%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO111-1 : TPTP v8.1.0. Released v2.4.0.
% 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 : Sat Jul 16 06:22:25 EDT 2022
% Result : Unsatisfiable 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 40 ( 23 unt; 2 nHn; 40 RR)
% Number of literals : 68 ( 0 equ; 32 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
between_c(sk15,sk16,sk17,sk18),
file('GEO111-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ incident_c(sk16,sk15)
| ~ incident_c(sk17,sk15)
| ~ incident_c(sk18,sk15)
| equal(sk17,sk16)
| equal(sk18,sk17)
| equal(sk18,sk16) ),
file('GEO111-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ incident_c(u,v)
| ~ part_of(v,w)
| incident_c(u,w) ),
file('GEO111-1.p',unknown),
[] ).
cnf(15,axiom,
( ~ end_point(u,v)
| incident_c(u,v) ),
file('GEO111-1.p',unknown),
[] ).
cnf(23,axiom,
( ~ inner_point(u,v)
| incident_c(u,v) ),
file('GEO111-1.p',unknown),
[] ).
cnf(24,axiom,
( ~ end_point(u,v)
| ~ inner_point(u,v) ),
file('GEO111-1.p',unknown),
[] ).
cnf(51,axiom,
( ~ equal(u,v)
| ~ between_c(w,u,x,v) ),
file('GEO111-1.p',unknown),
[] ).
cnf(52,axiom,
( ~ between_c(u,v,w,x)
| part_of(ax1_sk1(x,w,v,u),u) ),
file('GEO111-1.p',unknown),
[] ).
cnf(53,axiom,
( ~ between_c(u,v,w,x)
| end_point(v,ax1_sk1(x,w,v,u)) ),
file('GEO111-1.p',unknown),
[] ).
cnf(54,axiom,
( ~ between_c(u,v,w,x)
| end_point(x,ax1_sk1(x,w,v,u)) ),
file('GEO111-1.p',unknown),
[] ).
cnf(55,axiom,
( ~ between_c(u,v,w,x)
| inner_point(w,ax1_sk1(x,w,v,u)) ),
file('GEO111-1.p',unknown),
[] ).
cnf(57,plain,
part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15),
inference(res,[status(thm),theory(equality)],[1,52]),
[iquote('0:Res:1.0,52.0')] ).
cnf(58,plain,
end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(res,[status(thm),theory(equality)],[1,53]),
[iquote('0:Res:1.0,53.0')] ).
cnf(59,plain,
end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(res,[status(thm),theory(equality)],[1,54]),
[iquote('0:Res:1.0,54.0')] ).
cnf(60,plain,
inner_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(res,[status(thm),theory(equality)],[1,55]),
[iquote('0:Res:1.0,55.0')] ).
cnf(61,plain,
~ equal(sk18,sk16),
inference(res,[status(thm),theory(equality)],[1,51]),
[iquote('0:Res:1.0,51.0')] ).
cnf(62,plain,
( ~ incident_c(sk18,sk15)
| ~ incident_c(sk17,sk15)
| ~ incident_c(sk16,sk15)
| equal(sk18,sk17)
| equal(sk17,sk16) ),
inference(mrr,[status(thm)],[2,61]),
[iquote('0:MRR:2.5,61.0')] ).
cnf(63,plain,
equal(sk18,sk17),
inference(spt,[spt(split,[position(s1)])],[62]),
[iquote('1:Spt:62.3')] ).
cnf(64,plain,
inner_point(sk17,ax1_sk1(sk17,sk17,sk16,sk15)),
inference(rew,[status(thm),theory(equality)],[63,60]),
[iquote('1:Rew:63.0,60.0')] ).
cnf(69,plain,
end_point(sk17,ax1_sk1(sk17,sk17,sk16,sk15)),
inference(rew,[status(thm),theory(equality)],[63,59]),
[iquote('1:Rew:63.0,59.0')] ).
cnf(86,plain,
~ end_point(sk17,ax1_sk1(sk17,sk17,sk16,sk15)),
inference(res,[status(thm),theory(equality)],[64,24]),
[iquote('1:Res:64.0,24.1')] ).
cnf(87,plain,
$false,
inference(mrr,[status(thm)],[86,69]),
[iquote('1:MRR:86.0,69.0')] ).
cnf(88,plain,
~ equal(sk18,sk17),
inference(spt,[spt(split,[position(sa)])],[87,63]),
[iquote('1:Spt:87.0,62.3,63.0')] ).
cnf(89,plain,
( ~ incident_c(sk18,sk15)
| ~ incident_c(sk17,sk15)
| ~ incident_c(sk16,sk15)
| equal(sk17,sk16) ),
inference(spt,[spt(split,[position(s2)])],[62]),
[iquote('1:Spt:87.0,62.0,62.1,62.2,62.4')] ).
