TSTP Solution File: SEU277+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU277+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 14:35:46 EDT 2022
% Result : Theorem 0.13s 0.48s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of clauses : 54 ( 17 unt; 11 nHn; 54 RR)
% Number of literals : 132 ( 0 equ; 75 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 9 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc12),
file('SEU277+1.p',unknown),
[] ).
cnf(2,axiom,
relation(skc11),
file('SEU277+1.p',unknown),
[] ).
cnf(3,axiom,
function(skc11),
file('SEU277+1.p',unknown),
[] ).
cnf(37,axiom,
( in(skf13(u),u)
| in(skf13(u),cartesian_product2(skc13,skc13)) ),
file('SEU277+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ equal(skf23(u,v),skf23(u,v))
| skP0(w,x) ),
file('SEU277+1.p',unknown),
[] ).
cnf(40,axiom,
( in(skf13(u),u)
| equal(ordered_pair(skf15(u),skf14(u)),skf13(u)) ),
file('SEU277+1.p',unknown),
[] ).
cnf(43,axiom,
( in(skf13(u),u)
| in(ordered_pair(apply(skc11,skf15(v)),apply(skc11,skf14(v))),skc12) ),
file('SEU277+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ relation(u)
| ~ relation(v)
| ~ function(v)
| ~ skP0(u,v)
| ~ in(w,skf20(u,v,x))
| in(w,cartesian_product2(x,x)) ),
file('SEU277+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ equal(u,ordered_pair(v,w))
| ~ in(u,cartesian_product2(x,x))
| ~ in(ordered_pair(apply(y,v),apply(y,w)),z)
| in(u,skf20(z,y,x)) ),
file('SEU277+1.p',unknown),
[] ).
cnf(48,axiom,
( ~ in(skf13(u),u)
| ~ equal(skf13(u),ordered_pair(v,w))
| ~ in(skf13(u),cartesian_product2(skc13,skc13))
| ~ in(ordered_pair(apply(skc11,v),apply(skc11,w)),skc12) ),
file('SEU277+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ relation(u)
| ~ relation(v)
| ~ function(v)
| ~ skP0(u,v)
| ~ in(w,skf20(u,v,x))
| equal(ordered_pair(skf22(w,y,z),skf21(w,y,z)),w) ),
file('SEU277+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ relation(u)
| ~ relation(v)
| ~ function(v)
| ~ skP0(u,v)
| ~ in(w,skf20(u,v,x))
| in(ordered_pair(apply(v,skf22(w,u,v)),apply(v,skf21(w,u,v))),u) ),
file('SEU277+1.p',unknown),
[] ).
cnf(51,plain,
skP0(u,v),
inference(obv,[status(thm),theory(equality)],[39]),
[iquote('0:Obv:39.0')] ).
cnf(53,plain,
( ~ function(u)
| ~ relation(u)
| ~ relation(v)
| ~ in(w,skf20(v,u,x))
| in(w,cartesian_product2(x,x)) ),
inference(mrr,[status(thm)],[46,51]),
[iquote('0:MRR:46.3,51.0')] ).
cnf(54,plain,
( ~ function(u)
| ~ relation(u)
| ~ relation(v)
| ~ in(w,skf20(v,u,x))
| equal(ordered_pair(skf22(w,y,z),skf21(w,y,z)),w) ),
inference(mrr,[status(thm)],[49,51]),
[iquote('0:MRR:49.3,51.0')] ).
cnf(55,plain,
( ~ function(u)
| ~ relation(u)
| ~ relation(v)
| ~ in(w,skf20(v,u,x))
| in(ordered_pair(apply(u,skf22(w,v,u)),apply(u,skf21(w,v,u))),v) ),
inference(mrr,[status(thm)],[50,51]),
[iquote('0:MRR:50.3,51.0')] ).
cnf(58,plain,
( ~ relation(u)
| ~ relation(skc11)
| ~ in(v,skf20(u,skc11,w))
| in(v,cartesian_product2(w,w)) ),
inference(res,[status(thm),theory(equality)],[3,53]),
[iquote('0:Res:3.0,53.2')] ).
cnf(63,plain,
( ~ relation(u)
| ~ function(skc11)
| ~ in(v,skf20(u,skc11,w))
| in(ordered_pair(apply(skc11,skf22(v,u,skc11)),apply(skc11,skf21(v,u,skc11))),u) ),
inference(res,[status(thm),theory(equality)],[2,55]),
[iquote('0:Res:2.0,55.1')] ).
