TSTP Solution File: GRP130-3.003 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP130-3.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 10:36:52 EDT 2022
% Result : Unsatisfiable 0.48s 0.65s
% Output : CNFRefutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 11
% Syntax : Number of clauses : 110 ( 11 unt; 70 nHn; 110 RR)
% Number of literals : 330 ( 0 equ; 92 neg)
% Maximal clause size : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 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(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3) ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1) ).
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) ) ).
cnf(product_right_cancellation,axiom,
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ) ).
cnf(product_left_cancellation,axiom,
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ) ).
cnf(qg3,negated_conjecture,
( ~ product(X,Y,Z1)
| ~ product(X,Z1,Z2)
| product(Z2,Y,X) ) ).
cnf(refute_0_0,plain,
( ~ product(e_1,Z,e_1)
| ~ product(e_1,e_3,e_1)
| equalish(e_3,Z) ),
inference(subst,[],[product_right_cancellation:[bind(W,$fot(e_3)),bind(X,$fot(e_1)),bind(Y,$fot(e_1))]]) ).
cnf(refute_0_1,plain,
( ~ product(e_2,Z,e_1)
| ~ product(e_2,e_3,e_1)
| equalish(e_3,Z) ),
inference(subst,[],[product_right_cancellation:[bind(W,$fot(e_3)),bind(X,$fot(e_2)),bind(Y,$fot(e_1))]]) ).
cnf(refute_0_2,plain,
( ~ product(W,e_3,e_2)
| ~ product(e_1,e_3,e_2)
| equalish(W,e_1) ),
inference(subst,[],[product_left_cancellation:[bind(X,$fot(e_2)),bind(Y,$fot(e_3)),bind(Z,$fot(e_1))]]) ).
cnf(refute_0_3,plain,
( ~ product(Z,e_3,e_3)
| ~ product(e_1,e_3,e_3)
| equalish(e_1,Z) ),
inference(subst,[],[product_left_cancellation:[bind(W,$fot(e_1)),bind(X,$fot(e_3)),bind(Y,$fot(e_3))]]) ).
cnf(refute_0_4,plain,
( ~ group_element(X_64)
| ~ group_element(e_3)
| product(X_64,e_3,e_1)
| product(X_64,e_3,e_2)
| product(X_64,e_3,e_3) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(X_64)),bind(Y,$fot(e_3))]]) ).
cnf(refute_0_5,plain,
( ~ group_element(X_64)
| product(X_64,e_3,e_1)
| product(X_64,e_3,e_2)
| product(X_64,e_3,e_3) ),
inference(resolve,[$cnf( group_element(e_3) )],[element_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ group_element(e_1)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(subst,[],[refute_0_5:[bind(X_64,$fot(e_1))]]) ).
cnf(refute_0_7,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ product(Z,e_3,e_3)
| equalish(e_1,Z)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(resolve,[$cnf( product(e_1,e_3,e_3) )],[refute_0_7,refute_0_3]) ).
cnf(refute_0_9,plain,
( ~ product(e_2,e_3,e_3)
| equalish(e_1,e_2)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(subst,[],[refute_0_8:[bind(Z,$fot(e_2))]]) ).
cnf(refute_0_10,plain,
( ~ product(e_3,Z,e_1)
| ~ product(e_3,e_3,e_1)
| equalish(e_3,Z) ),
inference(subst,[],[product_right_cancellation:[bind(W,$fot(e_3)),bind(X,$fot(e_3)),bind(Y,$fot(e_1))]]) ).
cnf(refute_0_11,plain,
( ~ product(e_1,e_3,e_3)
| product(e_3,e_3,e_1) ),
inference(subst,[],[qg3:[bind(X,$fot(e_1)),bind(Y,$fot(e_3)),bind(Z1,$fot(e_3)),bind(Z2,$fot(e_3))]]) ).
cnf(refute_0_12,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(resolve,[$cnf( product(e_1,e_3,e_3) )],[refute_0_7,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ product(e_3,Z,e_1)
| equalish(e_3,Z)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(resolve,[$cnf( product(e_3,e_3,e_1) )],[refute_0_12,refute_0_10]) ).
cnf(refute_0_14,plain,
( ~ product(e_3,e_1,e_1)
| equalish(e_3,e_1)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(subst,[],[refute_0_13:[bind(Z,$fot(e_1))]]) ).
cnf(refute_0_15,plain,
( ~ product(e_3,e_3,e_3)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(subst,[],[refute_0_8:[bind(Z,$fot(e_3))]]) ).
