TSTP Solution File: SEU281+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU281+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 14:35:48 EDT 2022
% Result : Theorem 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of clauses : 39 ( 14 unt; 7 nHn; 39 RR)
% Number of literals : 87 ( 0 equ; 49 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(19,axiom,
( in(skf8(u),u)
| in(skf9(v),skc7) ),
file('SEU281+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ equal(skf15(u),skf15(u))
| skP0(v) ),
file('SEU281+1.p',unknown),
[] ).
cnf(23,axiom,
( in(skf8(u),u)
| in(skf8(u),cartesian_product2(skc7,skc6)) ),
file('SEU281+1.p',unknown),
[] ).
cnf(26,axiom,
( in(skf8(u),u)
| equal(ordered_pair(skf9(u),singleton(skf9(u))),skf8(u)) ),
file('SEU281+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ skP0(u)
| ~ in(v,skf13(w,u))
| in(v,cartesian_product2(u,w)) ),
file('SEU281+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ skP0(u)
| ~ in(v,skf13(w,u))
| in(skf14(u,x),u) ),
file('SEU281+1.p',unknown),
[] ).
cnf(29,axiom,
( ~ skP0(u)
| ~ in(v,skf13(w,u))
| equal(ordered_pair(skf14(u,v),singleton(skf14(u,v))),v) ),
file('SEU281+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ in(u,v)
| ~ in(w,cartesian_product2(v,x))
| ~ equal(ordered_pair(u,singleton(u)),w)
| in(w,skf13(x,v)) ),
file('SEU281+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ in(u,skc7)
| ~ in(skf8(v),v)
| ~ in(skf8(v),cartesian_product2(skc7,skc6))
| ~ equal(ordered_pair(u,singleton(u)),skf8(v)) ),
file('SEU281+1.p',unknown),
[] ).
cnf(32,plain,
skP0(u),
inference(obv,[status(thm),theory(equality)],[22]),
[iquote('0:Obv:22.0')] ).
cnf(33,plain,
( ~ in(u,skf13(v,w))
| in(skf14(w,x),w) ),
inference(mrr,[status(thm)],[28,32]),
[iquote('0:MRR:28.0,32.0')] ).
cnf(34,plain,
( ~ in(u,skf13(v,w))
| in(u,cartesian_product2(w,v)) ),
inference(mrr,[status(thm)],[27,32]),
[iquote('0:MRR:27.0,32.0')] ).
cnf(35,plain,
( ~ in(u,skf13(v,w))
| equal(ordered_pair(skf14(w,u),singleton(skf14(w,u))),u) ),
inference(mrr,[status(thm)],[29,32]),
[iquote('0:MRR:29.0,32.0')] ).
cnf(36,plain,
in(skf8(u),u),
inference(spt,[spt(split,[position(s1)])],[19]),
[iquote('1:Spt:19.0')] ).
cnf(37,plain,
( ~ in(u,skc7)
| ~ in(skf8(v),cartesian_product2(skc7,skc6))
| ~ equal(ordered_pair(u,singleton(u)),skf8(v)) ),
inference(mrr,[status(thm)],[31,36]),
[iquote('1:MRR:31.1,36.0')] ).
cnf(39,plain,
in(skf8(skf13(u,v)),cartesian_product2(v,u)),
inference(res,[status(thm),theory(equality)],[36,34]),
[iquote('1:Res:36.0,34.0')] ).
cnf(41,plain,
in(skf14(u,v),u),
inference(res,[status(thm),theory(equality)],[36,33]),
[iquote('1:Res:36.0,33.0')] ).
cnf(42,plain,
equal(ordered_pair(skf14(u,skf8(skf13(v,u))),singleton(skf14(u,skf8(skf13(v,u))))),skf8(skf13(v,u))),
inference(res,[status(thm),theory(equality)],[36,35]),
[iquote('1:Res:36.0,35.0')] ).
cnf(49,plain,
( ~ in(skf14(u,skf8(skf13(v,u))),skc7)
| ~ in(skf8(w),cartesian_product2(skc7,skc6))
| ~ equal(skf8(skf13(v,u)),skf8(w)) ),
inference(spl,[status(thm),theory(equality)],[42,37]),
[iquote('1:SpL:42.0,37.2')] ).
cnf(67,plain,
( ~ in(skf8(u),cartesian_product2(skc7,skc6))
| ~ equal(skf8(skf13(v,skc7)),skf8(u)) ),
inference(res,[status(thm),theory(equality)],[41,49]),
[iquote('1:Res:41.0,49.0')] ).
cnf(68,plain,
~ in(skf8(skf13(u,skc7)),cartesian_product2(skc7,skc6)),
inference(eqr,[status(thm),theory(equality)],[67]),
[iquote('1:EqR:67.1')] ).
cnf(69,plain,
$false,
inference(unc,[status(thm)],[68,39]),
[iquote('1:UnC:68.0,39.0')] ).
cnf(70,plain,
in(skf9(u),skc7),
inference(spt,[spt(split,[position(s2)])],[19]),
[iquote('1:Spt:69.0,19.1')] ).
cnf(75,plain,
( in(skf8(skf13(u,v)),cartesian_product2(skc7,skc6))
| in(skf8(skf13(u,v)),cartesian_product2(v,u)) ),
inference(res,[status(thm),theory(equality)],[23,34]),
[iquote('0:Res:23.0,34.0')] ).
cnf(83,plain,
( ~ in(skf9(u),v)
| ~ in(w,cartesian_product2(v,x))
| ~ equal(skf8(u),w)
| in(skf8(u),u)
| in(w,skf13(x,v)) ),
inference(spl,[status(thm),theory(equality)],[26,30]),
[iquote('0:SpL:26.1,30.2')] ).
