TSTP Solution File: SEU203+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU203+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 14:34:58 EDT 2022
% Result : Theorem 1.01s 1.18s
% Output : Refutation 1.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 18
% Syntax : Number of clauses : 60 ( 16 unt; 9 nHn; 60 RR)
% Number of literals : 145 ( 0 equ; 93 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 11 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc8),
file('SEU203+1.p',unknown),
[] ).
cnf(3,axiom,
empty(empty_set),
file('SEU203+1.p',unknown),
[] ).
cnf(4,axiom,
relation(empty_set),
file('SEU203+1.p',unknown),
[] ).
cnf(11,axiom,
element(skf15(u),u),
file('SEU203+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ empty(u)
| relation(u) ),
file('SEU203+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ empty(u)
| empty(relation_dom(u)) ),
file('SEU203+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ empty(u)
| equal(u,empty_set) ),
file('SEU203+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ empty(u)
| ~ in(v,u) ),
file('SEU203+1.p',unknown),
[] ).
cnf(22,axiom,
( in(skc11,skc9)
| in(skc10,relation_image(skc8,skc9)) ),
file('SEU203+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ element(u,v)
| empty(v)
| in(u,v) ),
file('SEU203+1.p',unknown),
[] ).
cnf(28,axiom,
( in(skc10,relation_image(skc8,skc9))
| in(ordered_pair(skc11,skc10),skc8) ),
file('SEU203+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ relation(u)
| ~ equal(v,relation_dom(u))
| ~ in(ordered_pair(w,x),u)
| in(w,v) ),
file('SEU203+1.p',unknown),
[] ).
cnf(32,axiom,
( ~ relation(u)
| ~ in(v,w)
| ~ equal(w,relation_image(u,x))
| in(skf7(x,y,z),x) ),
file('SEU203+1.p',unknown),
[] ).
cnf(33,axiom,
( ~ relation(u)
| ~ in(v,w)
| ~ equal(w,relation_dom(u))
| in(ordered_pair(v,skf11(u,v)),u) ),
file('SEU203+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ relation(u)
| equal(v,relation_dom(u))
| in(skf13(u,v),v)
| in(ordered_pair(skf13(u,v),skf14(v,u)),u) ),
file('SEU203+1.p',unknown),
[] ).
cnf(37,axiom,
( ~ relation(u)
| ~ in(v,w)
| ~ equal(w,relation_image(u,x))
| in(ordered_pair(skf7(x,u,v),v),u) ),
file('SEU203+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ in(u,skc9)
| ~ in(u,relation_dom(skc8))
| ~ in(skc10,relation_image(skc8,skc9))
| ~ in(ordered_pair(u,skc10),skc8) ),
file('SEU203+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ relation(u)
| ~ in(v,w)
| ~ equal(x,relation_image(u,w))
| ~ in(ordered_pair(v,y),u)
| in(y,x) ),
file('SEU203+1.p',unknown),
[] ).
cnf(43,plain,
( ~ in(u,v)
| ~ equal(w,relation_image(skc8,v))
| ~ in(ordered_pair(u,x),skc8)
| in(x,w) ),
inference(res,[status(thm),theory(equality)],[1,39]),
[iquote('0:Res:1.0,39.0')] ).
cnf(47,plain,
( ~ in(u,v)
| ~ equal(v,relation_image(skc8,w))
| in(skf7(w,x,y),w) ),
inference(res,[status(thm),theory(equality)],[1,32]),
[iquote('0:Res:1.0,32.0')] ).
cnf(49,plain,
( ~ equal(u,relation_dom(skc8))
| ~ in(ordered_pair(v,w),skc8)
| in(v,u) ),
inference(res,[status(thm),theory(equality)],[1,31]),
[iquote('0:Res:1.0,31.0')] ).
cnf(51,plain,
in(skc10,relation_image(skc8,skc9)),
inference(spt,[spt(split,[position(s1)])],[22]),
[iquote('1:Spt:22.1')] ).
cnf(52,plain,
( ~ in(u,skc9)
| ~ in(u,relation_dom(skc8))
| ~ in(ordered_pair(u,skc10),skc8) ),
inference(mrr,[status(thm)],[38,51]),
[iquote('1:MRR:38.2,51.0')] ).
cnf(61,plain,
( ~ empty(u)
| equal(relation_dom(u),empty_set) ),
inference(ems,[status(thm)],[18,16]),
[iquote('0:EmS:18.0,16.1')] ).
cnf(77,plain,
( empty(u)
| in(skf15(u),u) ),
inference(res,[status(thm),theory(equality)],[11,26]),
[iquote('0:Res:11.0,26.0')] ).
cnf(166,plain,
( ~ relation(u)
| ~ in(v,relation_dom(u))
| in(ordered_pair(v,skf11(u,v)),u) ),
inference(eqr,[status(thm),theory(equality)],[33]),
[iquote('0:EqR:33.2')] ).
