TSTP Solution File: SEU245+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU245+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 14:35:29 EDT 2022
% Result : Theorem 0.48s 0.70s
% Output : Refutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 26 ( 12 unt; 2 nHn; 26 RR)
% Number of literals : 46 ( 0 equ; 23 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc8),
file('SEU245+1.p',unknown),
[] ).
cnf(18,axiom,
equal(set_intersection2(u,v),set_intersection2(v,u)),
file('SEU245+1.p',unknown),
[] ).
cnf(22,axiom,
( in(skc10,skc8)
| in(skc10,relation_restriction(skc8,skc9)) ),
file('SEU245+1.p',unknown),
[] ).
cnf(26,axiom,
( in(skc10,cartesian_product2(skc9,skc9))
| in(skc10,relation_restriction(skc8,skc9)) ),
file('SEU245+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ relation(u)
| equal(set_intersection2(u,cartesian_product2(v,v)),relation_restriction(u,v)) ),
file('SEU245+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ in(u,v)
| ~ equal(v,set_intersection2(w,x))
| in(u,x) ),
file('SEU245+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ in(skc10,skc8)
| ~ in(skc10,cartesian_product2(skc9,skc9))
| ~ in(skc10,relation_restriction(skc8,skc9)) ),
file('SEU245+1.p',unknown),
[] ).
cnf(32,axiom,
( ~ in(u,v)
| ~ in(u,w)
| ~ equal(x,set_intersection2(w,v))
| in(u,x) ),
file('SEU245+1.p',unknown),
[] ).
cnf(37,plain,
equal(set_intersection2(skc8,cartesian_product2(u,u)),relation_restriction(skc8,u)),
inference(res,[status(thm),theory(equality)],[1,28]),
[iquote('0:Res:1.0,28.0')] ).
cnf(40,plain,
in(skc10,relation_restriction(skc8,skc9)),
inference(spt,[spt(split,[position(s1)])],[22]),
[iquote('1:Spt:22.1')] ).
cnf(41,plain,
( ~ in(skc10,skc8)
| ~ in(skc10,cartesian_product2(skc9,skc9)) ),
inference(mrr,[status(thm)],[31,40]),
[iquote('1:MRR:31.2,40.0')] ).
cnf(96,plain,
( ~ in(u,set_intersection2(v,w))
| in(u,w) ),
inference(eqr,[status(thm),theory(equality)],[30]),
[iquote('0:EqR:30.1')] ).
cnf(107,plain,
( ~ in(u,set_intersection2(v,w))
| in(u,v) ),
inference(spl,[status(thm),theory(equality)],[18,96]),
[iquote('0:SpL:18.0,96.0')] ).
cnf(112,plain,
( ~ in(u,relation_restriction(skc8,v))
| in(u,cartesian_product2(v,v)) ),
inference(spl,[status(thm),theory(equality)],[37,96]),
[iquote('0:SpL:37.0,96.0')] ).
cnf(122,plain,
( ~ in(u,relation_restriction(skc8,v))
| in(u,skc8) ),
inference(spl,[status(thm),theory(equality)],[37,107]),
[iquote('0:SpL:37.0,107.0')] ).
cnf(124,plain,
in(skc10,skc8),
inference(res,[status(thm),theory(equality)],[40,122]),
[iquote('1:Res:40.0,122.0')] ).
cnf(126,plain,
~ in(skc10,cartesian_product2(skc9,skc9)),
inference(mrr,[status(thm)],[41,124]),
[iquote('1:MRR:41.0,124.0')] ).
cnf(158,plain,
( ~ in(u,v)
| ~ in(u,w)
| in(u,set_intersection2(w,v)) ),
inference(eqr,[status(thm),theory(equality)],[32]),
[iquote('0:EqR:32.2')] ).
cnf(170,plain,
~ in(skc10,relation_restriction(skc8,skc9)),
inference(res,[status(thm),theory(equality)],[112,126]),
[iquote('1:Res:112.1,126.0')] ).
cnf(176,plain,
$false,
inference(mrr,[status(thm)],[170,40]),
[iquote('1:MRR:170.0,40.0')] ).
cnf(177,plain,
~ in(skc10,relation_restriction(skc8,skc9)),
inference(spt,[spt(split,[position(sa)])],[176,40]),
[iquote('1:Spt:176.0,22.1,40.0')] ).
cnf(178,plain,
in(skc10,skc8),
inference(spt,[spt(split,[position(s2)])],[22]),
[iquote('1:Spt:176.0,22.0')] ).
cnf(179,plain,
in(skc10,cartesian_product2(skc9,skc9)),
inference(mrr,[status(thm)],[26,112]),
[iquote('0:MRR:26.1,112.0')] ).
cnf(474,plain,
( ~ in(u,cartesian_product2(v,v))
| ~ in(u,skc8)
| in(u,relation_restriction(skc8,v)) ),
inference(spr,[status(thm),theory(equality)],[37,158]),
[iquote('0:SpR:37.0,158.2')] ).
cnf(1789,plain,
( ~ in(skc10,skc8)
| in(skc10,relation_restriction(skc8,skc9)) ),
inference(res,[status(thm),theory(equality)],[179,474]),
[iquote('0:Res:179.0,474.0')] ).
cnf(1814,plain,
$false,
inference(mrr,[status(thm)],[1789,178,177]),
[iquote('1:MRR:1789.0,1789.1,178.0,177.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU245+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n006.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 : Mon Jun 20 11:36:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.48/0.70
% 0.48/0.70 SPASS V 3.9
% 0.48/0.70 SPASS beiseite: Proof found.
% 0.48/0.70 % SZS status Theorem
% 0.48/0.70 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.48/0.70 SPASS derived 1493 clauses, backtracked 5 clauses, performed 1 splits and kept 732 clauses.
% 0.48/0.70 SPASS allocated 99117 KBytes.
% 0.48/0.70 SPASS spent 0:00:00.35 on the problem.
% 0.48/0.70 0:00:00.03 for the input.
% 0.48/0.70 0:00:00.03 for the FLOTTER CNF translation.
% 0.48/0.70 0:00:00.02 for inferences.
% 0.48/0.70 0:00:00.00 for the backtracking.
% 0.48/0.70 0:00:00.24 for the reduction.
% 0.48/0.70
% 0.48/0.70
% 0.48/0.70 Here is a proof with depth 4, length 26 :
% 0.48/0.70 % SZS output start Refutation
% See solution above
% 0.48/0.70 Formulae used in the proof : t16_wellord1 commutativity_k3_xboole_0 d6_wellord1 d3_xboole_0
% 0.48/0.70
%------------------------------------------------------------------------------