TSTP Solution File: SEU344+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU344+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 0.21s 0.51s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of clauses : 36 ( 16 unt; 7 nHn; 36 RR)
% Number of literals : 83 ( 0 equ; 47 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 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(13,axiom,
latt_str(boole_lattice(u)),
file('SEU344+1.p',unknown),
[] ).
cnf(14,axiom,
strict_latt_str(boole_lattice(u)),
file('SEU344+1.p',unknown),
[] ).
cnf(21,axiom,
~ empty_carrier(boole_lattice(u)),
file('SEU344+1.p',unknown),
[] ).
cnf(24,axiom,
element(skc14,the_carrier(boole_lattice(skc12))),
file('SEU344+1.p',unknown),
[] ).
cnf(25,axiom,
element(skc13,the_carrier(boole_lattice(skc12))),
file('SEU344+1.p',unknown),
[] ).
cnf(29,axiom,
( ~ latt_str(u)
| join_semilatt_str(u) ),
file('SEU344+1.p',unknown),
[] ).
cnf(37,axiom,
subset(u,set_union2(u,v)),
file('SEU344+1.p',unknown),
[] ).
cnf(52,axiom,
( subset(skc13,skc14)
| below(boole_lattice(skc12),skc13,skc14) ),
file('SEU344+1.p',unknown),
[] ).
cnf(62,axiom,
( ~ subset(u,v)
| equal(set_union2(u,v),v) ),
file('SEU344+1.p',unknown),
[] ).
cnf(65,axiom,
( ~ subset(skc13,skc14)
| ~ below(boole_lattice(skc12),skc13,skc14) ),
file('SEU344+1.p',unknown),
[] ).
cnf(77,axiom,
( ~ element(u,the_carrier(boole_lattice(v)))
| ~ element(w,the_carrier(boole_lattice(v)))
| equal(join(boole_lattice(v),w,u),set_union2(w,u)) ),
file('SEU344+1.p',unknown),
[] ).
cnf(80,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('SEU344+1.p',unknown),
[] ).
cnf(81,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('SEU344+1.p',unknown),
[] ).
cnf(99,plain,
( ~ join_semilatt_str(boole_lattice(skc12))
| ~ below(boole_lattice(skc12),skc13,u)
| ~ element(u,the_carrier(boole_lattice(skc12)))
| equal(join(boole_lattice(skc12),skc13,u),u)
| empty_carrier(boole_lattice(skc12)) ),
inference(res,[status(thm),theory(equality)],[25,81]),
[iquote('0:Res:25.0,81.2')] ).
cnf(100,plain,
( ~ join_semilatt_str(boole_lattice(skc12))
| ~ equal(join(boole_lattice(skc12),skc13,u),u)
| ~ element(u,the_carrier(boole_lattice(skc12)))
| below(boole_lattice(skc12),skc13,u)
| empty_carrier(boole_lattice(skc12)) ),
inference(res,[status(thm),theory(equality)],[25,80]),
[iquote('0:Res:25.0,80.2')] ).
cnf(110,plain,
( ~ element(u,the_carrier(boole_lattice(skc12)))
| equal(join(boole_lattice(skc12),skc13,u),set_union2(skc13,u)) ),
inference(res,[status(thm),theory(equality)],[25,77]),
[iquote('0:Res:25.0,77.0')] ).
cnf(165,plain,
( ~ join_semilatt_str(boole_lattice(skc12))
| ~ equal(set_union2(skc13,u),u)
| ~ element(u,the_carrier(boole_lattice(skc12)))
| below(boole_lattice(skc12),skc13,u)
| empty_carrier(boole_lattice(skc12)) ),
inference(rew,[status(thm),theory(equality)],[110,100]),
[iquote('0:Rew:110.1,100.1')] ).
cnf(166,plain,
( ~ join_semilatt_str(boole_lattice(skc12))
| ~ element(u,the_carrier(boole_lattice(skc12)))
| ~ equal(set_union2(skc13,u),u)
| below(boole_lattice(skc12),skc13,u) ),
inference(mrr,[status(thm)],[165,21]),
[iquote('0:MRR:165.4,21.0')] ).
cnf(167,plain,
( ~ join_semilatt_str(boole_lattice(skc12))
| ~ below(boole_lattice(skc12),skc13,u)
| ~ element(u,the_carrier(boole_lattice(skc12)))
| equal(set_union2(skc13,u),u)
| empty_carrier(boole_lattice(skc12)) ),
inference(rew,[status(thm),theory(equality)],[110,99]),
[iquote('0:Rew:110.1,99.3')] ).
cnf(168,plain,
( ~ join_semilatt_str(boole_lattice(skc12))
| ~ element(u,the_carrier(boole_lattice(skc12)))
| ~ below(boole_lattice(skc12),skc13,u)
| equal(set_union2(skc13,u),u) ),
inference(mrr,[status(thm)],[167,21]),
[iquote('0:MRR:167.4,21.0')] ).
