TSTP Solution File: NUM401+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM401+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 14:25:53 EDT 2022
% Result : Theorem 29.69s 29.87s
% Output : Refutation 29.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 18
% Syntax : Number of clauses : 67 ( 27 unt; 13 nHn; 67 RR)
% Number of literals : 134 ( 0 equ; 64 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ordinal(skc16),
file('NUM401+1.p',unknown),
[] ).
cnf(2,axiom,
ordinal(skc15),
file('NUM401+1.p',unknown),
[] ).
cnf(56,axiom,
in(u,succ(u)),
file('NUM401+1.p',unknown),
[] ).
cnf(58,axiom,
( ~ ordinal(u)
| epsilon_transitive(u) ),
file('NUM401+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ ordinal(u)
| epsilon_connected(u) ),
file('NUM401+1.p',unknown),
[] ).
cnf(71,axiom,
( ~ ordinal(u)
| ordinal_subset(u,u) ),
file('NUM401+1.p',unknown),
[] ).
cnf(73,axiom,
( ordinal_subset(skc15,skc16)
| in(skc15,succ(skc16)) ),
file('NUM401+1.p',unknown),
[] ).
cnf(77,axiom,
equal(set_union2(u,singleton(u)),succ(u)),
file('NUM401+1.p',unknown),
[] ).
cnf(88,axiom,
( ~ ordinal_subset(skc15,skc16)
| ~ in(skc15,succ(skc16)) ),
file('NUM401+1.p',unknown),
[] ).
cnf(92,axiom,
( ~ epsilon_transitive(u)
| ~ in(v,u)
| subset(v,u) ),
file('NUM401+1.p',unknown),
[] ).
cnf(95,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| equal(v,u) ),
file('NUM401+1.p',unknown),
[] ).
cnf(96,axiom,
( ~ ordinal(u)
| ~ ordinal(v)
| ordinal_subset(u,v)
| ordinal_subset(v,u) ),
file('NUM401+1.p',unknown),
[] ).
cnf(97,axiom,
( ~ in(u,v)
| ~ equal(v,singleton(w))
| equal(u,w) ),
file('NUM401+1.p',unknown),
[] ).
cnf(101,axiom,
( ~ in(u,v)
| ~ equal(w,set_union2(v,x))
| in(u,w) ),
file('NUM401+1.p',unknown),
[] ).
cnf(103,axiom,
( ~ ordinal(u)
| ~ ordinal(v)
| ~ ordinal_subset(v,u)
| subset(v,u) ),
file('NUM401+1.p',unknown),
[] ).
cnf(104,axiom,
( ~ ordinal(u)
| ~ ordinal(v)
| ~ subset(v,u)
| ordinal_subset(v,u) ),
file('NUM401+1.p',unknown),
[] ).
cnf(107,axiom,
( ~ ordinal(u)
| ~ ordinal(v)
| in(u,v)
| equal(v,u)
| in(v,u) ),
file('NUM401+1.p',unknown),
[] ).
cnf(109,axiom,
( ~ in(u,v)
| ~ equal(v,set_union2(w,x))
| in(u,x)
| in(u,w) ),
file('NUM401+1.p',unknown),
[] ).
cnf(112,plain,
( ~ ordinal(u)
| in(u,skc15)
| equal(skc15,u)
| in(skc15,u) ),
inference(res,[status(thm),theory(equality)],[2,107]),
[iquote('0:Res:2.0,107.0')] ).
cnf(113,plain,
( ~ ordinal(u)
| ~ ordinal_subset(skc15,u)
| subset(skc15,u) ),
inference(res,[status(thm),theory(equality)],[2,103]),
[iquote('0:Res:2.0,103.0')] ).
cnf(114,plain,
( ~ ordinal(u)
| ~ subset(skc15,u)
| ordinal_subset(skc15,u) ),
inference(res,[status(thm),theory(equality)],[2,104]),
[iquote('0:Res:2.0,104.0')] ).
cnf(115,plain,
( ~ ordinal(u)
| ordinal_subset(u,skc15)
| ordinal_subset(skc15,u) ),
inference(res,[status(thm),theory(equality)],[2,96]),
[iquote('0:Res:2.0,96.0')] ).
cnf(119,plain,
ordinal_subset(skc15,skc15),
inference(res,[status(thm),theory(equality)],[2,71]),
[iquote('0:Res:2.0,71.0')] ).
cnf(120,plain,
epsilon_transitive(skc15),
inference(res,[status(thm),theory(equality)],[2,58]),
[iquote('0:Res:2.0,58.0')] ).
cnf(121,plain,
epsilon_connected(skc15),
inference(res,[status(thm),theory(equality)],[2,59]),
[iquote('0:Res:2.0,59.0')] ).
cnf(123,plain,
( ~ ordinal(u)
| ~ ordinal_subset(u,skc15)
| subset(u,skc15) ),
inference(res,[status(thm),theory(equality)],[2,103]),
[iquote('0:Res:2.0,103.1')] ).
