TSTP Solution File: SEU304+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU304+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 14:36:04 EDT 2022
% Result : Theorem 0.20s 0.49s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of clauses : 33 ( 14 unt; 13 nHn; 33 RR)
% Number of literals : 96 ( 0 equ; 52 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
meet_commutative(skc8),
file('SEU304+1.p',unknown),
[] ).
cnf(2,axiom,
meet_absorbing(skc8),
file('SEU304+1.p',unknown),
[] ).
cnf(3,axiom,
latt_str(skc8),
file('SEU304+1.p',unknown),
[] ).
cnf(9,axiom,
~ empty_carrier(skc8),
file('SEU304+1.p',unknown),
[] ).
cnf(15,axiom,
element(skc10,the_carrier(skc8)),
file('SEU304+1.p',unknown),
[] ).
cnf(16,axiom,
element(skc9,the_carrier(skc8)),
file('SEU304+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ latt_str(u)
| meet_semilatt_str(u) ),
file('SEU304+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ latt_str(u)
| join_semilatt_str(u) ),
file('SEU304+1.p',unknown),
[] ).
cnf(35,axiom,
~ below(skc8,meet_commut(skc8,skc9,skc10),skc9),
file('SEU304+1.p',unknown),
[] ).
cnf(56,axiom,
( ~ meet_semilatt_str(u)
| ~ meet_commutative(u)
| ~ element(v,the_carrier(u))
| ~ element(w,the_carrier(u))
| empty_carrier(u)
| element(meet_commut(u,w,v),the_carrier(u)) ),
file('SEU304+1.p',unknown),
[] ).
cnf(57,axiom,
( ~ join_semilatt_str(u)
| ~ element(v,the_carrier(u))
| ~ element(w,the_carrier(u))
| ~ equal(join(u,w,v),v)
| empty_carrier(u)
| below(u,w,v) ),
file('SEU304+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ meet_semilatt_str(u)
| ~ meet_commutative(u)
| ~ element(v,the_carrier(u))
| ~ element(w,the_carrier(u))
| empty_carrier(u)
| equal(meet(u,w,v),meet_commut(u,w,v)) ),
file('SEU304+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ latt_str(u)
| ~ meet_absorbing(u)
| ~ element(v,the_carrier(u))
| ~ element(w,the_carrier(u))
| empty_carrier(u)
| equal(join(u,meet(u,v,w),w),w) ),
file('SEU304+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ meet_semilatt_str(u)
| ~ meet_commutative(u)
| ~ element(v,the_carrier(u))
| ~ element(w,the_carrier(u))
| empty_carrier(u)
| equal(meet_commut(u,w,v),meet_commut(u,v,w)) ),
file('SEU304+1.p',unknown),
[] ).
cnf(69,plain,
meet_semilatt_str(skc8),
inference(res,[status(thm),theory(equality)],[3,25]),
[iquote('0:Res:3.0,25.0')] ).
cnf(70,plain,
join_semilatt_str(skc8),
inference(res,[status(thm),theory(equality)],[3,26]),
[iquote('0:Res:3.0,26.0')] ).
cnf(91,plain,
( ~ meet_absorbing(skc8)
| ~ latt_str(skc8)
| ~ element(u,the_carrier(skc8))
| equal(join(skc8,meet(skc8,u,skc9),skc9),skc9)
| empty_carrier(skc8) ),
inference(res,[status(thm),theory(equality)],[16,60]),
[iquote('0:Res:16.0,60.2')] ).
cnf(95,plain,
( ~ meet_commutative(skc8)
| ~ meet_semilatt_str(skc8)
| ~ element(u,the_carrier(skc8))
| element(meet_commut(skc8,skc9,u),the_carrier(skc8))
| empty_carrier(skc8) ),
inference(res,[status(thm),theory(equality)],[16,56]),
[iquote('0:Res:16.0,56.2')] ).
cnf(100,plain,
( ~ meet_commutative(skc8)
| ~ meet_semilatt_str(skc8)
| ~ element(u,the_carrier(skc8))
| equal(meet_commut(skc8,u,skc9),meet_commut(skc8,skc9,u))
| empty_carrier(skc8) ),
inference(res,[status(thm),theory(equality)],[16,61]),
[iquote('0:Res:16.0,61.3')] ).
cnf(102,plain,
( ~ meet_commutative(skc8)
| ~ meet_semilatt_str(skc8)
| ~ element(u,the_carrier(skc8))
| equal(meet(skc8,u,skc9),meet_commut(skc8,u,skc9))
| empty_carrier(skc8) ),
inference(res,[status(thm),theory(equality)],[16,59]),
[iquote('0:Res:16.0,59.3')] ).
cnf(150,plain,
( ~ element(u,the_carrier(skc8))
| element(meet_commut(skc8,skc9,u),the_carrier(skc8)) ),
inference(mrr,[status(thm)],[95,1,69,9]),
[iquote('0:MRR:95.0,95.1,95.4,1.0,69.0,9.0')] ).
