TSTP Solution File: GRP132-1.002 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP132-1.002 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 10:36:54 EDT 2022
% Result : Unsatisfiable 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 8
% Syntax : Number of clauses : 63 ( 10 unt; 34 nHn; 63 RR)
% Number of literals : 166 ( 0 equ; 70 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 36 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(element_1,axiom,
group_element(e_1) ).
cnf(element_2,axiom,
group_element(e_2) ).
cnf(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2) ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1) ).
cnf(product_total_function1,axiom,
( ~ group_element(X)
| ~ group_element(Y)
| product(X,Y,e_1)
| product(X,Y,e_2) ) ).
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(qg2_1,negated_conjecture,
( ~ product(X1,Y1,Z1)
| ~ product(X2,Y2,Z1)
| ~ product(Z2,X1,Y1)
| ~ product(Z2,X2,Y2)
| equalish(X1,X2) ) ).
cnf(refute_0_0,plain,
( ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(e_1)),bind(Y,$fot(e_1))]]) ).
cnf(refute_0_1,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ group_element(e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(e_2)),bind(Y,$fot(e_2))]]) ).
cnf(refute_0_3,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(resolve,[$cnf( group_element(e_2) )],[element_2,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ product(X_11,e_2,e_2)
| ~ product(e_2,e_2,e_2)
| equalish(X_11,e_2) ),
inference(subst,[],[product_left_cancellation:[bind(W,$fot(X_11)),bind(X,$fot(e_2)),bind(Y,$fot(e_2)),bind(Z,$fot(e_2))]]) ).
cnf(refute_0_5,plain,
( ~ product(X_11,e_2,e_2)
| equalish(X_11,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[$cnf( product(e_2,e_2,e_2) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ product(e_1,e_2,e_2)
| equalish(e_1,e_2)
| product(e_2,e_2,e_1) ),
inference(subst,[],[refute_0_5:[bind(X_11,$fot(e_1))]]) ).
cnf(refute_0_7,plain,
( ~ group_element(X_20)
| ~ group_element(e_1)
| product(e_1,X_20,e_1)
| product(e_1,X_20,e_2) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(e_1)),bind(Y,$fot(X_20))]]) ).
cnf(refute_0_8,plain,
( ~ group_element(X_20)
| product(e_1,X_20,e_1)
| product(e_1,X_20,e_2) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ group_element(e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(subst,[],[refute_0_8:[bind(X_20,$fot(e_2))]]) ).
cnf(refute_0_10,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(resolve,[$cnf( group_element(e_2) )],[element_2,refute_0_9]) ).
cnf(refute_0_11,plain,
( equalish(e_1,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_2,e_1) ),
inference(resolve,[$cnf( product(e_1,e_2,e_2) )],[refute_0_10,refute_0_6]) ).
cnf(refute_0_12,plain,
( product(e_1,e_2,e_1)
| product(e_2,e_2,e_1) ),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_11,e_1_is_not_e_2]) ).
cnf(refute_0_13,plain,
( ~ product(e_2,X_49,e_1)
| ~ product(e_2,e_2,e_1)
| equalish(X_49,e_2) ),
inference(subst,[],[product_right_cancellation:[bind(W,$fot(X_49)),bind(X,$fot(e_2)),bind(Y,$fot(e_1)),bind(Z,$fot(e_2))]]) ).
cnf(refute_0_14,plain,
( ~ product(e_2,X_49,e_1)
| equalish(X_49,e_2)
| product(e_1,e_2,e_1) ),
inference(resolve,[$cnf( product(e_2,e_2,e_1) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_1) ),
inference(subst,[],[refute_0_14:[bind(X_49,$fot(e_1))]]) ).
cnf(refute_0_16,plain,
( ~ group_element(X_20)
| ~ group_element(e_2)
| product(e_2,X_20,e_1)
| product(e_2,X_20,e_2) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(e_2)),bind(Y,$fot(X_20))]]) ).
