TSTP Solution File: NUM404+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM404+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 : Mon Jul 18 14:25:54 EDT 2022
% Result : Theorem 0.21s 0.53s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of clauses : 41 ( 15 unt; 12 nHn; 41 RR)
% Number of literals : 76 ( 0 equ; 32 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(62,axiom,
( ~ in(u,skc14)
| ordinal(u) ),
file('NUM404+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ ordinal(u)
| in(u,skc14) ),
file('NUM404+1.p',unknown),
[] ).
cnf(64,axiom,
( epsilon_transitive(u)
| in(skf5(u),u) ),
file('NUM404+1.p',unknown),
[] ).
cnf(65,axiom,
~ in(skf7(u),skf6(u)),
file('NUM404+1.p',unknown),
[] ).
cnf(66,axiom,
( epsilon_connected(u)
| in(skf7(u),u) ),
file('NUM404+1.p',unknown),
[] ).
cnf(67,axiom,
( epsilon_connected(u)
| in(skf6(u),u) ),
file('NUM404+1.p',unknown),
[] ).
cnf(68,axiom,
~ in(skf8(u,v),u),
file('NUM404+1.p',unknown),
[] ).
cnf(70,axiom,
( ~ subset(skf5(u),u)
| epsilon_transitive(u) ),
file('NUM404+1.p',unknown),
[] ).
cnf(73,axiom,
( ~ in(u,v)
| ~ in(v,u) ),
file('NUM404+1.p',unknown),
[] ).
cnf(75,axiom,
( ~ equal(skf7(u),skf6(u))
| epsilon_connected(u) ),
file('NUM404+1.p',unknown),
[] ).
cnf(76,axiom,
( ~ in(skf6(u),skf7(u))
| epsilon_connected(u) ),
file('NUM404+1.p',unknown),
[] ).
cnf(77,axiom,
( subset(u,v)
| in(skf8(v,u),u) ),
file('NUM404+1.p',unknown),
[] ).
cnf(78,axiom,
( ~ epsilon_connected(u)
| ~ epsilon_transitive(u)
| ordinal(u) ),
file('NUM404+1.p',unknown),
[] ).
cnf(81,axiom,
( ~ ordinal(u)
| ~ in(v,u)
| ordinal(v) ),
file('NUM404+1.p',unknown),
[] ).
cnf(89,axiom,
( ~ ordinal(u)
| ~ ordinal(v)
| in(u,v)
| equal(v,u)
| in(v,u) ),
file('NUM404+1.p',unknown),
[] ).
cnf(96,plain,
~ ordinal(skf8(skc14,u)),
inference(res,[status(thm),theory(equality)],[63,68]),
[iquote('0:Res:63.1,68.0')] ).
cnf(130,plain,
( epsilon_transitive(skc14)
| ordinal(skf5(skc14)) ),
inference(res,[status(thm),theory(equality)],[64,62]),
[iquote('0:Res:64.1,62.0')] ).
cnf(131,plain,
( epsilon_connected(skc14)
| ordinal(skf6(skc14)) ),
inference(res,[status(thm),theory(equality)],[67,62]),
[iquote('0:Res:67.1,62.0')] ).
cnf(132,plain,
( epsilon_connected(skc14)
| ordinal(skf7(skc14)) ),
inference(res,[status(thm),theory(equality)],[66,62]),
[iquote('0:Res:66.1,62.0')] ).
cnf(148,plain,
( ~ ordinal(u)
| ~ in(skc14,u) ),
inference(res,[status(thm),theory(equality)],[63,73]),
[iquote('0:Res:63.1,73.0')] ).
cnf(157,plain,
( ~ ordinal(skc14)
| ~ ordinal(skc14) ),
inference(res,[status(thm),theory(equality)],[63,148]),
[iquote('0:Res:63.1,148.1')] ).
cnf(158,plain,
~ ordinal(skc14),
inference(obv,[status(thm),theory(equality)],[157]),
[iquote('0:Obv:157.0')] ).
cnf(160,plain,
( ~ epsilon_transitive(skc14)
| ~ epsilon_connected(skc14) ),
inference(sor,[status(thm)],[158,78]),
[iquote('0:SoR:158.0,78.2')] ).
cnf(176,plain,
( ~ ordinal(u)
| subset(u,v)
| ordinal(skf8(v,u)) ),
inference(res,[status(thm),theory(equality)],[77,81]),
[iquote('0:Res:77.1,81.1')] ).
cnf(197,plain,
( ~ ordinal(u)
| subset(u,skc14) ),
inference(sor,[status(thm)],[96,176]),
[iquote('0:SoR:96.0,176.2')] ).