cnf(170,plain,
( ~ element(u,the_carrier(skc8))
| equal(meet(skc8,u,skc9),meet_commut(skc8,u,skc9)) ),
inference(mrr,[status(thm)],[102,1,69,9]),
[iquote('0:MRR:102.0,102.1,102.4,1.0,69.0,9.0')] ).
cnf(173,plain,
( ~ element(u,the_carrier(skc8))
| equal(meet_commut(skc8,u,skc9),meet_commut(skc8,skc9,u)) ),
inference(mrr,[status(thm)],[100,1,69,9]),
[iquote('0:MRR:100.0,100.1,100.4,1.0,69.0,9.0')] ).
cnf(177,plain,
( ~ meet_absorbing(skc8)
| ~ latt_str(skc8)
| ~ element(u,the_carrier(skc8))
| equal(join(skc8,meet_commut(skc8,u,skc9),skc9),skc9)
| empty_carrier(skc8) ),
inference(rew,[status(thm),theory(equality)],[170,91]),
[iquote('0:Rew:170.1,91.3')] ).
cnf(178,plain,
( ~ element(u,the_carrier(skc8))
| equal(join(skc8,meet_commut(skc8,u,skc9),skc9),skc9) ),
inference(mrr,[status(thm)],[177,2,3,9]),
[iquote('0:MRR:177.0,177.1,177.4,2.0,3.0,9.0')] ).
cnf(229,plain,
equal(join(skc8,meet_commut(skc8,skc10,skc9),skc9),skc9),
inference(res,[status(thm),theory(equality)],[15,178]),
[iquote('0:Res:15.0,178.0')] ).
cnf(232,plain,
equal(meet_commut(skc8,skc10,skc9),meet_commut(skc8,skc9,skc10)),
inference(res,[status(thm),theory(equality)],[15,173]),
[iquote('0:Res:15.0,173.0')] ).
cnf(248,plain,
element(meet_commut(skc8,skc9,skc10),the_carrier(skc8)),
inference(res,[status(thm),theory(equality)],[15,150]),
[iquote('0:Res:15.0,150.0')] ).
cnf(257,plain,
equal(join(skc8,meet_commut(skc8,skc9,skc10),skc9),skc9),
inference(rew,[status(thm),theory(equality)],[232,229]),
[iquote('0:Rew:232.0,229.0')] ).
cnf(431,plain,
( ~ join_semilatt_str(skc8)
| ~ element(skc9,the_carrier(skc8))
| ~ element(meet_commut(skc8,skc9,skc10),the_carrier(skc8))
| ~ equal(skc9,skc9)
| empty_carrier(skc8)
| below(skc8,meet_commut(skc8,skc9,skc10),skc9) ),
inference(spl,[status(thm),theory(equality)],[257,57]),
[iquote('0:SpL:257.0,57.3')] ).
cnf(432,plain,
( ~ join_semilatt_str(skc8)
| ~ element(skc9,the_carrier(skc8))
| ~ element(meet_commut(skc8,skc9,skc10),the_carrier(skc8))
| empty_carrier(skc8)
| below(skc8,meet_commut(skc8,skc9,skc10),skc9) ),
inference(obv,[status(thm),theory(equality)],[431]),
[iquote('0:Obv:431.3')] ).
cnf(433,plain,
( ~ element(skc9,the_carrier(skc8))
| ~ element(meet_commut(skc8,skc9,skc10),the_carrier(skc8))
| empty_carrier(skc8)
| below(skc8,meet_commut(skc8,skc9,skc10),skc9) ),
inference(ssi,[status(thm)],[432,2,1,3,70,69]),
[iquote('0:SSi:432.0,2.0,1.0,3.0,70.0,69.0')] ).
cnf(434,plain,
$false,
inference(mrr,[status(thm)],[433,16,248,9,35]),
[iquote('0:MRR:433.0,433.1,433.2,433.3,16.0,248.0,9.0,35.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU304+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jun 19 18:26:04 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.20/0.49
% 0.20/0.49 SPASS V 3.9
% 0.20/0.49 SPASS beiseite: Proof found.
% 0.20/0.49 % SZS status Theorem
% 0.20/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.49 SPASS derived 273 clauses, backtracked 4 clauses, performed 1 splits and kept 227 clauses.
% 0.20/0.49 SPASS allocated 98011 KBytes.
% 0.20/0.49 SPASS spent 0:00:00.13 on the problem.
% 0.20/0.49 0:00:00.04 for the input.
% 0.20/0.49 0:00:00.04 for the FLOTTER CNF translation.
% 0.20/0.49 0:00:00.00 for inferences.
% 0.20/0.49 0:00:00.00 for the backtracking.
% 0.20/0.49 0:00:00.01 for the reduction.
% 0.20/0.49
% 0.20/0.49
% 0.20/0.49 Here is a proof with depth 3, length 33 :
% 0.20/0.49 % SZS output start Refutation
% See solution above
% 0.20/0.49 Formulae used in the proof : t23_lattices dt_l3_lattices dt_k4_lattices d3_lattices redefinition_k4_lattices d8_lattices existence_m1_subset_1 commutativity_k4_lattices
% 0.20/0.49
%------------------------------------------------------------------------------