cnf(64,plain,
( ~ relation(u)
| ~ function(skc11)
| ~ in(v,skf20(u,skc11,w))
| equal(ordered_pair(skf22(v,x,y),skf21(v,x,y)),v) ),
inference(res,[status(thm),theory(equality)],[2,54]),
[iquote('0:Res:2.0,54.1')] ).
cnf(73,plain,
( ~ relation(u)
| ~ in(v,skf20(u,skc11,w))
| in(v,cartesian_product2(w,w)) ),
inference(mrr,[status(thm)],[58,2]),
[iquote('0:MRR:58.1,2.0')] ).
cnf(74,plain,
( ~ relation(u)
| ~ in(v,skf20(u,skc11,w))
| equal(ordered_pair(skf22(v,x,y),skf21(v,x,y)),v) ),
inference(mrr,[status(thm)],[64,3]),
[iquote('0:MRR:64.1,3.0')] ).
cnf(75,plain,
( ~ relation(u)
| ~ in(v,skf20(u,skc11,w))
| in(ordered_pair(apply(skc11,skf22(v,u,skc11)),apply(skc11,skf21(v,u,skc11))),u) ),
inference(mrr,[status(thm)],[63,3]),
[iquote('0:MRR:63.1,3.0')] ).
cnf(77,plain,
( ~ in(u,skf20(skc12,skc11,v))
| in(ordered_pair(apply(skc11,skf22(u,skc12,skc11)),apply(skc11,skf21(u,skc12,skc11))),skc12) ),
inference(res,[status(thm),theory(equality)],[1,75]),
[iquote('0:Res:1.0,75.0')] ).
cnf(81,plain,
( ~ in(u,skf20(skc12,skc11,v))
| equal(ordered_pair(skf22(u,w,x),skf21(u,w,x)),u) ),
inference(res,[status(thm),theory(equality)],[1,74]),
[iquote('0:Res:1.0,74.0')] ).
cnf(87,plain,
( ~ in(u,skf20(skc12,skc11,v))
| in(u,cartesian_product2(v,v)) ),
inference(res,[status(thm),theory(equality)],[1,73]),
[iquote('0:Res:1.0,73.0')] ).
cnf(106,plain,
in(skf13(u),u),
inference(spt,[spt(split,[position(s1)])],[43]),
[iquote('1:Spt:43.0')] ).
cnf(107,plain,
( ~ equal(skf13(u),ordered_pair(v,w))
| ~ in(skf13(u),cartesian_product2(skc13,skc13))
| ~ in(ordered_pair(apply(skc11,v),apply(skc11,w)),skc12) ),
inference(mrr,[status(thm)],[48,106]),
[iquote('1:MRR:48.0,106.0')] ).
cnf(109,plain,
in(skf13(skf20(skc12,skc11,u)),cartesian_product2(u,u)),
inference(res,[status(thm),theory(equality)],[106,87]),
[iquote('1:Res:106.0,87.0')] ).
cnf(126,plain,
equal(ordered_pair(skf22(skf13(skf20(skc12,skc11,u)),v,w),skf21(skf13(skf20(skc12,skc11,u)),v,w)),skf13(skf20(skc12,skc11,u))),
inference(res,[status(thm),theory(equality)],[106,81]),
[iquote('1:Res:106.0,81.0')] ).
cnf(132,plain,
in(ordered_pair(apply(skc11,skf22(skf13(skf20(skc12,skc11,u)),skc12,skc11)),apply(skc11,skf21(skf13(skf20(skc12,skc11,u)),skc12,skc11))),skc12),
inference(res,[status(thm),theory(equality)],[106,77]),
[iquote('1:Res:106.0,77.0')] ).
cnf(136,plain,
( ~ equal(skf13(u),ordered_pair(skf22(skf13(skf20(skc12,skc11,v)),skc12,skc11),skf21(skf13(skf20(skc12,skc11,v)),skc12,skc11)))
| ~ in(skf13(u),cartesian_product2(skc13,skc13)) ),
inference(res,[status(thm),theory(equality)],[132,107]),
[iquote('1:Res:132.0,107.2')] ).
