TSTP Solution File: SEU345+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU345+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 : Tue Jul 19 14:36:27 EDT 2022
% Result : Theorem 0.62s 0.84s
% Output : Refutation 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 26
% Syntax : Number of clauses : 61 ( 28 unt; 19 nHn; 61 RR)
% Number of literals : 181 ( 0 equ; 103 neg)
% Maximal clause size : 11 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 16 ( 15 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(22,axiom,
latt_str(boole_lattice(u)),
file('SEU345+1.p',unknown),
[] ).
cnf(24,axiom,
strict_latt_str(boole_lattice(u)),
file('SEU345+1.p',unknown),
[] ).
cnf(25,axiom,
join_commutative(boole_lattice(u)),
file('SEU345+1.p',unknown),
[] ).
cnf(26,axiom,
join_associative(boole_lattice(u)),
file('SEU345+1.p',unknown),
[] ).
cnf(27,axiom,
meet_commutative(boole_lattice(u)),
file('SEU345+1.p',unknown),
[] ).
cnf(28,axiom,
meet_associative(boole_lattice(u)),
file('SEU345+1.p',unknown),
[] ).
cnf(29,axiom,
meet_absorbing(boole_lattice(u)),
file('SEU345+1.p',unknown),
[] ).
cnf(30,axiom,
join_absorbing(boole_lattice(u)),
file('SEU345+1.p',unknown),
[] ).
cnf(31,axiom,
lattice(boole_lattice(u)),
file('SEU345+1.p',unknown),
[] ).
cnf(32,axiom,
empty(skf20(u)),
file('SEU345+1.p',unknown),
[] ).
cnf(42,axiom,
~ empty_carrier(boole_lattice(u)),
file('SEU345+1.p',unknown),
[] ).
cnf(44,axiom,
element(skf11(u),the_carrier(u)),
file('SEU345+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ latt_str(u)
| meet_semilatt_str(u) ),
file('SEU345+1.p',unknown),
[] ).
cnf(53,axiom,
element(skf20(u),powerset(u)),
file('SEU345+1.p',unknown),
[] ).
cnf(55,axiom,
equal(set_intersection2(u,empty_set),empty_set),
file('SEU345+1.p',unknown),
[] ).
cnf(56,axiom,
element(skf12(u,v),the_carrier(v)),
file('SEU345+1.p',unknown),
[] ).
cnf(57,axiom,
element(skf13(u,v),the_carrier(v)),
file('SEU345+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ empty(u)
| equal(u,empty_set) ),
file('SEU345+1.p',unknown),
[] ).
cnf(69,axiom,
equal(set_intersection2(u,v),set_intersection2(v,u)),
file('SEU345+1.p',unknown),
[] ).
cnf(85,axiom,
( ~ lower_bounded_semilattstr(boole_lattice(skc12))
| ~ equal(bottom_of_semilattstr(boole_lattice(skc13)),empty_set) ),
file('SEU345+1.p',unknown),
[] ).
cnf(117,axiom,
( ~ strict_latt_str(u)
| ~ latt_str(u)
| ~ equal(u,boole_lattice(v))
| equal(the_carrier(u),powerset(v)) ),
file('SEU345+1.p',unknown),
[] ).
cnf(132,axiom,
( ~ element(u,the_carrier(boole_lattice(v)))
| ~ element(w,the_carrier(boole_lattice(v)))
| equal(meet(boole_lattice(v),w,u),set_intersection2(w,u)) ),
file('SEU345+1.p',unknown),
[] ).
cnf(134,axiom,
( ~ meet_semilatt_str(u)
| ~ lower_bounded_semilattstr(u)
| ~ element(v,the_carrier(u))
| empty_carrier(u)
| equal(meet(u,v,skf11(u)),skf11(u)) ),
file('SEU345+1.p',unknown),
[] ).
cnf(135,axiom,
( ~ meet_semilatt_str(u)
| ~ lower_bounded_semilattstr(u)
| ~ element(v,the_carrier(u))
| empty_carrier(u)
| equal(meet(u,skf11(u),v),skf11(u)) ),
file('SEU345+1.p',unknown),
[] ).
