[refute_0_6:[bind(X_27,$fot(e_2)),bind(X_28,$fot(e_4))]]) ).
cnf(refute_0_38,plain,
( ~ group_element(X_44)
| ~ group_element(e_4)
| product(X_44,e_4,e_1)
| product(X_44,e_4,e_2)
| product(X_44,e_4,e_3)
| product(X_44,e_4,e_4) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(X_44)),bind(Y,$fot(e_4))]]) ).
cnf(refute_0_39,plain,
( ~ group_element(X_44)
| product(X_44,e_4,e_1)
| product(X_44,e_4,e_2)
| product(X_44,e_4,e_3)
| product(X_44,e_4,e_4) ),
inference(resolve,[$cnf( group_element(e_4) )],[element_4,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ group_element(e_2)
| product(e_2,e_4,e_1)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_4) ),
inference(subst,[],[refute_0_39:[bind(X_44,$fot(e_2))]]) ).
cnf(refute_0_41,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_4) ),
inference(resolve,[$cnf( group_element(e_2) )],[element_2,refute_0_40]) ).
cnf(refute_0_42,plain,
( equalish(e_2,e_4)
| product(e_2,e_4,e_1)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_3) ),
inference(resolve,[$cnf( product(e_2,e_4,e_4) )],[refute_0_41,refute_0_37]) ).
cnf(refute_0_43,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_3) ),
inference(resolve,[$cnf( equalish(e_2,e_4) )],[refute_0_42,e_2_is_not_e_4]) ).
cnf(refute_0_44,plain,
( ~ product(W,e_4,e_3)
| equalish(W,e_2)
| product(e_2,e_4,e_1)
| product(e_2,e_4,e_2) ),
inference(resolve,[$cnf( product(e_2,e_4,e_3) )],[refute_0_43,refute_0_36]) ).
cnf(refute_0_45,plain,
( ~ product(e_1,e_4,e_3)
| equalish(e_1,e_2)
| product(e_2,e_4,e_1)
| product(e_2,e_4,e_2) ),
inference(subst,[],[refute_0_44:[bind(W,$fot(e_1))]]) ).
cnf(refute_0_46,plain,
( equalish(e_1,e_2)
| product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_2,e_4,e_1)
| product(e_2,e_4,e_2) ),
inference(resolve,[$cnf( product(e_1,e_4,e_3) )],[refute_0_35,refute_0_45]) ).
cnf(refute_0_47,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_2,e_4,e_1)
| product(e_2,e_4,e_2) ),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_46,e_1_is_not_e_2]) ).
cnf(refute_0_48,plain,
( equalish(e_2,e_4)
| product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(resolve,[$cnf( product(e_2,e_4,e_2) )],[refute_0_47,refute_0_28]) ).
cnf(refute_0_49,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(resolve,[$cnf( equalish(e_2,e_4) )],[refute_0_48,e_2_is_not_e_4]) ).
cnf(refute_0_50,plain,
( ~ product(Z,e_4,e_1)
| equalish(e_2,Z)
| product(e_1,e_4,e_1)
| product(e_1,e_4,e_2) ),
inference(resolve,[$cnf( product(e_2,e_4,e_1) )],[refute_0_49,refute_0_27]) ).
cnf(refute_0_51,plain,
( ~ product(e_3,e_4,e_1)
| equalish(e_2,e_3)
| product(e_1,e_4,e_1)
| product(e_1,e_4,e_2) ),
inference(subst,[],[refute_0_50:[bind(Z,$fot(e_3))]]) ).
cnf(refute_0_52,plain,
( ~ product(e_3,Z,e_2)
| ~ product(e_3,e_4,e_2)
| equalish(e_4,Z) ),
inference(subst,[],[product_right_cancellation:[bind(W,$fot(e_4)),bind(X,$fot(e_3)),bind(Y,$fot(e_2))]]) ).
cnf(refute_0_53,plain,
( ~ product(e_3,Z,e_2)
| equalish(e_4,Z)
| product(e_3,e_4,e_1) ),
inference(resolve,[$cnf( product(e_3,e_4,e_2) )],[refute_0_20,refute_0_52]) ).
