TSTP Solution File: GRP124-9.004 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP124-9.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 10:36:37 EDT 2022
% Result : Unsatisfiable 0.19s 0.52s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 20
% Syntax : Number of clauses : 151 ( 21 unt; 95 nHn; 146 RR)
% Number of literals : 488 ( 0 equ; 101 neg)
% Maximal clause size : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 63 ( 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_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_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_2,axiom,
~ equalish(e_4,e_2) ).
cnf(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3) ).
cnf(product1_total_function1,axiom,
( ~ group_element(X)
| ~ group_element(Y)
| product1(X,Y,e_1)
| product1(X,Y,e_2)
| product1(X,Y,e_3)
| product1(X,Y,e_4) ) ).
cnf(product1_right_cancellation,axiom,
( ~ product1(X,W,Y)
| ~ product1(X,Z,Y)
| equalish(W,Z) ) ).
cnf(product1_left_cancellation,axiom,
( ~ product1(W,Y,X)
| ~ product1(Z,Y,X)
| equalish(W,Z) ) ).
cnf(product1_idempotence,axiom,
product1(X,X,X) ).
cnf(product2_total_function2,axiom,
( ~ product2(X,Y,W)
| ~ product2(X,Y,Z)
| equalish(W,Z) ) ).
cnf(product2_idempotence,axiom,
product2(X,X,X) ).
cnf(qg2a,negated_conjecture,
( ~ product1(X,Y,Z1)
| ~ product1(Z1,X,Z2)
| product2(Z2,Y,X) ) ).
cnf(refute_0_0,plain,
product1(X_16,X_16,X_16),
inference(subst,[],[product1_idempotence:[bind(X,$fot(X_16))]]) ).
cnf(refute_0_1,plain,
( ~ product1(X_16,X_16,X_16)
| ~ product1(X_16,X_17,X_16)
| equalish(X_16,X_17) ),
inference(subst,[],[product1_right_cancellation:[bind(W,$fot(X_16)),bind(X,$fot(X_16)),bind(Y,$fot(X_16)),bind(Z,$fot(X_17))]]) ).
cnf(refute_0_2,plain,
( ~ product1(X_16,X_17,X_16)
| equalish(X_16,X_17) ),
inference(resolve,[$cnf( product1(X_16,X_16,X_16) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ product1(e_1,e_4,e_1)
| equalish(e_1,e_4) ),
inference(subst,[],[refute_0_2:[bind(X_16,$fot(e_1)),bind(X_17,$fot(e_4))]]) ).
cnf(refute_0_4,plain,
( ~ product1(Z,e_4,e_1)
| ~ product1(e_3,e_4,e_1)
| equalish(e_3,Z) ),
inference(subst,[],[product1_left_cancellation:[bind(W,$fot(e_3)),bind(X,$fot(e_1)),bind(Y,$fot(e_4))]]) ).
cnf(refute_0_5,plain,
( ~ product1(Z,e_4,e_2)
| ~ product1(e_3,e_4,e_2)
| equalish(e_3,Z) ),
inference(subst,[],[product1_left_cancellation:[bind(W,$fot(e_3)),bind(X,$fot(e_2)),bind(Y,$fot(e_4))]]) ).
cnf(refute_0_6,plain,
( ~ product1(e_3,e_4,e_3)
| equalish(e_3,e_4) ),
inference(subst,[],[refute_0_2:[bind(X_16,$fot(e_3)),bind(X_17,$fot(e_4))]]) ).
cnf(refute_0_7,plain,
product1(X_23,X_23,X_23),
inference(subst,[],[product1_idempotence:[bind(X,$fot(X_23))]]) ).
cnf(refute_0_8,plain,
( ~ product1(X_22,X_23,X_23)
| ~ product1(X_23,X_23,X_23)
| equalish(X_22,X_23) ),
inference(subst,[],[product1_left_cancellation:[bind(W,$fot(X_22)),bind(X,$fot(X_23)),bind(Y,$fot(X_23)),bind(Z,$fot(X_23))]]) ).
cnf(refute_0_9,plain,
( ~ product1(X_22,X_23,X_23)
| equalish(X_22,X_23) ),
inference(resolve,[$cnf( product1(X_23,X_23,X_23) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ product1(e_3,e_4,e_4)
| equalish(e_3,e_4) ),
inference(subst,[],[refute_0_9:[bind(X_22,$fot(e_3)),bind(X_23,$fot(e_4))]]) ).
cnf(refute_0_11,plain,
( ~ group_element(X_87)
| ~ group_element(e_3)
| product1(e_3,X_87,e_1)
| product1(e_3,X_87,e_2)
| product1(e_3,X_87,e_3)
| product1(e_3,X_87,e_4) ),
inference(subst,[],[product1_total_function1:[bind(X,$fot(e_3)),bind(Y,$fot(X_87))]]) ).