cnf(144,axiom,
( ~ meet_semilatt_str(u)
| ~ element(v,the_carrier(u))
| ~ equal(meet(u,v,skf12(v,u)),v)
| ~ equal(meet(u,skf12(v,u),v),v)
| empty_carrier(u)
| lower_bounded_semilattstr(u) ),
file('SEU345+1.p',unknown),
[] ).
cnf(149,axiom,
( ~ lower_bounded_semilattstr(u)
| ~ meet_semilatt_str(u)
| ~ element(v,the_carrier(u))
| ~ equal(meet(u,v,skf13(v,u)),v)
| ~ equal(meet(u,skf13(v,u),v),v)
| empty_carrier(u)
| equal(v,bottom_of_semilattstr(u)) ),
file('SEU345+1.p',unknown),
[] ).
cnf(174,plain,
equal(skf20(u),empty_set),
inference(ems,[status(thm)],[66,32]),
[iquote('0:EmS:66.0,32.0')] ).
cnf(179,plain,
element(empty_set,powerset(u)),
inference(rew,[status(thm),theory(equality)],[174,53]),
[iquote('0:Rew:174.0,53.0')] ).
cnf(186,plain,
equal(set_intersection2(empty_set,u),empty_set),
inference(spr,[status(thm),theory(equality)],[69,55]),
[iquote('0:SpR:69.0,55.0')] ).
cnf(546,plain,
( ~ strict_latt_str(boole_lattice(u))
| ~ latt_str(boole_lattice(u))
| equal(the_carrier(boole_lattice(u)),powerset(u)) ),
inference(eqr,[status(thm),theory(equality)],[117]),
[iquote('0:EqR:117.2')] ).
cnf(547,plain,
equal(the_carrier(boole_lattice(u)),powerset(u)),
inference(ssi,[status(thm)],[546,30,29,28,26,25,31,27,24,22]),
[iquote('0:SSi:546.1,546.0,30.0,29.0,28.0,26.0,25.0,31.0,27.0,24.0,22.0,30.0,29.0,28.0,26.0,25.0,31.0,27.0,24.0,22.0')] ).
cnf(548,plain,
( ~ element(u,powerset(v))
| ~ element(w,the_carrier(boole_lattice(v)))
| equal(meet(boole_lattice(v),w,u),set_intersection2(w,u)) ),
inference(rew,[status(thm),theory(equality)],[547,132]),
[iquote('0:Rew:547.0,132.0')] ).
cnf(550,plain,
( ~ element(u,powerset(v))
| ~ element(w,powerset(v))
| equal(meet(boole_lattice(v),w,u),set_intersection2(w,u)) ),
inference(rew,[status(thm),theory(equality)],[547,548]),
[iquote('0:Rew:547.0,548.1')] ).
cnf(552,plain,
element(skf11(boole_lattice(u)),powerset(u)),
inference(spr,[status(thm),theory(equality)],[547,44]),
[iquote('0:SpR:547.0,44.0')] ).
cnf(571,plain,
element(skf12(u,boole_lattice(v)),powerset(v)),
inference(spr,[status(thm),theory(equality)],[547,56]),
[iquote('0:SpR:547.0,56.0')] ).
cnf(794,plain,
( ~ meet_semilatt_str(boole_lattice(u))
| ~ lower_bounded_semilattstr(boole_lattice(u))
| ~ element(v,the_carrier(boole_lattice(u)))
| ~ element(v,powerset(u))
| ~ element(skf11(boole_lattice(u)),powerset(u))
| empty_carrier(boole_lattice(u))
| equal(set_intersection2(skf11(boole_lattice(u)),v),skf11(boole_lattice(u))) ),
inference(spr,[status(thm),theory(equality)],[135,550]),
[iquote('0:SpR:135.4,550.2')] ).
