TSTP Solution File: SEU003+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU003+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 14:33:30 EDT 2022
% Result : Theorem 12.26s 12.49s
% Output : Refutation 12.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of clauses : 33 ( 13 unt; 4 nHn; 33 RR)
% Number of literals : 86 ( 0 equ; 54 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc9),
file('SEU003+1.p',unknown),
[] ).
cnf(2,axiom,
relation(skc8),
file('SEU003+1.p',unknown),
[] ).
cnf(3,axiom,
function(skc8),
file('SEU003+1.p',unknown),
[] ).
cnf(4,axiom,
function(skc9),
file('SEU003+1.p',unknown),
[] ).
cnf(23,axiom,
element(skf12(u),u),
file('SEU003+1.p',unknown),
[] ).
cnf(29,axiom,
~ subset(relation_rng(skc9),relation_dom(skc8)),
file('SEU003+1.p',unknown),
[] ).
cnf(30,axiom,
~ in(skf7(u,v),u),
file('SEU003+1.p',unknown),
[] ).
cnf(37,axiom,
equal(relation_dom(relation_composition(skc9,skc8)),relation_dom(skc9)),
file('SEU003+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ empty(u)
| ~ in(v,u) ),
file('SEU003+1.p',unknown),
[] ).
cnf(41,axiom,
( subset(u,v)
| in(skf7(v,u),u) ),
file('SEU003+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ element(u,v)
| empty(v)
| in(u,v) ),
file('SEU003+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ function(u)
| ~ relation(u)
| ~ in(v,w)
| ~ equal(w,relation_rng(u))
| in(skf8(u,x),relation_dom(u)) ),
file('SEU003+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ function(u)
| ~ relation(u)
| ~ in(v,w)
| ~ equal(w,relation_rng(u))
| equal(apply(u,skf8(u,v)),v) ),
file('SEU003+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ relation(u)
| ~ function(u)
| ~ relation(v)
| ~ function(v)
| ~ in(w,relation_dom(relation_composition(v,u)))
| in(apply(v,w),relation_dom(u)) ),
file('SEU003+1.p',unknown),
[] ).
cnf(73,plain,
( ~ relation(skc9)
| ~ in(u,v)
| ~ equal(v,relation_rng(skc9))
| in(skf8(skc9,w),relation_dom(skc9)) ),
inference(res,[status(thm),theory(equality)],[4,60]),
[iquote('0:Res:4.0,60.1')] ).
cnf(106,plain,
( ~ function(u)
| ~ relation(u)
| ~ function(skc8)
| ~ in(v,relation_dom(relation_composition(u,skc8)))
| in(apply(u,v),relation_dom(skc8)) ),
inference(res,[status(thm),theory(equality)],[2,64]),
[iquote('0:Res:2.0,64.3')] ).
cnf(139,plain,
( ~ in(u,v)
| ~ equal(v,relation_rng(skc9))
| in(skf8(skc9,w),relation_dom(skc9)) ),
inference(mrr,[status(thm)],[73,1]),
[iquote('0:MRR:73.0,1.0')] ).
cnf(154,plain,
( ~ relation(u)
| ~ function(u)
| ~ in(v,relation_dom(relation_composition(u,skc8)))
| in(apply(u,v),relation_dom(skc8)) ),
inference(mrr,[status(thm)],[106,3]),
[iquote('0:MRR:106.2,3.0')] ).
cnf(395,plain,
( ~ empty(u)
| subset(u,v) ),
inference(res,[status(thm),theory(equality)],[41,39]),
[iquote('0:Res:41.1,39.1')] ).
cnf(440,plain,
~ empty(relation_rng(skc9)),
inference(res,[status(thm),theory(equality)],[395,29]),
[iquote('0:Res:395.1,29.0')] ).
cnf(507,plain,
( empty(u)
| in(skf12(u),u) ),
inference(res,[status(thm),theory(equality)],[23,46]),
[iquote('0:Res:23.0,46.0')] ).
cnf(711,plain,
( ~ function(u)
| ~ relation(u)
| ~ in(v,relation_rng(u))
| equal(apply(u,skf8(u,v)),v) ),
inference(eqr,[status(thm),theory(equality)],[61]),
[iquote('0:EqR:61.3')] ).