cnf(refute_0_17,plain,
( ~ group_element(X_20)
| product(e_2,X_20,e_1)
| product(e_2,X_20,e_2) ),
inference(resolve,[$cnf( group_element(e_2) )],[element_2,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ group_element(e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(subst,[],[refute_0_17:[bind(X_20,$fot(e_1))]]) ).
cnf(refute_0_19,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ product(e_2,X_52,e_2)
| ~ product(e_2,e_1,e_2)
| equalish(e_1,X_52) ),
inference(subst,[],[product_right_cancellation:[bind(W,$fot(e_1)),bind(X,$fot(e_2)),bind(Y,$fot(e_2)),bind(Z,$fot(X_52))]]) ).
cnf(refute_0_21,plain,
( ~ product(e_2,X_52,e_2)
| equalish(e_1,X_52)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( product(e_2,e_1,e_2) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ product(e_2,e_2,e_2)
| equalish(e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(subst,[],[refute_0_21:[bind(X_52,$fot(e_2))]]) ).
cnf(refute_0_23,plain,
( equalish(e_1,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_2,e_1) ),
inference(resolve,[$cnf( product(e_2,e_2,e_2) )],[refute_0_3,refute_0_22]) ).
cnf(refute_0_24,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_2,e_1) ),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_23,e_1_is_not_e_2]) ).
cnf(refute_0_25,plain,
( ~ product(e_1,X_81,X_81)
| ~ product(e_2,e_1,X_81)
| ~ product(e_2,e_2,e_1)
| equalish(e_2,e_1) ),
inference(subst,[],[qg2_1:[bind(X1,$fot(e_2)),bind(X2,$fot(e_1)),bind(Y1,$fot(e_1)),bind(Y2,$fot(X_81)),bind(Z1,$fot(X_81)),bind(Z2,$fot(e_2))]]) ).
cnf(refute_0_26,plain,
( ~ product(e_1,X_81,X_81)
| ~ product(e_2,e_1,X_81)
| equalish(e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( product(e_2,e_2,e_1) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ product(e_1,X_81,X_81)
| ~ product(e_2,e_1,X_81)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( equalish(e_2,e_1) )],[refute_0_26,e_2_is_not_e_1]) ).
cnf(refute_0_28,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(subst,[],[refute_0_27:[bind(X_81,$fot(e_2))]]) ).
cnf(refute_0_29,plain,
( ~ product(e_1,e_2,e_2)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( product(e_2,e_1,e_2) )],[refute_0_19,refute_0_28]) ).
cnf(refute_0_30,plain,
( product(e_1,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( product(e_1,e_2,e_2) )],[refute_0_10,refute_0_29]) ).
cnf(refute_0_31,plain,
( equalish(e_1,e_2)
| product(e_1,e_2,e_1) ),
inference(resolve,[$cnf( product(e_2,e_1,e_1) )],[refute_0_30,refute_0_15]) ).
cnf(refute_0_32,plain,
product(e_1,e_2,e_1),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_31,e_1_is_not_e_2]) ).
cnf(refute_0_33,plain,
( ~ product(X_11,e_1,e_2)
| ~ product(e_1,e_1,e_2)
| equalish(X_11,e_1) ),
inference(subst,[],[product_left_cancellation:[bind(W,$fot(X_11)),bind(X,$fot(e_2)),bind(Y,$fot(e_1)),bind(Z,$fot(e_1))]]) ).
cnf(refute_0_34,plain,
( ~ product(X_11,e_1,e_2)
| equalish(X_11,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[$cnf( product(e_1,e_1,e_2) )],[refute_0_1,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ product(e_2,e_1,e_2)
| equalish(e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(subst,[],[refute_0_34:[bind(X_11,$fot(e_2))]]) ).
cnf(refute_0_36,plain,
( equalish(e_2,e_1)
| product(e_1,e_1,e_1)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( product(e_2,e_1,e_2) )],[refute_0_19,refute_0_35]) ).
cnf(refute_0_37,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( equalish(e_2,e_1) )],[refute_0_36,e_2_is_not_e_1]) ).
