TSTP Solution File: SEU243+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU243+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 14:35:27 EDT 2022
% Result : Theorem 0.20s 0.50s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of clauses : 39 ( 12 unt; 15 nHn; 39 RR)
% Number of literals : 103 ( 0 equ; 55 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 : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc6),
file('SEU243+1.p',unknown),
[] ).
cnf(16,axiom,
subset(skf6(u),relation_field(u)),
file('SEU243+1.p',unknown),
[] ).
cnf(17,axiom,
subset(skf8(u,v),v),
file('SEU243+1.p',unknown),
[] ).
cnf(20,axiom,
( well_founded_relation(skc6)
| is_well_founded_in(skc6,relation_field(skc6)) ),
file('SEU243+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ well_founded_relation(skc6)
| ~ is_well_founded_in(skc6,relation_field(skc6)) ),
file('SEU243+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ relation(u)
| ~ equal(skf6(u),empty_set)
| well_founded_relation(u) ),
file('SEU243+1.p',unknown),
[] ).
cnf(37,axiom,
( ~ relation(u)
| ~ equal(skf8(u,v),empty_set)
| is_well_founded_in(u,v) ),
file('SEU243+1.p',unknown),
[] ).
cnf(40,axiom,
( ~ relation(u)
| ~ in(v,skf6(u))
| ~ disjoint(fiber(u,v),skf6(u))
| well_founded_relation(u) ),
file('SEU243+1.p',unknown),
[] ).
cnf(41,axiom,
( ~ relation(u)
| ~ well_founded_relation(u)
| ~ subset(v,relation_field(u))
| equal(v,empty_set)
| in(skf5(v,w),v) ),
file('SEU243+1.p',unknown),
[] ).
cnf(42,axiom,
( ~ relation(u)
| ~ is_well_founded_in(u,v)
| ~ subset(w,v)
| equal(w,empty_set)
| in(skf7(w,x),w) ),
file('SEU243+1.p',unknown),
[] ).
cnf(43,axiom,
( ~ relation(u)
| ~ in(v,skf8(u,w))
| ~ disjoint(fiber(u,v),skf8(u,w))
| is_well_founded_in(u,w) ),
file('SEU243+1.p',unknown),
[] ).
cnf(44,axiom,
( ~ relation(u)
| ~ is_well_founded_in(u,v)
| ~ subset(w,v)
| equal(w,empty_set)
| disjoint(fiber(u,skf7(w,u)),w) ),
file('SEU243+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ relation(u)
| ~ well_founded_relation(u)
| ~ subset(v,relation_field(u))
| equal(v,empty_set)
| disjoint(fiber(u,skf5(v,u)),v) ),
file('SEU243+1.p',unknown),
[] ).
cnf(47,plain,
( ~ well_founded_relation(skc6)
| ~ subset(u,relation_field(skc6))
| equal(u,empty_set)
| disjoint(fiber(skc6,skf5(u,skc6)),u) ),
inference(res,[status(thm),theory(equality)],[1,45]),
[iquote('0:Res:1.0,45.1')] ).
cnf(50,plain,
( ~ well_founded_relation(skc6)
| ~ subset(u,relation_field(skc6))
| equal(u,empty_set)
| in(skf5(u,v),u) ),
inference(res,[status(thm),theory(equality)],[1,41]),
[iquote('0:Res:1.0,41.1')] ).
cnf(52,plain,
( ~ in(u,skf6(skc6))
| ~ disjoint(fiber(skc6,u),skf6(skc6))
| well_founded_relation(skc6) ),
inference(res,[status(thm),theory(equality)],[1,40]),
[iquote('0:Res:1.0,40.0')] ).
cnf(53,plain,
( ~ equal(skf8(skc6,u),empty_set)
| is_well_founded_in(skc6,u) ),
inference(res,[status(thm),theory(equality)],[1,37]),
[iquote('0:Res:1.0,37.0')] ).
cnf(56,plain,
( ~ equal(skf6(skc6),empty_set)
| well_founded_relation(skc6) ),
inference(res,[status(thm),theory(equality)],[1,34]),
[iquote('0:Res:1.0,34.0')] ).
cnf(57,plain,
well_founded_relation(skc6),
inference(spt,[spt(split,[position(s1)])],[20]),
[iquote('1:Spt:20.0')] ).
cnf(58,plain,
~ is_well_founded_in(skc6,relation_field(skc6)),
inference(mrr,[status(thm)],[28,57]),
[iquote('1:MRR:28.0,57.0')] ).
cnf(59,plain,
( ~ subset(u,relation_field(skc6))
| equal(u,empty_set)
| in(skf5(u,v),u) ),
inference(mrr,[status(thm)],[50,57]),
[iquote('1:MRR:50.0,57.0')] ).
cnf(60,plain,
( ~ subset(u,relation_field(skc6))
| equal(u,empty_set)
| disjoint(fiber(skc6,skf5(u,skc6)),u) ),
inference(mrr,[status(thm)],[47,57]),
[iquote('1:MRR:47.0,57.0')] ).
cnf(315,plain,
( ~ relation(skc6)
| ~ subset(skf8(skc6,u),relation_field(skc6))
| ~ in(skf5(skf8(skc6,u),skc6),skf8(skc6,u))
| equal(skf8(skc6,u),empty_set)
| is_well_founded_in(skc6,u) ),
inference(res,[status(thm),theory(equality)],[60,43]),
[iquote('1:Res:60.2,43.2')] ).
