TSTP Solution File: SYN084-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SYN084-2 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 : Thu Jul 21 12:18:30 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of clauses : 27 ( 15 unt; 4 nHn; 27 RR)
% Number of literals : 46 ( 0 equ; 22 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
big_p(a),
file('SYN084-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ big_p(a)
| big_p(f(f(u)))
| big_p(u) ),
file('SYN084-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ big_p(f(u))
| ~ big_p(a)
| big_p(f(f(u))) ),
file('SYN084-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ big_p(f(f(sk2)))
| ~ big_p(f(f(sk1))) ),
file('SYN084-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ big_p(sk2)
| ~ big_p(sk1)
| big_p(f(sk2))
| big_p(f(sk1)) ),
file('SYN084-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ big_p(sk1)
| ~ big_p(f(f(sk2)))
| big_p(f(sk1)) ),
file('SYN084-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ big_p(sk2)
| ~ big_p(f(f(sk1)))
| big_p(f(sk2)) ),
file('SYN084-2.p',unknown),
[] ).
cnf(8,plain,
( big_p(u)
| big_p(f(f(u))) ),
inference(mrr,[status(thm)],[2,1]),
[iquote('0:MRR:2.0,1.0')] ).
cnf(9,plain,
( ~ big_p(f(u))
| big_p(f(f(u))) ),
inference(mrr,[status(thm)],[3,1]),
[iquote('0:MRR:3.1,1.0')] ).
cnf(10,plain,
~ big_p(f(f(sk2))),
inference(spt,[spt(split,[position(s1)])],[4]),
[iquote('1:Spt:4.0')] ).
cnf(11,plain,
~ big_p(f(sk2)),
inference(res,[status(thm),theory(equality)],[9,10]),
[iquote('1:Res:9.1,10.0')] ).
cnf(12,plain,
big_p(sk2),
inference(res,[status(thm),theory(equality)],[8,10]),
[iquote('1:Res:8.1,10.0')] ).
cnf(13,plain,
( ~ big_p(f(f(sk1)))
| big_p(f(sk2)) ),
inference(mrr,[status(thm)],[7,12]),
[iquote('1:MRR:7.0,12.0')] ).
cnf(14,plain,
( ~ big_p(sk1)
| big_p(f(sk2))
| big_p(f(sk1)) ),
inference(mrr,[status(thm)],[5,12]),
[iquote('1:MRR:5.0,12.0')] ).
cnf(15,plain,
~ big_p(f(f(sk1))),
inference(mrr,[status(thm)],[13,11]),
[iquote('1:MRR:13.1,11.0')] ).
cnf(16,plain,
( ~ big_p(sk1)
| big_p(f(sk1)) ),
inference(mrr,[status(thm)],[14,11]),
[iquote('1:MRR:14.1,11.0')] ).
cnf(17,plain,
~ big_p(f(sk1)),
inference(res,[status(thm),theory(equality)],[9,15]),
[iquote('1:Res:9.1,15.0')] ).
cnf(18,plain,
big_p(sk1),
inference(res,[status(thm),theory(equality)],[8,15]),
[iquote('1:Res:8.1,15.0')] ).
cnf(19,plain,
big_p(f(sk1)),
inference(mrr,[status(thm)],[16,18]),
[iquote('1:MRR:16.0,18.0')] ).
cnf(20,plain,
$false,
inference(mrr,[status(thm)],[17,19]),
[iquote('1:MRR:17.0,19.0')] ).
cnf(21,plain,
big_p(f(f(sk2))),
inference(spt,[spt(split,[position(sa)])],[20,10]),
[iquote('1:Spt:20.0,4.0,10.0')] ).
cnf(22,plain,
~ big_p(f(f(sk1))),
inference(spt,[spt(split,[position(s2)])],[4]),
[iquote('1:Spt:20.0,4.1')] ).
cnf(23,plain,
( ~ big_p(sk1)
| big_p(f(sk1)) ),
inference(mrr,[status(thm)],[6,21]),
[iquote('1:MRR:6.1,21.0')] ).
cnf(24,plain,
~ big_p(f(sk1)),
inference(res,[status(thm),theory(equality)],[9,22]),
[iquote('1:Res:9.1,22.0')] ).
cnf(25,plain,
big_p(sk1),
inference(res,[status(thm),theory(equality)],[8,22]),
[iquote('1:Res:8.1,22.0')] ).
cnf(26,plain,
big_p(f(sk1)),
inference(mrr,[status(thm)],[23,25]),
[iquote('1:MRR:23.0,25.0')] ).
cnf(27,plain,
$false,
inference(mrr,[status(thm)],[24,26]),
[iquote('1:MRR:24.0,26.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN084-2 : TPTP v8.1.0. Released v1.2.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jul 12 01:16:57 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.42
% 0.19/0.42 SPASS V 3.9
% 0.19/0.42 SPASS beiseite: Proof found.
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.42 SPASS derived 11 clauses, backtracked 5 clauses, performed 1 splits and kept 21 clauses.
% 0.19/0.42 SPASS allocated 63091 KBytes.
% 0.19/0.42 SPASS spent 0:00:00.06 on the problem.
% 0.19/0.42 0:00:00.04 for the input.
% 0.19/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42 0:00:00.00 for inferences.
% 0.19/0.42 0:00:00.00 for the backtracking.
% 0.19/0.42 0:00:00.00 for the reduction.
% 0.19/0.42
% 0.19/0.42
% 0.19/0.42 Here is a proof with depth 2, length 27 :
% 0.19/0.42 % SZS output start Refutation
% See solution above
% 0.19/0.42 Formulae used in the proof : pel62_1 pel62_2 pel62_3 pel62_4 pel62_5 pel62_6 pel62_7
% 0.19/0.42
%------------------------------------------------------------------------------