cnf(refute_0_54,plain,
( ~ product(e_3,e_1,e_2)
| equalish(e_4,e_1)
| product(e_3,e_4,e_1) ),
inference(subst,[],[refute_0_53:[bind(Z,$fot(e_1))]]) ).
cnf(refute_0_55,plain,
( ~ product(e_4,Z,e_1)
| ~ product(e_4,e_3,e_1)
| equalish(e_3,Z) ),
inference(subst,[],[product_right_cancellation:[bind(W,$fot(e_3)),bind(X,$fot(e_4)),bind(Y,$fot(e_1))]]) ).
cnf(refute_0_56,plain,
( ~ product(e_3,e_4,Z2)
| ~ product(e_4,e_3,e_2)
| product(e_2,Z2,e_3) ),
inference(subst,[],[qg4:[bind(X,$fot(e_4)),bind(Y,$fot(e_3)),bind(Z1,$fot(e_2))]]) ).
cnf(refute_0_57,plain,
( ~ product(e_4,e_3,e_3)
| equalish(e_4,e_3) ),
inference(subst,[],[refute_0_6:[bind(X_27,$fot(e_4)),bind(X_28,$fot(e_3))]]) ).
cnf(refute_0_58,plain,
( ~ product(e_4,e_3,e_4)
| equalish(e_4,e_3) ),
inference(subst,[],[refute_0_2:[bind(X_21,$fot(e_4)),bind(X_22,$fot(e_3))]]) ).
cnf(refute_0_59,plain,
( ~ group_element(X_45)
| ~ group_element(e_4)
| product(e_4,X_45,e_1)
| product(e_4,X_45,e_2)
| product(e_4,X_45,e_3)
| product(e_4,X_45,e_4) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(e_4)),bind(Y,$fot(X_45))]]) ).
cnf(refute_0_60,plain,
( ~ group_element(X_45)
| product(e_4,X_45,e_1)
| product(e_4,X_45,e_2)
| product(e_4,X_45,e_3)
| product(e_4,X_45,e_4) ),
inference(resolve,[$cnf( group_element(e_4) )],[element_4,refute_0_59]) ).
cnf(refute_0_61,plain,
( ~ group_element(e_3)
| product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_4) ),
inference(subst,[],[refute_0_60:[bind(X_45,$fot(e_3))]]) ).
cnf(refute_0_62,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,[$cnf( group_element(e_3) )],[element_3,refute_0_61]) ).
cnf(refute_0_63,plain,
( equalish(e_4,e_3)
| product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3) ),
inference(resolve,[$cnf( product(e_4,e_3,e_4) )],[refute_0_62,refute_0_58]) ).
cnf(refute_0_64,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3) ),
inference(resolve,[$cnf( equalish(e_4,e_3) )],[refute_0_63,e_4_is_not_e_3]) ).
cnf(refute_0_65,plain,
( equalish(e_4,e_3)
| product(e_4,e_3,e_1)
| product(e_4,e_3,e_2) ),
inference(resolve,[$cnf( product(e_4,e_3,e_3) )],[refute_0_64,refute_0_57]) ).
cnf(refute_0_66,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2) ),
inference(resolve,[$cnf( equalish(e_4,e_3) )],[refute_0_65,e_4_is_not_e_3]) ).
cnf(refute_0_67,plain,
( ~ product(e_3,e_4,Z2)
| product(e_2,Z2,e_3)
| product(e_4,e_3,e_1) ),
inference(resolve,[$cnf( product(e_4,e_3,e_2) )],[refute_0_66,refute_0_56]) ).
cnf(refute_0_68,plain,
( ~ product(e_3,e_4,e_2)
| product(e_2,e_2,e_3)
| product(e_4,e_3,e_1) ),
inference(subst,[],[refute_0_67:[bind(Z2,$fot(e_2))]]) ).
cnf(refute_0_69,plain,
( product(e_2,e_2,e_3)
| product(e_3,e_4,e_1)
| product(e_4,e_3,e_1) ),
inference(resolve,[$cnf( product(e_3,e_4,e_2) )],[refute_0_20,refute_0_68]) ).