cnf(800,plain,
( ~ meet_semilatt_str(boole_lattice(u))
| ~ lower_bounded_semilattstr(boole_lattice(u))
| ~ element(v,powerset(u))
| ~ element(v,powerset(u))
| ~ element(skf11(boole_lattice(u)),powerset(u))
| empty_carrier(boole_lattice(u))
| equal(set_intersection2(skf11(boole_lattice(u)),v),skf11(boole_lattice(u))) ),
inference(rew,[status(thm),theory(equality)],[547,794]),
[iquote('0:Rew:547.0,794.2')] ).
cnf(801,plain,
( ~ meet_semilatt_str(boole_lattice(u))
| ~ lower_bounded_semilattstr(boole_lattice(u))
| ~ element(v,powerset(u))
| ~ element(skf11(boole_lattice(u)),powerset(u))
| empty_carrier(boole_lattice(u))
| equal(set_intersection2(skf11(boole_lattice(u)),v),skf11(boole_lattice(u))) ),
inference(obv,[status(thm),theory(equality)],[800]),
[iquote('0:Obv:800.2')] ).
cnf(802,plain,
( ~ lower_bounded_semilattstr(boole_lattice(u))
| ~ element(v,powerset(u))
| ~ element(skf11(boole_lattice(u)),powerset(u))
| empty_carrier(boole_lattice(u))
| equal(set_intersection2(skf11(boole_lattice(u)),v),skf11(boole_lattice(u))) ),
inference(ssi,[status(thm)],[801,47,30,29,28,26,25,31,27,24,22]),
[iquote('0:SSi:801.0,47.0,30.0,29.0,28.0,26.0,25.0,31.0,27.0,24.0,22.1')] ).
cnf(803,plain,
( ~ lower_bounded_semilattstr(boole_lattice(u))
| ~ element(v,powerset(u))
| equal(set_intersection2(skf11(boole_lattice(u)),v),skf11(boole_lattice(u))) ),
inference(mrr,[status(thm)],[802,552,42]),
[iquote('0:MRR:802.2,802.3,552.0,42.0')] ).
cnf(1164,plain,
( ~ meet_semilatt_str(boole_lattice(u))
| ~ element(v,powerset(u))
| ~ element(skf12(v,boole_lattice(u)),powerset(u))
| ~ element(v,the_carrier(boole_lattice(u)))
| ~ equal(meet(boole_lattice(u),v,skf12(v,boole_lattice(u))),v)
| ~ equal(set_intersection2(skf12(v,boole_lattice(u)),v),v)
| empty_carrier(boole_lattice(u))
| lower_bounded_semilattstr(boole_lattice(u)) ),
inference(spl,[status(thm),theory(equality)],[550,144]),
[iquote('0:SpL:550.2,144.3')] ).
cnf(1172,plain,
( ~ meet_semilatt_str(boole_lattice(u))
| ~ element(v,powerset(u))
| ~ element(skf12(v,boole_lattice(u)),powerset(u))
| ~ element(v,powerset(u))
| ~ equal(set_intersection2(v,skf12(v,boole_lattice(u))),v)
| ~ equal(set_intersection2(v,skf12(v,boole_lattice(u))),v)
| empty_carrier(boole_lattice(u))
| lower_bounded_semilattstr(boole_lattice(u)) ),
inference(rew,[status(thm),theory(equality)],[69,1164,550,547]),
[iquote('0:Rew:69.0,1164.5,550.2,1164.4,547.0,1164.3')] ).
cnf(1173,plain,
( ~ meet_semilatt_str(boole_lattice(u))
| ~ element(skf12(v,boole_lattice(u)),powerset(u))
| ~ element(v,powerset(u))
| ~ equal(set_intersection2(v,skf12(v,boole_lattice(u))),v)
| empty_carrier(boole_lattice(u))
| lower_bounded_semilattstr(boole_lattice(u)) ),
inference(obv,[status(thm),theory(equality)],[1172]),
[iquote('0:Obv:1172.4')] ).