cnf(91,plain,
incident_c(sk18,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(res,[status(thm),theory(equality)],[59,15]),
[iquote('0:Res:59.0,15.0')] ).
cnf(94,plain,
incident_c(sk16,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(res,[status(thm),theory(equality)],[58,15]),
[iquote('0:Res:58.0,15.0')] ).
cnf(96,plain,
~ end_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(res,[status(thm),theory(equality)],[60,24]),
[iquote('0:Res:60.0,24.1')] ).
cnf(97,plain,
incident_c(sk17,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(res,[status(thm),theory(equality)],[60,23]),
[iquote('0:Res:60.0,23.0')] ).
cnf(112,plain,
( ~ part_of(ax1_sk1(sk18,sk17,sk16,sk15),u)
| incident_c(sk18,u) ),
inference(res,[status(thm),theory(equality)],[91,3]),
[iquote('0:Res:91.0,3.0')] ).
cnf(113,plain,
( ~ part_of(ax1_sk1(sk18,sk17,sk16,sk15),u)
| incident_c(sk16,u) ),
inference(res,[status(thm),theory(equality)],[94,3]),
[iquote('0:Res:94.0,3.0')] ).
cnf(114,plain,
( ~ part_of(ax1_sk1(sk18,sk17,sk16,sk15),u)
| incident_c(sk17,u) ),
inference(res,[status(thm),theory(equality)],[97,3]),
[iquote('0:Res:97.0,3.0')] ).
cnf(123,plain,
incident_c(sk18,sk15),
inference(res,[status(thm),theory(equality)],[57,112]),
[iquote('0:Res:57.0,112.0')] ).
cnf(124,plain,
( ~ incident_c(sk17,sk15)
| ~ incident_c(sk16,sk15)
| equal(sk17,sk16) ),
inference(mrr,[status(thm)],[89,123]),
[iquote('1:MRR:89.0,123.0')] ).
cnf(129,plain,
incident_c(sk16,sk15),
inference(res,[status(thm),theory(equality)],[57,113]),
[iquote('0:Res:57.0,113.0')] ).
cnf(130,plain,
( ~ incident_c(sk17,sk15)
| equal(sk17,sk16) ),
inference(mrr,[status(thm)],[124,129]),
[iquote('1:MRR:124.1,129.0')] ).
cnf(135,plain,
incident_c(sk17,sk15),
inference(res,[status(thm),theory(equality)],[57,114]),
[iquote('0:Res:57.0,114.0')] ).
cnf(136,plain,
equal(sk17,sk16),
inference(mrr,[status(thm)],[130,135]),
[iquote('1:MRR:130.0,135.0')] ).
cnf(142,plain,
end_point(sk16,ax1_sk1(sk18,sk16,sk16,sk15)),
inference(rew,[status(thm),theory(equality)],[136,58]),
[iquote('1:Rew:136.0,58.0')] ).
cnf(150,plain,
~ end_point(sk16,ax1_sk1(sk18,sk16,sk16,sk15)),
inference(rew,[status(thm),theory(equality)],[136,96]),
[iquote('1:Rew:136.0,96.0')] ).
cnf(153,plain,
$false,
inference(mrr,[status(thm)],[150,142]),
[iquote('1:MRR:150.0,142.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO111-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % 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 : Fri Jun 17 20:28:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.45
% 0.19/0.45 SPASS V 3.9
% 0.19/0.45 SPASS beiseite: Proof found.
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 SPASS derived 91 clauses, backtracked 8 clauses, performed 1 splits and kept 126 clauses.
% 0.19/0.45 SPASS allocated 75722 KBytes.
% 0.19/0.45 SPASS spent 0:00:00.09 on the problem.
% 0.19/0.45 0:00:00.05 for the input.
% 0.19/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.45 0:00:00.00 for inferences.
% 0.19/0.45 0:00:00.00 for the backtracking.
% 0.19/0.45 0:00:00.01 for the reduction.
% 0.19/0.45
% 0.19/0.45
% 0.19/0.45 Here is a proof with depth 4, length 40 :
% 0.19/0.45 % SZS output start Refutation
% See solution above
% 0.19/0.45 Formulae used in the proof : theorem_3_8_1_77 theorem_3_8_1_78 part_of_defn_1 end_point_defn_13 inner_point_defn_21 inner_point_defn_22 between_c_defn_1 between_c_defn_2 between_c_defn_3 between_c_defn_4 between_c_defn_5
% 0.19/0.45
%------------------------------------------------------------------------------