cnf(124,plain,
( ~ ordinal(u)
| ~ subset(u,skc15)
| ordinal_subset(u,skc15) ),
inference(res,[status(thm),theory(equality)],[2,104]),
[iquote('0:Res:2.0,104.1')] ).
cnf(134,plain,
epsilon_transitive(skc16),
inference(res,[status(thm),theory(equality)],[1,58]),
[iquote('0:Res:1.0,58.0')] ).
cnf(135,plain,
epsilon_connected(skc16),
inference(res,[status(thm),theory(equality)],[1,59]),
[iquote('0:Res:1.0,59.0')] ).
cnf(141,plain,
( in(skc16,skc15)
| equal(skc16,skc15)
| in(skc15,skc16) ),
inference(res,[status(thm),theory(equality)],[1,112]),
[iquote('0:Res:1.0,112.0')] ).
cnf(146,plain,
( ~ subset(skc16,skc15)
| ordinal_subset(skc16,skc15) ),
inference(res,[status(thm),theory(equality)],[1,124]),
[iquote('0:Res:1.0,124.0')] ).
cnf(147,plain,
( ~ ordinal_subset(skc16,skc15)
| subset(skc16,skc15) ),
inference(res,[status(thm),theory(equality)],[1,123]),
[iquote('0:Res:1.0,123.0')] ).
cnf(148,plain,
( ~ subset(skc15,skc16)
| ordinal_subset(skc15,skc16) ),
inference(res,[status(thm),theory(equality)],[1,114]),
[iquote('0:Res:1.0,114.0')] ).
cnf(149,plain,
( ~ ordinal_subset(skc15,skc16)
| subset(skc15,skc16) ),
inference(res,[status(thm),theory(equality)],[1,113]),
[iquote('0:Res:1.0,113.0')] ).
cnf(151,plain,
( ordinal_subset(skc16,skc15)
| ordinal_subset(skc15,skc16) ),
inference(res,[status(thm),theory(equality)],[1,115]),
[iquote('0:Res:1.0,115.0')] ).
cnf(166,plain,
equal(skc16,skc15),
inference(spt,[spt(split,[position(s1)])],[141]),
[iquote('1:Spt:141.1')] ).
cnf(167,plain,
( ~ ordinal_subset(skc15,skc16)
| ~ in(skc15,succ(skc15)) ),
inference(rew,[status(thm),theory(equality)],[166,88]),
[iquote('1:Rew:166.0,88.1')] ).
cnf(189,plain,
( ~ ordinal_subset(skc15,skc15)
| ~ in(skc15,succ(skc15)) ),
inference(rew,[status(thm),theory(equality)],[166,167]),
[iquote('1:Rew:166.0,167.0')] ).
cnf(190,plain,
$false,
inference(mrr,[status(thm)],[189,119,56]),
[iquote('1:MRR:189.0,189.1,119.0,56.0')] ).
cnf(197,plain,
~ equal(skc16,skc15),
inference(spt,[spt(split,[position(sa)])],[190,166]),
[iquote('1:Spt:190.0,141.1,166.0')] ).
cnf(198,plain,
( in(skc16,skc15)
| in(skc15,skc16) ),
inference(spt,[spt(split,[position(s2)])],[141]),
[iquote('1:Spt:190.0,141.0,141.2')] ).
cnf(199,plain,
ordinal_subset(skc15,skc16),
inference(spt,[spt(split,[position(s2s1)])],[151]),
[iquote('2:Spt:151.1')] ).
cnf(200,plain,
subset(skc15,skc16),
inference(mrr,[status(thm)],[149,199]),
[iquote('2:MRR:149.0,199.0')] ).
cnf(201,plain,
~ in(skc15,succ(skc16)),
inference(mrr,[status(thm)],[88,199]),
[iquote('2:MRR:88.0,199.0')] ).
cnf(290,plain,
( ~ epsilon_transitive(skc15)
| ~ in(skc16,skc15)
| ordinal_subset(skc16,skc15) ),
inference(res,[status(thm),theory(equality)],[92,146]),
[iquote('0:Res:92.2,146.0')] ).
cnf(291,plain,
( ~ in(skc16,skc15)
| ordinal_subset(skc16,skc15) ),
inference(ssi,[status(thm)],[290,2,121,120]),
[iquote('0:SSi:290.0,2.0,121.0,120.0')] ).
cnf(328,plain,
( ~ subset(skc16,skc15)
| equal(skc16,skc15) ),
inference(res,[status(thm),theory(equality)],[200,95]),
[iquote('2:Res:200.0,95.0')] ).
cnf(331,plain,
~ subset(skc16,skc15),
inference(mrr,[status(thm)],[328,197]),
[iquote('2:MRR:328.1,197.0')] ).
cnf(332,plain,
~ ordinal_subset(skc16,skc15),
inference(mrr,[status(thm)],[147,331]),
[iquote('2:MRR:147.1,331.0')] ).