cnf(refute_0_38,plain,
( ~ product(X_82,X_82,e_2)
| ~ product(X_82,e_2,e_1)
| ~ product(e_2,e_1,e_1)
| equalish(X_82,e_2) ),
inference(subst,[],[qg2_1:[bind(X1,$fot(X_82)),bind(X2,$fot(e_2)),bind(Y1,$fot(e_2)),bind(Y2,$fot(e_1)),bind(Z1,$fot(e_1)),bind(Z2,$fot(X_82))]]) ).
cnf(refute_0_39,plain,
( ~ product(X_82,X_82,e_2)
| ~ product(X_82,e_2,e_1)
| equalish(X_82,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[$cnf( product(e_2,e_1,e_1) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_1,e_2,e_1)
| ~ product(e_2,e_1,e_1)
| equalish(e_1,e_2) ),
inference(subst,[],[qg2_1:[bind(X1,$fot(e_1)),bind(X2,$fot(e_2)),bind(Y1,$fot(e_1)),bind(Y2,$fot(e_1)),bind(Z1,$fot(e_1)),bind(Z2,$fot(e_1))]]) ).
cnf(refute_0_41,plain,
( ~ product(Z,e_2,e_1)
| ~ product(e_2,e_2,e_1)
| equalish(e_2,Z) ),
inference(subst,[],[product_left_cancellation:[bind(W,$fot(e_2)),bind(X,$fot(e_1)),bind(Y,$fot(e_2))]]) ).
cnf(refute_0_42,plain,
( ~ product(Z,e_2,e_1)
| equalish(e_2,Z)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( product(e_2,e_2,e_1) )],[refute_0_24,refute_0_41]) ).
cnf(refute_0_43,plain,
( ~ product(e_1,e_2,e_1)
| equalish(e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(subst,[],[refute_0_42:[bind(Z,$fot(e_1))]]) ).
cnf(refute_0_44,plain,
( equalish(e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( product(e_1,e_2,e_1) )],[refute_0_32,refute_0_43]) ).
cnf(refute_0_45,plain,
product(e_2,e_1,e_1),
inference(resolve,[$cnf( equalish(e_2,e_1) )],[refute_0_44,e_2_is_not_e_1]) ).
cnf(refute_0_46,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_1,e_2,e_1)
| equalish(e_1,e_2) ),
inference(resolve,[$cnf( product(e_2,e_1,e_1) )],[refute_0_45,refute_0_40]) ).
cnf(refute_0_47,plain,
( ~ product(e_1,e_1,e_1)
| equalish(e_1,e_2) ),
inference(resolve,[$cnf( product(e_1,e_2,e_1) )],[refute_0_32,refute_0_46]) ).
cnf(refute_0_48,plain,
~ product(e_1,e_1,e_1),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_47,e_1_is_not_e_2]) ).
cnf(refute_0_49,plain,
( ~ product(X_82,X_82,e_2)
| ~ product(X_82,e_2,e_1)
| equalish(X_82,e_2) ),
inference(resolve,[$cnf( product(e_1,e_1,e_1) )],[refute_0_39,refute_0_48]) ).
cnf(refute_0_50,plain,
( ~ product(e_1,e_1,e_2)
| ~ product(e_1,e_2,e_1)
| equalish(e_1,e_2) ),
inference(subst,[],[refute_0_49:[bind(X_82,$fot(e_1))]]) ).
cnf(refute_0_51,plain,
( ~ product(e_1,e_1,e_2)
| equalish(e_1,e_2) ),
inference(resolve,[$cnf( product(e_1,e_2,e_1) )],[refute_0_32,refute_0_50]) ).
cnf(refute_0_52,plain,
~ product(e_1,e_1,e_2),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_51,e_1_is_not_e_2]) ).
cnf(refute_0_53,plain,
product(e_1,e_1,e_1),
inference(resolve,[$cnf( product(e_1,e_1,e_2) )],[refute_0_1,refute_0_52]) ).
cnf(refute_0_54,plain,
$false,
inference(resolve,[$cnf( product(e_1,e_1,e_1) )],[refute_0_53,refute_0_48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP132-1.002 : TPTP v8.1.0. Released v1.2.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n008.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 12:17:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.38
%------------------------------------------------------------------------------