cnf(refute_0_16,plain,
( ~ product(e_3,Y,e_1)
| ~ product(e_3,e_1,e_3)
| product(e_3,Y,e_3) ),
inference(subst,[],[qg3:[bind(X,$fot(e_3)),bind(Z1,$fot(e_1)),bind(Z2,$fot(e_3))]]) ).
cnf(refute_0_17,plain,
( ~ group_element(X_65)
| ~ group_element(e_3)
| product(e_3,X_65,e_1)
| product(e_3,X_65,e_2)
| product(e_3,X_65,e_3) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(e_3)),bind(Y,$fot(X_65))]]) ).
cnf(refute_0_18,plain,
( ~ group_element(X_65)
| product(e_3,X_65,e_1)
| product(e_3,X_65,e_2)
| product(e_3,X_65,e_3) ),
inference(resolve,[$cnf( group_element(e_3) )],[element_3,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ group_element(e_1)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(subst,[],[refute_0_18:[bind(X_65,$fot(e_1))]]) ).
cnf(refute_0_20,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ product(e_3,Y,e_1)
| product(e_3,Y,e_3)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2) ),
inference(resolve,[$cnf( product(e_3,e_1,e_3) )],[refute_0_20,refute_0_16]) ).
cnf(refute_0_22,plain,
( ~ product(e_3,e_3,e_1)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_3,e_3) ),
inference(subst,[],[refute_0_21:[bind(Y,$fot(e_3))]]) ).
cnf(refute_0_23,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_3,e_3) ),
inference(resolve,[$cnf( product(e_3,e_3,e_1) )],[refute_0_12,refute_0_22]) ).
cnf(refute_0_24,plain,
( equalish(e_1,e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2) ),
inference(resolve,[$cnf( product(e_3,e_3,e_3) )],[refute_0_23,refute_0_15]) ).
cnf(refute_0_25,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2) ),
inference(resolve,[$cnf( equalish(e_1,e_3) )],[refute_0_24,e_1_is_not_e_3]) ).
cnf(refute_0_26,plain,
( ~ product(e_3,e_1,Z2)
| ~ product(e_3,e_3,e_1)
| product(Z2,e_3,e_3) ),
inference(subst,[],[qg3:[bind(X,$fot(e_3)),bind(Y,$fot(e_3)),bind(Z1,$fot(e_1))]]) ).
cnf(refute_0_27,plain,
( ~ product(e_3,e_1,Z2)
| product(Z2,e_3,e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(resolve,[$cnf( product(e_3,e_3,e_1) )],[refute_0_12,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ product(e_3,e_1,e_2)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(subst,[],[refute_0_27:[bind(Z2,$fot(e_2))]]) ).
cnf(refute_0_29,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_2,e_3,e_3)
| product(e_3,e_1,e_1) ),
inference(resolve,[$cnf( product(e_3,e_1,e_2) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
( equalish(e_3,e_1)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(resolve,[$cnf( product(e_3,e_1,e_1) )],[refute_0_29,refute_0_14]) ).
cnf(refute_0_31,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(resolve,[$cnf( equalish(e_3,e_1) )],[refute_0_30,e_3_is_not_e_1]) ).
cnf(refute_0_32,plain,
( equalish(e_1,e_2)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(resolve,[$cnf( product(e_2,e_3,e_3) )],[refute_0_31,refute_0_9]) ).
cnf(refute_0_33,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_32,e_1_is_not_e_2]) ).
cnf(refute_0_34,plain,
( ~ product(W,e_3,e_2)
| equalish(W,e_1)
| product(e_1,e_3,e_1) ),
inference(resolve,[$cnf( product(e_1,e_3,e_2) )],[refute_0_33,refute_0_2]) ).
cnf(refute_0_35,plain,
( ~ product(e_2,e_3,e_2)
| equalish(e_2,e_1)
| product(e_1,e_3,e_1) ),
inference(subst,[],[refute_0_34:[bind(W,$fot(e_2))]]) ).
cnf(refute_0_36,plain,
( ~ product(e_2,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(subst,[],[qg3:[bind(X,$fot(e_2)),bind(Y,$fot(e_3)),bind(Z1,$fot(e_3)),bind(Z2,$fot(e_3))]]) ).
cnf(refute_0_37,plain,
( ~ group_element(X_65)
| ~ group_element(e_2)
| product(e_2,X_65,e_1)
| product(e_2,X_65,e_2)
| product(e_2,X_65,e_3) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(e_2)),bind(Y,$fot(X_65))]]) ).