cnf(167,plain,
( ~ empty(u)
| ~ relation(u)
| ~ in(v,w)
| ~ equal(w,empty_set)
| in(ordered_pair(v,skf11(u,v)),u) ),
inference(spl,[status(thm),theory(equality)],[61,33]),
[iquote('0:SpL:61.1,33.2')] ).
cnf(168,plain,
( ~ empty(u)
| ~ in(v,w)
| ~ equal(w,empty_set)
| in(ordered_pair(v,skf11(u,v)),u) ),
inference(ssi,[status(thm)],[167,13]),
[iquote('0:SSi:167.1,13.1')] ).
cnf(169,plain,
( ~ empty(u)
| ~ in(v,w)
| ~ equal(w,empty_set) ),
inference(mrr,[status(thm)],[168,21]),
[iquote('0:MRR:168.3,21.1')] ).
cnf(170,plain,
( ~ in(u,v)
| ~ equal(v,empty_set) ),
inference(ems,[status(thm)],[169,3]),
[iquote('0:EmS:169.0,3.0')] ).
cnf(171,plain,
~ equal(relation_image(skc8,skc9),empty_set),
inference(res,[status(thm),theory(equality)],[51,170]),
[iquote('1:Res:51.0,170.0')] ).
cnf(261,plain,
( ~ relation(u)
| ~ in(v,relation_image(u,w))
| in(ordered_pair(skf7(w,u,v),v),u) ),
inference(eqr,[status(thm),theory(equality)],[37]),
[iquote('0:EqR:37.2')] ).
cnf(440,plain,
( ~ relation(u)
| ~ empty(u)
| ~ in(v,relation_dom(u)) ),
inference(res,[status(thm),theory(equality)],[166,21]),
[iquote('0:Res:166.2,21.1')] ).
cnf(448,plain,
( ~ relation(u)
| ~ empty(u)
| ~ in(v,empty_set) ),
inference(rew,[status(thm),theory(equality)],[61,440]),
[iquote('0:Rew:61.1,440.2')] ).
cnf(449,plain,
( ~ empty(u)
| ~ in(v,empty_set) ),
inference(ssi,[status(thm)],[448,13]),
[iquote('0:SSi:448.0,13.1')] ).
cnf(452,plain,
~ in(u,empty_set),
inference(ems,[status(thm)],[449,3]),
[iquote('0:EmS:449.0,3.0')] ).
cnf(456,plain,
( ~ relation(empty_set)
| equal(u,relation_dom(empty_set))
| in(skf13(empty_set,u),u) ),
inference(res,[status(thm),theory(equality)],[36,452]),
[iquote('0:Res:36.3,452.0')] ).
cnf(457,plain,
( ~ relation(empty_set)
| ~ in(u,relation_dom(empty_set)) ),
inference(res,[status(thm),theory(equality)],[166,452]),
[iquote('0:Res:166.2,452.0')] ).
cnf(463,plain,
~ in(u,relation_dom(empty_set)),
inference(ssi,[status(thm)],[457,4,3]),
[iquote('0:SSi:457.0,4.0,3.0')] ).
cnf(545,plain,
( equal(u,relation_dom(empty_set))
| in(skf13(empty_set,u),u) ),
inference(ssi,[status(thm)],[456,4,3]),
[iquote('0:SSi:456.0,4.0,3.0')] ).
cnf(624,plain,
empty(relation_dom(empty_set)),
inference(res,[status(thm),theory(equality)],[77,463]),
[iquote('0:Res:77.1,463.0')] ).
cnf(646,plain,
equal(relation_dom(empty_set),empty_set),
inference(ems,[status(thm)],[18,624]),
[iquote('0:EmS:18.0,624.0')] ).
cnf(652,plain,
( equal(u,empty_set)
| in(skf13(empty_set,u),u) ),
inference(rew,[status(thm),theory(equality)],[646,545]),
[iquote('0:Rew:646.0,545.0')] ).
cnf(750,plain,
( ~ in(u,relation_image(skc8,v))
| in(skf7(v,w,x),v) ),
inference(eqr,[status(thm),theory(equality)],[47]),
[iquote('0:EqR:47.1')] ).
cnf(880,plain,
( ~ relation(skc8)
| ~ in(u,relation_image(skc8,v))
| ~ equal(w,relation_dom(skc8))
| in(skf7(v,skc8,u),w) ),
inference(res,[status(thm),theory(equality)],[261,49]),
[iquote('0:Res:261.2,49.1')] ).
cnf(881,plain,
( ~ relation(skc8)
| ~ in(skc10,relation_image(skc8,u))
| ~ in(skf7(u,skc8,skc10),skc9)
| ~ in(skf7(u,skc8,skc10),relation_dom(skc8)) ),
inference(res,[status(thm),theory(equality)],[261,52]),
[iquote('1:Res:261.2,52.2')] ).