cnf(91,plain,
( ~ in(skf9(u),skc7)
| ~ in(skf8(v),v)
| ~ in(skf8(v),cartesian_product2(skc7,skc6))
| ~ equal(skf8(u),skf8(v))
| in(skf8(u),u) ),
inference(spl,[status(thm),theory(equality)],[26,31]),
[iquote('0:SpL:26.1,31.3')] ).
cnf(92,plain,
( ~ in(skf8(u),u)
| ~ in(skf8(u),cartesian_product2(skc7,skc6))
| ~ equal(skf8(v),skf8(u))
| in(skf8(v),v) ),
inference(mrr,[status(thm)],[91,70]),
[iquote('1:MRR:91.0,70.0')] ).
cnf(98,plain,
in(skf8(skf13(skc6,skc7)),cartesian_product2(skc7,skc6)),
inference(fac,[status(thm)],[75]),
[iquote('0:Fac:75.0,75.1')] ).
cnf(115,plain,
( ~ in(skf8(skf13(skc6,skc7)),skf13(skc6,skc7))
| ~ equal(skf8(u),skf8(skf13(skc6,skc7)))
| in(skf8(u),u) ),
inference(res,[status(thm),theory(equality)],[98,92]),
[iquote('1:Res:98.0,92.1')] ).
cnf(127,plain,
( ~ in(skf9(u),skc7)
| ~ equal(skf8(u),skf8(skf13(skc6,skc7)))
| in(skf8(u),u)
| in(skf8(skf13(skc6,skc7)),skf13(skc6,skc7)) ),
inference(res,[status(thm),theory(equality)],[98,83]),
[iquote('0:Res:98.0,83.1')] ).
cnf(130,plain,
( ~ equal(skf8(u),skf8(skf13(skc6,skc7)))
| in(skf8(u),u)
| in(skf8(skf13(skc6,skc7)),skf13(skc6,skc7)) ),
inference(mrr,[status(thm)],[127,70]),
[iquote('1:MRR:127.0,70.0')] ).
cnf(131,plain,
( ~ equal(skf8(u),skf8(skf13(skc6,skc7)))
| in(skf8(u),u) ),
inference(mrr,[status(thm)],[130,115]),
[iquote('1:MRR:130.2,115.0')] ).
cnf(136,plain,
in(skf8(skf13(skc6,skc7)),skf13(skc6,skc7)),
inference(eqr,[status(thm),theory(equality)],[131]),
[iquote('1:EqR:131.0')] ).
cnf(138,plain,
in(skf14(skc7,u),skc7),
inference(res,[status(thm),theory(equality)],[136,33]),
[iquote('1:Res:136.0,33.0')] ).
cnf(139,plain,
equal(ordered_pair(skf14(skc7,skf8(skf13(skc6,skc7))),singleton(skf14(skc7,skf8(skf13(skc6,skc7))))),skf8(skf13(skc6,skc7))),
inference(res,[status(thm),theory(equality)],[136,35]),
[iquote('1:Res:136.0,35.0')] ).
cnf(176,plain,
( ~ in(skf14(skc7,skf8(skf13(skc6,skc7))),skc7)
| ~ in(skf8(u),u)
| ~ in(skf8(u),cartesian_product2(skc7,skc6))
| ~ equal(skf8(skf13(skc6,skc7)),skf8(u)) ),
inference(spl,[status(thm),theory(equality)],[139,31]),
[iquote('1:SpL:139.0,31.3')] ).
cnf(177,plain,
( ~ in(skf8(u),cartesian_product2(skc7,skc6))
| ~ equal(skf8(skf13(skc6,skc7)),skf8(u)) ),
inference(mrr,[status(thm)],[176,138,131]),
[iquote('1:MRR:176.0,176.1,138.0,131.1')] ).
cnf(190,plain,
~ equal(skf8(skf13(skc6,skc7)),skf8(skf13(skc6,skc7))),
inference(res,[status(thm),theory(equality)],[98,177]),
[iquote('1:Res:98.0,177.0')] ).
cnf(191,plain,
$false,
inference(obv,[status(thm),theory(equality)],[190]),
[iquote('1:Obv:190.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU281+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n004.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 : Sun Jun 19 02:43:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.48
% 0.18/0.48 SPASS V 3.9
% 0.18/0.48 SPASS beiseite: Proof found.
% 0.18/0.48 % SZS status Theorem
% 0.18/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.48 SPASS derived 132 clauses, backtracked 5 clauses, performed 1 splits and kept 141 clauses.
% 0.18/0.48 SPASS allocated 97973 KBytes.
% 0.18/0.48 SPASS spent 0:00:00.13 on the problem.
% 0.18/0.48 0:00:00.03 for the input.
% 0.18/0.48 0:00:00.05 for the FLOTTER CNF translation.
% 0.18/0.48 0:00:00.01 for inferences.
% 0.18/0.48 0:00:00.00 for the backtracking.
% 0.18/0.48 0:00:00.02 for the reduction.
% 0.18/0.48
% 0.18/0.48
% 0.18/0.48 Here is a proof with depth 7, length 39 :
% 0.18/0.48 % SZS output start Refutation
% See solution above
% 0.18/0.48 Formulae used in the proof : s1_xboole_0__e16_22__wellord2__1 antisymmetry_r2_hidden s1_tarski__e16_22__wellord2__2
% 0.18/0.48
%------------------------------------------------------------------------------