TSTP Solution File: SEU353+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU353+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 14:36:32 EDT 2022
% Result : Theorem 0.18s 0.47s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 23
% Syntax : Number of clauses : 52 ( 30 unt; 3 nHn; 52 RR)
% Number of literals : 98 ( 0 equ; 51 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 17 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
one_sorted_str(skc7),
file('SEU353+1.p',unknown),
[] ).
cnf(10,axiom,
~ empty_carrier(skc7),
file('SEU353+1.p',unknown),
[] ).
cnf(12,axiom,
relation(identity_relation(u)),
file('SEU353+1.p',unknown),
[] ).
cnf(14,axiom,
reflexive(identity_relation(u)),
file('SEU353+1.p',unknown),
[] ).
cnf(15,axiom,
symmetric(identity_relation(u)),
file('SEU353+1.p',unknown),
[] ).
cnf(16,axiom,
antisymmetric(identity_relation(u)),
file('SEU353+1.p',unknown),
[] ).
cnf(17,axiom,
transitive(identity_relation(u)),
file('SEU353+1.p',unknown),
[] ).
cnf(30,axiom,
element(skc8,the_carrier(skc7)),
file('SEU353+1.p',unknown),
[] ).
cnf(37,axiom,
v1_partfun1(identity_as_relation_of(u),u,u),
file('SEU353+1.p',unknown),
[] ).
cnf(47,axiom,
equal(identity_as_relation_of(u),identity_relation(u)),
file('SEU353+1.p',unknown),
[] ).
cnf(48,axiom,
( ~ one_sorted_str(u)
| function(identity_on_carrier(u)) ),
file('SEU353+1.p',unknown),
[] ).
cnf(58,axiom,
( ~ empty(u)
| ~ in(v,u) ),
file('SEU353+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ one_sorted_str(u)
| equal(identity_as_relation_of(the_carrier(u)),identity_on_carrier(u)) ),
file('SEU353+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ one_sorted_str(u)
| ~ empty(the_carrier(u))
| empty_carrier(u) ),
file('SEU353+1.p',unknown),
[] ).
cnf(67,axiom,
( ~ relation_of2_as_subset(u,v,w)
| relation_of2(u,v,w) ),
file('SEU353+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ element(u,v)
| empty(v)
| in(u,v) ),
file('SEU353+1.p',unknown),
[] ).
cnf(71,axiom,
( ~ one_sorted_str(u)
| quasi_total(identity_on_carrier(u),the_carrier(u),the_carrier(u)) ),
file('SEU353+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ one_sorted_str(u)
| relation_of2_as_subset(identity_on_carrier(u),the_carrier(u),the_carrier(u)) ),
file('SEU353+1.p',unknown),
[] ).
cnf(73,axiom,
( ~ in(u,v)
| equal(apply(identity_relation(v),u),u) ),
file('SEU353+1.p',unknown),
[] ).
cnf(74,axiom,
~ equal(apply_as_element(the_carrier(skc7),the_carrier(skc7),identity_on_carrier(skc7),skc8),skc8),
file('SEU353+1.p',unknown),
[] ).
cnf(79,axiom,
( ~ function(u)
| ~ relation_of2(u,v,w)
| ~ v1_partfun1(u,v,w)
| quasi_total(u,v,w) ),
file('SEU353+1.p',unknown),
[] ).
cnf(85,axiom,
( ~ reflexive(u)
| ~ function(u)
| ~ quasi_total(u,v,v)
| ~ relation_of2(u,v,v)
| ~ v1_partfun1(u,v,v)
| one_to_one(u) ),
file('SEU353+1.p',unknown),
[] ).
cnf(90,axiom,
( ~ function(u)
| ~ element(v,w)
| ~ quasi_total(u,w,x)
| ~ relation_of2(u,w,x)
| empty(w)
| equal(apply_as_element(w,x,u,v),apply(u,v)) ),
file('SEU353+1.p',unknown),
[] ).
cnf(92,plain,
v1_partfun1(identity_relation(u),u,u),
inference(rew,[status(thm),theory(equality)],[47,37]),
[iquote('0:Rew:47.0,37.0')] ).
cnf(93,plain,
( ~ one_sorted_str(u)
| equal(identity_relation(the_carrier(u)),identity_on_carrier(u)) ),
inference(rew,[status(thm),theory(equality)],[47,63]),
[iquote('0:Rew:47.0,63.1')] ).