cnf(138,plain,
( ~ equal(skf13(u),skf13(skf20(skc12,skc11,v)))
| ~ in(skf13(u),cartesian_product2(skc13,skc13)) ),
inference(rew,[status(thm),theory(equality)],[126,136]),
[iquote('1:Rew:126.0,136.0')] ).
cnf(140,plain,
~ in(skf13(skf20(skc12,skc11,u)),cartesian_product2(skc13,skc13)),
inference(eqr,[status(thm),theory(equality)],[138]),
[iquote('1:EqR:138.0')] ).
cnf(141,plain,
$false,
inference(unc,[status(thm)],[140,109]),
[iquote('1:UnC:140.0,109.0')] ).
cnf(142,plain,
in(ordered_pair(apply(skc11,skf15(u)),apply(skc11,skf14(u))),skc12),
inference(spt,[spt(split,[position(s2)])],[43]),
[iquote('1:Spt:141.0,43.1')] ).
cnf(144,plain,
( ~ equal(u,ordered_pair(skf15(v),skf14(v)))
| ~ in(u,cartesian_product2(w,w))
| in(u,skf20(skc12,skc11,w)) ),
inference(res,[status(thm),theory(equality)],[142,47]),
[iquote('1:Res:142.0,47.2')] ).
cnf(149,plain,
( in(skf13(skf20(skc12,skc11,u)),cartesian_product2(skc13,skc13))
| in(skf13(skf20(skc12,skc11,u)),cartesian_product2(u,u)) ),
inference(res,[status(thm),theory(equality)],[37,87]),
[iquote('0:Res:37.0,87.0')] ).
cnf(185,plain,
in(skf13(skf20(skc12,skc11,skc13)),cartesian_product2(skc13,skc13)),
inference(fac,[status(thm)],[149]),
[iquote('0:Fac:149.0,149.1')] ).
cnf(205,plain,
( ~ in(ordered_pair(skf15(u),skf14(u)),cartesian_product2(v,v))
| in(ordered_pair(skf15(u),skf14(u)),skf20(skc12,skc11,v)) ),
inference(eqr,[status(thm),theory(equality)],[144]),
[iquote('1:EqR:144.0')] ).
cnf(207,plain,
( ~ in(skf13(u),cartesian_product2(v,v))
| in(skf13(u),u)
| in(ordered_pair(skf15(u),skf14(u)),skf20(skc12,skc11,v)) ),
inference(spl,[status(thm),theory(equality)],[40,205]),
[iquote('1:SpL:40.1,205.0')] ).
cnf(208,plain,
( ~ in(skf13(u),cartesian_product2(v,v))
| in(skf13(u),u)
| in(skf13(u),skf20(skc12,skc11,v)) ),
inference(rew,[status(thm),theory(equality)],[40,207]),
[iquote('1:Rew:40.1,207.2')] ).
cnf(213,plain,
( in(skf13(u),u)
| in(skf13(u),u)
| in(skf13(u),skf20(skc12,skc11,skc13)) ),
inference(res,[status(thm),theory(equality)],[37,208]),
[iquote('1:Res:37.1,208.0')] ).
cnf(216,plain,
( in(skf13(skf20(skc12,skc11,skc13)),skf20(skc12,skc11,skc13))
| in(skf13(skf20(skc12,skc11,skc13)),skf20(skc12,skc11,skc13)) ),
inference(res,[status(thm),theory(equality)],[185,208]),
[iquote('1:Res:185.0,208.0')] ).
cnf(229,plain,
( in(skf13(u),u)
| in(skf13(u),skf20(skc12,skc11,skc13)) ),
inference(obv,[status(thm),theory(equality)],[213]),
[iquote('1:Obv:213.0')] ).
cnf(230,plain,
in(skf13(skf20(skc12,skc11,skc13)),skf20(skc12,skc11,skc13)),
inference(obv,[status(thm),theory(equality)],[216]),
[iquote('1:Obv:216.0')] ).
cnf(249,plain,
( in(skf13(skf20(skc12,skc11,u)),skf20(skc12,skc11,skc13))
| in(ordered_pair(apply(skc11,skf22(skf13(skf20(skc12,skc11,u)),skc12,skc11)),apply(skc11,skf21(skf13(skf20(skc12,skc11,u)),skc12,skc11))),skc12) ),
inference(res,[status(thm),theory(equality)],[229,77]),
[iquote('1:Res:229.0,77.0')] ).