cnf(169,plain,
( ~ join_semilatt_str(boole_lattice(skc12))
| ~ below(boole_lattice(skc12),skc13,skc14)
| equal(set_union2(skc13,skc14),skc14) ),
inference(res,[status(thm),theory(equality)],[24,168]),
[iquote('0:Res:24.0,168.2')] ).
cnf(170,plain,
( ~ join_semilatt_str(boole_lattice(skc12))
| ~ equal(set_union2(skc13,skc14),skc14)
| below(boole_lattice(skc12),skc13,skc14) ),
inference(res,[status(thm),theory(equality)],[24,166]),
[iquote('0:Res:24.0,166.2')] ).
cnf(249,plain,
below(boole_lattice(skc12),skc13,skc14),
inference(spt,[spt(split,[position(s1)])],[52]),
[iquote('1:Spt:52.1')] ).
cnf(250,plain,
~ subset(skc13,skc14),
inference(mrr,[status(thm)],[65,249]),
[iquote('1:MRR:65.1,249.0')] ).
cnf(251,plain,
( ~ join_semilatt_str(boole_lattice(skc12))
| equal(set_union2(skc13,skc14),skc14) ),
inference(mrr,[status(thm)],[169,249]),
[iquote('1:MRR:169.1,249.0')] ).
cnf(586,plain,
( ~ latt_str(boole_lattice(skc12))
| equal(set_union2(skc13,skc14),skc14) ),
inference(sor,[status(thm)],[251,29]),
[iquote('1:SoR:251.0,29.1')] ).
cnf(587,plain,
equal(set_union2(skc13,skc14),skc14),
inference(ssi,[status(thm)],[586,14,13]),
[iquote('1:SSi:586.0,14.0,13.0')] ).
cnf(590,plain,
subset(skc13,skc14),
inference(spr,[status(thm),theory(equality)],[587,37]),
[iquote('1:SpR:587.0,37.0')] ).
cnf(596,plain,
$false,
inference(mrr,[status(thm)],[590,250]),
[iquote('1:MRR:590.0,250.0')] ).
cnf(597,plain,
~ below(boole_lattice(skc12),skc13,skc14),
inference(spt,[spt(split,[position(sa)])],[596,249]),
[iquote('1:Spt:596.0,52.1,249.0')] ).
cnf(598,plain,
subset(skc13,skc14),
inference(spt,[spt(split,[position(s2)])],[52]),
[iquote('1:Spt:596.0,52.0')] ).
cnf(600,plain,
( ~ equal(set_union2(skc13,skc14),skc14)
| below(boole_lattice(skc12),skc13,skc14) ),
inference(ssi,[status(thm)],[170,29,14,13]),
[iquote('0:SSi:170.0,29.0,14.0,13.1')] ).
cnf(601,plain,
~ equal(set_union2(skc13,skc14),skc14),
inference(mrr,[status(thm)],[600,597]),
[iquote('1:MRR:600.1,597.0')] ).
cnf(604,plain,
( ~ subset(skc13,skc14)
| ~ equal(skc14,skc14) ),
inference(spl,[status(thm),theory(equality)],[62,601]),
[iquote('1:SpL:62.1,601.0')] ).
cnf(605,plain,
~ subset(skc13,skc14),
inference(obv,[status(thm),theory(equality)],[604]),
[iquote('1:Obv:604.1')] ).
cnf(606,plain,
$false,
inference(mrr,[status(thm)],[605,598]),
[iquote('1:MRR:605.0,598.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU344+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 20 11:26:31 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.21/0.51
% 0.21/0.51 SPASS V 3.9
% 0.21/0.51 SPASS beiseite: Proof found.
% 0.21/0.51 % SZS status Theorem
% 0.21/0.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.51 SPASS derived 359 clauses, backtracked 47 clauses, performed 2 splits and kept 302 clauses.
% 0.21/0.51 SPASS allocated 98056 KBytes.
% 0.21/0.51 SPASS spent 0:00:00.16 on the problem.
% 0.21/0.51 0:00:00.04 for the input.
% 0.21/0.51 0:00:00.05 for the FLOTTER CNF translation.
% 0.21/0.51 0:00:00.00 for inferences.
% 0.21/0.51 0:00:00.00 for the backtracking.
% 0.21/0.51 0:00:00.02 for the reduction.
% 0.21/0.51
% 0.21/0.51
% 0.21/0.51 Here is a proof with depth 4, length 36 :
% 0.21/0.51 % SZS output start Refutation
% See solution above
% 0.21/0.51 Formulae used in the proof : dt_k1_lattice3 fc1_lattice3 t2_lattice3 dt_l3_lattices t7_xboole_1 t12_xboole_1 t1_lattice3 d3_lattices
% 0.21/0.51
%------------------------------------------------------------------------------