TSTP Solution File: SEU406+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU406+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 14:37:00 EDT 2022
% Result : Theorem 0.18s 0.66s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of clauses : 28 ( 12 unt; 3 nHn; 28 RR)
% Number of literals : 52 ( 0 equ; 30 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
r2_hidden(skc9,k2_xboole_0(skc7,skc8)),
file('SEU406+1.p',unknown),
[] ).
cnf(6,axiom,
r2_hidden(skc6,k2_xboole_0(skc7,skc8)),
file('SEU406+1.p',unknown),
[] ).
cnf(12,axiom,
equal(k2_xboole_0(u,v),k2_xboole_0(v,u)),
file('SEU406+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ r2_hidden(skc6,skc8)
| ~ r2_hidden(skc9,skc8) ),
file('SEU406+1.p',unknown),
[] ).
cnf(20,axiom,
equal(k2_xboole_0(u,k4_xboole_0(v,u)),k2_xboole_0(u,v)),
file('SEU406+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ r2_hidden(skc6,skc8)
| ~ r2_hidden(skc9,k4_xboole_0(skc7,skc8)) ),
file('SEU406+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ r2_hidden(skc9,skc8)
| ~ r2_hidden(skc6,k4_xboole_0(skc7,skc8)) ),
file('SEU406+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ r2_hidden(skc6,k4_xboole_0(skc7,skc8))
| ~ r2_hidden(skc9,k4_xboole_0(skc7,skc8)) ),
file('SEU406+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ r2_hidden(u,v)
| ~ equal(v,k2_xboole_0(w,x))
| r2_hidden(u,x)
| r2_hidden(u,w) ),
file('SEU406+1.p',unknown),
[] ).
cnf(80,plain,
~ r2_hidden(skc6,skc8),
inference(spt,[spt(split,[position(s1)])],[17]),
[iquote('1:Spt:17.0')] ).
cnf(189,plain,
( ~ r2_hidden(u,k2_xboole_0(v,w))
| r2_hidden(u,w)
| r2_hidden(u,v) ),
inference(eqr,[status(thm),theory(equality)],[27]),
[iquote('0:EqR:27.1')] ).
cnf(306,plain,
( ~ r2_hidden(u,k2_xboole_0(v,w))
| r2_hidden(u,k4_xboole_0(w,v))
| r2_hidden(u,v) ),
inference(spl,[status(thm),theory(equality)],[20,189]),
[iquote('0:SpL:20.0,189.0')] ).
cnf(1589,plain,
( ~ r2_hidden(skc6,k2_xboole_0(skc8,skc7))
| ~ r2_hidden(skc9,skc8)
| r2_hidden(skc6,skc8) ),
inference(res,[status(thm),theory(equality)],[306,23]),
[iquote('0:Res:306.1,23.1')] ).
cnf(1590,plain,
( ~ r2_hidden(skc9,k2_xboole_0(skc8,skc7))
| ~ r2_hidden(skc6,k4_xboole_0(skc7,skc8))
| r2_hidden(skc9,skc8) ),
inference(res,[status(thm),theory(equality)],[306,24]),
[iquote('0:Res:306.1,24.1')] ).
cnf(1593,plain,
( ~ r2_hidden(skc6,k2_xboole_0(skc7,skc8))
| ~ r2_hidden(skc9,skc8)
| r2_hidden(skc6,skc8) ),
inference(rew,[status(thm),theory(equality)],[12,1589]),
[iquote('0:Rew:12.0,1589.0')] ).
cnf(1594,plain,
~ r2_hidden(skc9,skc8),
inference(mrr,[status(thm)],[1593,6,80]),
[iquote('1:MRR:1593.0,1593.2,6.0,80.0')] ).
cnf(1601,plain,
( ~ r2_hidden(skc9,k2_xboole_0(skc7,skc8))
| ~ r2_hidden(skc6,k4_xboole_0(skc7,skc8))
| r2_hidden(skc9,skc8) ),
inference(rew,[status(thm),theory(equality)],[12,1590]),
[iquote('0:Rew:12.0,1590.0')] ).