cnf(refute_0_70,plain,
( ~ product(e_4,Z,e_1)
| equalish(e_3,Z)
| product(e_2,e_2,e_3)
| product(e_3,e_4,e_1) ),
inference(resolve,[$cnf( product(e_4,e_3,e_1) )],[refute_0_69,refute_0_55]) ).
cnf(refute_0_71,plain,
( ~ product(e_4,e_2,e_1)
| equalish(e_3,e_2)
| product(e_2,e_2,e_3)
| product(e_3,e_4,e_1) ),
inference(subst,[],[refute_0_70:[bind(Z,$fot(e_2))]]) ).
cnf(refute_0_72,plain,
( ~ product(e_4,e_2,e_2)
| equalish(e_4,e_2) ),
inference(subst,[],[refute_0_6:[bind(X_27,$fot(e_4)),bind(X_28,$fot(e_2))]]) ).
cnf(refute_0_73,plain,
( ~ product(e_2,e_4,Z2)
| ~ product(e_4,e_2,e_3)
| product(e_3,Z2,e_2) ),
inference(subst,[],[qg4:[bind(X,$fot(e_4)),bind(Y,$fot(e_2)),bind(Z1,$fot(e_3))]]) ).
cnf(refute_0_74,plain,
( ~ product(e_4,e_2,e_4)
| equalish(e_4,e_2) ),
inference(subst,[],[refute_0_2:[bind(X_21,$fot(e_4)),bind(X_22,$fot(e_2))]]) ).
cnf(refute_0_75,plain,
( ~ group_element(e_2)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_4) ),
inference(subst,[],[refute_0_60:[bind(X_45,$fot(e_2))]]) ).
cnf(refute_0_76,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,[$cnf( group_element(e_2) )],[element_2,refute_0_75]) ).
cnf(refute_0_77,plain,
( equalish(e_4,e_2)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3) ),
inference(resolve,[$cnf( product(e_4,e_2,e_4) )],[refute_0_76,refute_0_74]) ).
cnf(refute_0_78,plain,
( product(e_4,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3) ),
inference(resolve,[$cnf( equalish(e_4,e_2) )],[refute_0_77,e_4_is_not_e_2]) ).
cnf(refute_0_79,plain,
( ~ product(e_2,e_4,Z2)
| product(e_3,Z2,e_2)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2) ),
inference(resolve,[$cnf( product(e_4,e_2,e_3) )],[refute_0_78,refute_0_73]) ).
cnf(refute_0_80,plain,
( ~ product(e_2,e_4,e_1)
| product(e_3,e_1,e_2)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2) ),
inference(subst,[],[refute_0_79:[bind(Z2,$fot(e_1))]]) ).
cnf(refute_0_81,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_3,e_1,e_2)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2) ),
inference(resolve,[$cnf( product(e_2,e_4,e_1) )],[refute_0_49,refute_0_80]) ).
cnf(refute_0_82,plain,
( equalish(e_4,e_2)
| product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_3,e_1,e_2)
| product(e_4,e_2,e_1) ),
inference(resolve,[$cnf( product(e_4,e_2,e_2) )],[refute_0_81,refute_0_72]) ).
cnf(refute_0_83,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_3,e_1,e_2)
| product(e_4,e_2,e_1) ),
inference(resolve,[$cnf( equalish(e_4,e_2) )],[refute_0_82,e_4_is_not_e_2]) ).
cnf(refute_0_84,plain,
( equalish(e_3,e_2)
| product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_2,e_2,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_4,e_1) ),
inference(resolve,[$cnf( product(e_4,e_2,e_1) )],[refute_0_83,refute_0_71]) ).
cnf(refute_0_85,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_2,e_2,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_4,e_1) ),
inference(resolve,[$cnf( equalish(e_3,e_2) )],[refute_0_84,e_3_is_not_e_2]) ).
cnf(refute_0_86,plain,
( equalish(e_2,e_3)
| product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_2,e_2,e_3)
| product(e_3,e_1,e_2) ),
inference(resolve,[$cnf( product(e_3,e_4,e_1) )],[refute_0_85,refute_0_51]) ).