cnf(refute_0_12,plain,
( ~ group_element(X_87)
| product1(e_3,X_87,e_1)
| product1(e_3,X_87,e_2)
| product1(e_3,X_87,e_3)
| product1(e_3,X_87,e_4) ),
inference(resolve,[$cnf( group_element(e_3) )],[element_3,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ group_element(e_4)
| product1(e_3,e_4,e_1)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_3)
| product1(e_3,e_4,e_4) ),
inference(subst,[],[refute_0_12:[bind(X_87,$fot(e_4))]]) ).
cnf(refute_0_14,plain,
( product1(e_3,e_4,e_1)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_3)
| product1(e_3,e_4,e_4) ),
inference(resolve,[$cnf( group_element(e_4) )],[element_4,refute_0_13]) ).
cnf(refute_0_15,plain,
( equalish(e_3,e_4)
| product1(e_3,e_4,e_1)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_3) ),
inference(resolve,[$cnf( product1(e_3,e_4,e_4) )],[refute_0_14,refute_0_10]) ).
cnf(refute_0_16,plain,
( product1(e_3,e_4,e_1)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_3) ),
inference(resolve,[$cnf( equalish(e_3,e_4) )],[refute_0_15,e_3_is_not_e_4]) ).
cnf(refute_0_17,plain,
( equalish(e_3,e_4)
| product1(e_3,e_4,e_1)
| product1(e_3,e_4,e_2) ),
inference(resolve,[$cnf( product1(e_3,e_4,e_3) )],[refute_0_16,refute_0_6]) ).
cnf(refute_0_18,plain,
( product1(e_3,e_4,e_1)
| product1(e_3,e_4,e_2) ),
inference(resolve,[$cnf( equalish(e_3,e_4) )],[refute_0_17,e_3_is_not_e_4]) ).
cnf(refute_0_19,plain,
( ~ product1(Z,e_4,e_2)
| equalish(e_3,Z)
| product1(e_3,e_4,e_1) ),
inference(resolve,[$cnf( product1(e_3,e_4,e_2) )],[refute_0_18,refute_0_5]) ).
cnf(refute_0_20,plain,
( ~ product1(e_1,e_4,e_2)
| equalish(e_3,e_1)
| product1(e_3,e_4,e_1) ),
inference(subst,[],[refute_0_19:[bind(Z,$fot(e_1))]]) ).
cnf(refute_0_21,plain,
( ~ product1(e_2,e_3,e_2)
| equalish(e_2,e_3) ),
inference(subst,[],[refute_0_2:[bind(X_16,$fot(e_2)),bind(X_17,$fot(e_3))]]) ).
cnf(refute_0_22,plain,
( ~ product1(e_2,e_3,e_3)
| equalish(e_2,e_3) ),
inference(subst,[],[refute_0_9:[bind(X_22,$fot(e_2)),bind(X_23,$fot(e_3))]]) ).
cnf(refute_0_23,plain,
( ~ product1(Z,e_4,e_1)
| ~ product1(e_2,e_4,e_1)
| equalish(e_2,Z) ),
inference(subst,[],[product1_left_cancellation:[bind(W,$fot(e_2)),bind(X,$fot(e_1)),bind(Y,$fot(e_4))]]) ).
cnf(refute_0_24,plain,
( ~ product1(e_2,e_4,e_2)
| equalish(e_2,e_4) ),
inference(subst,[],[refute_0_2:[bind(X_16,$fot(e_2)),bind(X_17,$fot(e_4))]]) ).
cnf(refute_0_25,plain,
( ~ product1(Z,e_4,e_3)
| ~ product1(e_1,e_4,e_3)
| equalish(e_1,Z) ),
inference(subst,[],[product1_left_cancellation:[bind(W,$fot(e_1)),bind(X,$fot(e_3)),bind(Y,$fot(e_4))]]) ).
cnf(refute_0_26,plain,
( ~ product1(e_1,e_4,e_4)
| equalish(e_1,e_4) ),
inference(subst,[],[refute_0_9:[bind(X_22,$fot(e_1)),bind(X_23,$fot(e_4))]]) ).
cnf(refute_0_27,plain,
( ~ group_element(X_87)
| ~ group_element(e_1)
| product1(e_1,X_87,e_1)
| product1(e_1,X_87,e_2)
| product1(e_1,X_87,e_3)
| product1(e_1,X_87,e_4) ),
inference(subst,[],[product1_total_function1:[bind(X,$fot(e_1)),bind(Y,$fot(X_87))]]) ).
cnf(refute_0_28,plain,
( ~ group_element(X_87)
| product1(e_1,X_87,e_1)
| product1(e_1,X_87,e_2)
| product1(e_1,X_87,e_3)
| product1(e_1,X_87,e_4) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ group_element(e_4)
| product1(e_1,e_4,e_1)
| product1(e_1,e_4,e_2)
| product1(e_1,e_4,e_3)
| product1(e_1,e_4,e_4) ),
inference(subst,[],[refute_0_28:[bind(X_87,$fot(e_4))]]) ).