cnf(1602,plain,
( ~ r2_hidden(skc6,k4_xboole_0(skc7,skc8))
| r2_hidden(skc9,skc8) ),
inference(mrr,[status(thm)],[1601,5]),
[iquote('0:MRR:1601.0,5.0')] ).
cnf(1603,plain,
~ r2_hidden(skc6,k4_xboole_0(skc7,skc8)),
inference(mrr,[status(thm)],[1602,1594]),
[iquote('1:MRR:1602.1,1594.0')] ).
cnf(1644,plain,
( ~ r2_hidden(skc6,k2_xboole_0(skc8,skc7))
| r2_hidden(skc6,skc8) ),
inference(res,[status(thm),theory(equality)],[306,1603]),
[iquote('1:Res:306.1,1603.0')] ).
cnf(1645,plain,
( ~ r2_hidden(skc6,k2_xboole_0(skc7,skc8))
| r2_hidden(skc6,skc8) ),
inference(rew,[status(thm),theory(equality)],[12,1644]),
[iquote('1:Rew:12.0,1644.0')] ).
cnf(1646,plain,
$false,
inference(mrr,[status(thm)],[1645,6,80]),
[iquote('1:MRR:1645.0,1645.1,6.0,80.0')] ).
cnf(1647,plain,
r2_hidden(skc6,skc8),
inference(spt,[spt(split,[position(sa)])],[1646,80]),
[iquote('1:Spt:1646.0,17.0,80.0')] ).
cnf(1648,plain,
~ r2_hidden(skc9,skc8),
inference(spt,[spt(split,[position(s2)])],[17]),
[iquote('1:Spt:1646.0,17.1')] ).
cnf(1653,plain,
~ r2_hidden(skc9,k4_xboole_0(skc7,skc8)),
inference(mrr,[status(thm)],[22,1647]),
[iquote('1:MRR:22.0,1647.0')] ).
cnf(1672,plain,
( ~ r2_hidden(skc9,k2_xboole_0(skc8,skc7))
| r2_hidden(skc9,skc8) ),
inference(res,[status(thm),theory(equality)],[306,1653]),
[iquote('1:Res:306.1,1653.0')] ).
cnf(1673,plain,
( ~ r2_hidden(skc9,k2_xboole_0(skc7,skc8))
| r2_hidden(skc9,skc8) ),
inference(rew,[status(thm),theory(equality)],[12,1672]),
[iquote('1:Rew:12.0,1672.0')] ).
cnf(1674,plain,
$false,
inference(mrr,[status(thm)],[1673,5,1648]),
[iquote('1:MRR:1673.0,1673.1,5.0,1648.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU406+1 : TPTP v8.1.0. Released v3.4.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n008.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 19 16:49:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.66
% 0.18/0.66 SPASS V 3.9
% 0.18/0.66 SPASS beiseite: Proof found.
% 0.18/0.66 % SZS status Theorem
% 0.18/0.66 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.66 SPASS derived 1433 clauses, backtracked 135 clauses, performed 2 splits and kept 634 clauses.
% 0.18/0.66 SPASS allocated 98875 KBytes.
% 0.18/0.66 SPASS spent 0:00:00.31 on the problem.
% 0.18/0.66 0:00:00.04 for the input.
% 0.18/0.66 0:00:00.04 for the FLOTTER CNF translation.
% 0.18/0.66 0:00:00.02 for inferences.
% 0.18/0.66 0:00:00.00 for the backtracking.
% 0.18/0.66 0:00:00.18 for the reduction.
% 0.18/0.66
% 0.18/0.66
% 0.18/0.66 Here is a proof with depth 4, length 28 :
% 0.18/0.66 % SZS output start Refutation
% See solution above
% 0.18/0.66 Formulae used in the proof : t1_latsum_1 commutativity_k2_xboole_0 t39_xboole_1 d2_xboole_0
% 0.18/0.66
%------------------------------------------------------------------------------