cnf(333,plain,
~ in(skc16,skc15),
inference(mrr,[status(thm)],[291,332]),
[iquote('2:MRR:291.1,332.0')] ).
cnf(334,plain,
in(skc15,skc16),
inference(mrr,[status(thm)],[198,333]),
[iquote('2:MRR:198.0,333.0')] ).
cnf(400,plain,
( ~ in(u,singleton(v))
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[97]),
[iquote('0:EqR:97.1')] ).
cnf(497,plain,
( ~ in(u,v)
| in(u,set_union2(v,w)) ),
inference(eqr,[status(thm),theory(equality)],[101]),
[iquote('0:EqR:101.1')] ).
cnf(650,plain,
( ~ in(u,set_union2(v,w))
| in(u,w)
| in(u,v) ),
inference(eqr,[status(thm),theory(equality)],[109]),
[iquote('0:EqR:109.1')] ).
cnf(732,plain,
( ~ in(u,v)
| in(u,succ(v)) ),
inference(spr,[status(thm),theory(equality)],[77,497]),
[iquote('0:SpR:77.0,497.1')] ).
cnf(838,plain,
~ in(skc15,skc16),
inference(res,[status(thm),theory(equality)],[732,201]),
[iquote('2:Res:732.1,201.0')] ).
cnf(861,plain,
$false,
inference(mrr,[status(thm)],[838,334]),
[iquote('2:MRR:838.0,334.0')] ).
cnf(862,plain,
~ ordinal_subset(skc15,skc16),
inference(spt,[spt(split,[position(s2sa)])],[861,199]),
[iquote('2:Spt:861.0,151.1,199.0')] ).
cnf(863,plain,
ordinal_subset(skc16,skc15),
inference(spt,[spt(split,[position(s2s2)])],[151]),
[iquote('2:Spt:861.0,151.0')] ).
cnf(864,plain,
~ subset(skc15,skc16),
inference(mrr,[status(thm)],[148,862]),
[iquote('2:MRR:148.1,862.0')] ).
cnf(865,plain,
in(skc15,succ(skc16)),
inference(mrr,[status(thm)],[73,862]),
[iquote('2:MRR:73.0,862.0')] ).
cnf(874,plain,
( ~ epsilon_transitive(skc16)
| ~ in(skc15,skc16) ),
inference(res,[status(thm),theory(equality)],[92,864]),
[iquote('2:Res:92.2,864.0')] ).
cnf(878,plain,
~ in(skc15,skc16),
inference(ssi,[status(thm)],[874,1,134,135]),
[iquote('2:SSi:874.0,1.0,134.0,135.0')] ).
cnf(1842,plain,
( ~ in(u,succ(v))
| in(u,singleton(v))
| in(u,v) ),
inference(spl,[status(thm),theory(equality)],[77,650]),
[iquote('0:SpL:77.0,650.0')] ).
cnf(4478,plain,
( ~ in(u,succ(v))
| in(u,v)
| equal(u,v) ),
inference(res,[status(thm),theory(equality)],[1842,400]),
[iquote('0:Res:1842.1,400.0')] ).
cnf(33529,plain,
( in(skc15,skc16)
| equal(skc16,skc15) ),
inference(res,[status(thm),theory(equality)],[865,4478]),
[iquote('2:Res:865.0,4478.0')] ).
cnf(33543,plain,
$false,
inference(mrr,[status(thm)],[33529,878,197]),
[iquote('2:MRR:33529.0,33529.1,878.0,197.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : NUM401+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n004.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 : Thu Jul 7 08:57:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 29.69/29.87
% 29.69/29.87 SPASS V 3.9
% 29.69/29.87 SPASS beiseite: Proof found.
% 29.69/29.87 % SZS status Theorem
% 29.69/29.87 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.69/29.87 SPASS derived 28987 clauses, backtracked 121 clauses, performed 5 splits and kept 10060 clauses.
% 29.69/29.87 SPASS allocated 129094 KBytes.
% 29.69/29.87 SPASS spent 0:0:28.77 on the problem.
% 29.69/29.87 0:00:00.03 for the input.
% 29.69/29.87 0:00:00.04 for the FLOTTER CNF translation.
% 29.69/29.87 0:00:00.58 for inferences.
% 29.69/29.87 0:00:00.96 for the backtracking.
% 29.69/29.87 0:0:26.87 for the reduction.
% 29.69/29.87
% 29.69/29.87
% 29.69/29.87 Here is a proof with depth 4, length 67 :
% 29.69/29.87 % SZS output start Refutation
% See solution above
% 29.69/29.87 Formulae used in the proof : t34_ordinal1 t10_ordinal1 cc1_ordinal1 reflexivity_r1_ordinal1 d1_ordinal1 d2_ordinal1 d10_xboole_0 connectedness_r1_ordinal1 d1_tarski t1_boole d2_xboole_0 antisymmetry_r2_hidden redefinition_r1_ordinal1 t24_ordinal1
% 29.69/29.87
%------------------------------------------------------------------------------