TSTP Solution File: GRP125-4.003 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP125-4.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n005.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 10:36:39 EDT 2022
% Result : Unsatisfiable 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of clauses : 47 ( 14 unt; 15 nHn; 43 RR)
% Number of literals : 109 ( 0 equ; 39 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 : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 40 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(row_surjectivity,axiom,
( ~ group_element(X)
| ~ group_element(Y)
| product(e_1,X,Y)
| product(e_2,X,Y)
| product(e_3,X,Y) ) ).
cnf(qg3_1,negated_conjecture,
( product(X,Y,Z1)
| ~ product(Z1,Z2,X)
| ~ product(Y,X,Z2) ) ).
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_2_is_not_e_3,axiom,
~ equalish(e_2,e_3) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2) ).
cnf(product_total_function2,axiom,
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ) ).
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(product_idempotence,axiom,
product(X,X,X) ).
cnf(refute_0_0,plain,
product(X_39,X_39,X_39),
inference(subst,[],[product_idempotence:[bind(X,$fot(X_39))]]) ).
cnf(refute_0_1,plain,
( ~ product(X_39,X_39,X_39)
| ~ product(X_41,X_39,X_39)
| equalish(X_39,X_41) ),
inference(subst,[],[product_left_cancellation:[bind(W,$fot(X_39)),bind(X,$fot(X_39)),bind(Y,$fot(X_39)),bind(Z,$fot(X_41))]]) ).
cnf(refute_0_2,plain,
( ~ product(X_41,X_39,X_39)
| equalish(X_39,X_41) ),
inference(resolve,[$cnf( product(X_39,X_39,X_39) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ product(e_2,e_1,e_1)
| equalish(e_1,e_2) ),
inference(subst,[],[refute_0_2:[bind(X_39,$fot(e_1)),bind(X_41,$fot(e_2))]]) ).
cnf(refute_0_4,plain,
( ~ product(Y,e_2,e_3)
| ~ product(e_1,e_3,e_2)
| product(e_2,Y,e_1) ),
inference(subst,[],[qg3_1:[bind(X,$fot(e_2)),bind(Z1,$fot(e_1)),bind(Z2,$fot(e_3))]]) ).
cnf(refute_0_5,plain,
product(X_32,X_32,X_32),
inference(subst,[],[product_idempotence:[bind(X,$fot(X_32))]]) ).
cnf(refute_0_6,plain,
( ~ product(X_32,X_32,X_32)
| ~ product(X_32,X_33,X_32)
| equalish(X_32,X_33) ),
inference(subst,[],[product_right_cancellation:[bind(W,$fot(X_32)),bind(X,$fot(X_32)),bind(Y,$fot(X_32)),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_7,plain,
( ~ product(X_32,X_33,X_32)
| equalish(X_32,X_33) ),
inference(resolve,[$cnf( product(X_32,X_32,X_32) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ product(e_2,e_3,e_2)
| equalish(e_2,e_3) ),
inference(subst,[],[refute_0_7:[bind(X_32,$fot(e_2)),bind(X_33,$fot(e_3))]]) ).
cnf(refute_0_9,plain,
product(X_25,X_25,X_25),
inference(subst,[],[product_idempotence:[bind(X,$fot(X_25))]]) ).
cnf(refute_0_10,plain,
( ~ product(X_25,X_25,X_22)
| ~ product(X_25,X_25,X_25)
| equalish(X_22,X_25) ),
inference(subst,[],[product_total_function2:[bind(W,$fot(X_22)),bind(X,$fot(X_25)),bind(Y,$fot(X_25)),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_11,plain,
( ~ product(X_25,X_25,X_22)
| equalish(X_22,X_25) ),
inference(resolve,[$cnf( product(X_25,X_25,X_25) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ product(e_3,e_3,e_2)
| equalish(e_2,e_3) ),
inference(subst,[],[refute_0_11:[bind(X_22,$fot(e_2)),bind(X_25,$fot(e_3))]]) ).
cnf(refute_0_13,plain,
( ~ group_element(X_62)
| ~ group_element(e_2)
| product(e_1,X_62,e_2)
| product(e_2,X_62,e_2)
| product(e_3,X_62,e_2) ),
inference(subst,[],[row_surjectivity:[bind(X,$fot(X_62)),bind(Y,$fot(e_2))]]) ).
cnf(refute_0_14,plain,
( ~ group_element(X_62)
| product(e_1,X_62,e_2)
| product(e_2,X_62,e_2)
| product(e_3,X_62,e_2) ),
inference(resolve,[$cnf( group_element(e_2) )],[element_2,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ group_element(e_3)
| product(e_1,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_3,e_3,e_2) ),
inference(subst,[],[refute_0_14:[bind(X_62,$fot(e_3))]]) ).
