TSTP Solution File: GRP123-1.003 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP123-1.003 : 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 10:36:28 EDT 2022
% Result : Unsatisfiable 0.21s 0.38s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of clauses : 47 ( 16 unt; 14 nHn; 44 RR)
% Number of literals : 111 ( 0 equ; 46 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 : 38 ( 5 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_3,axiom,
~ equalish(e_2,e_3) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2) ).
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_left_cancellation,axiom,
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ) ).
cnf(product_idempotence,axiom,
product(X,X,X) ).
cnf(qg1_1,negated_conjecture,
( ~ product(X1,Y1,Z1)
| ~ product(X2,Y2,Z1)
| ~ product(Z2,Y1,X1)
| ~ product(Z2,Y2,X2)
| equalish(X1,X2) ) ).
cnf(qg1_2,negated_conjecture,
( ~ product(X1,Y1,Z1)
| ~ product(X2,Y2,Z1)
| ~ product(Z2,Y1,X1)
| ~ product(Z2,Y2,X2)
| equalish(Y1,Y2) ) ).
cnf(refute_0_0,plain,
product(X_5,X_5,X_5),
inference(subst,[],[product_idempotence:[bind(X,$fot(X_5))]]) ).
cnf(refute_0_1,plain,
( ~ product(X_5,X_5,X_5)
| ~ product(X_5,X_6,X_5)
| equalish(X_5,X_6) ),
inference(subst,[],[qg1_2:[bind(X1,$fot(X_5)),bind(X2,$fot(X_5)),bind(Y1,$fot(X_5)),bind(Y2,$fot(X_6)),bind(Z1,$fot(X_5)),bind(Z2,$fot(X_5))]]) ).
cnf(refute_0_2,plain,
( ~ product(X_5,X_6,X_5)
| equalish(X_5,X_6) ),
inference(resolve,[$cnf( product(X_5,X_5,X_5) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ product(e_1,e_3,e_1)
| equalish(e_1,e_3) ),
inference(subst,[],[refute_0_2:[bind(X_5,$fot(e_1)),bind(X_6,$fot(e_3))]]) ).
cnf(refute_0_4,plain,
product(e_1,e_1,e_1),
inference(subst,[],[product_idempotence:[bind(X,$fot(e_1))]]) ).
cnf(refute_0_5,plain,
product(X_25,X_25,X_25),
inference(subst,[],[product_idempotence:[bind(X,$fot(X_25))]]) ).
cnf(refute_0_6,plain,
( ~ product(X_25,X_25,X_25)
| ~ product(X_27,X_25,X_25)
| equalish(X_25,X_27) ),
inference(subst,[],[product_left_cancellation:[bind(W,$fot(X_25)),bind(X,$fot(X_25)),bind(Y,$fot(X_25)),bind(Z,$fot(X_27))]]) ).
cnf(refute_0_7,plain,
( ~ product(X_27,X_25,X_25)
| equalish(X_25,X_27) ),
inference(resolve,[$cnf( product(X_25,X_25,X_25) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ product(e_1,e_3,e_3)
| equalish(e_3,e_1) ),
inference(subst,[],[refute_0_7:[bind(X_25,$fot(e_3)),bind(X_27,$fot(e_1))]]) ).
cnf(refute_0_9,plain,
( ~ group_element(X_33)
| ~ group_element(e_1)
| product(e_1,X_33,e_1)
| product(e_1,X_33,e_2)
| product(e_1,X_33,e_3) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(e_1)),bind(Y,$fot(X_33))]]) ).
cnf(refute_0_10,plain,
( ~ group_element(X_33)
| product(e_1,X_33,e_1)
| product(e_1,X_33,e_2)
| product(e_1,X_33,e_3) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ group_element(e_3)
| 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_10:[bind(X_33,$fot(e_3))]]) ).
cnf(refute_0_12,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(resolve,[$cnf( group_element(e_3) )],[element_3,refute_0_11]) ).
cnf(refute_0_13,plain,
( equalish(e_3,e_1)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(resolve,[$cnf( product(e_1,e_3,e_3) )],[refute_0_12,refute_0_8]) ).
cnf(refute_0_14,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(resolve,[$cnf( equalish(e_3,e_1) )],[refute_0_13,e_3_is_not_e_1]) ).
cnf(refute_0_15,plain,
( ~ product(e_2,e_3,e_2)
| equalish(e_2,e_3) ),
inference(subst,[],[refute_0_2:[bind(X_5,$fot(e_2)),bind(X_6,$fot(e_3))]]) ).