cnf(94,plain,
( ~ function(u)
| ~ reflexive(u)
| ~ v1_partfun1(u,v,v)
| ~ relation_of2(u,v,v)
| one_to_one(u) ),
inference(mrr,[status(thm)],[85,79]),
[iquote('0:MRR:85.2,79.3')] ).
cnf(98,plain,
quasi_total(identity_on_carrier(skc7),the_carrier(skc7),the_carrier(skc7)),
inference(res,[status(thm),theory(equality)],[1,71]),
[iquote('0:Res:1.0,71.0')] ).
cnf(99,plain,
relation_of2_as_subset(identity_on_carrier(skc7),the_carrier(skc7),the_carrier(skc7)),
inference(res,[status(thm),theory(equality)],[1,72]),
[iquote('0:Res:1.0,72.0')] ).
cnf(100,plain,
equal(identity_relation(the_carrier(skc7)),identity_on_carrier(skc7)),
inference(res,[status(thm),theory(equality)],[1,93]),
[iquote('0:Res:1.0,93.0')] ).
cnf(101,plain,
( ~ empty(the_carrier(skc7))
| empty_carrier(skc7) ),
inference(res,[status(thm),theory(equality)],[1,64]),
[iquote('0:Res:1.0,64.0')] ).
cnf(103,plain,
function(identity_on_carrier(skc7)),
inference(res,[status(thm),theory(equality)],[1,48]),
[iquote('0:Res:1.0,48.0')] ).
cnf(106,plain,
( in(skc8,the_carrier(skc7))
| empty(the_carrier(skc7)) ),
inference(res,[status(thm),theory(equality)],[30,69]),
[iquote('0:Res:30.0,69.0')] ).
cnf(111,plain,
~ empty(the_carrier(skc7)),
inference(mrr,[status(thm)],[101,10]),
[iquote('0:MRR:101.1,10.0')] ).
cnf(113,plain,
in(skc8,the_carrier(skc7)),
inference(mrr,[status(thm)],[106,111]),
[iquote('0:MRR:106.1,111.0')] ).
cnf(116,plain,
antisymmetric(identity_on_carrier(skc7)),
inference(spr,[status(thm),theory(equality)],[100,16]),
[iquote('0:SpR:100.0,16.0')] ).
cnf(117,plain,
transitive(identity_on_carrier(skc7)),
inference(spr,[status(thm),theory(equality)],[100,17]),
[iquote('0:SpR:100.0,17.0')] ).
cnf(118,plain,
symmetric(identity_on_carrier(skc7)),
inference(spr,[status(thm),theory(equality)],[100,15]),
[iquote('0:SpR:100.0,15.0')] ).
cnf(119,plain,
reflexive(identity_on_carrier(skc7)),
inference(spr,[status(thm),theory(equality)],[100,14]),
[iquote('0:SpR:100.0,14.0')] ).
cnf(120,plain,
relation(identity_on_carrier(skc7)),
inference(spr,[status(thm),theory(equality)],[100,12]),
[iquote('0:SpR:100.0,12.0')] ).
cnf(123,plain,
v1_partfun1(identity_on_carrier(skc7),the_carrier(skc7),the_carrier(skc7)),
inference(spr,[status(thm),theory(equality)],[100,92]),
[iquote('0:SpR:100.0,92.0')] ).
cnf(139,plain,
~ empty(the_carrier(skc7)),
inference(res,[status(thm),theory(equality)],[113,58]),
[iquote('0:Res:113.0,58.1')] ).
cnf(188,plain,
relation_of2(identity_on_carrier(skc7),the_carrier(skc7),the_carrier(skc7)),
inference(res,[status(thm),theory(equality)],[99,67]),
[iquote('0:Res:99.0,67.0')] ).
cnf(206,plain,
( ~ in(u,the_carrier(skc7))
| equal(apply(identity_on_carrier(skc7),u),u) ),
inference(spr,[status(thm),theory(equality)],[100,73]),
[iquote('0:SpR:100.0,73.1')] ).
cnf(287,plain,
( ~ function(identity_on_carrier(skc7))
| ~ reflexive(identity_on_carrier(skc7))
| ~ relation_of2(identity_on_carrier(skc7),the_carrier(skc7),the_carrier(skc7))
| one_to_one(identity_on_carrier(skc7)) ),
inference(res,[status(thm),theory(equality)],[123,94]),
[iquote('0:Res:123.0,94.2')] ).