cnf(316,plain,
( ~ subset(skf8(skc6,u),relation_field(skc6))
| ~ in(skf5(skf8(skc6,u),skc6),skf8(skc6,u))
| equal(skf8(skc6,u),empty_set)
| is_well_founded_in(skc6,u) ),
inference(ssi,[status(thm)],[315,57,1]),
[iquote('1:SSi:315.0,57.0,1.0')] ).
cnf(317,plain,
( ~ subset(skf8(skc6,u),relation_field(skc6))
| is_well_founded_in(skc6,u) ),
inference(mrr,[status(thm)],[316,59,53]),
[iquote('1:MRR:316.1,316.2,59.2,53.0')] ).
cnf(319,plain,
is_well_founded_in(skc6,relation_field(skc6)),
inference(res,[status(thm),theory(equality)],[17,317]),
[iquote('1:Res:17.0,317.0')] ).
cnf(320,plain,
$false,
inference(mrr,[status(thm)],[319,58]),
[iquote('1:MRR:319.0,58.0')] ).
cnf(321,plain,
~ well_founded_relation(skc6),
inference(spt,[spt(split,[position(sa)])],[320,57]),
[iquote('1:Spt:320.0,20.0,57.0')] ).
cnf(322,plain,
is_well_founded_in(skc6,relation_field(skc6)),
inference(spt,[spt(split,[position(s2)])],[20]),
[iquote('1:Spt:320.0,20.1')] ).
cnf(323,plain,
~ equal(skf6(skc6),empty_set),
inference(mrr,[status(thm)],[56,321]),
[iquote('1:MRR:56.1,321.0')] ).
cnf(325,plain,
( ~ in(u,skf6(skc6))
| ~ disjoint(fiber(skc6,u),skf6(skc6)) ),
inference(mrr,[status(thm)],[52,321]),
[iquote('1:MRR:52.2,321.0')] ).
cnf(328,plain,
( ~ relation(skc6)
| ~ subset(u,relation_field(skc6))
| equal(u,empty_set)
| disjoint(fiber(skc6,skf7(u,skc6)),u) ),
inference(res,[status(thm),theory(equality)],[322,44]),
[iquote('1:Res:322.0,44.1')] ).
cnf(329,plain,
( ~ relation(skc6)
| ~ subset(u,relation_field(skc6))
| equal(u,empty_set)
| in(skf7(u,v),u) ),
inference(res,[status(thm),theory(equality)],[322,42]),
[iquote('1:Res:322.0,42.1')] ).
cnf(330,plain,
( ~ subset(u,relation_field(skc6))
| equal(u,empty_set)
| in(skf7(u,v),u) ),
inference(ssi,[status(thm)],[329,1]),
[iquote('1:SSi:329.0,1.0')] ).
cnf(331,plain,
( ~ subset(u,relation_field(skc6))
| equal(u,empty_set)
| disjoint(fiber(skc6,skf7(u,skc6)),u) ),
inference(ssi,[status(thm)],[328,1]),
[iquote('1:SSi:328.0,1.0')] ).
cnf(411,plain,
( ~ subset(skf6(skc6),relation_field(skc6))
| ~ in(skf7(skf6(skc6),skc6),skf6(skc6))
| equal(skf6(skc6),empty_set) ),
inference(res,[status(thm),theory(equality)],[331,325]),
[iquote('1:Res:331.2,325.1')] ).
cnf(412,plain,
~ in(skf7(skf6(skc6),skc6),skf6(skc6)),
inference(mrr,[status(thm)],[411,16,323]),
[iquote('1:MRR:411.0,411.2,16.0,323.0')] ).
cnf(419,plain,
( ~ subset(skf6(skc6),relation_field(skc6))
| equal(skf6(skc6),empty_set) ),
inference(res,[status(thm),theory(equality)],[330,412]),
[iquote('1:Res:330.2,412.0')] ).
cnf(421,plain,
$false,
inference(mrr,[status(thm)],[419,16,323]),
[iquote('1:MRR:419.0,419.1,16.0,323.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU243+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n003.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 : Sun Jun 19 20:17:59 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.50
% 0.20/0.50 SPASS V 3.9
% 0.20/0.50 SPASS beiseite: Proof found.
% 0.20/0.50 % SZS status Theorem
% 0.20/0.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.50 SPASS derived 304 clauses, backtracked 18 clauses, performed 1 splits and kept 198 clauses.
% 0.20/0.50 SPASS allocated 97987 KBytes.
% 0.20/0.50 SPASS spent 0:00:00.14 on the problem.
% 0.20/0.50 0:00:00.04 for the input.
% 0.20/0.50 0:00:00.04 for the FLOTTER CNF translation.
% 0.20/0.50 0:00:00.01 for inferences.
% 0.20/0.50 0:00:00.00 for the backtracking.
% 0.20/0.50 0:00:00.03 for the reduction.
% 0.20/0.50
% 0.20/0.50
% 0.20/0.50 Here is a proof with depth 4, length 39 :
% 0.20/0.50 % SZS output start Refutation
% See solution above
% 0.20/0.50 Formulae used in the proof : t5_wellord1 d2_wellord1 reflexivity_r1_tarski t3_subset d3_wellord1
% 0.20/0.50
%------------------------------------------------------------------------------