cnf(1268,plain,
( ~ in(u,relation_rng(skc9))
| in(skf8(skc9,v),relation_dom(skc9)) ),
inference(eqr,[status(thm),theory(equality)],[139]),
[iquote('0:EqR:139.1')] ).
cnf(2162,plain,
( ~ function(u)
| ~ relation(u)
| ~ relation(u)
| ~ function(u)
| ~ in(v,relation_rng(u))
| ~ in(skf8(u,v),relation_dom(relation_composition(u,skc8)))
| in(v,relation_dom(skc8)) ),
inference(spr,[status(thm),theory(equality)],[711,154]),
[iquote('0:SpR:711.3,154.3')] ).
cnf(2179,plain,
( ~ relation(u)
| ~ function(u)
| ~ in(v,relation_rng(u))
| ~ in(skf8(u,v),relation_dom(relation_composition(u,skc8)))
| in(v,relation_dom(skc8)) ),
inference(obv,[status(thm),theory(equality)],[2162]),
[iquote('0:Obv:2162.1')] ).
cnf(3766,plain,
( empty(relation_rng(skc9))
| in(skf8(skc9,u),relation_dom(skc9)) ),
inference(res,[status(thm),theory(equality)],[507,1268]),
[iquote('0:Res:507.1,1268.0')] ).
cnf(3788,plain,
in(skf8(skc9,u),relation_dom(skc9)),
inference(mrr,[status(thm)],[3766,440]),
[iquote('0:MRR:3766.0,440.0')] ).
cnf(18510,plain,
( ~ relation(skc9)
| ~ function(skc9)
| ~ in(u,relation_rng(skc9))
| ~ in(skf8(skc9,u),relation_dom(skc9))
| in(u,relation_dom(skc8)) ),
inference(spl,[status(thm),theory(equality)],[37,2179]),
[iquote('0:SpL:37.0,2179.3')] ).
cnf(18514,plain,
( ~ in(u,relation_rng(skc9))
| ~ in(skf8(skc9,u),relation_dom(skc9))
| in(u,relation_dom(skc8)) ),
inference(ssi,[status(thm)],[18510,4,1]),
[iquote('0:SSi:18510.1,18510.0,4.0,1.0,4.0,1.0')] ).
cnf(18515,plain,
( ~ in(u,relation_rng(skc9))
| in(u,relation_dom(skc8)) ),
inference(mrr,[status(thm)],[18514,3788]),
[iquote('0:MRR:18514.1,3788.0')] ).
cnf(18524,plain,
~ in(skf7(relation_dom(skc8),u),relation_rng(skc9)),
inference(res,[status(thm),theory(equality)],[18515,30]),
[iquote('0:Res:18515.1,30.0')] ).
cnf(18542,plain,
subset(relation_rng(skc9),relation_dom(skc8)),
inference(res,[status(thm),theory(equality)],[41,18524]),
[iquote('0:Res:41.1,18524.0')] ).
cnf(18544,plain,
$false,
inference(mrr,[status(thm)],[18542,29]),
[iquote('0:MRR:18542.0,29.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU003+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n022.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 : Sat Jun 18 21:24:17 EDT 2022
% 0.12/0.34 % CPUTime :
% 12.26/12.49
% 12.26/12.49 SPASS V 3.9
% 12.26/12.49 SPASS beiseite: Proof found.
% 12.26/12.49 % SZS status Theorem
% 12.26/12.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.26/12.49 SPASS derived 15249 clauses, backtracked 862 clauses, performed 9 splits and kept 7751 clauses.
% 12.26/12.49 SPASS allocated 115477 KBytes.
% 12.26/12.49 SPASS spent 0:0:11.73 on the problem.
% 12.26/12.49 0:00:00.04 for the input.
% 12.26/12.49 0:00:00.05 for the FLOTTER CNF translation.
% 12.26/12.49 0:00:00.19 for inferences.
% 12.26/12.49 0:00:00.48 for the backtracking.
% 12.26/12.49 0:0:10.86 for the reduction.
% 12.26/12.49
% 12.26/12.49
% 12.26/12.49 Here is a proof with depth 5, length 33 :
% 12.26/12.49 % SZS output start Refutation
% See solution above
% 12.26/12.49 Formulae used in the proof : t27_funct_1 existence_m1_subset_1 d3_tarski antisymmetry_r2_hidden t7_boole t2_subset d5_funct_1 t21_funct_1
% 12.26/12.49
%------------------------------------------------------------------------------