cnf(refute_0_30,plain,
( product1(e_1,e_4,e_1)
| product1(e_1,e_4,e_2)
| product1(e_1,e_4,e_3)
| product1(e_1,e_4,e_4) ),
inference(resolve,[$cnf( group_element(e_4) )],[element_4,refute_0_29]) ).
cnf(refute_0_31,plain,
( equalish(e_1,e_4)
| product1(e_1,e_4,e_1)
| product1(e_1,e_4,e_2)
| product1(e_1,e_4,e_3) ),
inference(resolve,[$cnf( product1(e_1,e_4,e_4) )],[refute_0_30,refute_0_26]) ).
cnf(refute_0_32,plain,
( product1(e_1,e_4,e_1)
| product1(e_1,e_4,e_2)
| product1(e_1,e_4,e_3) ),
inference(resolve,[$cnf( equalish(e_1,e_4) )],[refute_0_31,e_1_is_not_e_4]) ).
cnf(refute_0_33,plain,
( ~ product1(Z,e_4,e_3)
| equalish(e_1,Z)
| product1(e_1,e_4,e_1)
| product1(e_1,e_4,e_2) ),
inference(resolve,[$cnf( product1(e_1,e_4,e_3) )],[refute_0_32,refute_0_25]) ).
cnf(refute_0_34,plain,
( ~ product1(e_2,e_4,e_3)
| equalish(e_1,e_2)
| product1(e_1,e_4,e_1)
| product1(e_1,e_4,e_2) ),
inference(subst,[],[refute_0_33:[bind(Z,$fot(e_2))]]) ).
cnf(refute_0_35,plain,
( ~ product1(e_2,e_4,e_4)
| equalish(e_2,e_4) ),
inference(subst,[],[refute_0_9:[bind(X_22,$fot(e_2)),bind(X_23,$fot(e_4))]]) ).
cnf(refute_0_36,plain,
( ~ group_element(X_87)
| ~ group_element(e_2)
| product1(e_2,X_87,e_1)
| product1(e_2,X_87,e_2)
| product1(e_2,X_87,e_3)
| product1(e_2,X_87,e_4) ),
inference(subst,[],[product1_total_function1:[bind(X,$fot(e_2)),bind(Y,$fot(X_87))]]) ).
cnf(refute_0_37,plain,
( ~ group_element(X_87)
| product1(e_2,X_87,e_1)
| product1(e_2,X_87,e_2)
| product1(e_2,X_87,e_3)
| product1(e_2,X_87,e_4) ),
inference(resolve,[$cnf( group_element(e_2) )],[element_2,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ group_element(e_4)
| product1(e_2,e_4,e_1)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_3)
| product1(e_2,e_4,e_4) ),
inference(subst,[],[refute_0_37:[bind(X_87,$fot(e_4))]]) ).
cnf(refute_0_39,plain,
( product1(e_2,e_4,e_1)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_3)
| product1(e_2,e_4,e_4) ),
inference(resolve,[$cnf( group_element(e_4) )],[element_4,refute_0_38]) ).
cnf(refute_0_40,plain,
( equalish(e_2,e_4)
| product1(e_2,e_4,e_1)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_3) ),
inference(resolve,[$cnf( product1(e_2,e_4,e_4) )],[refute_0_39,refute_0_35]) ).
cnf(refute_0_41,plain,
( product1(e_2,e_4,e_1)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_3) ),
inference(resolve,[$cnf( equalish(e_2,e_4) )],[refute_0_40,e_2_is_not_e_4]) ).
cnf(refute_0_42,plain,
( equalish(e_1,e_2)
| product1(e_1,e_4,e_1)
| product1(e_1,e_4,e_2)
| product1(e_2,e_4,e_1)
| product1(e_2,e_4,e_2) ),
inference(resolve,[$cnf( product1(e_2,e_4,e_3) )],[refute_0_41,refute_0_34]) ).
cnf(refute_0_43,plain,
( product1(e_1,e_4,e_1)
| product1(e_1,e_4,e_2)
| product1(e_2,e_4,e_1)
| product1(e_2,e_4,e_2) ),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_42,e_1_is_not_e_2]) ).
cnf(refute_0_44,plain,
( equalish(e_2,e_4)
| product1(e_1,e_4,e_1)
| product1(e_1,e_4,e_2)
| product1(e_2,e_4,e_1) ),
inference(resolve,[$cnf( product1(e_2,e_4,e_2) )],[refute_0_43,refute_0_24]) ).