cnf(250,plain,
( in(skf13(skf20(skc12,skc11,u)),skf20(skc12,skc11,skc13))
| equal(ordered_pair(skf22(skf13(skf20(skc12,skc11,u)),v,w),skf21(skf13(skf20(skc12,skc11,u)),v,w)),skf13(skf20(skc12,skc11,u))) ),
inference(res,[status(thm),theory(equality)],[229,81]),
[iquote('1:Res:229.0,81.0')] ).
cnf(282,plain,
equal(ordered_pair(skf22(skf13(skf20(skc12,skc11,u)),v,w),skf21(skf13(skf20(skc12,skc11,u)),v,w)),skf13(skf20(skc12,skc11,u))),
inference(mrr,[status(thm)],[250,81]),
[iquote('1:MRR:250.0,81.0')] ).
cnf(283,plain,
in(ordered_pair(apply(skc11,skf22(skf13(skf20(skc12,skc11,u)),skc12,skc11)),apply(skc11,skf21(skf13(skf20(skc12,skc11,u)),skc12,skc11))),skc12),
inference(mrr,[status(thm)],[249,77]),
[iquote('1:MRR:249.0,77.0')] ).
cnf(447,plain,
( ~ in(skf13(u),u)
| ~ equal(skf13(u),ordered_pair(skf22(skf13(skf20(skc12,skc11,v)),skc12,skc11),skf21(skf13(skf20(skc12,skc11,v)),skc12,skc11)))
| ~ in(skf13(u),cartesian_product2(skc13,skc13)) ),
inference(res,[status(thm),theory(equality)],[283,48]),
[iquote('1:Res:283.0,48.3')] ).
cnf(449,plain,
( ~ in(skf13(u),u)
| ~ equal(skf13(u),skf13(skf20(skc12,skc11,v)))
| ~ in(skf13(u),cartesian_product2(skc13,skc13)) ),
inference(rew,[status(thm),theory(equality)],[282,447]),
[iquote('1:Rew:282.0,447.1')] ).
cnf(482,plain,
( ~ in(skf13(skf20(skc12,skc11,u)),skf20(skc12,skc11,u))
| ~ in(skf13(skf20(skc12,skc11,u)),cartesian_product2(skc13,skc13)) ),
inference(eqr,[status(thm),theory(equality)],[449]),
[iquote('1:EqR:449.1')] ).
cnf(486,plain,
~ in(skf13(skf20(skc12,skc11,skc13)),cartesian_product2(skc13,skc13)),
inference(res,[status(thm),theory(equality)],[230,482]),
[iquote('1:Res:230.0,482.0')] ).
cnf(489,plain,
$false,
inference(mrr,[status(thm)],[486,185]),
[iquote('1:MRR:486.0,185.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU277+1 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.10 % Command : run_spass %d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 600
% 0.10/0.29 % DateTime : Sun Jun 19 21:16:33 EDT 2022
% 0.13/0.29 % CPUTime :
% 0.13/0.48
% 0.13/0.48 SPASS V 3.9
% 0.13/0.48 SPASS beiseite: Proof found.
% 0.13/0.48 % SZS status Theorem
% 0.13/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.48 SPASS derived 402 clauses, backtracked 4 clauses, performed 2 splits and kept 287 clauses.
% 0.13/0.48 SPASS allocated 98620 KBytes.
% 0.13/0.48 SPASS spent 0:00:00.18 on the problem.
% 0.13/0.48 0:00:00.02 for the input.
% 0.13/0.48 0:00:00.07 for the FLOTTER CNF translation.
% 0.13/0.48 0:00:00.01 for inferences.
% 0.13/0.48 0:00:00.00 for the backtracking.
% 0.13/0.48 0:00:00.05 for the reduction.
% 0.13/0.48
% 0.13/0.48
% 0.13/0.48 Here is a proof with depth 9, length 54 :
% 0.13/0.48 % SZS output start Refutation
% See solution above
% 0.13/0.48 Formulae used in the proof : s1_xboole_0__e6_21__wellord2__1 antisymmetry_r2_hidden s1_tarski__e6_21__wellord2__1
% 0.13/0.48
%------------------------------------------------------------------------------