cnf(refute_0_38,plain,
( ~ group_element(X_65)
| product(e_2,X_65,e_1)
| product(e_2,X_65,e_2)
| product(e_2,X_65,e_3) ),
inference(resolve,[$cnf( group_element(e_2) )],[element_2,refute_0_37]) ).
cnf(refute_0_39,plain,
( ~ group_element(e_3)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(subst,[],[refute_0_38:[bind(X_65,$fot(e_3))]]) ).
cnf(refute_0_40,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(resolve,[$cnf( group_element(e_3) )],[element_3,refute_0_39]) ).
cnf(refute_0_41,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_3,e_3,e_2) ),
inference(resolve,[$cnf( product(e_2,e_3,e_3) )],[refute_0_40,refute_0_36]) ).
cnf(refute_0_42,plain,
( ~ product(e_3,e_3,e_2)
| equalish(e_3,e_1)
| product(e_1,e_3,e_1) ),
inference(subst,[],[refute_0_34:[bind(W,$fot(e_3))]]) ).
cnf(refute_0_43,plain,
( equalish(e_3,e_1)
| product(e_1,e_3,e_1)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2) ),
inference(resolve,[$cnf( product(e_3,e_3,e_2) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
( product(e_1,e_3,e_1)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2) ),
inference(resolve,[$cnf( equalish(e_3,e_1) )],[refute_0_43,e_3_is_not_e_1]) ).
cnf(refute_0_45,plain,
( equalish(e_2,e_1)
| product(e_1,e_3,e_1)
| product(e_2,e_3,e_1) ),
inference(resolve,[$cnf( product(e_2,e_3,e_2) )],[refute_0_44,refute_0_35]) ).
cnf(refute_0_46,plain,
( product(e_1,e_3,e_1)
| product(e_2,e_3,e_1) ),
inference(resolve,[$cnf( equalish(e_2,e_1) )],[refute_0_45,e_2_is_not_e_1]) ).
cnf(refute_0_47,plain,
( ~ product(e_2,Z,e_1)
| equalish(e_3,Z)
| product(e_1,e_3,e_1) ),
inference(resolve,[$cnf( product(e_2,e_3,e_1) )],[refute_0_46,refute_0_1]) ).
cnf(refute_0_48,plain,
( ~ product(e_2,e_1,e_1)
| equalish(e_3,e_1)
| product(e_1,e_3,e_1) ),
inference(subst,[],[refute_0_47:[bind(Z,$fot(e_1))]]) ).
cnf(refute_0_49,plain,
( ~ product(Z,e_3,e_2)
| ~ product(e_1,e_3,e_2)
| equalish(e_1,Z) ),
inference(subst,[],[product_left_cancellation:[bind(W,$fot(e_1)),bind(X,$fot(e_2)),bind(Y,$fot(e_3))]]) ).
cnf(refute_0_50,plain,
( ~ product(Z,e_3,e_2)
| equalish(e_1,Z)
| product(e_1,e_3,e_1) ),
inference(resolve,[$cnf( product(e_1,e_3,e_2) )],[refute_0_33,refute_0_49]) ).
cnf(refute_0_51,plain,
( ~ product(e_2,e_3,e_2)
| equalish(e_1,e_2)
| product(e_1,e_3,e_1) ),
inference(subst,[],[refute_0_50:[bind(Z,$fot(e_2))]]) ).
cnf(refute_0_52,plain,
( ~ product(e_2,e_1,Z2)
| ~ product(e_2,e_3,e_1)
| product(Z2,e_3,e_2) ),
inference(subst,[],[qg3:[bind(X,$fot(e_2)),bind(Y,$fot(e_3)),bind(Z1,$fot(e_1))]]) ).
cnf(refute_0_53,plain,
( ~ product(e_2,e_1,Z2)
| product(Z2,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[$cnf( product(e_2,e_3,e_1) )],[refute_0_46,refute_0_52]) ).
cnf(refute_0_54,plain,
( ~ product(e_2,e_1,e_2)
| product(e_1,e_3,e_1)
| product(e_2,e_3,e_2) ),
inference(subst,[],[refute_0_53:[bind(Z2,$fot(e_2))]]) ).
cnf(refute_0_55,plain,
( ~ product(e_3,e_3,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(subst,[],[refute_0_50:[bind(Z,$fot(e_3))]]) ).
cnf(refute_0_56,plain,
( ~ product(e_2,Y,e_1)
| ~ product(e_2,e_1,e_3)
| product(e_3,Y,e_2) ),
inference(subst,[],[qg3:[bind(X,$fot(e_2)),bind(Z1,$fot(e_1)),bind(Z2,$fot(e_3))]]) ).
