TSTP Solution File: GRP123-6.003 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP123-6.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 10:36:30 EDT 2022
% Result : Unsatisfiable 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of clauses : 50 ( 15 unt; 19 nHn; 45 RR)
% Number of literals : 121 ( 0 equ; 40 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 41 ( 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(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) ) ).
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(qg1a,negated_conjecture,
( ~ product1(X,Y,Z1)
| ~ product1(Z1,Y,Z2)
| product2(Z2,X,Y) ) ).
cnf(refute_0_0,plain,
product1(X_27,X_27,X_27),
inference(subst,[],[product1_idempotence:[bind(X,$fot(X_27))]]) ).
cnf(refute_0_1,plain,
( ~ product1(X_27,X_27,X_27)
| ~ product1(X_29,X_27,X_27)
| equalish(X_27,X_29) ),
inference(subst,[],[product1_left_cancellation:[bind(W,$fot(X_27)),bind(X,$fot(X_27)),bind(Y,$fot(X_27)),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_2,plain,
( ~ product1(X_29,X_27,X_27)
| equalish(X_27,X_29) ),
inference(resolve,[$cnf( product1(X_27,X_27,X_27) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ product1(e_2,e_1,e_1)
| equalish(e_1,e_2) ),
inference(subst,[],[refute_0_2:[bind(X_27,$fot(e_1)),bind(X_29,$fot(e_2))]]) ).
cnf(refute_0_4,plain,
product1(X_10,X_10,X_10),
inference(subst,[],[product1_idempotence:[bind(X,$fot(X_10))]]) ).
cnf(refute_0_5,plain,
( ~ product1(X_10,X_10,X_10)
| ~ product1(X_10,X_11,X_10)
| equalish(X_10,X_11) ),
inference(subst,[],[product1_right_cancellation:[bind(W,$fot(X_10)),bind(X,$fot(X_10)),bind(Y,$fot(X_10)),bind(Z,$fot(X_11))]]) ).
cnf(refute_0_6,plain,
( ~ product1(X_10,X_11,X_10)
| equalish(X_10,X_11) ),
inference(resolve,[$cnf( product1(X_10,X_10,X_10) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ product1(e_2,e_1,e_2)
| equalish(e_2,e_1) ),
inference(subst,[],[refute_0_6:[bind(X_10,$fot(e_2)),bind(X_11,$fot(e_1))]]) ).
cnf(refute_0_8,plain,
( ~ product1(e_3,e_1,e_1)
| equalish(e_1,e_3) ),
inference(subst,[],[refute_0_2:[bind(X_27,$fot(e_1)),bind(X_29,$fot(e_3))]]) ).
cnf(refute_0_9,plain,
product2(X_37,X_37,X_37),
inference(subst,[],[product2_idempotence:[bind(X,$fot(X_37))]]) ).
cnf(refute_0_10,plain,
( ~ product2(X_37,X_37,X_34)
| ~ product2(X_37,X_37,X_37)
| equalish(X_34,X_37) ),
inference(subst,[],[product2_total_function2:[bind(W,$fot(X_34)),bind(X,$fot(X_37)),bind(Y,$fot(X_37)),bind(Z,$fot(X_37))]]) ).
cnf(refute_0_11,plain,
( ~ product2(X_37,X_37,X_34)
| equalish(X_34,X_37) ),
inference(resolve,[$cnf( product2(X_37,X_37,X_37) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ product2(e_2,e_2,e_1)
| equalish(e_1,e_2) ),
inference(subst,[],[refute_0_11:[bind(X_34,$fot(e_1)),bind(X_37,$fot(e_2))]]) ).
cnf(refute_0_13,plain,
( ~ product1(X,e_1,e_3)
| ~ product1(e_3,e_1,e_2)
| product2(e_2,X,e_1) ),
inference(subst,[],[qg1a:[bind(Y,$fot(e_1)),bind(Z1,$fot(e_3)),bind(Z2,$fot(e_2))]]) ).
cnf(refute_0_14,plain,
( ~ product1(e_3,e_1,e_3)
| equalish(e_3,e_1) ),
inference(subst,[],[refute_0_6:[bind(X_10,$fot(e_3)),bind(X_11,$fot(e_1))]]) ).
cnf(refute_0_15,plain,
( ~ group_element(X_67)
| ~ group_element(e_3)
| product1(e_3,X_67,e_1)
| product1(e_3,X_67,e_2)
| product1(e_3,X_67,e_3) ),
inference(subst,[],[product1_total_function1:[bind(X,$fot(e_3)),bind(Y,$fot(X_67))]]) ).