cnf(293,plain,
( ~ relation_of2(identity_on_carrier(skc7),the_carrier(skc7),the_carrier(skc7))
| one_to_one(identity_on_carrier(skc7)) ),
inference(ssi,[status(thm)],[287,103,116,117,118,119,120]),
[iquote('0:SSi:287.1,287.0,103.0,116.0,117.0,118.0,119.0,120.0,103.0,116.0,117.0,118.0,119.0,120.0')] ).
cnf(294,plain,
one_to_one(identity_on_carrier(skc7)),
inference(mrr,[status(thm)],[293,188]),
[iquote('0:MRR:293.0,188.0')] ).
cnf(445,plain,
( ~ function(identity_on_carrier(skc7))
| ~ element(skc8,the_carrier(skc7))
| ~ quasi_total(identity_on_carrier(skc7),the_carrier(skc7),the_carrier(skc7))
| ~ relation_of2(identity_on_carrier(skc7),the_carrier(skc7),the_carrier(skc7))
| ~ equal(apply(identity_on_carrier(skc7),skc8),skc8)
| empty(the_carrier(skc7)) ),
inference(spl,[status(thm),theory(equality)],[90,74]),
[iquote('0:SpL:90.5,74.0')] ).
cnf(446,plain,
( ~ element(skc8,the_carrier(skc7))
| ~ quasi_total(identity_on_carrier(skc7),the_carrier(skc7),the_carrier(skc7))
| ~ relation_of2(identity_on_carrier(skc7),the_carrier(skc7),the_carrier(skc7))
| ~ equal(apply(identity_on_carrier(skc7),skc8),skc8)
| empty(the_carrier(skc7)) ),
inference(ssi,[status(thm)],[445,103,116,117,118,119,120,294]),
[iquote('0:SSi:445.0,103.0,116.0,117.0,118.0,119.0,120.0,294.0')] ).
cnf(447,plain,
~ equal(apply(identity_on_carrier(skc7),skc8),skc8),
inference(mrr,[status(thm)],[446,30,98,188,139]),
[iquote('0:MRR:446.0,446.1,446.2,446.4,30.0,98.0,188.0,139.0')] ).
cnf(448,plain,
( ~ in(skc8,the_carrier(skc7))
| ~ equal(skc8,skc8) ),
inference(spl,[status(thm),theory(equality)],[206,447]),
[iquote('0:SpL:206.1,447.0')] ).
cnf(449,plain,
~ in(skc8,the_carrier(skc7)),
inference(obv,[status(thm),theory(equality)],[448]),
[iquote('0:Obv:448.1')] ).
cnf(450,plain,
$false,
inference(mrr,[status(thm)],[449,113]),
[iquote('0:MRR:449.0,113.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU353+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n025.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 : Mon Jun 20 11:56:29 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.47
% 0.18/0.47 SPASS V 3.9
% 0.18/0.47 SPASS beiseite: Proof found.
% 0.18/0.47 % SZS status Theorem
% 0.18/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.47 SPASS derived 281 clauses, backtracked 0 clauses, performed 0 splits and kept 247 clauses.
% 0.18/0.47 SPASS allocated 98010 KBytes.
% 0.18/0.47 SPASS spent 0:00:00.13 on the problem.
% 0.18/0.47 0:00:00.04 for the input.
% 0.18/0.47 0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.47 0:00:00.01 for inferences.
% 0.18/0.47 0:00:00.00 for the backtracking.
% 0.18/0.47 0:00:00.02 for the reduction.
% 0.18/0.47
% 0.18/0.47
% 0.18/0.47 Here is a proof with depth 3, length 52 :
% 0.18/0.47 % SZS output start Refutation
% See solution above
% 0.18/0.48 Formulae used in the proof : t91_tmap_1 fc2_partfun1 dt_k6_partfun1 redefinition_k6_partfun1 dt_k7_grcat_1 t7_boole d11_grcat_1 fc1_struct_0 redefinition_m2_relset_1 t2_subset t35_funct_1 cc1_funct_2 cc4_funct_2 redefinition_k8_funct_2
% 0.18/0.48
%------------------------------------------------------------------------------