%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP135-2.002 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 10:36:59 EDT 2022
% Result : Unsatisfiable 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of clauses : 47 ( 7 unt; 25 nHn; 47 RR)
% Number of literals : 116 ( 0 equ; 43 neg)
% Maximal clause size : 4 ( 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 : 30 ( 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(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(qg3,negated_conjecture,
( ~ product(Y,X,Z1)
| ~ product(Z1,Y,Z2)
| product(Z2,Y,X) ) ).
cnf(refute_0_0,plain,
( ~ product(e_1,Z,e_1)
| ~ product(e_1,e_1,e_1)
| equalish(e_1,Z) ),
inference(subst,[],[product_right_cancellation:[bind(W,$fot(e_1)),bind(X,$fot(e_1)),bind(Y,$fot(e_1))]]) ).
cnf(refute_0_1,plain,
( ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(e_1)),bind(Y,$fot(e_1))]]) ).
cnf(refute_0_2,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ group_element(X_15)
| ~ group_element(e_2)
| product(e_2,X_15,e_1)
| product(e_2,X_15,e_2) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(e_2)),bind(Y,$fot(X_15))]]) ).
cnf(refute_0_4,plain,
( ~ group_element(X_15)
| product(e_2,X_15,e_1)
| product(e_2,X_15,e_2) ),
inference(resolve,[$cnf( group_element(e_2) )],[element_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ group_element(e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(subst,[],[refute_0_4:[bind(X_15,$fot(e_1))]]) ).
cnf(refute_0_6,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ product(X_56,e_1,e_2)
| ~ product(e_1,e_1,e_2)
| equalish(e_1,X_56) ),
inference(subst,[],[product_left_cancellation:[bind(W,$fot(e_1)),bind(X,$fot(e_2)),bind(Y,$fot(e_1)),bind(Z,$fot(X_56))]]) ).
cnf(refute_0_8,plain,
( ~ product(X_56,e_1,e_2)
| equalish(e_1,X_56)
| product(e_1,e_1,e_1) ),
inference(resolve,[$cnf( product(e_1,e_1,e_2) )],[refute_0_2,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ product(e_2,e_1,e_2)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(subst,[],[refute_0_8:[bind(X_56,$fot(e_2))]]) ).
cnf(refute_0_10,plain,
( equalish(e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( product(e_2,e_1,e_2) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_10,e_1_is_not_e_2]) ).
cnf(refute_0_12,plain,
( ~ product(e_1,X_82,e_2)
| ~ product(e_2,e_1,e_1)
| product(e_1,e_1,X_82) ),
inference(subst,[],[qg3:[bind(X,$fot(X_82)),bind(Y,$fot(e_1)),bind(Z1,$fot(e_2)),bind(Z2,$fot(e_1))]]) ).
cnf(refute_0_13,plain,
( ~ product(e_1,X_82,e_2)
| product(e_1,e_1,X_82)
| product(e_1,e_1,e_1) ),
inference(resolve,[$cnf( product(e_2,e_1,e_1) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(subst,[],[refute_0_13:[bind(X_82,$fot(e_1))]]) ).
cnf(refute_0_15,plain,
product(e_1,e_1,e_1),
inference(resolve,[$cnf( product(e_1,e_1,e_2) )],[refute_0_2,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ product(e_1,Z,e_1)
| equalish(e_1,Z) ),
inference(resolve,[$cnf( product(e_1,e_1,e_1) )],[refute_0_15,refute_0_0]) ).
cnf(refute_0_17,plain,
( ~ product(e_1,e_2,e_1)
| equalish(e_1,e_2) ),
inference(subst,[],[refute_0_16:[bind(Z,$fot(e_2))]]) ).
cnf(refute_0_18,plain,
( ~ product(Z,e_1,e_1)
| ~ product(e_1,e_1,e_1)
| equalish(e_1,Z) ),
inference(subst,[],[product_left_cancellation:[bind(W,$fot(e_1)),bind(X,$fot(e_1)),bind(Y,$fot(e_1))]]) ).