cnf(refute_0_45,plain,
( product1(e_1,e_4,e_1)
| product1(e_1,e_4,e_2)
| product1(e_2,e_4,e_1) ),
inference(resolve,[$cnf( equalish(e_2,e_4) )],[refute_0_44,e_2_is_not_e_4]) ).
cnf(refute_0_46,plain,
( ~ product1(Z,e_4,e_1)
| equalish(e_2,Z)
| product1(e_1,e_4,e_1)
| product1(e_1,e_4,e_2) ),
inference(resolve,[$cnf( product1(e_2,e_4,e_1) )],[refute_0_45,refute_0_23]) ).
cnf(refute_0_47,plain,
( ~ product1(e_3,e_4,e_1)
| equalish(e_2,e_3)
| product1(e_1,e_4,e_1)
| product1(e_1,e_4,e_2) ),
inference(subst,[],[refute_0_46:[bind(Z,$fot(e_3))]]) ).
cnf(refute_0_48,plain,
product2(X_30,X_30,X_30),
inference(subst,[],[product2_idempotence:[bind(X,$fot(X_30))]]) ).
cnf(refute_0_49,plain,
( ~ product2(X_30,X_30,X_30)
| ~ product2(X_30,X_30,X_33)
| equalish(X_30,X_33) ),
inference(subst,[],[product2_total_function2:[bind(W,$fot(X_30)),bind(X,$fot(X_30)),bind(Y,$fot(X_30)),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_50,plain,
( ~ product2(X_30,X_30,X_33)
| equalish(X_30,X_33) ),
inference(resolve,[$cnf( product2(X_30,X_30,X_30) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
( ~ product2(e_4,e_4,e_3)
| equalish(e_4,e_3) ),
inference(subst,[],[refute_0_50:[bind(X_30,$fot(e_4)),bind(X_33,$fot(e_3))]]) ).
cnf(refute_0_52,plain,
( ~ group_element(e_3)
| product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_4) ),
inference(subst,[],[refute_0_37:[bind(X_87,$fot(e_3))]]) ).
cnf(refute_0_53,plain,
( product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_4) ),
inference(resolve,[$cnf( group_element(e_3) )],[element_3,refute_0_52]) ).
cnf(refute_0_54,plain,
( ~ product1(e_2,e_3,Z2)
| ~ product1(e_3,e_4,e_2)
| product2(Z2,e_4,e_3) ),
inference(subst,[],[qg2a:[bind(X,$fot(e_3)),bind(Y,$fot(e_4)),bind(Z1,$fot(e_2))]]) ).
cnf(refute_0_55,plain,
( ~ product1(e_2,e_3,Z2)
| product1(e_3,e_4,e_1)
| product2(Z2,e_4,e_3) ),
inference(resolve,[$cnf( product1(e_3,e_4,e_2) )],[refute_0_18,refute_0_54]) ).
cnf(refute_0_56,plain,
( ~ product1(e_2,e_3,e_4)
| product1(e_3,e_4,e_1)
| product2(e_4,e_4,e_3) ),
inference(subst,[],[refute_0_55:[bind(Z2,$fot(e_4))]]) ).
cnf(refute_0_57,plain,
( product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_3)
| product1(e_3,e_4,e_1)
| product2(e_4,e_4,e_3) ),
inference(resolve,[$cnf( product1(e_2,e_3,e_4) )],[refute_0_53,refute_0_56]) ).
cnf(refute_0_58,plain,
( equalish(e_4,e_3)
| product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_3)
| product1(e_3,e_4,e_1) ),
inference(resolve,[$cnf( product2(e_4,e_4,e_3) )],[refute_0_57,refute_0_51]) ).
cnf(refute_0_59,plain,
( product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_3)
| product1(e_3,e_4,e_1) ),
inference(resolve,[$cnf( equalish(e_4,e_3) )],[refute_0_58,e_4_is_not_e_3]) ).
cnf(refute_0_60,plain,
( equalish(e_2,e_3)
| product1(e_1,e_4,e_1)
| product1(e_1,e_4,e_2)
| product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_3) ),
inference(resolve,[$cnf( product1(e_3,e_4,e_1) )],[refute_0_59,refute_0_47]) ).
cnf(refute_0_61,plain,
( product1(e_1,e_4,e_1)
| product1(e_1,e_4,e_2)
| product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_3) ),
inference(resolve,[$cnf( equalish(e_2,e_3) )],[refute_0_60,e_2_is_not_e_3]) ).
cnf(refute_0_62,plain,
( equalish(e_2,e_3)
| product1(e_1,e_4,e_1)
| product1(e_1,e_4,e_2)
| product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2) ),
inference(resolve,[$cnf( product1(e_2,e_3,e_3) )],[refute_0_61,refute_0_22]) ).
