%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP123-8.003 : 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 10:36:31 EDT 2022
% Result : Unsatisfiable 0.13s 0.40s
% 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_42,X_42,X_42),
inference(subst,[],[product1_idempotence:[bind(X,$fot(X_42))]]) ).
cnf(refute_0_1,plain,
( ~ product1(X_41,X_42,X_42)
| ~ product1(X_42,X_42,X_42)
| equalish(X_41,X_42) ),
inference(subst,[],[product1_left_cancellation:[bind(W,$fot(X_41)),bind(X,$fot(X_42)),bind(Y,$fot(X_42)),bind(Z,$fot(X_42))]]) ).
cnf(refute_0_2,plain,
( ~ product1(X_41,X_42,X_42)
| equalish(X_41,X_42) ),
inference(resolve,[$cnf( product1(X_42,X_42,X_42) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ product1(e_2,e_1,e_1)
| equalish(e_2,e_1) ),
inference(subst,[],[refute_0_2:[bind(X_41,$fot(e_2)),bind(X_42,$fot(e_1))]]) ).
cnf(refute_0_4,plain,
product1(X_35,X_35,X_35),
inference(subst,[],[product1_idempotence:[bind(X,$fot(X_35))]]) ).
cnf(refute_0_5,plain,
( ~ product1(X_35,X_33,X_35)
| ~ product1(X_35,X_35,X_35)
| equalish(X_33,X_35) ),
inference(subst,[],[product1_right_cancellation:[bind(W,$fot(X_33)),bind(X,$fot(X_35)),bind(Y,$fot(X_35)),bind(Z,$fot(X_35))]]) ).
cnf(refute_0_6,plain,
( ~ product1(X_35,X_33,X_35)
| equalish(X_33,X_35) ),
inference(resolve,[$cnf( product1(X_35,X_35,X_35) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ product1(e_2,e_1,e_2)
| equalish(e_1,e_2) ),
inference(subst,[],[refute_0_6:[bind(X_33,$fot(e_1)),bind(X_35,$fot(e_2))]]) ).
cnf(refute_0_8,plain,
( ~ product1(e_3,e_1,e_1)
| equalish(e_3,e_1) ),
inference(subst,[],[refute_0_2:[bind(X_41,$fot(e_3)),bind(X_42,$fot(e_1))]]) ).
cnf(refute_0_9,plain,
product2(X_49,X_49,X_49),
inference(subst,[],[product2_idempotence:[bind(X,$fot(X_49))]]) ).
cnf(refute_0_10,plain,
( ~ product2(X_49,X_49,X_49)
| ~ product2(X_49,X_49,X_52)
| equalish(X_49,X_52) ),
inference(subst,[],[product2_total_function2:[bind(W,$fot(X_49)),bind(X,$fot(X_49)),bind(Y,$fot(X_49)),bind(Z,$fot(X_52))]]) ).
cnf(refute_0_11,plain,
( ~ product2(X_49,X_49,X_52)
| equalish(X_49,X_52) ),
inference(resolve,[$cnf( product2(X_49,X_49,X_49) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ product2(e_2,e_2,e_1)
| equalish(e_2,e_1) ),
inference(subst,[],[refute_0_11:[bind(X_49,$fot(e_2)),bind(X_52,$fot(e_1))]]) ).
cnf(refute_0_13,plain,
( ~ group_element(X_126)
| ~ group_element(e_2)
| product1(e_2,X_126,e_1)
| product1(e_2,X_126,e_2)
| product1(e_2,X_126,e_3) ),
inference(subst,[],[product1_total_function1:[bind(X,$fot(e_2)),bind(Y,$fot(X_126))]]) ).
cnf(refute_0_14,plain,
( ~ group_element(X_126)
| product1(e_2,X_126,e_1)
| product1(e_2,X_126,e_2)
| product1(e_2,X_126,e_3) ),
inference(resolve,[$cnf( group_element(e_2) )],[element_2,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ group_element(e_1)
| product1(e_2,e_1,e_1)
| product1(e_2,e_1,e_2)
| product1(e_2,e_1,e_3) ),
inference(subst,[],[refute_0_14:[bind(X_126,$fot(e_1))]]) ).