cnf(refute_0_16,plain,
( ~ product(e_2,e_3,e_3)
| equalish(e_3,e_2) ),
inference(subst,[],[refute_0_7:[bind(X_25,$fot(e_3)),bind(X_27,$fot(e_2))]]) ).
cnf(refute_0_17,plain,
( ~ group_element(X_33)
| ~ group_element(e_2)
| product(e_2,X_33,e_1)
| product(e_2,X_33,e_2)
| product(e_2,X_33,e_3) ),
inference(subst,[],[product_total_function1:[bind(X,$fot(e_2)),bind(Y,$fot(X_33))]]) ).
cnf(refute_0_18,plain,
( ~ group_element(X_33)
| product(e_2,X_33,e_1)
| product(e_2,X_33,e_2)
| product(e_2,X_33,e_3) ),
inference(resolve,[$cnf( group_element(e_2) )],[element_2,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ group_element(e_3)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(subst,[],[refute_0_18:[bind(X_33,$fot(e_3))]]) ).
cnf(refute_0_20,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(resolve,[$cnf( group_element(e_3) )],[element_3,refute_0_19]) ).
cnf(refute_0_21,plain,
( equalish(e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2) ),
inference(resolve,[$cnf( product(e_2,e_3,e_3) )],[refute_0_20,refute_0_16]) ).
cnf(refute_0_22,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2) ),
inference(resolve,[$cnf( equalish(e_3,e_2) )],[refute_0_21,e_3_is_not_e_2]) ).
cnf(refute_0_23,plain,
( equalish(e_2,e_3)
| product(e_2,e_3,e_1) ),
inference(resolve,[$cnf( product(e_2,e_3,e_2) )],[refute_0_22,refute_0_15]) ).
cnf(refute_0_24,plain,
product(e_2,e_3,e_1),
inference(resolve,[$cnf( equalish(e_2,e_3) )],[refute_0_23,e_2_is_not_e_3]) ).
cnf(refute_0_25,plain,
( ~ product(e_1,X_77,e_1)
| ~ product(e_1,e_3,e_2)
| ~ product(e_2,e_3,e_1)
| equalish(e_1,e_2) ),
inference(subst,[],[qg1_1:[bind(X1,$fot(e_1)),bind(X2,$fot(e_2)),bind(Y1,$fot(X_77)),bind(Y2,$fot(e_3)),bind(Z1,$fot(e_1)),bind(Z2,$fot(e_1))]]) ).
cnf(refute_0_26,plain,
( ~ product(e_1,X_77,e_1)
| ~ product(e_1,e_3,e_2)
| equalish(e_1,e_2) ),
inference(resolve,[$cnf( product(e_2,e_3,e_1) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ product(e_1,X_77,e_1)
| ~ product(e_1,e_3,e_2) ),
inference(resolve,[$cnf( equalish(e_1,e_2) )],[refute_0_26,e_1_is_not_e_2]) ).
cnf(refute_0_28,plain,
( ~ product(e_1,X_80,e_1)
| ~ product(e_1,e_3,e_2) ),
inference(subst,[],[refute_0_27:[bind(X_77,$fot(X_80))]]) ).
cnf(refute_0_29,plain,
( ~ product(e_1,X_80,e_1)
| product(e_1,e_3,e_1) ),
inference(resolve,[$cnf( product(e_1,e_3,e_2) )],[refute_0_14,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ product(e_1,e_1,e_1)
| product(e_1,e_3,e_1) ),
inference(subst,[],[refute_0_29:[bind(X_80,$fot(e_1))]]) ).
cnf(refute_0_31,plain,
product(e_1,e_3,e_1),
inference(resolve,[$cnf( product(e_1,e_1,e_1) )],[refute_0_4,refute_0_30]) ).
cnf(refute_0_32,plain,
equalish(e_1,e_3),
inference(resolve,[$cnf( product(e_1,e_3,e_1) )],[refute_0_31,refute_0_3]) ).
cnf(refute_0_33,plain,
$false,
inference(resolve,[$cnf( equalish(e_1,e_3) )],[refute_0_32,e_1_is_not_e_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP123-1.003 : TPTP v8.1.0. Released v1.2.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 13 04:57:07 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.38
% 0.21/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.21/0.38
%------------------------------------------------------------------------------