cnf(refute_0_19,plain,
( ~ product(Z,e_1,e_1)
| equalish(e_1,Z) ),
inference(resolve,[$cnf( product(e_1,e_1,e_1) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ product(e_2,e_1,e_1)
| equalish(e_1,e_2) ),
inference(subst,[],[refute_0_19:[bind(Z,$fot(e_2))]]) ).
cnf(refute_0_21,plain,
( ~ group_element(e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(e_2)),bind(Y,$fot(e_2))]]) ).
cnf(refute_0_22,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(resolve,[$cnf( group_element(e_2) )],[element_2,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ group_element(X_15)
| ~ group_element(e_1)
| product(e_1,X_15,e_1)
| product(e_1,X_15,e_2) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(e_1)),bind(Y,$fot(X_15))]]) ).
cnf(refute_0_24,plain,
( ~ group_element(X_15)
| product(e_1,X_15,e_1)
| product(e_1,X_15,e_2) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ group_element(e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(subst,[],[refute_0_24:[bind(X_15,$fot(e_2))]]) ).
cnf(refute_0_26,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(resolve,[$cnf( group_element(e_2) )],[element_2,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ product(X_56,e_2,e_2)
| ~ product(e_1,e_2,e_2)
| equalish(e_1,X_56) ),
inference(subst,[],[product_left_cancellation:[bind(W,$fot(e_1)),bind(X,$fot(e_2)),bind(Y,$fot(e_2)),bind(Z,$fot(X_56))]]) ).
cnf(refute_0_28,plain,
( ~ product(X_56,e_2,e_2)
| equalish(e_1,X_56)
| product(e_1,e_2,e_1) ),
inference(resolve,[$cnf( product(e_1,e_2,e_2) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ product(e_2,e_2,e_2)
| equalish(e_1,e_2)
| product(e_1,e_2,e_1) ),
inference(subst,[],[refute_0_28:[bind(X_56,$fot(e_2))]]) ).
cnf(refute_0_30,plain,
( equalish(e_1,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_2,e_1) ),
inference(resolve,[$cnf( product(e_2,e_2,e_2) )],[refute_0_22,refute_0_29]) ).
cnf(refute_0_31,plain,
( product(e_1,e_2,e_1)
| product(e_2,e_2,e_1) ),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_30,e_1_is_not_e_2]) ).
cnf(refute_0_32,plain,
( ~ product(e_2,X_82,e_2)
| ~ product(e_2,e_2,e_1)
| product(e_1,e_2,X_82) ),
inference(subst,[],[qg3:[bind(X,$fot(X_82)),bind(Y,$fot(e_2)),bind(Z1,$fot(e_2)),bind(Z2,$fot(e_1))]]) ).
cnf(refute_0_33,plain,
( ~ product(e_2,X_82,e_2)
| product(e_1,e_2,X_82)
| product(e_1,e_2,e_1) ),
inference(resolve,[$cnf( product(e_2,e_2,e_1) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( ~ product(e_2,e_1,e_2)
| product(e_1,e_2,e_1) ),
inference(subst,[],[refute_0_33:[bind(X_82,$fot(e_1))]]) ).
cnf(refute_0_35,plain,
( product(e_1,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(resolve,[$cnf( product(e_2,e_1,e_2) )],[refute_0_6,refute_0_34]) ).
cnf(refute_0_36,plain,
( equalish(e_1,e_2)
| product(e_1,e_2,e_1) ),
inference(resolve,[$cnf( product(e_2,e_1,e_1) )],[refute_0_35,refute_0_20]) ).
cnf(refute_0_37,plain,
product(e_1,e_2,e_1),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_36,e_1_is_not_e_2]) ).
cnf(refute_0_38,plain,
equalish(e_1,e_2),
inference(resolve,[$cnf( product(e_1,e_2,e_1) )],[refute_0_37,refute_0_17]) ).
cnf(refute_0_39,plain,
$false,
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_38,e_1_is_not_e_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP135-2.002 : TPTP v8.1.0. Released v1.2.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 12:20:09 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.38
%------------------------------------------------------------------------------