cnf(1174,plain,
( ~ element(skf12(u,boole_lattice(v)),powerset(v))
| ~ element(u,powerset(v))
| ~ equal(set_intersection2(u,skf12(u,boole_lattice(v))),u)
| empty_carrier(boole_lattice(v))
| lower_bounded_semilattstr(boole_lattice(v)) ),
inference(ssi,[status(thm)],[1173,47,30,29,28,26,25,31,27,24,22]),
[iquote('0:SSi:1173.0,47.0,30.0,29.0,28.0,26.0,25.0,31.0,27.0,24.0,22.1')] ).
cnf(1175,plain,
( ~ element(u,powerset(v))
| ~ equal(set_intersection2(u,skf12(u,boole_lattice(v))),u)
| lower_bounded_semilattstr(boole_lattice(v)) ),
inference(mrr,[status(thm)],[1174,571,42]),
[iquote('0:MRR:1174.0,1174.3,571.0,42.0')] ).
cnf(1301,plain,
( ~ meet_semilatt_str(u)
| ~ lower_bounded_semilattstr(u)
| ~ lower_bounded_semilattstr(u)
| ~ meet_semilatt_str(u)
| ~ element(skf13(skf11(u),u),the_carrier(u))
| ~ element(skf11(u),the_carrier(u))
| ~ equal(meet(u,skf11(u),skf13(skf11(u),u)),skf11(u))
| ~ equal(skf11(u),skf11(u))
| empty_carrier(u)
| empty_carrier(u)
| equal(skf11(u),bottom_of_semilattstr(u)) ),
inference(spl,[status(thm),theory(equality)],[134,149]),
[iquote('0:SpL:134.4,149.4')] ).
cnf(1308,plain,
( ~ lower_bounded_semilattstr(u)
| ~ meet_semilatt_str(u)
| ~ element(skf13(skf11(u),u),the_carrier(u))
| ~ element(skf11(u),the_carrier(u))
| ~ equal(meet(u,skf11(u),skf13(skf11(u),u)),skf11(u))
| empty_carrier(u)
| equal(skf11(u),bottom_of_semilattstr(u)) ),
inference(obv,[status(thm),theory(equality)],[1301]),
[iquote('0:Obv:1301.8')] ).
cnf(1309,plain,
( ~ lower_bounded_semilattstr(u)
| ~ meet_semilatt_str(u)
| ~ element(skf13(skf11(u),u),the_carrier(u))
| ~ element(skf11(u),the_carrier(u))
| ~ equal(skf11(u),skf11(u))
| empty_carrier(u)
| equal(skf11(u),bottom_of_semilattstr(u)) ),
inference(rew,[status(thm),theory(equality)],[135,1308]),
[iquote('0:Rew:135.4,1308.4')] ).
cnf(1310,plain,
( ~ lower_bounded_semilattstr(u)
| ~ meet_semilatt_str(u)
| ~ element(skf13(skf11(u),u),the_carrier(u))
| ~ element(skf11(u),the_carrier(u))
| empty_carrier(u)
| equal(skf11(u),bottom_of_semilattstr(u)) ),
inference(obv,[status(thm),theory(equality)],[1309]),
[iquote('0:Obv:1309.4')] ).
cnf(1311,plain,
( ~ lower_bounded_semilattstr(u)
| ~ meet_semilatt_str(u)
| empty_carrier(u)
| equal(skf11(u),bottom_of_semilattstr(u)) ),
inference(mrr,[status(thm)],[1310,57,44]),
[iquote('0:MRR:1310.2,1310.3,57.0,44.0')] ).
cnf(2211,plain,
( ~ element(empty_set,powerset(u))
| ~ equal(empty_set,empty_set)
| lower_bounded_semilattstr(boole_lattice(u)) ),
inference(spl,[status(thm),theory(equality)],[186,1175]),
[iquote('0:SpL:186.0,1175.1')] ).
cnf(2212,plain,
( ~ element(empty_set,powerset(u))
| lower_bounded_semilattstr(boole_lattice(u)) ),
inference(obv,[status(thm),theory(equality)],[2211]),
[iquote('0:Obv:2211.1')] ).
