TSTP Solution File: SEU305+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU305+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 14:36:05 EDT 2022
% Result : Theorem 0.19s 0.46s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 26 ( 13 unt; 11 nHn; 26 RR)
% Number of literals : 77 ( 0 equ; 42 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
join_commutative(skc6),
file('SEU305+1.p',unknown),
[] ).
cnf(2,axiom,
join_semilatt_str(skc6),
file('SEU305+1.p',unknown),
[] ).
cnf(6,axiom,
~ empty_carrier(skc6),
file('SEU305+1.p',unknown),
[] ).
cnf(12,axiom,
element(skc8,the_carrier(skc6)),
file('SEU305+1.p',unknown),
[] ).
cnf(13,axiom,
element(skc7,the_carrier(skc6)),
file('SEU305+1.p',unknown),
[] ).
cnf(14,axiom,
below(skc6,skc7,skc8),
file('SEU305+1.p',unknown),
[] ).
cnf(15,axiom,
below(skc6,skc8,skc7),
file('SEU305+1.p',unknown),
[] ).
cnf(16,axiom,
~ equal(skc8,skc7),
file('SEU305+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ join_semilatt_str(u)
| one_sorted_str(u) ),
file('SEU305+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ join_semilatt_str(u)
| ~ element(v,the_carrier(u))
| ~ element(w,the_carrier(u))
| ~ below(u,w,v)
| empty_carrier(u)
| equal(join(u,w,v),v) ),
file('SEU305+1.p',unknown),
[] ).
cnf(48,axiom,
( ~ join_semilatt_str(u)
| ~ join_commutative(u)
| ~ element(v,the_carrier(u))
| ~ element(w,the_carrier(u))
| empty_carrier(u)
| equal(join(u,w,v),join_commut(u,w,v)) ),
file('SEU305+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ join_semilatt_str(u)
| ~ join_commutative(u)
| ~ element(v,the_carrier(u))
| ~ element(w,the_carrier(u))
| empty_carrier(u)
| equal(join_commut(u,w,v),join_commut(u,v,w)) ),
file('SEU305+1.p',unknown),
[] ).
cnf(64,plain,
one_sorted_str(skc6),
inference(res,[status(thm),theory(equality)],[2,21]),
[iquote('0:Res:2.0,21.0')] ).
cnf(65,plain,
( ~ join_semilatt_str(skc6)
| ~ element(u,the_carrier(skc6))
| ~ element(v,the_carrier(skc6))
| equal(join_commut(skc6,u,v),join_commut(skc6,v,u))
| empty_carrier(skc6) ),
inference(res,[status(thm),theory(equality)],[1,49]),
[iquote('0:Res:1.0,49.0')] ).
cnf(79,plain,
( ~ join_semilatt_str(skc6)
| ~ element(skc8,the_carrier(skc6))
| ~ element(skc7,the_carrier(skc6))
| equal(join(skc6,skc8,skc7),skc7)
| empty_carrier(skc6) ),
inference(res,[status(thm),theory(equality)],[15,47]),
[iquote('0:Res:15.0,47.1')] ).
cnf(80,plain,
( ~ join_semilatt_str(skc6)
| ~ element(skc7,the_carrier(skc6))
| ~ element(skc8,the_carrier(skc6))
| equal(join(skc6,skc7,skc8),skc8)
| empty_carrier(skc6) ),
inference(res,[status(thm),theory(equality)],[14,47]),
[iquote('0:Res:14.0,47.1')] ).
cnf(140,plain,
equal(join(skc6,skc7,skc8),skc8),
inference(mrr,[status(thm)],[80,2,13,12,6]),
[iquote('0:MRR:80.0,80.1,80.2,80.4,2.0,13.0,12.0,6.0')] ).
cnf(141,plain,
equal(join(skc6,skc8,skc7),skc7),
inference(mrr,[status(thm)],[79,2,12,13,6]),
[iquote('0:MRR:79.0,79.1,79.2,79.4,2.0,12.0,13.0,6.0')] ).