cnf(885,plain,
( ~ in(u,relation_image(skc8,v))
| ~ equal(w,relation_dom(skc8))
| in(skf7(v,skc8,u),w) ),
inference(ssi,[status(thm)],[880,1]),
[iquote('0:SSi:880.0,1.0')] ).
cnf(887,plain,
( ~ in(skc10,relation_image(skc8,u))
| ~ in(skf7(u,skc8,skc10),skc9)
| ~ in(skf7(u,skc8,skc10),relation_dom(skc8)) ),
inference(ssi,[status(thm)],[881,1]),
[iquote('1:SSi:881.0,1.0')] ).
cnf(1013,plain,
( equal(relation_image(skc8,u),empty_set)
| in(skf7(u,v,w),u) ),
inference(res,[status(thm),theory(equality)],[652,750]),
[iquote('0:Res:652.1,750.0')] ).
cnf(1225,plain,
( ~ in(u,v)
| ~ in(ordered_pair(u,w),skc8)
| in(w,relation_image(skc8,v)) ),
inference(eqr,[status(thm),theory(equality)],[43]),
[iquote('0:EqR:43.1')] ).
cnf(3191,plain,
( ~ in(skc10,relation_image(skc8,u))
| ~ equal(relation_dom(skc8),relation_dom(skc8))
| ~ in(skc10,relation_image(skc8,u))
| ~ in(skf7(u,skc8,skc10),skc9) ),
inference(res,[status(thm),theory(equality)],[885,887]),
[iquote('1:Res:885.2,887.2')] ).
cnf(3194,plain,
( ~ in(skc10,relation_image(skc8,u))
| ~ in(skf7(u,skc8,skc10),skc9) ),
inference(obv,[status(thm),theory(equality)],[3191]),
[iquote('1:Obv:3191.1')] ).
cnf(3304,plain,
( ~ in(skc10,relation_image(skc8,skc9))
| equal(relation_image(skc8,skc9),empty_set) ),
inference(res,[status(thm),theory(equality)],[1013,3194]),
[iquote('1:Res:1013.1,3194.1')] ).
cnf(3310,plain,
$false,
inference(mrr,[status(thm)],[3304,51,171]),
[iquote('1:MRR:3304.0,3304.1,51.0,171.0')] ).
cnf(3314,plain,
~ in(skc10,relation_image(skc8,skc9)),
inference(spt,[spt(split,[position(sa)])],[3310,51]),
[iquote('1:Spt:3310.0,22.1,51.0')] ).
cnf(3315,plain,
in(skc11,skc9),
inference(spt,[spt(split,[position(s2)])],[22]),
[iquote('1:Spt:3310.0,22.0')] ).
cnf(3319,plain,
in(ordered_pair(skc11,skc10),skc8),
inference(mrr,[status(thm)],[28,3314]),
[iquote('1:MRR:28.0,3314.0')] ).
cnf(3384,plain,
( ~ in(skc11,u)
| in(skc10,relation_image(skc8,u)) ),
inference(res,[status(thm),theory(equality)],[3319,1225]),
[iquote('1:Res:3319.0,1225.1')] ).
cnf(3492,plain,
~ in(skc11,skc9),
inference(res,[status(thm),theory(equality)],[3384,3314]),
[iquote('1:Res:3384.1,3314.0')] ).
cnf(3497,plain,
$false,
inference(mrr,[status(thm)],[3492,3315]),
[iquote('1:MRR:3492.0,3315.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU203+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 : Sat Jun 18 21:09:49 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.01/1.18
% 1.01/1.18 SPASS V 3.9
% 1.01/1.18 SPASS beiseite: Proof found.
% 1.01/1.18 % SZS status Theorem
% 1.01/1.18 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.01/1.18 SPASS derived 2826 clauses, backtracked 87 clauses, performed 2 splits and kept 1247 clauses.
% 1.01/1.18 SPASS allocated 101021 KBytes.
% 1.01/1.18 SPASS spent 0:00:00.81 on the problem.
% 1.01/1.18 0:00:00.04 for the input.
% 1.01/1.18 0:00:00.07 for the FLOTTER CNF translation.
% 1.01/1.18 0:00:00.04 for inferences.
% 1.01/1.18 0:00:00.02 for the backtracking.
% 1.01/1.18 0:00:00.61 for the reduction.
% 1.01/1.18
% 1.01/1.18
% 1.01/1.18 Here is a proof with depth 6, length 60 :
% 1.01/1.18 % SZS output start Refutation
% See solution above
% 1.01/1.18 Formulae used in the proof : t143_relat_1 fc4_relat_1 existence_m1_subset_1 cc1_relat_1 fc7_relat_1 t6_boole t7_boole t2_subset d4_relat_1 antisymmetry_r2_hidden d13_relat_1
% 1.01/1.18
%------------------------------------------------------------------------------