cnf(refute_0_63,plain,
( product1(e_1,e_4,e_1)
| product1(e_1,e_4,e_2)
| product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2) ),
inference(resolve,[$cnf( equalish(e_2,e_3) )],[refute_0_62,e_2_is_not_e_3]) ).
cnf(refute_0_64,plain,
( equalish(e_2,e_3)
| product1(e_1,e_4,e_1)
| product1(e_1,e_4,e_2)
| product1(e_2,e_3,e_1) ),
inference(resolve,[$cnf( product1(e_2,e_3,e_2) )],[refute_0_63,refute_0_21]) ).
cnf(refute_0_65,plain,
( product1(e_1,e_4,e_1)
| product1(e_1,e_4,e_2)
| product1(e_2,e_3,e_1) ),
inference(resolve,[$cnf( equalish(e_2,e_3) )],[refute_0_64,e_2_is_not_e_3]) ).
cnf(refute_0_66,plain,
( ~ product1(e_2,W,e_1)
| ~ product1(e_2,e_4,e_1)
| equalish(W,e_4) ),
inference(subst,[],[product1_right_cancellation:[bind(X,$fot(e_2)),bind(Y,$fot(e_1)),bind(Z,$fot(e_4))]]) ).
cnf(refute_0_67,plain,
( ~ product1(e_2,W,e_1)
| equalish(W,e_4)
| product1(e_1,e_4,e_1)
| product1(e_1,e_4,e_2) ),
inference(resolve,[$cnf( product1(e_2,e_4,e_1) )],[refute_0_45,refute_0_66]) ).
cnf(refute_0_68,plain,
( ~ product1(e_2,e_3,e_1)
| equalish(e_3,e_4)
| product1(e_1,e_4,e_1)
| product1(e_1,e_4,e_2) ),
inference(subst,[],[refute_0_67:[bind(W,$fot(e_3))]]) ).
cnf(refute_0_69,plain,
( equalish(e_3,e_4)
| product1(e_1,e_4,e_1)
| product1(e_1,e_4,e_2) ),
inference(resolve,[$cnf( product1(e_2,e_3,e_1) )],[refute_0_65,refute_0_68]) ).
cnf(refute_0_70,plain,
( product1(e_1,e_4,e_1)
| product1(e_1,e_4,e_2) ),
inference(resolve,[$cnf( equalish(e_3,e_4) )],[refute_0_69,e_3_is_not_e_4]) ).
cnf(refute_0_71,plain,
( equalish(e_3,e_1)
| product1(e_1,e_4,e_1)
| product1(e_3,e_4,e_1) ),
inference(resolve,[$cnf( product1(e_1,e_4,e_2) )],[refute_0_70,refute_0_20]) ).
cnf(refute_0_72,plain,
( product1(e_1,e_4,e_1)
| product1(e_3,e_4,e_1) ),
inference(resolve,[$cnf( equalish(e_3,e_1) )],[refute_0_71,e_3_is_not_e_1]) ).
cnf(refute_0_73,plain,
( ~ product1(Z,e_4,e_1)
| equalish(e_3,Z)
| product1(e_1,e_4,e_1) ),
inference(resolve,[$cnf( product1(e_3,e_4,e_1) )],[refute_0_72,refute_0_4]) ).
cnf(refute_0_74,plain,
( ~ product1(e_2,e_4,e_1)
| equalish(e_3,e_2)
| product1(e_1,e_4,e_1) ),
inference(subst,[],[refute_0_73:[bind(Z,$fot(e_2))]]) ).
cnf(refute_0_75,plain,
( ~ product1(Z,e_3,e_1)
| ~ product1(e_4,e_3,e_1)
| equalish(e_4,Z) ),
inference(subst,[],[product1_left_cancellation:[bind(W,$fot(e_4)),bind(X,$fot(e_1)),bind(Y,$fot(e_3))]]) ).
cnf(refute_0_76,plain,
( ~ product2(e_3,e_3,e_4)
| equalish(e_3,e_4) ),
inference(subst,[],[refute_0_50:[bind(X_30,$fot(e_3)),bind(X_33,$fot(e_4))]]) ).
cnf(refute_0_77,plain,
( ~ product1(e_2,e_4,Z2)
| ~ product1(e_4,e_3,e_2)
| product2(Z2,e_3,e_4) ),
inference(subst,[],[qg2a:[bind(X,$fot(e_4)),bind(Y,$fot(e_3)),bind(Z1,$fot(e_2))]]) ).
cnf(refute_0_78,plain,
( ~ product1(e_4,e_3,e_3)
| equalish(e_4,e_3) ),
inference(subst,[],[refute_0_9:[bind(X_22,$fot(e_4)),bind(X_23,$fot(e_3))]]) ).
cnf(refute_0_79,plain,
( ~ product1(e_4,e_3,e_4)
| equalish(e_4,e_3) ),
inference(subst,[],[refute_0_2:[bind(X_16,$fot(e_4)),bind(X_17,$fot(e_3))]]) ).
