TSTP Solution File: LAT005-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LAT005-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 : Sun Jul 17 05:58:47 EDT 2022
% Result : Unsatisfiable 4.14s 4.30s
% Output : CNFRefutation 4.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 17
% Syntax : Number of clauses : 97 ( 39 unt; 0 nHn; 95 RR)
% Number of literals : 192 ( 0 equ; 96 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 11 con; 0-0 aty)
% Number of variables : 80 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(join_x_and_0,axiom,
join(X,n0,X) ).
cnf(meet_x_and_0,axiom,
meet(X,n0,n0) ).
cnf(commutativity_of_meet,axiom,
( ~ meet(X,Y,Z)
| meet(Y,X,Z) ) ).
cnf(commutativity_of_join,axiom,
( ~ join(X,Y,Z)
| join(Y,X,Z) ) ).
cnf(absorbtion1,axiom,
( ~ meet(X,Y,Z)
| join(X,Z,X) ) ).
cnf(absorbtion2,axiom,
( ~ join(X,Y,Z)
| meet(X,Z,X) ) ).
cnf(associativity_of_meet1,axiom,
( ~ meet(X,Y,Xy)
| ~ meet(Y,Z,Yz)
| ~ meet(X,Yz,Xyz)
| meet(Xy,Z,Xyz) ) ).
cnf(modularity2,axiom,
( ~ meet(X,Z,X)
| ~ join(X,Y,X1)
| ~ meet(Y,Z,Y1)
| ~ join(X,Y1,Z1)
| meet(Z,X1,Z1) ) ).
cnf(meet_a2_and_b2,negated_conjecture,
~ meet(a2,b2,r1) ).
cnf(meet_a_and_b,negated_conjecture,
meet(a,b,c) ).
cnf(meet_c_and_r2,negated_conjecture,
meet(c,r2,n0) ).
cnf(meet_r2_and_b,negated_conjecture,
meet(r2,b,e) ).
cnf(join_a_and_b,negated_conjecture,
join(a,b,c2) ).
cnf(meet_c2_and_r1,negated_conjecture,
meet(c2,r1,n0) ).
cnf(meet_r2_and_a,negated_conjecture,
meet(r2,a,d) ).
cnf(join_r1_and_e,negated_conjecture,
join(r1,e,a2) ).
cnf(join_r1_and_d,negated_conjecture,
join(r1,d,b2) ).
cnf(refute_0_0,plain,
join(r1,n0,r1),
inference(subst,[],[join_x_and_0:[bind(X,$fot(r1))]]) ).
cnf(refute_0_1,plain,
( ~ meet(e,a,n0)
| meet(a,e,n0) ),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(e)),bind(Y,$fot(a)),bind(Z,$fot(n0))]]) ).
cnf(refute_0_2,plain,
( ~ meet(c,r2,n0)
| meet(r2,c,n0) ),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(c)),bind(Y,$fot(r2)),bind(Z,$fot(n0))]]) ).
cnf(refute_0_3,plain,
meet(r2,c,n0),
inference(resolve,[$cnf( meet(c,r2,n0) )],[meet_c_and_r2,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ meet(a,b,c)
| meet(b,a,c) ),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(c))]]) ).
cnf(refute_0_5,plain,
meet(b,a,c),
inference(resolve,[$cnf( meet(a,b,c) )],[meet_a_and_b,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ meet(X_663,b,X_664)
| ~ meet(X_663,c,X_665)
| ~ meet(b,a,c)
| meet(X_664,a,X_665) ),
inference(subst,[],[associativity_of_meet1:[bind(X,$fot(X_663)),bind(Xy,$fot(X_664)),bind(Xyz,$fot(X_665)),bind(Y,$fot(b)),bind(Yz,$fot(c)),bind(Z,$fot(a))]]) ).
cnf(refute_0_7,plain,
( ~ meet(X_663,b,X_664)
| ~ meet(X_663,c,X_665)
| meet(X_664,a,X_665) ),
inference(resolve,[$cnf( meet(b,a,c) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ meet(r2,b,X_920)
| ~ meet(r2,c,n0)
| meet(X_920,a,n0) ),
inference(subst,[],[refute_0_7:[bind(X_663,$fot(r2)),bind(X_664,$fot(X_920)),bind(X_665,$fot(n0))]]) ).