cnf(refute_0_16,plain,
( ~ group_element(X_67)
| product1(e_3,X_67,e_1)
| product1(e_3,X_67,e_2)
| product1(e_3,X_67,e_3) ),
inference(resolve,[$cnf( group_element(e_3) )],[element_3,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ group_element(e_1)
| product1(e_3,e_1,e_1)
| product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_3) ),
inference(subst,[],[refute_0_16:[bind(X_67,$fot(e_1))]]) ).
cnf(refute_0_18,plain,
( product1(e_3,e_1,e_1)
| product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_3) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_17]) ).
cnf(refute_0_19,plain,
( equalish(e_3,e_1)
| product1(e_3,e_1,e_1)
| product1(e_3,e_1,e_2) ),
inference(resolve,[$cnf( product1(e_3,e_1,e_3) )],[refute_0_18,refute_0_14]) ).
cnf(refute_0_20,plain,
( product1(e_3,e_1,e_1)
| product1(e_3,e_1,e_2) ),
inference(resolve,[$cnf( equalish(e_3,e_1) )],[refute_0_19,e_3_is_not_e_1]) ).
cnf(refute_0_21,plain,
( ~ product1(X,e_1,e_3)
| product1(e_3,e_1,e_1)
| product2(e_2,X,e_1) ),
inference(resolve,[$cnf( product1(e_3,e_1,e_2) )],[refute_0_20,refute_0_13]) ).
cnf(refute_0_22,plain,
( ~ product1(e_2,e_1,e_3)
| product1(e_3,e_1,e_1)
| product2(e_2,e_2,e_1) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(e_2))]]) ).
cnf(refute_0_23,plain,
( ~ group_element(X_66)
| ~ group_element(e_1)
| product1(X_66,e_1,e_1)
| product1(X_66,e_1,e_2)
| product1(X_66,e_1,e_3) ),
inference(subst,[],[product1_total_function1:[bind(X,$fot(X_66)),bind(Y,$fot(e_1))]]) ).
cnf(refute_0_24,plain,
( ~ group_element(X_66)
| product1(X_66,e_1,e_1)
| product1(X_66,e_1,e_2)
| product1(X_66,e_1,e_3) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ group_element(e_2)
| product1(e_2,e_1,e_1)
| product1(e_2,e_1,e_2)
| product1(e_2,e_1,e_3) ),
inference(subst,[],[refute_0_24:[bind(X_66,$fot(e_2))]]) ).
cnf(refute_0_26,plain,
( product1(e_2,e_1,e_1)
| product1(e_2,e_1,e_2)
| product1(e_2,e_1,e_3) ),
inference(resolve,[$cnf( group_element(e_2) )],[element_2,refute_0_25]) ).
cnf(refute_0_27,plain,
( product1(e_2,e_1,e_1)
| product1(e_2,e_1,e_2)
| product1(e_3,e_1,e_1)
| product2(e_2,e_2,e_1) ),
inference(resolve,[$cnf( product1(e_2,e_1,e_3) )],[refute_0_26,refute_0_22]) ).
cnf(refute_0_28,plain,
( equalish(e_1,e_2)
| product1(e_2,e_1,e_1)
| product1(e_2,e_1,e_2)
| product1(e_3,e_1,e_1) ),
inference(resolve,[$cnf( product2(e_2,e_2,e_1) )],[refute_0_27,refute_0_12]) ).
cnf(refute_0_29,plain,
( product1(e_2,e_1,e_1)
| product1(e_2,e_1,e_2)
| product1(e_3,e_1,e_1) ),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_28,e_1_is_not_e_2]) ).
cnf(refute_0_30,plain,
( equalish(e_1,e_3)
| product1(e_2,e_1,e_1)
| product1(e_2,e_1,e_2) ),
inference(resolve,[$cnf( product1(e_3,e_1,e_1) )],[refute_0_29,refute_0_8]) ).
cnf(refute_0_31,plain,
( product1(e_2,e_1,e_1)
| product1(e_2,e_1,e_2) ),
inference(resolve,[$cnf( equalish(e_1,e_3) )],[refute_0_30,e_1_is_not_e_3]) ).
cnf(refute_0_32,plain,
( equalish(e_2,e_1)
| product1(e_2,e_1,e_1) ),
inference(resolve,[$cnf( product1(e_2,e_1,e_2) )],[refute_0_31,refute_0_7]) ).
cnf(refute_0_33,plain,
product1(e_2,e_1,e_1),
inference(resolve,[$cnf( equalish(e_2,e_1) )],[refute_0_32,e_2_is_not_e_1]) ).
cnf(refute_0_34,plain,
equalish(e_1,e_2),
inference(resolve,[$cnf( product1(e_2,e_1,e_1) )],[refute_0_33,refute_0_3]) ).
cnf(refute_0_35,plain,
$false,
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_34,e_1_is_not_e_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP123-6.003 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 15:45:17 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.37
%------------------------------------------------------------------------------