TSTP Solution File: SET955+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET955+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 05:30:02 EDT 2022
% Result : Theorem 3.20s 3.38s
% Output : Refutation 3.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of clauses : 23 ( 6 unt; 6 nHn; 23 RR)
% Number of literals : 53 ( 0 equ; 21 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
~ equal(cartesian_product2(skc8,skc9),cartesian_product2(skc6,skc7)),
file('SET955+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ in(skf7(u,v),u)
| ~ in(skf7(u,v),v) ),
file('SET955+1.p',unknown),
[] ).
cnf(11,axiom,
( equal(u,v)
| in(skf7(v,u),v)
| in(skf7(v,u),u) ),
file('SET955+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ in(u,v)
| ~ equal(v,cartesian_product2(w,x))
| skP0(u,x,w) ),
file('SET955+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ in(ordered_pair(u,v),cartesian_product2(skc6,skc7))
| in(ordered_pair(u,v),cartesian_product2(skc8,skc9)) ),
file('SET955+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ in(ordered_pair(u,v),cartesian_product2(skc8,skc9))
| in(ordered_pair(u,v),cartesian_product2(skc6,skc7)) ),
file('SET955+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ skP0(u,v,w)
| equal(ordered_pair(skf6(w,v,u),skf5(v,u,w)),u) ),
file('SET955+1.p',unknown),
[] ).
cnf(65,plain,
( ~ in(u,cartesian_product2(v,w))
| skP0(u,w,v) ),
inference(eqr,[status(thm),theory(equality)],[12]),
[iquote('0:EqR:12.1')] ).
cnf(67,plain,
( equal(cartesian_product2(u,v),w)
| in(skf7(w,cartesian_product2(u,v)),w)
| skP0(skf7(w,cartesian_product2(u,v)),v,u) ),
inference(res,[status(thm),theory(equality)],[11,65]),
[iquote('0:Res:11.2,65.0')] ).
cnf(144,plain,
( ~ skP0(u,v,w)
| ~ in(ordered_pair(skf6(w,v,u),skf5(v,u,w)),cartesian_product2(skc6,skc7))
| in(u,cartesian_product2(skc8,skc9)) ),
inference(spr,[status(thm),theory(equality)],[17,14]),
[iquote('0:SpR:17.1,14.1')] ).
cnf(151,plain,
( ~ skP0(u,v,w)
| ~ in(u,cartesian_product2(skc8,skc9))
| in(ordered_pair(skf6(w,v,u),skf5(v,u,w)),cartesian_product2(skc6,skc7)) ),
inference(spl,[status(thm),theory(equality)],[17,15]),
[iquote('0:SpL:17.1,15.0')] ).
cnf(168,plain,
( ~ skP0(u,v,w)
| ~ in(u,cartesian_product2(skc8,skc9))
| in(u,cartesian_product2(skc6,skc7)) ),
inference(rew,[status(thm),theory(equality)],[17,151]),
[iquote('0:Rew:17.1,151.2')] ).
cnf(169,plain,
( ~ skP0(u,v,w)
| ~ in(u,cartesian_product2(skc6,skc7))
| in(u,cartesian_product2(skc8,skc9)) ),
inference(rew,[status(thm),theory(equality)],[17,144]),
[iquote('0:Rew:17.1,144.1')] ).
cnf(241,plain,
( ~ skP0(skf7(u,cartesian_product2(skc8,skc9)),v,w)
| equal(cartesian_product2(skc8,skc9),u)
| in(skf7(u,cartesian_product2(skc8,skc9)),u)
| in(skf7(u,cartesian_product2(skc8,skc9)),cartesian_product2(skc6,skc7)) ),
inference(res,[status(thm),theory(equality)],[11,168]),
[iquote('0:Res:11.2,168.1')] ).