cnf(refute_0_9,plain,
( ~ meet(r2,b,X_920)
| meet(X_920,a,n0) ),
inference(resolve,[$cnf( meet(r2,c,n0) )],[refute_0_3,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ meet(r2,b,e)
| meet(e,a,n0) ),
inference(subst,[],[refute_0_9:[bind(X_920,$fot(e))]]) ).
cnf(refute_0_11,plain,
meet(e,a,n0),
inference(resolve,[$cnf( meet(r2,b,e) )],[meet_r2_and_b,refute_0_10]) ).
cnf(refute_0_12,plain,
meet(a,e,n0),
inference(resolve,[$cnf( meet(e,a,n0) )],[refute_0_11,refute_0_1]) ).
cnf(refute_0_13,plain,
meet(d,n0,n0),
inference(subst,[],[meet_x_and_0:[bind(X,$fot(d))]]) ).
cnf(refute_0_14,plain,
( ~ join(a,d,a)
| join(d,a,a) ),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(a)),bind(Y,$fot(d)),bind(Z,$fot(a))]]) ).
cnf(refute_0_15,plain,
( ~ meet(r2,a,d)
| meet(a,r2,d) ),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(r2)),bind(Y,$fot(a)),bind(Z,$fot(d))]]) ).
cnf(refute_0_16,plain,
meet(a,r2,d),
inference(resolve,[$cnf( meet(r2,a,d) )],[meet_r2_and_a,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ meet(a,r2,d)
| join(a,d,a) ),
inference(subst,[],[absorbtion1:[bind(X,$fot(a)),bind(Y,$fot(r2)),bind(Z,$fot(d))]]) ).
cnf(refute_0_18,plain,
join(a,d,a),
inference(resolve,[$cnf( meet(a,r2,d) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
join(d,a,a),
inference(resolve,[$cnf( join(a,d,a) )],[refute_0_18,refute_0_14]) ).
cnf(refute_0_20,plain,
( ~ join(d,a,a)
| meet(d,a,d) ),
inference(subst,[],[absorbtion2:[bind(X,$fot(d)),bind(Y,$fot(a)),bind(Z,$fot(a))]]) ).
cnf(refute_0_21,plain,
meet(d,a,d),
inference(resolve,[$cnf( join(d,a,a) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ meet(a,X_668,X_667)
| ~ meet(d,X_667,X_665)
| ~ meet(d,a,d)
| meet(d,X_668,X_665) ),
inference(subst,[],[associativity_of_meet1:[bind(X,$fot(d)),bind(Xy,$fot(d)),bind(Xyz,$fot(X_665)),bind(Y,$fot(a)),bind(Yz,$fot(X_667)),bind(Z,$fot(X_668))]]) ).
cnf(refute_0_23,plain,
( ~ meet(a,X_668,X_667)
| ~ meet(d,X_667,X_665)
| meet(d,X_668,X_665) ),
inference(resolve,[$cnf( meet(d,a,d) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ meet(a,X_1257,n0)
| ~ meet(d,n0,n0)
| meet(d,X_1257,n0) ),
inference(subst,[],[refute_0_23:[bind(X_665,$fot(n0)),bind(X_667,$fot(n0)),bind(X_668,$fot(X_1257))]]) ).
cnf(refute_0_25,plain,
( ~ meet(a,X_1257,n0)
| meet(d,X_1257,n0) ),
inference(resolve,[$cnf( meet(d,n0,n0) )],[refute_0_13,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ meet(a,e,n0)
| meet(d,e,n0) ),
inference(subst,[],[refute_0_25:[bind(X_1257,$fot(e))]]) ).
cnf(refute_0_27,plain,
meet(d,e,n0),
inference(resolve,[$cnf( meet(a,e,n0) )],[refute_0_12,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ join(a,b,c2)
| meet(a,c2,a) ),
inference(subst,[],[absorbtion2:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(c2))]]) ).