cnf(refute_0_16,plain,
( product1(e_2,e_1,e_1)
| product1(e_2,e_1,e_2)
| product1(e_2,e_1,e_3) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ product1(X,e_1,e_3)
| ~ product1(e_3,e_1,e_2)
| product2(e_2,X,e_1) ),
inference(subst,[],[qg1a:[bind(Y,$fot(e_1)),bind(Z1,$fot(e_3)),bind(Z2,$fot(e_2))]]) ).
cnf(refute_0_18,plain,
( ~ product1(e_3,e_1,e_3)
| equalish(e_1,e_3) ),
inference(subst,[],[refute_0_6:[bind(X_33,$fot(e_1)),bind(X_35,$fot(e_3))]]) ).
cnf(refute_0_19,plain,
( ~ group_element(X_126)
| ~ group_element(e_3)
| product1(e_3,X_126,e_1)
| product1(e_3,X_126,e_2)
| product1(e_3,X_126,e_3) ),
inference(subst,[],[product1_total_function1:[bind(X,$fot(e_3)),bind(Y,$fot(X_126))]]) ).
cnf(refute_0_20,plain,
( ~ group_element(X_126)
| product1(e_3,X_126,e_1)
| product1(e_3,X_126,e_2)
| product1(e_3,X_126,e_3) ),
inference(resolve,[$cnf( group_element(e_3) )],[element_3,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ group_element(e_1)
| product1(e_3,e_1,e_1)
| product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_3) ),
inference(subst,[],[refute_0_20:[bind(X_126,$fot(e_1))]]) ).
cnf(refute_0_22,plain,
( product1(e_3,e_1,e_1)
| product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_3) ),
inference(resolve,[$cnf( group_element(e_1) )],[element_1,refute_0_21]) ).
cnf(refute_0_23,plain,
( equalish(e_1,e_3)
| product1(e_3,e_1,e_1)
| product1(e_3,e_1,e_2) ),
inference(resolve,[$cnf( product1(e_3,e_1,e_3) )],[refute_0_22,refute_0_18]) ).
cnf(refute_0_24,plain,
( product1(e_3,e_1,e_1)
| product1(e_3,e_1,e_2) ),
inference(resolve,[$cnf( equalish(e_1,e_3) )],[refute_0_23,e_1_is_not_e_3]) ).
cnf(refute_0_25,plain,
( ~ product1(X,e_1,e_3)
| product1(e_3,e_1,e_1)
| product2(e_2,X,e_1) ),
inference(resolve,[$cnf( product1(e_3,e_1,e_2) )],[refute_0_24,refute_0_17]) ).
cnf(refute_0_26,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_25:[bind(X,$fot(e_2))]]) ).
cnf(refute_0_27,plain,
( product1(e_2,e_1,e_1)
| product1(e_2,e_1,e_2)
| product1(e_3,e_1,e_1)
| product2(e_2,e_2,e_1) ),
inference(resolve,[$cnf( product1(e_2,e_1,e_3) )],[refute_0_16,refute_0_26]) ).
cnf(refute_0_28,plain,
( equalish(e_2,e_1)
| 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_2,e_1) )],[refute_0_28,e_2_is_not_e_1]) ).
cnf(refute_0_30,plain,
( equalish(e_3,e_1)
| 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_3,e_1) )],[refute_0_30,e_3_is_not_e_1]) ).
cnf(refute_0_32,plain,
( equalish(e_1,e_2)
| 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_1,e_2) )],[refute_0_32,e_1_is_not_e_2]) ).
cnf(refute_0_34,plain,
equalish(e_2,e_1),
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_2,e_1) )],[refute_0_34,e_2_is_not_e_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP123-8.003 : TPTP v8.1.0. Released v1.2.0.
% 0.10/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n008.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 05:16:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.40
% 0.13/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.40
%------------------------------------------------------------------------------