cnf(refute_0_80,plain,
( ~ group_element(X_87)
| ~ group_element(e_4)
| product1(e_4,X_87,e_1)
| product1(e_4,X_87,e_2)
| product1(e_4,X_87,e_3)
| product1(e_4,X_87,e_4) ),
inference(subst,[],[product1_total_function1:[bind(X,$fot(e_4)),bind(Y,$fot(X_87))]]) ).
cnf(refute_0_81,plain,
( ~ group_element(X_87)
| product1(e_4,X_87,e_1)
| product1(e_4,X_87,e_2)
| product1(e_4,X_87,e_3)
| product1(e_4,X_87,e_4) ),
inference(resolve,[$cnf( group_element(e_4) )],[element_4,refute_0_80]) ).
cnf(refute_0_82,plain,
( ~ group_element(e_3)
| product1(e_4,e_3,e_1)
| product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_3)
| product1(e_4,e_3,e_4) ),
inference(subst,[],[refute_0_81:[bind(X_87,$fot(e_3))]]) ).
cnf(refute_0_83,plain,
( product1(e_4,e_3,e_1)
| product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_3)
| product1(e_4,e_3,e_4) ),
inference(resolve,[$cnf( group_element(e_3) )],[element_3,refute_0_82]) ).
cnf(refute_0_84,plain,
( equalish(e_4,e_3)
| product1(e_4,e_3,e_1)
| product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_3) ),
inference(resolve,[$cnf( product1(e_4,e_3,e_4) )],[refute_0_83,refute_0_79]) ).
cnf(refute_0_85,plain,
( product1(e_4,e_3,e_1)
| product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_3) ),
inference(resolve,[$cnf( equalish(e_4,e_3) )],[refute_0_84,e_4_is_not_e_3]) ).
cnf(refute_0_86,plain,
( equalish(e_4,e_3)
| product1(e_4,e_3,e_1)
| product1(e_4,e_3,e_2) ),
inference(resolve,[$cnf( product1(e_4,e_3,e_3) )],[refute_0_85,refute_0_78]) ).
cnf(refute_0_87,plain,
( product1(e_4,e_3,e_1)
| product1(e_4,e_3,e_2) ),
inference(resolve,[$cnf( equalish(e_4,e_3) )],[refute_0_86,e_4_is_not_e_3]) ).
cnf(refute_0_88,plain,
( ~ product1(e_2,e_4,Z2)
| product1(e_4,e_3,e_1)
| product2(Z2,e_3,e_4) ),
inference(resolve,[$cnf( product1(e_4,e_3,e_2) )],[refute_0_87,refute_0_77]) ).
cnf(refute_0_89,plain,
( ~ product1(e_2,e_4,e_3)
| product1(e_4,e_3,e_1)
| product2(e_3,e_3,e_4) ),
inference(subst,[],[refute_0_88:[bind(Z2,$fot(e_3))]]) ).
cnf(refute_0_90,plain,
( product1(e_2,e_4,e_1)
| product1(e_2,e_4,e_2)
| product1(e_4,e_3,e_1)
| product2(e_3,e_3,e_4) ),
inference(resolve,[$cnf( product1(e_2,e_4,e_3) )],[refute_0_41,refute_0_89]) ).
cnf(refute_0_91,plain,
( equalish(e_3,e_4)
| product1(e_2,e_4,e_1)
| product1(e_2,e_4,e_2)
| product1(e_4,e_3,e_1) ),
inference(resolve,[$cnf( product2(e_3,e_3,e_4) )],[refute_0_90,refute_0_76]) ).
cnf(refute_0_92,plain,
( product1(e_2,e_4,e_1)
| product1(e_2,e_4,e_2)
| product1(e_4,e_3,e_1) ),
inference(resolve,[$cnf( equalish(e_3,e_4) )],[refute_0_91,e_3_is_not_e_4]) ).
cnf(refute_0_93,plain,
( ~ product1(Z,e_3,e_1)
| equalish(e_4,Z)
| product1(e_2,e_4,e_1)
| product1(e_2,e_4,e_2) ),
inference(resolve,[$cnf( product1(e_4,e_3,e_1) )],[refute_0_92,refute_0_75]) ).
cnf(refute_0_94,plain,
( ~ product1(e_2,e_3,e_1)
| equalish(e_4,e_2)
| product1(e_2,e_4,e_1)
| product1(e_2,e_4,e_2) ),
inference(subst,[],[refute_0_93:[bind(Z,$fot(e_2))]]) ).
cnf(refute_0_95,plain,
( ~ product1(e_4,e_2,e_2)
| equalish(e_4,e_2) ),
inference(subst,[],[refute_0_9:[bind(X_22,$fot(e_4)),bind(X_23,$fot(e_2))]]) ).