cnf(refute_0_87,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_2,e_2,e_3)
| product(e_3,e_1,e_2) ),
inference(resolve,[$cnf( equalish(e_2,e_3) )],[refute_0_86,e_2_is_not_e_3]) ).
cnf(refute_0_88,plain,
( equalish(e_4,e_1)
| product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_2,e_2,e_3)
| product(e_3,e_4,e_1) ),
inference(resolve,[$cnf( product(e_3,e_1,e_2) )],[refute_0_87,refute_0_54]) ).
cnf(refute_0_89,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_2,e_2,e_3)
| product(e_3,e_4,e_1) ),
inference(resolve,[$cnf( equalish(e_4,e_1) )],[refute_0_88,e_4_is_not_e_1]) ).
cnf(refute_0_90,plain,
( equalish(e_2,e_3)
| product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_2,e_2,e_3) ),
inference(resolve,[$cnf( product(e_3,e_4,e_1) )],[refute_0_89,refute_0_51]) ).
cnf(refute_0_91,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_2,e_2,e_3) ),
inference(resolve,[$cnf( equalish(e_2,e_3) )],[refute_0_90,e_2_is_not_e_3]) ).
cnf(refute_0_92,plain,
( equalish(e_2,e_3)
| product(e_1,e_4,e_1)
| product(e_1,e_4,e_2) ),
inference(resolve,[$cnf( product(e_2,e_2,e_3) )],[refute_0_91,refute_0_26]) ).
cnf(refute_0_93,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2) ),
inference(resolve,[$cnf( equalish(e_2,e_3) )],[refute_0_92,e_2_is_not_e_3]) ).
cnf(refute_0_94,plain,
( equalish(e_3,e_1)
| product(e_1,e_4,e_1)
| product(e_3,e_4,e_1) ),
inference(resolve,[$cnf( product(e_1,e_4,e_2) )],[refute_0_93,refute_0_22]) ).
cnf(refute_0_95,plain,
( product(e_1,e_4,e_1)
| product(e_3,e_4,e_1) ),
inference(resolve,[$cnf( equalish(e_3,e_1) )],[refute_0_94,e_3_is_not_e_1]) ).
cnf(refute_0_96,plain,
( ~ product(Z,e_4,e_1)
| equalish(e_3,Z)
| product(e_1,e_4,e_1) ),
inference(resolve,[$cnf( product(e_3,e_4,e_1) )],[refute_0_95,refute_0_9]) ).
cnf(refute_0_97,plain,
( ~ product(e_2,e_4,e_1)
| equalish(e_3,e_2)
| product(e_1,e_4,e_1) ),
inference(subst,[],[refute_0_96:[bind(Z,$fot(e_2))]]) ).
cnf(refute_0_98,plain,
( ~ product(e_2,Z,e_3)
| ~ product(e_2,e_4,e_3)
| equalish(e_4,Z) ),
inference(subst,[],[product_right_cancellation:[bind(W,$fot(e_4)),bind(X,$fot(e_2)),bind(Y,$fot(e_3))]]) ).
cnf(refute_0_99,plain,
( ~ product(e_2,Z,e_3)
| equalish(e_4,Z)
| product(e_2,e_4,e_1)
| product(e_2,e_4,e_2) ),
inference(resolve,[$cnf( product(e_2,e_4,e_3) )],[refute_0_43,refute_0_98]) ).
cnf(refute_0_100,plain,
( ~ product(e_2,e_1,e_3)
| equalish(e_4,e_1)
| product(e_2,e_4,e_1)
| product(e_2,e_4,e_2) ),
inference(subst,[],[refute_0_99:[bind(Z,$fot(e_1))]]) ).
cnf(refute_0_101,plain,
( ~ greater(e_4,X1)
| ~ next(e_2,X1)
| ~ product(e_2,e_1,e_4) ),
inference(subst,[],[no_redundancy:[bind(X,$fot(e_2)),bind(Y,$fot(e_4))]]) ).
cnf(refute_0_102,plain,
( ~ group_element(X_45)
| ~ group_element(e_2)
| product(e_2,X_45,e_1)
| product(e_2,X_45,e_2)
| product(e_2,X_45,e_3)
| product(e_2,X_45,e_4) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(e_2)),bind(Y,$fot(X_45))]]) ).