cnf(3241,plain,
( equal(cartesian_product2(skc8,skc9),u)
| in(skf7(u,cartesian_product2(skc8,skc9)),u)
| equal(cartesian_product2(skc8,skc9),u)
| in(skf7(u,cartesian_product2(skc8,skc9)),u)
| in(skf7(u,cartesian_product2(skc8,skc9)),cartesian_product2(skc6,skc7)) ),
inference(res,[status(thm),theory(equality)],[67,241]),
[iquote('0:Res:67.2,241.0')] ).
cnf(3242,plain,
( equal(cartesian_product2(skc8,skc9),u)
| in(skf7(u,cartesian_product2(skc8,skc9)),u)
| in(skf7(u,cartesian_product2(skc8,skc9)),cartesian_product2(skc6,skc7)) ),
inference(obv,[status(thm),theory(equality)],[3241]),
[iquote('0:Obv:3241.1')] ).
cnf(8326,plain,
( equal(cartesian_product2(skc8,skc9),cartesian_product2(skc6,skc7))
| in(skf7(cartesian_product2(skc6,skc7),cartesian_product2(skc8,skc9)),cartesian_product2(skc6,skc7)) ),
inference(fac,[status(thm)],[3242]),
[iquote('0:Fac:3242.1,3242.2')] ).
cnf(8356,plain,
in(skf7(cartesian_product2(skc6,skc7),cartesian_product2(skc8,skc9)),cartesian_product2(skc6,skc7)),
inference(mrr,[status(thm)],[8326,5]),
[iquote('0:MRR:8326.0,5.0')] ).
cnf(8368,plain,
~ in(skf7(cartesian_product2(skc6,skc7),cartesian_product2(skc8,skc9)),cartesian_product2(skc8,skc9)),
inference(res,[status(thm),theory(equality)],[8356,10]),
[iquote('0:Res:8356.0,10.0')] ).
cnf(8369,plain,
skP0(skf7(cartesian_product2(skc6,skc7),cartesian_product2(skc8,skc9)),skc7,skc6),
inference(res,[status(thm),theory(equality)],[8356,65]),
[iquote('0:Res:8356.0,65.0')] ).
cnf(8372,plain,
( ~ skP0(skf7(cartesian_product2(skc6,skc7),cartesian_product2(skc8,skc9)),u,v)
| in(skf7(cartesian_product2(skc6,skc7),cartesian_product2(skc8,skc9)),cartesian_product2(skc8,skc9)) ),
inference(res,[status(thm),theory(equality)],[8356,169]),
[iquote('0:Res:8356.0,169.1')] ).
cnf(8373,plain,
~ skP0(skf7(cartesian_product2(skc6,skc7),cartesian_product2(skc8,skc9)),u,v),
inference(mrr,[status(thm)],[8372,8368]),
[iquote('0:MRR:8372.1,8368.0')] ).
cnf(8374,plain,
$false,
inference(unc,[status(thm)],[8373,8369]),
[iquote('0:UnC:8373.0,8369.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET955+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n019.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 Jul 10 21:43:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 3.20/3.38
% 3.20/3.38 SPASS V 3.9
% 3.20/3.38 SPASS beiseite: Proof found.
% 3.20/3.38 % SZS status Theorem
% 3.20/3.38 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.20/3.38 SPASS derived 7209 clauses, backtracked 0 clauses, performed 7 splits and kept 2769 clauses.
% 3.20/3.38 SPASS allocated 92014 KBytes.
% 3.20/3.38 SPASS spent 0:00:03.00 on the problem.
% 3.20/3.38 0:00:00.03 for the input.
% 3.20/3.38 0:00:00.04 for the FLOTTER CNF translation.
% 3.20/3.38 0:00:00.15 for inferences.
% 3.20/3.38 0:00:00.05 for the backtracking.
% 3.20/3.38 0:00:02.69 for the reduction.
% 3.20/3.38
% 3.20/3.38
% 3.20/3.38 Here is a proof with depth 5, length 23 :
% 3.20/3.38 % SZS output start Refutation
% See solution above
% 3.20/3.38 Formulae used in the proof : t108_zfmisc_1 t2_tarski antisymmetry_r2_hidden d2_zfmisc_1
% 3.20/3.38
%------------------------------------------------------------------------------