TSTP Solution File: SET957+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET957+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 05:30:03 EDT 2022
% Result : Theorem 0.18s 0.45s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 29 ( 12 unt; 3 nHn; 29 RR)
% Number of literals : 52 ( 0 equ; 24 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 12 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
~ equal(skc11,skc8),
file('SET957+1.p',unknown),
[] ).
cnf(5,axiom,
subset(skc11,cartesian_product2(skc13,skc12)),
file('SET957+1.p',unknown),
[] ).
cnf(6,axiom,
subset(skc8,cartesian_product2(skc9,skc10)),
file('SET957+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ in(ordered_pair(u,v),skc11)
| in(ordered_pair(u,v),skc8) ),
file('SET957+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ in(ordered_pair(u,v),skc8)
| in(ordered_pair(u,v),skc11) ),
file('SET957+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ in(skf5(u,v),u)
| ~ in(skf5(u,v),v) ),
file('SET957+1.p',unknown),
[] ).
cnf(14,axiom,
( equal(u,v)
| in(skf5(v,u),v)
| in(skf5(v,u),u) ),
file('SET957+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ in(u,v)
| ~ subset(v,cartesian_product2(w,x))
| in(skf3(x,y,z),x) ),
file('SET957+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ in(u,v)
| ~ subset(v,cartesian_product2(w,x))
| equal(ordered_pair(skf4(w,x,u),skf3(x,u,w)),u) ),
file('SET957+1.p',unknown),
[] ).
cnf(19,plain,
( in(skf5(skc8,skc11),skc8)
| in(skf5(skc8,skc11),skc11) ),
inference(res,[status(thm),theory(equality)],[14,4]),
[iquote('0:Res:14.2,4.0')] ).
cnf(21,plain,
( ~ in(u,skc8)
| equal(ordered_pair(skf4(skc9,skc10,u),skf3(skc10,u,skc9)),u) ),
inference(res,[status(thm),theory(equality)],[6,17]),
[iquote('0:Res:6.0,17.0')] ).
cnf(24,plain,
( ~ in(u,skc11)
| equal(ordered_pair(skf4(skc13,skc12,u),skf3(skc12,u,skc13)),u) ),
inference(res,[status(thm),theory(equality)],[5,17]),
[iquote('0:Res:5.0,17.0')] ).
cnf(26,plain,
( ~ in(u,skc11)
| in(skf3(skc12,v,w),skc12) ),
inference(res,[status(thm),theory(equality)],[5,16]),
[iquote('0:Res:5.0,16.0')] ).
cnf(38,plain,
( in(skf5(skc8,skc11),skc8)
| in(skf3(skc12,u,v),skc12) ),
inference(res,[status(thm),theory(equality)],[19,26]),
[iquote('0:Res:19.1,26.0')] ).
cnf(68,plain,
in(skf5(skc8,skc11),skc8),
inference(spt,[spt(split,[position(s1)])],[38]),
[iquote('1:Spt:38.0')] ).
cnf(70,plain,
~ in(skf5(skc8,skc11),skc11),
inference(res,[status(thm),theory(equality)],[68,13]),
[iquote('1:Res:68.0,13.0')] ).
cnf(130,plain,
( ~ in(u,skc11)
| ~ in(u,skc11)
| in(ordered_pair(skf4(skc13,skc12,u),skf3(skc12,u,skc13)),skc8) ),
inference(spl,[status(thm),theory(equality)],[24,11]),
[iquote('0:SpL:24.1,11.0')] ).
cnf(131,plain,
( ~ in(u,skc11)
| in(ordered_pair(skf4(skc13,skc12,u),skf3(skc12,u,skc13)),skc8) ),
inference(obv,[status(thm),theory(equality)],[130]),
[iquote('0:Obv:130.0')] ).
cnf(132,plain,
( ~ in(u,skc11)
| in(u,skc8) ),
inference(rew,[status(thm),theory(equality)],[24,131]),
[iquote('0:Rew:24.1,131.1')] ).
cnf(135,plain,
( ~ in(u,skc8)
| ~ in(ordered_pair(skf4(skc9,skc10,u),skf3(skc10,u,skc9)),skc8)
| in(u,skc11) ),
inference(spr,[status(thm),theory(equality)],[21,12]),
[iquote('0:SpR:21.1,12.1')] ).
cnf(140,plain,
( ~ in(u,skc8)
| ~ in(u,skc8)
| in(u,skc11) ),
inference(rew,[status(thm),theory(equality)],[21,135]),
[iquote('0:Rew:21.1,135.1')] ).
cnf(141,plain,
( ~ in(u,skc8)
| in(u,skc11) ),
inference(obv,[status(thm),theory(equality)],[140]),
[iquote('0:Obv:140.0')] ).
cnf(163,plain,
~ in(skf5(skc8,skc11),skc8),
inference(res,[status(thm),theory(equality)],[141,70]),
[iquote('1:Res:141.1,70.0')] ).
cnf(164,plain,
$false,
inference(mrr,[status(thm)],[163,68]),
[iquote('1:MRR:163.0,68.0')] ).
cnf(165,plain,
~ in(skf5(skc8,skc11),skc8),
inference(spt,[spt(split,[position(sa)])],[164,68]),
[iquote('1:Spt:164.0,38.0,68.0')] ).
cnf(166,plain,
in(skf3(skc12,u,v),skc12),
inference(spt,[spt(split,[position(s2)])],[38]),
[iquote('1:Spt:164.0,38.1')] ).
cnf(167,plain,
in(skf5(skc8,skc11),skc11),
inference(mrr,[status(thm)],[19,141]),
[iquote('0:MRR:19.0,141.0')] ).
cnf(172,plain,
in(skf5(skc8,skc11),skc8),
inference(res,[status(thm),theory(equality)],[167,132]),
[iquote('0:Res:167.0,132.0')] ).
cnf(174,plain,
$false,
inference(mrr,[status(thm)],[172,165]),
[iquote('1:MRR:172.0,165.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET957+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n003.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 07:47:44 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.45
% 0.18/0.45 SPASS V 3.9
% 0.18/0.45 SPASS beiseite: Proof found.
% 0.18/0.45 % SZS status Theorem
% 0.18/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 SPASS derived 133 clauses, backtracked 15 clauses, performed 4 splits and kept 106 clauses.
% 0.18/0.45 SPASS allocated 85264 KBytes.
% 0.18/0.45 SPASS spent 0:00:00.10 on the problem.
% 0.18/0.45 0:00:00.03 for the input.
% 0.18/0.45 0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.45 0:00:00.00 for inferences.
% 0.18/0.45 0:00:00.00 for the backtracking.
% 0.18/0.45 0:00:00.01 for the reduction.
% 0.18/0.45
% 0.18/0.45
% 0.18/0.45 Here is a proof with depth 5, length 29 :
% 0.18/0.45 % SZS output start Refutation
% See solution above
% 0.18/0.45 Formulae used in the proof : t110_zfmisc_1 t2_tarski antisymmetry_r2_hidden t103_zfmisc_1
% 0.18/0.45
%------------------------------------------------------------------------------