cnf(refute_0_29,plain,
meet(a,c2,a),
inference(resolve,[$cnf( join(a,b,c2) )],[join_a_and_b,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ meet(a,X_103,a)
| ~ meet(d,a,d)
| meet(d,X_103,d) ),
inference(subst,[],[associativity_of_meet1:[bind(X,$fot(d)),bind(Xy,$fot(d)),bind(Xyz,$fot(d)),bind(Y,$fot(a)),bind(Yz,$fot(a)),bind(Z,$fot(X_103))]]) ).
cnf(refute_0_31,plain,
( ~ meet(a,X_103,a)
| meet(d,X_103,d) ),
inference(resolve,[$cnf( meet(d,a,d) )],[refute_0_21,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ meet(a,c2,a)
| meet(d,c2,d) ),
inference(subst,[],[refute_0_31:[bind(X_103,$fot(c2))]]) ).
cnf(refute_0_33,plain,
meet(d,c2,d),
inference(resolve,[$cnf( meet(a,c2,a) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
( ~ meet(c2,X_668,X_667)
| ~ meet(d,X_667,X_665)
| ~ meet(d,c2,d)
| meet(d,X_668,X_665) ),
inference(subst,[],[associativity_of_meet1:[bind(X,$fot(d)),bind(Xy,$fot(d)),bind(Xyz,$fot(X_665)),bind(Y,$fot(c2)),bind(Yz,$fot(X_667)),bind(Z,$fot(X_668))]]) ).
cnf(refute_0_35,plain,
( ~ meet(c2,X_668,X_667)
| ~ meet(d,X_667,X_665)
| meet(d,X_668,X_665) ),
inference(resolve,[$cnf( meet(d,c2,d) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ meet(c2,X_1318,e)
| ~ meet(d,e,n0)
| meet(d,X_1318,n0) ),
inference(subst,[],[refute_0_35:[bind(X_665,$fot(n0)),bind(X_667,$fot(e)),bind(X_668,$fot(X_1318))]]) ).
cnf(refute_0_37,plain,
( ~ meet(c2,X_1318,e)
| meet(d,X_1318,n0) ),
inference(resolve,[$cnf( meet(d,e,n0) )],[refute_0_27,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ meet(c2,a2,e)
| meet(d,a2,n0) ),
inference(subst,[],[refute_0_37:[bind(X_1318,$fot(a2))]]) ).
cnf(refute_0_39,plain,
join(e,n0,e),
inference(subst,[],[join_x_and_0:[bind(X,$fot(e))]]) ).
cnf(refute_0_40,plain,
( ~ join(r1,e,a2)
| join(e,r1,a2) ),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(r1)),bind(Y,$fot(e)),bind(Z,$fot(a2))]]) ).
cnf(refute_0_41,plain,
join(e,r1,a2),
inference(resolve,[$cnf( join(r1,e,a2) )],[join_r1_and_e,refute_0_40]) ).
cnf(refute_0_42,plain,
( ~ join(a,b,c2)
| join(b,a,c2) ),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(c2))]]) ).
cnf(refute_0_43,plain,
join(b,a,c2),
inference(resolve,[$cnf( join(a,b,c2) )],[join_a_and_b,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ join(b,a,c2)
| meet(b,c2,b) ),
inference(subst,[],[absorbtion2:[bind(X,$fot(b)),bind(Y,$fot(a)),bind(Z,$fot(c2))]]) ).
cnf(refute_0_45,plain,
meet(b,c2,b),
inference(resolve,[$cnf( join(b,a,c2) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( ~ join(b,e,b)
| join(e,b,b) ),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(b)),bind(Y,$fot(e)),bind(Z,$fot(b))]]) ).
cnf(refute_0_47,plain,
( ~ meet(r2,b,e)
| meet(b,r2,e) ),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(r2)),bind(Y,$fot(b)),bind(Z,$fot(e))]]) ).
cnf(refute_0_48,plain,
meet(b,r2,e),
inference(resolve,[$cnf( meet(r2,b,e) )],[meet_r2_and_b,refute_0_47]) ).