cnf(refute_0_103,plain,
( ~ group_element(X_45)
| product(e_2,X_45,e_1)
| product(e_2,X_45,e_2)
| product(e_2,X_45,e_3)
| product(e_2,X_45,e_4) ),
inference(resolve,[$cnf( group_element(e_2) )],[element_2,refute_0_102]) ).
cnf(refute_0_104,plain,
( ~ group_element(e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_4) ),
inference(subst,[],[refute_0_103:[bind(X_45,$fot(e_1))]]) ).
cnf(refute_0_105,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_4) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_104]) ).
cnf(refute_0_106,plain,
( ~ greater(e_4,X1)
| ~ next(e_2,X1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(resolve,[$cnf( product(e_2,e_1,e_4) )],[refute_0_105,refute_0_101]) ).
cnf(refute_0_107,plain,
( ~ greater(e_4,e_3)
| ~ next(e_2,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(subst,[],[refute_0_106:[bind(X1,$fot(e_3))]]) ).
cnf(refute_0_108,plain,
( ~ greater(e_4,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(resolve,[$cnf( next(e_2,e_3) )],[e_2_then_e_3,refute_0_107]) ).
cnf(refute_0_109,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(resolve,[$cnf( greater(e_4,e_3) )],[e_4_greater_e_3,refute_0_108]) ).
cnf(refute_0_110,plain,
( equalish(e_4,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_4,e_1)
| product(e_2,e_4,e_2) ),
inference(resolve,[$cnf( product(e_2,e_1,e_3) )],[refute_0_109,refute_0_100]) ).
cnf(refute_0_111,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_4,e_1)
| product(e_2,e_4,e_2) ),
inference(resolve,[$cnf( equalish(e_4,e_1) )],[refute_0_110,e_4_is_not_e_1]) ).
cnf(refute_0_112,plain,
( equalish(e_2,e_4)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_4,e_1) ),
inference(resolve,[$cnf( product(e_2,e_4,e_2) )],[refute_0_111,refute_0_28]) ).
cnf(refute_0_113,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_4,e_1) ),
inference(resolve,[$cnf( equalish(e_2,e_4) )],[refute_0_112,e_2_is_not_e_4]) ).
cnf(refute_0_114,plain,
( equalish(e_3,e_2)
| product(e_1,e_4,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolve,[$cnf( product(e_2,e_4,e_1) )],[refute_0_113,refute_0_97]) ).
cnf(refute_0_115,plain,
( product(e_1,e_4,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolve,[$cnf( equalish(e_3,e_2) )],[refute_0_114,e_3_is_not_e_2]) ).
cnf(refute_0_116,plain,
( equalish(e_2,e_1)
| product(e_1,e_4,e_1)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( product(e_2,e_1,e_2) )],[refute_0_115,refute_0_8]) ).
cnf(refute_0_117,plain,
( product(e_1,e_4,e_1)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( equalish(e_2,e_1) )],[refute_0_116,e_2_is_not_e_1]) ).
cnf(refute_0_118,plain,
( equalish(e_2,e_1)
| product(e_1,e_4,e_1) ),
inference(resolve,[$cnf( product(e_2,e_1,e_1) )],[refute_0_117,refute_0_7]) ).
cnf(refute_0_119,plain,
product(e_1,e_4,e_1),
inference(resolve,[$cnf( equalish(e_2,e_1) )],[refute_0_118,e_2_is_not_e_1]) ).
cnf(refute_0_120,plain,
equalish(e_1,e_4),
inference(resolve,[$cnf( product(e_1,e_4,e_1) )],[refute_0_119,refute_0_3]) ).
cnf(refute_0_121,plain,
$false,
inference(resolve,[$cnf( equalish(e_1,e_4) )],[refute_0_120,e_1_is_not_e_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP126-2.004 : TPTP v8.1.0. Released v1.2.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n029.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 23:30:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.44/0.62 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.44/0.62
% 0.44/0.62 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.47/0.63
%------------------------------------------------------------------------------