cnf(refute_0_96,plain,
( ~ product2(e_3,e_3,e_2)
| equalish(e_3,e_2) ),
inference(subst,[],[refute_0_50:[bind(X_30,$fot(e_3)),bind(X_33,$fot(e_2))]]) ).
cnf(refute_0_97,plain,
( ~ product1(e_2,Y,e_4)
| ~ product1(e_4,e_2,e_3)
| product2(e_3,Y,e_2) ),
inference(subst,[],[qg2a:[bind(X,$fot(e_2)),bind(Z1,$fot(e_4)),bind(Z2,$fot(e_3))]]) ).
cnf(refute_0_98,plain,
( ~ product1(e_4,e_2,e_4)
| equalish(e_4,e_2) ),
inference(subst,[],[refute_0_2:[bind(X_16,$fot(e_4)),bind(X_17,$fot(e_2))]]) ).
cnf(refute_0_99,plain,
( ~ group_element(e_2)
| product1(e_4,e_2,e_1)
| product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_3)
| product1(e_4,e_2,e_4) ),
inference(subst,[],[refute_0_81:[bind(X_87,$fot(e_2))]]) ).
cnf(refute_0_100,plain,
( product1(e_4,e_2,e_1)
| product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_3)
| product1(e_4,e_2,e_4) ),
inference(resolve,[$cnf( group_element(e_2) )],[element_2,refute_0_99]) ).
cnf(refute_0_101,plain,
( equalish(e_4,e_2)
| product1(e_4,e_2,e_1)
| product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_3) ),
inference(resolve,[$cnf( product1(e_4,e_2,e_4) )],[refute_0_100,refute_0_98]) ).
cnf(refute_0_102,plain,
( product1(e_4,e_2,e_1)
| product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_3) ),
inference(resolve,[$cnf( equalish(e_4,e_2) )],[refute_0_101,e_4_is_not_e_2]) ).
cnf(refute_0_103,plain,
( ~ product1(e_2,Y,e_4)
| product1(e_4,e_2,e_1)
| product1(e_4,e_2,e_2)
| product2(e_3,Y,e_2) ),
inference(resolve,[$cnf( product1(e_4,e_2,e_3) )],[refute_0_102,refute_0_97]) ).
cnf(refute_0_104,plain,
( ~ product1(e_2,e_3,e_4)
| product1(e_4,e_2,e_1)
| product1(e_4,e_2,e_2)
| product2(e_3,e_3,e_2) ),
inference(subst,[],[refute_0_103:[bind(Y,$fot(e_3))]]) ).
cnf(refute_0_105,plain,
( product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_3)
| product1(e_4,e_2,e_1)
| product1(e_4,e_2,e_2)
| product2(e_3,e_3,e_2) ),
inference(resolve,[$cnf( product1(e_2,e_3,e_4) )],[refute_0_53,refute_0_104]) ).
cnf(refute_0_106,plain,
( equalish(e_3,e_2)
| product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_3)
| product1(e_4,e_2,e_1)
| product1(e_4,e_2,e_2) ),
inference(resolve,[$cnf( product2(e_3,e_3,e_2) )],[refute_0_105,refute_0_96]) ).
cnf(refute_0_107,plain,
( product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_3)
| product1(e_4,e_2,e_1)
| product1(e_4,e_2,e_2) ),
inference(resolve,[$cnf( equalish(e_3,e_2) )],[refute_0_106,e_3_is_not_e_2]) ).
cnf(refute_0_108,plain,
( equalish(e_4,e_2)
| product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_3)
| product1(e_4,e_2,e_1) ),
inference(resolve,[$cnf( product1(e_4,e_2,e_2) )],[refute_0_107,refute_0_95]) ).
cnf(refute_0_109,plain,
( product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_3)
| product1(e_4,e_2,e_1) ),
inference(resolve,[$cnf( equalish(e_4,e_2) )],[refute_0_108,e_4_is_not_e_2]) ).
cnf(refute_0_110,plain,
( ~ product1(e_4,W,e_1)
| ~ product1(e_4,e_3,e_1)
| equalish(W,e_3) ),
inference(subst,[],[product1_right_cancellation:[bind(X,$fot(e_4)),bind(Y,$fot(e_1)),bind(Z,$fot(e_3))]]) ).
cnf(refute_0_111,plain,
( ~ product1(e_4,W,e_1)
| equalish(W,e_3)
| product1(e_2,e_4,e_1)
| product1(e_2,e_4,e_2) ),
inference(resolve,[$cnf( product1(e_4,e_3,e_1) )],[refute_0_92,refute_0_110]) ).
cnf(refute_0_112,plain,
( ~ product1(e_4,e_2,e_1)
| equalish(e_2,e_3)
| product1(e_2,e_4,e_1)
| product1(e_2,e_4,e_2) ),
inference(subst,[],[refute_0_111:[bind(W,$fot(e_2))]]) ).