cnf(refute_0_16,plain,
( product(e_1,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_3,e_3,e_2) ),
inference(resolve,[$cnf( group_element(e_3) )],[element_3,refute_0_15]) ).
cnf(refute_0_17,plain,
( equalish(e_2,e_3)
| product(e_1,e_3,e_2)
| product(e_2,e_3,e_2) ),
inference(resolve,[$cnf( product(e_3,e_3,e_2) )],[refute_0_16,refute_0_12]) ).
cnf(refute_0_18,plain,
( product(e_1,e_3,e_2)
| product(e_2,e_3,e_2) ),
inference(resolve,[$cnf( equalish(e_2,e_3) )],[refute_0_17,e_2_is_not_e_3]) ).
cnf(refute_0_19,plain,
( equalish(e_2,e_3)
| product(e_1,e_3,e_2) ),
inference(resolve,[$cnf( product(e_2,e_3,e_2) )],[refute_0_18,refute_0_8]) ).
cnf(refute_0_20,plain,
product(e_1,e_3,e_2),
inference(resolve,[$cnf( equalish(e_2,e_3) )],[refute_0_19,e_2_is_not_e_3]) ).
cnf(refute_0_21,plain,
( ~ product(Y,e_2,e_3)
| product(e_2,Y,e_1) ),
inference(resolve,[$cnf( product(e_1,e_3,e_2) )],[refute_0_20,refute_0_4]) ).
cnf(refute_0_22,plain,
( ~ product(e_1,e_2,e_3)
| product(e_2,e_1,e_1) ),
inference(subst,[],[refute_0_21:[bind(Y,$fot(e_1))]]) ).
cnf(refute_0_23,plain,
( ~ product(e_2,e_2,e_3)
| equalish(e_3,e_2) ),
inference(subst,[],[refute_0_11:[bind(X_22,$fot(e_3)),bind(X_25,$fot(e_2))]]) ).
cnf(refute_0_24,plain,
( ~ product(e_3,e_2,e_3)
| equalish(e_3,e_2) ),
inference(subst,[],[refute_0_7:[bind(X_32,$fot(e_3)),bind(X_33,$fot(e_2))]]) ).
cnf(refute_0_25,plain,
( ~ group_element(X_63)
| ~ group_element(e_2)
| product(e_1,e_2,X_63)
| product(e_2,e_2,X_63)
| product(e_3,e_2,X_63) ),
inference(subst,[],[row_surjectivity:[bind(X,$fot(e_2)),bind(Y,$fot(X_63))]]) ).
cnf(refute_0_26,plain,
( ~ group_element(X_63)
| product(e_1,e_2,X_63)
| product(e_2,e_2,X_63)
| product(e_3,e_2,X_63) ),
inference(resolve,[$cnf( group_element(e_2) )],[element_2,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ group_element(e_3)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_3)
| product(e_3,e_2,e_3) ),
inference(subst,[],[refute_0_26:[bind(X_63,$fot(e_3))]]) ).
cnf(refute_0_28,plain,
( product(e_1,e_2,e_3)
| product(e_2,e_2,e_3)
| product(e_3,e_2,e_3) ),
inference(resolve,[$cnf( group_element(e_3) )],[element_3,refute_0_27]) ).
cnf(refute_0_29,plain,
( equalish(e_3,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_3) ),
inference(resolve,[$cnf( product(e_3,e_2,e_3) )],[refute_0_28,refute_0_24]) ).
cnf(refute_0_30,plain,
( product(e_1,e_2,e_3)
| product(e_2,e_2,e_3) ),
inference(resolve,[$cnf( equalish(e_3,e_2) )],[refute_0_29,e_3_is_not_e_2]) ).
cnf(refute_0_31,plain,
( equalish(e_3,e_2)
| product(e_1,e_2,e_3) ),
inference(resolve,[$cnf( product(e_2,e_2,e_3) )],[refute_0_30,refute_0_23]) ).
cnf(refute_0_32,plain,
product(e_1,e_2,e_3),
inference(resolve,[$cnf( equalish(e_3,e_2) )],[refute_0_31,e_3_is_not_e_2]) ).
cnf(refute_0_33,plain,
product(e_2,e_1,e_1),
inference(resolve,[$cnf( product(e_1,e_2,e_3) )],[refute_0_32,refute_0_22]) ).
cnf(refute_0_34,plain,
equalish(e_1,e_2),
inference(resolve,[$cnf( product(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
% 0.11/0.12 % Problem : GRP125-4.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n005.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 10:55:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.38
%------------------------------------------------------------------------------