cnf(207,plain,
( ~ ordinal(skf5(skc14))
| epsilon_transitive(skc14) ),
inference(res,[status(thm),theory(equality)],[197,70]),
[iquote('0:Res:197.1,70.0')] ).
cnf(208,plain,
epsilon_transitive(skc14),
inference(mrr,[status(thm)],[207,130]),
[iquote('0:MRR:207.0,130.1')] ).
cnf(209,plain,
~ epsilon_connected(skc14),
inference(mrr,[status(thm)],[160,208]),
[iquote('0:MRR:160.0,208.0')] ).
cnf(210,plain,
ordinal(skf6(skc14)),
inference(mrr,[status(thm)],[131,209]),
[iquote('0:MRR:131.0,209.0')] ).
cnf(211,plain,
ordinal(skf7(skc14)),
inference(mrr,[status(thm)],[132,209]),
[iquote('0:MRR:132.0,209.0')] ).
cnf(251,plain,
( ~ ordinal(skf7(u))
| ~ ordinal(skf6(u))
| equal(skf7(u),skf6(u))
| in(skf6(u),skf7(u)) ),
inference(res,[status(thm),theory(equality)],[89,65]),
[iquote('0:Res:89.2,65.0')] ).
cnf(672,plain,
( ~ ordinal(skf6(skc14))
| equal(skf7(skc14),skf6(skc14))
| in(skf6(skc14),skf7(skc14)) ),
inference(sor,[status(thm)],[251,211]),
[iquote('0:SoR:251.0,211.0')] ).
cnf(675,plain,
( equal(skf7(skc14),skf6(skc14))
| in(skf6(skc14),skf7(skc14)) ),
inference(ssi,[status(thm)],[672,210]),
[iquote('0:SSi:672.0,210.0')] ).
cnf(831,plain,
equal(skf7(skc14),skf6(skc14)),
inference(spt,[spt(split,[position(s1)])],[675]),
[iquote('1:Spt:675.0')] ).
cnf(838,plain,
( ~ equal(skf6(skc14),skf6(skc14))
| epsilon_connected(skc14) ),
inference(spl,[status(thm),theory(equality)],[831,75]),
[iquote('1:SpL:831.0,75.0')] ).
cnf(842,plain,
epsilon_connected(skc14),
inference(obv,[status(thm),theory(equality)],[838]),
[iquote('1:Obv:838.0')] ).
cnf(843,plain,
$false,
inference(mrr,[status(thm)],[842,209]),
[iquote('1:MRR:842.0,209.0')] ).
cnf(844,plain,
~ equal(skf7(skc14),skf6(skc14)),
inference(spt,[spt(split,[position(sa)])],[843,831]),
[iquote('1:Spt:843.0,675.0,831.0')] ).
cnf(845,plain,
in(skf6(skc14),skf7(skc14)),
inference(spt,[spt(split,[position(s2)])],[675]),
[iquote('1:Spt:843.0,675.1')] ).
cnf(852,plain,
epsilon_connected(skc14),
inference(res,[status(thm),theory(equality)],[845,76]),
[iquote('1:Res:845.0,76.0')] ).
cnf(853,plain,
$false,
inference(mrr,[status(thm)],[852,209]),
[iquote('1:MRR:852.0,209.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : NUM404+1 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.15 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n029.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Wed Jul 6 08:29:13 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.53
% 0.21/0.53 SPASS V 3.9
% 0.21/0.53 SPASS beiseite: Proof found.
% 0.21/0.53 % SZS status Theorem
% 0.21/0.53 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.53 SPASS derived 684 clauses, backtracked 4 clauses, performed 3 splits and kept 402 clauses.
% 0.21/0.53 SPASS allocated 98240 KBytes.
% 0.21/0.53 SPASS spent 0:00:00.16 on the problem.
% 0.21/0.53 0:00:00.03 for the input.
% 0.21/0.53 0:00:00.04 for the FLOTTER CNF translation.
% 0.21/0.53 0:00:00.01 for inferences.
% 0.21/0.53 0:00:00.00 for the backtracking.
% 0.21/0.53 0:00:00.05 for the reduction.
% 0.21/0.53
% 0.21/0.53
% 0.21/0.53 Here is a proof with depth 4, length 41 :
% 0.21/0.53 % SZS output start Refutation
% See solution above
% 0.21/0.53 Formulae used in the proof : t37_ordinal1 d2_ordinal1 d3_ordinal1 antisymmetry_r2_hidden d3_tarski d4_ordinal1 t23_ordinal1 t24_ordinal1
% 0.21/0.53
%------------------------------------------------------------------------------