cnf(167,plain,
( ~ element(u,the_carrier(skc6))
| ~ element(v,the_carrier(skc6))
| equal(join_commut(skc6,v,u),join_commut(skc6,u,v)) ),
inference(mrr,[status(thm)],[65,2,6]),
[iquote('0:MRR:65.0,65.4,2.0,6.0')] ).
cnf(314,plain,
( ~ join_semilatt_str(skc6)
| ~ join_commutative(skc6)
| ~ element(skc7,the_carrier(skc6))
| ~ element(skc8,the_carrier(skc6))
| empty_carrier(skc6)
| equal(join_commut(skc6,skc8,skc7),skc7) ),
inference(spr,[status(thm),theory(equality)],[48,141]),
[iquote('0:SpR:48.5,141.0')] ).
cnf(315,plain,
( ~ join_semilatt_str(skc6)
| ~ join_commutative(skc6)
| ~ element(skc8,the_carrier(skc6))
| ~ element(skc7,the_carrier(skc6))
| empty_carrier(skc6)
| equal(join_commut(skc6,skc7,skc8),skc8) ),
inference(spr,[status(thm),theory(equality)],[48,140]),
[iquote('0:SpR:48.5,140.0')] ).
cnf(320,plain,
( ~ element(skc8,the_carrier(skc6))
| ~ element(skc7,the_carrier(skc6))
| empty_carrier(skc6)
| equal(join_commut(skc6,skc7,skc8),skc8) ),
inference(ssi,[status(thm)],[315,1,2,64]),
[iquote('0:SSi:315.1,315.0,1.0,2.0,64.0,1.0,2.0,64.0')] ).
cnf(321,plain,
equal(join_commut(skc6,skc7,skc8),skc8),
inference(mrr,[status(thm)],[320,12,13,6]),
[iquote('0:MRR:320.0,320.1,320.2,12.0,13.0,6.0')] ).
cnf(322,plain,
( ~ join_semilatt_str(skc6)
| ~ join_commutative(skc6)
| ~ element(skc7,the_carrier(skc6))
| ~ element(skc8,the_carrier(skc6))
| empty_carrier(skc6)
| equal(skc8,skc7) ),
inference(rew,[status(thm),theory(equality)],[321,314,167]),
[iquote('0:Rew:321.0,314.5,167.2,314.5')] ).
cnf(323,plain,
( ~ element(skc7,the_carrier(skc6))
| ~ element(skc8,the_carrier(skc6))
| empty_carrier(skc6)
| equal(skc8,skc7) ),
inference(ssi,[status(thm)],[322,1,2,64]),
[iquote('0:SSi:322.1,322.0,1.0,2.0,64.0,1.0,2.0,64.0')] ).
cnf(324,plain,
$false,
inference(mrr,[status(thm)],[323,13,12,6,16]),
[iquote('0:MRR:323.0,323.1,323.2,323.3,13.0,12.0,6.0,16.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU305+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 19:31:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.46
% 0.19/0.46 SPASS V 3.9
% 0.19/0.46 SPASS beiseite: Proof found.
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 SPASS derived 194 clauses, backtracked 0 clauses, performed 0 splits and kept 174 clauses.
% 0.19/0.46 SPASS allocated 97903 KBytes.
% 0.19/0.46 SPASS spent 0:00:00.11 on the problem.
% 0.19/0.46 0:00:00.03 for the input.
% 0.19/0.46 0:00:00.04 for the FLOTTER CNF translation.
% 0.19/0.46 0:00:00.00 for inferences.
% 0.19/0.46 0:00:00.00 for the backtracking.
% 0.19/0.46 0:00:00.01 for the reduction.
% 0.19/0.46
% 0.19/0.46
% 0.19/0.46 Here is a proof with depth 2, length 26 :
% 0.19/0.46 % SZS output start Refutation
% See solution above
% 0.19/0.46 Formulae used in the proof : t26_lattices dt_l2_lattices d3_lattices redefinition_k3_lattices commutativity_k3_lattices
% 0.19/0.46
%------------------------------------------------------------------------------