cnf(refute_0_113,plain,
( equalish(e_2,e_3)
| product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_3)
| product1(e_2,e_4,e_1)
| product1(e_2,e_4,e_2) ),
inference(resolve,[$cnf( product1(e_4,e_2,e_1) )],[refute_0_109,refute_0_112]) ).
cnf(refute_0_114,plain,
( product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_3)
| product1(e_2,e_4,e_1)
| product1(e_2,e_4,e_2) ),
inference(resolve,[$cnf( equalish(e_2,e_3) )],[refute_0_113,e_2_is_not_e_3]) ).
cnf(refute_0_115,plain,
( equalish(e_2,e_4)
| product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_3)
| product1(e_2,e_4,e_1) ),
inference(resolve,[$cnf( product1(e_2,e_4,e_2) )],[refute_0_114,refute_0_24]) ).
cnf(refute_0_116,plain,
( product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_3)
| product1(e_2,e_4,e_1) ),
inference(resolve,[$cnf( equalish(e_2,e_4) )],[refute_0_115,e_2_is_not_e_4]) ).
cnf(refute_0_117,plain,
( equalish(e_3,e_2)
| product1(e_1,e_4,e_1)
| product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_3) ),
inference(resolve,[$cnf( product1(e_2,e_4,e_1) )],[refute_0_116,refute_0_74]) ).
cnf(refute_0_118,plain,
( product1(e_1,e_4,e_1)
| product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_3) ),
inference(resolve,[$cnf( equalish(e_3,e_2) )],[refute_0_117,e_3_is_not_e_2]) ).
cnf(refute_0_119,plain,
( equalish(e_2,e_3)
| product1(e_1,e_4,e_1)
| product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2) ),
inference(resolve,[$cnf( product1(e_2,e_3,e_3) )],[refute_0_118,refute_0_22]) ).
cnf(refute_0_120,plain,
( product1(e_1,e_4,e_1)
| product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2) ),
inference(resolve,[$cnf( equalish(e_2,e_3) )],[refute_0_119,e_2_is_not_e_3]) ).
cnf(refute_0_121,plain,
( equalish(e_2,e_3)
| product1(e_1,e_4,e_1)
| product1(e_2,e_3,e_1) ),
inference(resolve,[$cnf( product1(e_2,e_3,e_2) )],[refute_0_120,refute_0_21]) ).
cnf(refute_0_122,plain,
( product1(e_1,e_4,e_1)
| product1(e_2,e_3,e_1) ),
inference(resolve,[$cnf( equalish(e_2,e_3) )],[refute_0_121,e_2_is_not_e_3]) ).
cnf(refute_0_123,plain,
( equalish(e_4,e_2)
| product1(e_1,e_4,e_1)
| product1(e_2,e_4,e_1)
| product1(e_2,e_4,e_2) ),
inference(resolve,[$cnf( product1(e_2,e_3,e_1) )],[refute_0_122,refute_0_94]) ).
cnf(refute_0_124,plain,
( product1(e_1,e_4,e_1)
| product1(e_2,e_4,e_1)
| product1(e_2,e_4,e_2) ),
inference(resolve,[$cnf( equalish(e_4,e_2) )],[refute_0_123,e_4_is_not_e_2]) ).
cnf(refute_0_125,plain,
( equalish(e_2,e_4)
| product1(e_1,e_4,e_1)
| product1(e_2,e_4,e_1) ),
inference(resolve,[$cnf( product1(e_2,e_4,e_2) )],[refute_0_124,refute_0_24]) ).
cnf(refute_0_126,plain,
( product1(e_1,e_4,e_1)
| product1(e_2,e_4,e_1) ),
inference(resolve,[$cnf( equalish(e_2,e_4) )],[refute_0_125,e_2_is_not_e_4]) ).
cnf(refute_0_127,plain,
( equalish(e_3,e_2)
| product1(e_1,e_4,e_1) ),
inference(resolve,[$cnf( product1(e_2,e_4,e_1) )],[refute_0_126,refute_0_74]) ).
cnf(refute_0_128,plain,
product1(e_1,e_4,e_1),
inference(resolve,[$cnf( equalish(e_3,e_2) )],[refute_0_127,e_3_is_not_e_2]) ).
cnf(refute_0_129,plain,
equalish(e_1,e_4),
inference(resolve,[$cnf( product1(e_1,e_4,e_1) )],[refute_0_128,refute_0_3]) ).
cnf(refute_0_130,plain,
$false,
inference(resolve,[$cnf( equalish(e_1,e_4) )],[refute_0_129,e_1_is_not_e_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP124-9.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12 % 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 11:45:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.52 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.52
% 0.19/0.52 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.53
%------------------------------------------------------------------------------