TSTP Solution File: SEU210+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU210+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 14:35:01 EDT 2022
% Result : Theorem 1.30s 1.51s
% Output : Refutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of clauses : 34 ( 13 unt; 4 nHn; 34 RR)
% Number of literals : 79 ( 0 equ; 47 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc6),
file('SEU210+1.p',unknown),
[] ).
cnf(3,axiom,
empty(empty_set),
file('SEU210+1.p',unknown),
[] ).
cnf(10,axiom,
empty(skf15(u)),
file('SEU210+1.p',unknown),
[] ).
cnf(13,axiom,
~ equal(skc7,empty_set),
file('SEU210+1.p',unknown),
[] ).
cnf(14,axiom,
subset(skc7,relation_rng(skc6)),
file('SEU210+1.p',unknown),
[] ).
cnf(18,axiom,
equal(relation_inverse_image(skc6,skc7),empty_set),
file('SEU210+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ empty(u)
| relation(u) ),
file('SEU210+1.p',unknown),
[] ).
cnf(23,axiom,
element(skf15(u),powerset(u)),
file('SEU210+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ empty(u)
| empty(relation_rng(u)) ),
file('SEU210+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ empty(u)
| equal(u,empty_set) ),
file('SEU210+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ empty(u)
| ~ in(v,u) ),
file('SEU210+1.p',unknown),
[] ).
cnf(40,axiom,
( ~ in(u,v)
| ~ subset(v,w)
| in(u,w) ),
file('SEU210+1.p',unknown),
[] ).
cnf(42,axiom,
( ~ empty(u)
| ~ in(v,w)
| ~ element(w,powerset(u)) ),
file('SEU210+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ relation(u)
| ~ in(v,w)
| ~ equal(w,relation_rng(u))
| in(ordered_pair(skf9(u,v),v),u) ),
file('SEU210+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ relation(u)
| equal(v,relation_rng(u))
| in(skf11(u,v),v)
| in(ordered_pair(skf12(v,u),skf11(u,v)),u) ),
file('SEU210+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ relation(u)
| ~ in(v,w)
| ~ in(v,relation_rng(u))
| ~ in(ordered_pair(x,v),u)
| in(x,relation_inverse_image(u,w)) ),
file('SEU210+1.p',unknown),
[] ).
cnf(61,plain,
( ~ in(u,skc7)
| in(u,relation_rng(skc6)) ),
inference(res,[status(thm),theory(equality)],[14,40]),
[iquote('0:Res:14.0,40.0')] ).
cnf(67,plain,
equal(skf15(u),empty_set),
inference(ems,[status(thm)],[27,10]),
[iquote('0:EmS:27.0,10.0')] ).
cnf(75,plain,
element(empty_set,powerset(u)),
inference(rew,[status(thm),theory(equality)],[67,23]),
[iquote('0:Rew:67.0,23.0')] ).
cnf(79,plain,
( ~ empty(u)
| equal(relation_rng(u),empty_set) ),
inference(ems,[status(thm)],[27,24]),
[iquote('0:EmS:27.0,24.1')] ).
cnf(153,plain,
( ~ empty(u)
| ~ in(v,empty_set) ),
inference(res,[status(thm),theory(equality)],[75,42]),
[iquote('0:Res:75.0,42.2')] ).
cnf(157,plain,
~ in(u,empty_set),
inference(ems,[status(thm)],[153,3]),
[iquote('0:EmS:153.0,3.0')] ).
cnf(298,plain,
( ~ relation(u)
| ~ in(v,relation_rng(u))
| in(ordered_pair(skf9(u,v),v),u) ),
inference(eqr,[status(thm),theory(equality)],[47]),
[iquote('0:EqR:47.2')] ).
cnf(352,plain,
( ~ relation(u)
| ~ empty(u)
| equal(v,relation_rng(u))
| in(skf11(u,v),v) ),
inference(res,[status(thm),theory(equality)],[49,30]),
[iquote('0:Res:49.3,30.1')] ).