cnf(refute_0_49,plain,
( ~ meet(b,r2,e)
| join(b,e,b) ),
inference(subst,[],[absorbtion1:[bind(X,$fot(b)),bind(Y,$fot(r2)),bind(Z,$fot(e))]]) ).
cnf(refute_0_50,plain,
join(b,e,b),
inference(resolve,[$cnf( meet(b,r2,e) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
join(e,b,b),
inference(resolve,[$cnf( join(b,e,b) )],[refute_0_50,refute_0_46]) ).
cnf(refute_0_52,plain,
( ~ join(e,b,b)
| meet(e,b,e) ),
inference(subst,[],[absorbtion2:[bind(X,$fot(e)),bind(Y,$fot(b)),bind(Z,$fot(b))]]) ).
cnf(refute_0_53,plain,
meet(e,b,e),
inference(resolve,[$cnf( join(e,b,b) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
( ~ meet(b,X_103,b)
| ~ meet(e,b,e)
| meet(e,X_103,e) ),
inference(subst,[],[associativity_of_meet1:[bind(X,$fot(e)),bind(Xy,$fot(e)),bind(Xyz,$fot(e)),bind(Y,$fot(b)),bind(Yz,$fot(b)),bind(Z,$fot(X_103))]]) ).
cnf(refute_0_55,plain,
( ~ meet(b,X_103,b)
| meet(e,X_103,e) ),
inference(resolve,[$cnf( meet(e,b,e) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
( ~ meet(b,c2,b)
| meet(e,c2,e) ),
inference(subst,[],[refute_0_55:[bind(X_103,$fot(c2))]]) ).
cnf(refute_0_57,plain,
meet(e,c2,e),
inference(resolve,[$cnf( meet(b,c2,b) )],[refute_0_45,refute_0_56]) ).
cnf(refute_0_58,plain,
( ~ meet(c2,r1,n0)
| meet(r1,c2,n0) ),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(c2)),bind(Y,$fot(r1)),bind(Z,$fot(n0))]]) ).
cnf(refute_0_59,plain,
meet(r1,c2,n0),
inference(resolve,[$cnf( meet(c2,r1,n0) )],[meet_c2_and_r1,refute_0_58]) ).
cnf(refute_0_60,plain,
( ~ join(X_8565,n0,X_8570)
| ~ join(X_8565,r1,X_8566)
| ~ meet(X_8565,c2,X_8565)
| ~ meet(r1,c2,n0)
| meet(c2,X_8566,X_8570) ),
inference(subst,[],[modularity2:[bind(X,$fot(X_8565)),bind(X1,$fot(X_8566)),bind(Y,$fot(r1)),bind(Y1,$fot(n0)),bind(Z,$fot(c2)),bind(Z1,$fot(X_8570))]]) ).
cnf(refute_0_61,plain,
( ~ join(X_8565,n0,X_8570)
| ~ join(X_8565,r1,X_8566)
| ~ meet(X_8565,c2,X_8565)
| meet(c2,X_8566,X_8570) ),
inference(resolve,[$cnf( meet(r1,c2,n0) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
( ~ join(e,n0,X_9342)
| ~ join(e,r1,X_9341)
| ~ meet(e,c2,e)
| meet(c2,X_9341,X_9342) ),
inference(subst,[],[refute_0_61:[bind(X_8565,$fot(e)),bind(X_8566,$fot(X_9341)),bind(X_8570,$fot(X_9342))]]) ).
cnf(refute_0_63,plain,
( ~ join(e,n0,X_9342)
| ~ join(e,r1,X_9341)
| meet(c2,X_9341,X_9342) ),
inference(resolve,[$cnf( meet(e,c2,e) )],[refute_0_57,refute_0_62]) ).
cnf(refute_0_64,plain,
( ~ join(e,n0,X_9553)
| ~ join(e,r1,a2)
| meet(c2,a2,X_9553) ),
inference(subst,[],[refute_0_63:[bind(X_9341,$fot(a2)),bind(X_9342,$fot(X_9553))]]) ).