cnf(refute_0_57,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) ),
inference(subst,[],[refute_0_38:[bind(X_65,$fot(e_1))]]) ).
cnf(refute_0_58,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_57]) ).
cnf(refute_0_59,plain,
( ~ product(e_2,Y,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_3,Y,e_2) ),
inference(resolve,[$cnf( product(e_2,e_1,e_3) )],[refute_0_58,refute_0_56]) ).
cnf(refute_0_60,plain,
( ~ product(e_2,e_3,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_3,e_2) ),
inference(subst,[],[refute_0_59:[bind(Y,$fot(e_3))]]) ).
cnf(refute_0_61,plain,
( product(e_1,e_3,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_3,e_2) ),
inference(resolve,[$cnf( product(e_2,e_3,e_1) )],[refute_0_46,refute_0_60]) ).
cnf(refute_0_62,plain,
( equalish(e_1,e_3)
| product(e_1,e_3,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolve,[$cnf( product(e_3,e_3,e_2) )],[refute_0_61,refute_0_55]) ).
cnf(refute_0_63,plain,
( product(e_1,e_3,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolve,[$cnf( equalish(e_1,e_3) )],[refute_0_62,e_1_is_not_e_3]) ).
cnf(refute_0_64,plain,
( product(e_1,e_3,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_3,e_2) ),
inference(resolve,[$cnf( product(e_2,e_1,e_2) )],[refute_0_63,refute_0_54]) ).
cnf(refute_0_65,plain,
( equalish(e_1,e_2)
| product(e_1,e_3,e_1)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( product(e_2,e_3,e_2) )],[refute_0_64,refute_0_51]) ).
cnf(refute_0_66,plain,
( product(e_1,e_3,e_1)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_65,e_1_is_not_e_2]) ).
cnf(refute_0_67,plain,
( equalish(e_3,e_1)
| product(e_1,e_3,e_1) ),
inference(resolve,[$cnf( product(e_2,e_1,e_1) )],[refute_0_66,refute_0_48]) ).
cnf(refute_0_68,plain,
product(e_1,e_3,e_1),
inference(resolve,[$cnf( equalish(e_3,e_1) )],[refute_0_67,e_3_is_not_e_1]) ).
cnf(refute_0_69,plain,
( ~ product(e_1,Z,e_1)
| equalish(e_3,Z) ),
inference(resolve,[$cnf( product(e_1,e_3,e_1) )],[refute_0_68,refute_0_0]) ).
cnf(refute_0_70,plain,
( ~ product(e_1,e_1,e_1)
| equalish(e_3,e_1) ),
inference(subst,[],[refute_0_69:[bind(Z,$fot(e_1))]]) ).
cnf(refute_0_71,plain,
( ~ product(Z,e_3,e_1)
| ~ product(e_1,e_3,e_1)
| equalish(e_1,Z) ),
inference(subst,[],[product_left_cancellation:[bind(W,$fot(e_1)),bind(X,$fot(e_1)),bind(Y,$fot(e_3))]]) ).
cnf(refute_0_72,plain,
( ~ product(Z,e_3,e_1)
| equalish(e_1,Z) ),
inference(resolve,[$cnf( product(e_1,e_3,e_1) )],[refute_0_68,refute_0_71]) ).
cnf(refute_0_73,plain,
( ~ product(e_2,e_3,e_1)
| equalish(e_1,e_2) ),
inference(subst,[],[refute_0_72:[bind(Z,$fot(e_2))]]) ).
cnf(refute_0_74,plain,
( ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(e_1)),bind(Y,$fot(e_1))]]) ).
cnf(refute_0_75,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_74]) ).
cnf(refute_0_76,plain,
( ~ product(e_1,X_58,e_1)
| ~ product(e_1,e_1,e_3)
| product(e_3,X_58,e_1) ),
inference(subst,[],[qg3:[bind(X,$fot(e_1)),bind(Y,$fot(X_58)),bind(Z1,$fot(e_1)),bind(Z2,$fot(e_3))]]) ).
cnf(refute_0_77,plain,
( ~ product(e_1,X_58,e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_3,X_58,e_1) ),
inference(resolve,[$cnf( product(e_1,e_1,e_3) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
( ~ product(e_1,e_3,e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_3,e_3,e_1) ),
inference(subst,[],[refute_0_77:[bind(X_58,$fot(e_3))]]) ).