cnf(364,plain,
( ~ relation(u)
| ~ empty(u)
| equal(v,empty_set)
| in(skf11(u,v),v) ),
inference(rew,[status(thm),theory(equality)],[79,352]),
[iquote('0:Rew:79.1,352.2')] ).
cnf(365,plain,
( ~ empty(u)
| equal(v,empty_set)
| in(skf11(u,v),v) ),
inference(ssi,[status(thm)],[364,19]),
[iquote('0:SSi:364.0,19.1')] ).
cnf(906,plain,
( ~ relation(u)
| ~ relation(u)
| ~ in(v,relation_rng(u))
| ~ in(v,w)
| ~ in(v,relation_rng(u))
| in(skf9(u,v),relation_inverse_image(u,w)) ),
inference(res,[status(thm),theory(equality)],[298,50]),
[iquote('0:Res:298.2,50.3')] ).
cnf(923,plain,
( ~ relation(u)
| ~ in(v,w)
| ~ in(v,relation_rng(u))
| in(skf9(u,v),relation_inverse_image(u,w)) ),
inference(obv,[status(thm),theory(equality)],[906]),
[iquote('0:Obv:906.2')] ).
cnf(5486,plain,
( ~ relation(skc6)
| ~ in(u,skc7)
| ~ in(u,relation_rng(skc6))
| in(skf9(skc6,u),empty_set) ),
inference(spr,[status(thm),theory(equality)],[18,923]),
[iquote('0:SpR:18.0,923.3')] ).
cnf(5497,plain,
( ~ in(u,skc7)
| ~ in(u,relation_rng(skc6))
| in(skf9(skc6,u),empty_set) ),
inference(ssi,[status(thm)],[5486,1]),
[iquote('0:SSi:5486.0,1.0')] ).
cnf(5498,plain,
~ in(u,skc7),
inference(mrr,[status(thm)],[5497,61,157]),
[iquote('0:MRR:5497.1,5497.2,61.1,157.0')] ).
cnf(5519,plain,
( ~ empty(u)
| equal(skc7,empty_set) ),
inference(res,[status(thm),theory(equality)],[365,5498]),
[iquote('0:Res:365.2,5498.0')] ).
cnf(5544,plain,
~ empty(u),
inference(mrr,[status(thm)],[5519,13]),
[iquote('0:MRR:5519.1,13.0')] ).
cnf(5545,plain,
$false,
inference(unc,[status(thm)],[5544,3]),
[iquote('0:UnC:5544.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : SEU210+1 : TPTP v8.1.0. Released v3.3.0.
% 0.05/0.09 % Command : run_spass %d %s
% 0.08/0.29 % Computer : n015.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 600
% 0.08/0.29 % DateTime : Sun Jun 19 07:56:44 EDT 2022
% 0.08/0.29 % CPUTime :
% 1.30/1.51
% 1.30/1.51 SPASS V 3.9
% 1.30/1.51 SPASS beiseite: Proof found.
% 1.30/1.51 % SZS status Theorem
% 1.30/1.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.30/1.51 SPASS derived 4468 clauses, backtracked 152 clauses, performed 2 splits and kept 1826 clauses.
% 1.30/1.51 SPASS allocated 101862 KBytes.
% 1.30/1.51 SPASS spent 0:00:01.17 on the problem.
% 1.30/1.51 0:00:00.03 for the input.
% 1.30/1.51 0:00:00.04 for the FLOTTER CNF translation.
% 1.30/1.51 0:00:00.08 for inferences.
% 1.30/1.51 0:00:00.01 for the backtracking.
% 1.30/1.51 0:00:00.98 for the reduction.
% 1.30/1.51
% 1.30/1.51
% 1.30/1.51 Here is a proof with depth 4, length 34 :
% 1.30/1.51 % SZS output start Refutation
% See solution above
% 1.30/1.51 Formulae used in the proof : t174_relat_1 fc4_relat_1 rc2_subset_1 cc1_relat_1 fc8_relat_1 t6_boole t7_boole d3_tarski t5_subset d5_relat_1 t166_relat_1
% 1.30/1.51
%------------------------------------------------------------------------------