cnf(refute_0_65,plain,
( ~ join(e,n0,X_9553)
| meet(c2,a2,X_9553) ),
inference(resolve,[$cnf( join(e,r1,a2) )],[refute_0_41,refute_0_64]) ).
cnf(refute_0_66,plain,
( ~ join(e,n0,e)
| meet(c2,a2,e) ),
inference(subst,[],[refute_0_65:[bind(X_9553,$fot(e))]]) ).
cnf(refute_0_67,plain,
meet(c2,a2,e),
inference(resolve,[$cnf( join(e,n0,e) )],[refute_0_39,refute_0_66]) ).
cnf(refute_0_68,plain,
meet(d,a2,n0),
inference(resolve,[$cnf( meet(c2,a2,e) )],[refute_0_67,refute_0_38]) ).
cnf(refute_0_69,plain,
( ~ join(r1,e,a2)
| meet(r1,a2,r1) ),
inference(subst,[],[absorbtion2:[bind(X,$fot(r1)),bind(Y,$fot(e)),bind(Z,$fot(a2))]]) ).
cnf(refute_0_70,plain,
meet(r1,a2,r1),
inference(resolve,[$cnf( join(r1,e,a2) )],[join_r1_and_e,refute_0_69]) ).
cnf(refute_0_71,plain,
( ~ join(r1,X_8567,X_8566)
| ~ join(r1,X_8568,X_8570)
| ~ meet(X_8567,a2,X_8568)
| ~ meet(r1,a2,r1)
| meet(a2,X_8566,X_8570) ),
inference(subst,[],[modularity2:[bind(X,$fot(r1)),bind(X1,$fot(X_8566)),bind(Y,$fot(X_8567)),bind(Y1,$fot(X_8568)),bind(Z,$fot(a2)),bind(Z1,$fot(X_8570))]]) ).
cnf(refute_0_72,plain,
( ~ join(r1,X_8567,X_8566)
| ~ join(r1,X_8568,X_8570)
| ~ meet(X_8567,a2,X_8568)
| meet(a2,X_8566,X_8570) ),
inference(resolve,[$cnf( meet(r1,a2,r1) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
( ~ join(r1,d,X_10931)
| ~ join(r1,n0,X_10934)
| ~ meet(d,a2,n0)
| meet(a2,X_10931,X_10934) ),
inference(subst,[],[refute_0_72:[bind(X_8566,$fot(X_10931)),bind(X_8567,$fot(d)),bind(X_8568,$fot(n0)),bind(X_8570,$fot(X_10934))]]) ).
cnf(refute_0_74,plain,
( ~ join(r1,d,X_10931)
| ~ join(r1,n0,X_10934)
| meet(a2,X_10931,X_10934) ),
inference(resolve,[$cnf( meet(d,a2,n0) )],[refute_0_68,refute_0_73]) ).
cnf(refute_0_75,plain,
( ~ join(r1,d,X_10954)
| ~ join(r1,n0,r1)
| meet(a2,X_10954,r1) ),
inference(subst,[],[refute_0_74:[bind(X_10931,$fot(X_10954)),bind(X_10934,$fot(r1))]]) ).
cnf(refute_0_76,plain,
( ~ join(r1,d,X_10954)
| meet(a2,X_10954,r1) ),
inference(resolve,[$cnf( join(r1,n0,r1) )],[refute_0_0,refute_0_75]) ).
cnf(refute_0_77,plain,
( ~ join(r1,d,b2)
| meet(a2,b2,r1) ),
inference(subst,[],[refute_0_76:[bind(X_10954,$fot(b2))]]) ).
cnf(refute_0_78,plain,
meet(a2,b2,r1),
inference(resolve,[$cnf( join(r1,d,b2) )],[join_r1_and_d,refute_0_77]) ).
cnf(refute_0_79,plain,
$false,
inference(resolve,[$cnf( meet(a2,b2,r1) )],[refute_0_78,meet_a2_and_b2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LAT005-2 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n015.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 : Thu Jun 30 11:31:27 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4.14/4.30 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.14/4.30
% 4.14/4.30 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.14/4.30
%------------------------------------------------------------------------------