cnf(refute_0_79,plain,
( ~ product(e_2,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(subst,[],[qg3:[bind(X,$fot(e_2)),bind(Y,$fot(e_1)),bind(Z1,$fot(e_1)),bind(Z2,$fot(e_1))]]) ).
cnf(refute_0_80,plain,
( ~ product(e_1,Y,e_3)
| ~ product(e_1,e_3,e_2)
| product(e_2,Y,e_1) ),
inference(subst,[],[qg3:[bind(X,$fot(e_1)),bind(Z1,$fot(e_3)),bind(Z2,$fot(e_2))]]) ).
cnf(refute_0_81,plain,
( ~ product(e_1,Y,e_3)
| product(e_1,e_3,e_1)
| product(e_2,Y,e_1) ),
inference(resolve,[$cnf( product(e_1,e_3,e_2) )],[refute_0_33,refute_0_80]) ).
cnf(refute_0_82,plain,
( ~ product(e_1,e_1,e_3)
| product(e_1,e_3,e_1)
| product(e_2,e_1,e_1) ),
inference(subst,[],[refute_0_81:[bind(Y,$fot(e_1))]]) ).
cnf(refute_0_83,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_3,e_1)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( product(e_1,e_1,e_3) )],[refute_0_75,refute_0_82]) ).
cnf(refute_0_84,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[$cnf( product(e_2,e_1,e_1) )],[refute_0_83,refute_0_79]) ).
cnf(refute_0_85,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_3,e_3,e_1) ),
inference(resolve,[$cnf( product(e_1,e_3,e_1) )],[refute_0_84,refute_0_78]) ).
cnf(refute_0_86,plain,
( ~ product(W,e_3,e_1)
| ~ product(e_1,e_3,e_1)
| equalish(W,e_1) ),
inference(subst,[],[product_left_cancellation:[bind(X,$fot(e_1)),bind(Y,$fot(e_3)),bind(Z,$fot(e_1))]]) ).
cnf(refute_0_87,plain,
( ~ product(W,e_3,e_1)
| equalish(W,e_1) ),
inference(resolve,[$cnf( product(e_1,e_3,e_1) )],[refute_0_68,refute_0_86]) ).
cnf(refute_0_88,plain,
( ~ product(e_3,e_3,e_1)
| equalish(e_3,e_1) ),
inference(subst,[],[refute_0_87:[bind(W,$fot(e_3))]]) ).
cnf(refute_0_89,plain,
( equalish(e_3,e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(resolve,[$cnf( product(e_3,e_3,e_1) )],[refute_0_85,refute_0_88]) ).
cnf(refute_0_90,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(resolve,[$cnf( equalish(e_3,e_1) )],[refute_0_89,e_3_is_not_e_1]) ).
cnf(refute_0_91,plain,
( ~ product(e_1,e_1,Z2)
| ~ product(e_1,e_3,e_1)
| product(Z2,e_3,e_1) ),
inference(subst,[],[qg3:[bind(X,$fot(e_1)),bind(Y,$fot(e_3)),bind(Z1,$fot(e_1))]]) ).
cnf(refute_0_92,plain,
( ~ product(e_1,e_1,Z2)
| product(Z2,e_3,e_1) ),
inference(resolve,[$cnf( product(e_1,e_3,e_1) )],[refute_0_68,refute_0_91]) ).
cnf(refute_0_93,plain,
( ~ product(e_1,e_1,e_2)
| product(e_2,e_3,e_1) ),
inference(subst,[],[refute_0_92:[bind(Z2,$fot(e_2))]]) ).
cnf(refute_0_94,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_3,e_1) ),
inference(resolve,[$cnf( product(e_1,e_1,e_2) )],[refute_0_90,refute_0_93]) ).
cnf(refute_0_95,plain,
( equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[$cnf( product(e_2,e_3,e_1) )],[refute_0_94,refute_0_73]) ).
cnf(refute_0_96,plain,
product(e_1,e_1,e_1),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_95,e_1_is_not_e_2]) ).
cnf(refute_0_97,plain,
equalish(e_3,e_1),
inference(resolve,[$cnf( product(e_1,e_1,e_1) )],[refute_0_96,refute_0_70]) ).
cnf(refute_0_98,plain,
$false,
inference(resolve,[$cnf( equalish(e_3,e_1) )],[refute_0_97,e_3_is_not_e_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : GRP130-3.003 : TPTP v8.1.0. Released v1.2.0.
% 0.12/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n021.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jun 13 18:07:27 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.48/0.65 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.48/0.65
% 0.48/0.65 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.48/0.66
%------------------------------------------------------------------------------