cnf(2213,plain,
lower_bounded_semilattstr(boole_lattice(u)),
inference(mrr,[status(thm)],[2212,179]),
[iquote('0:MRR:2212.0,179.0')] ).
cnf(2214,plain,
~ equal(bottom_of_semilattstr(boole_lattice(skc13)),empty_set),
inference(mrr,[status(thm)],[85,2213]),
[iquote('0:MRR:85.0,2213.0')] ).
cnf(2217,plain,
( ~ element(u,powerset(v))
| equal(set_intersection2(skf11(boole_lattice(v)),u),skf11(boole_lattice(v))) ),
inference(mrr,[status(thm)],[803,2213]),
[iquote('0:MRR:803.0,2213.0')] ).
cnf(2230,plain,
( ~ element(empty_set,powerset(u))
| equal(skf11(boole_lattice(u)),empty_set) ),
inference(spr,[status(thm),theory(equality)],[2217,55]),
[iquote('0:SpR:2217.1,55.0')] ).
cnf(2240,plain,
equal(skf11(boole_lattice(u)),empty_set),
inference(mrr,[status(thm)],[2230,179]),
[iquote('0:MRR:2230.0,179.0')] ).
cnf(2317,plain,
( ~ lower_bounded_semilattstr(boole_lattice(u))
| ~ meet_semilatt_str(boole_lattice(u))
| empty_carrier(boole_lattice(u))
| equal(bottom_of_semilattstr(boole_lattice(u)),empty_set) ),
inference(spr,[status(thm),theory(equality)],[2240,1311]),
[iquote('0:SpR:2240.0,1311.3')] ).
cnf(2322,plain,
( empty_carrier(boole_lattice(u))
| equal(bottom_of_semilattstr(boole_lattice(u)),empty_set) ),
inference(ssi,[status(thm)],[2317,47,30,29,28,26,25,31,27,24,22,2213]),
[iquote('0:SSi:2317.1,2317.0,47.0,30.0,29.0,28.0,26.0,25.0,31.0,27.0,24.0,22.0,2213.0,30.0,29.0,28.0,26.0,25.0,31.0,27.0,24.0,22.0,2213.1')] ).
cnf(2323,plain,
equal(bottom_of_semilattstr(boole_lattice(u)),empty_set),
inference(mrr,[status(thm)],[2322,42]),
[iquote('0:MRR:2322.0,42.0')] ).
cnf(2324,plain,
$false,
inference(unc,[status(thm)],[2323,2214]),
[iquote('0:UnC:2323.0,2214.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU345+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n012.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 20 06:51:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.62/0.84
% 0.62/0.84 SPASS V 3.9
% 0.62/0.84 SPASS beiseite: Proof found.
% 0.62/0.84 % SZS status Theorem
% 0.62/0.84 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.62/0.84 SPASS derived 1784 clauses, backtracked 0 clauses, performed 0 splits and kept 994 clauses.
% 0.62/0.84 SPASS allocated 100065 KBytes.
% 0.62/0.84 SPASS spent 0:00:00.49 on the problem.
% 0.62/0.84 0:00:00.04 for the input.
% 0.62/0.84 0:00:00.05 for the FLOTTER CNF translation.
% 0.62/0.84 0:00:00.04 for inferences.
% 0.62/0.84 0:00:00.00 for the backtracking.
% 0.62/0.84 0:00:00.32 for the reduction.
% 0.62/0.84
% 0.62/0.84
% 0.62/0.84 Here is a proof with depth 3, length 61 :
% 0.62/0.84 % SZS output start Refutation
% See solution above
% 0.62/0.85 Formulae used in the proof : dt_k1_lattice3 fc2_lattice3 rc2_subset_1 d13_lattices existence_m1_subset_1 dt_l3_lattices t2_boole d16_lattices t6_boole commutativity_k3_xboole_0 t3_lattice3 d1_lattice3 t1_lattice3
% 0.62/0.85
%------------------------------------------------------------------------------