TSTP Solution File: COL074-3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COL074-3 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 : Fri Jul 15 00:42:35 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of clauses : 24 ( 22 unt; 2 nHn; 24 RR)
% Number of literals : 26 ( 0 equ; 2 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
equal(apply(eq,pair(u,u)),projection1),
file('COL074-3.p',unknown),
[] ).
cnf(6,axiom,
( equal(u,v)
| equal(apply(eq,pair(u,v)),projection2) ),
file('COL074-3.p',unknown),
[] ).
cnf(8,axiom,
~ equal(projection2,projection1),
file('COL074-3.p',unknown),
[] ).
cnf(9,axiom,
equal(apply(k,projection1),k_projection1),
file('COL074-3.p',unknown),
[] ).
cnf(10,axiom,
equal(apply(k,projection2),k_projection2),
file('COL074-3.p',unknown),
[] ).
cnf(11,axiom,
equal(apply(eq,pair(apply(k,s),apply(k,projection2))),s),
file('COL074-3.p',unknown),
[] ).
cnf(12,axiom,
equal(apply(apply(k,u),v),u),
file('COL074-3.p',unknown),
[] ).
cnf(14,plain,
equal(apply(eq,pair(apply(k,s),k_projection2)),s),
inference(rew,[status(thm),theory(equality)],[10,11]),
[iquote('0:Rew:10.0,11.0')] ).
cnf(21,plain,
equal(apply(k_projection2,u),projection2),
inference(spr,[status(thm),theory(equality)],[10,12]),
[iquote('0:SpR:10.0,12.0')] ).
cnf(22,plain,
equal(apply(k_projection1,u),projection1),
inference(spr,[status(thm),theory(equality)],[9,12]),
[iquote('0:SpR:9.0,12.0')] ).
cnf(30,plain,
( equal(apply(k,s),k_projection2)
| equal(s,projection2) ),
inference(spr,[status(thm),theory(equality)],[6,14]),
[iquote('0:SpR:6.1,14.0')] ).
cnf(31,plain,
equal(apply(k,s),k_projection2),
inference(spt,[spt(split,[position(s1)])],[30]),
[iquote('1:Spt:30.0')] ).
cnf(32,plain,
equal(apply(eq,pair(k_projection2,k_projection2)),s),
inference(rew,[status(thm),theory(equality)],[31,14]),
[iquote('1:Rew:31.0,14.0')] ).
cnf(33,plain,
equal(s,projection1),
inference(rew,[status(thm),theory(equality)],[5,32]),
[iquote('1:Rew:5.0,32.0')] ).
cnf(34,plain,
equal(apply(k,projection1),k_projection2),
inference(rew,[status(thm),theory(equality)],[33,31]),
[iquote('1:Rew:33.0,31.0')] ).
cnf(35,plain,
equal(k_projection2,k_projection1),
inference(rew,[status(thm),theory(equality)],[9,34]),
[iquote('1:Rew:9.0,34.0')] ).
cnf(37,plain,
equal(apply(k_projection1,u),projection2),
inference(rew,[status(thm),theory(equality)],[35,21]),
[iquote('1:Rew:35.0,21.0')] ).
cnf(38,plain,
equal(projection2,projection1),
inference(rew,[status(thm),theory(equality)],[22,37]),
[iquote('1:Rew:22.0,37.0')] ).
cnf(39,plain,
$false,
inference(mrr,[status(thm)],[38,8]),
[iquote('1:MRR:38.0,8.0')] ).
cnf(40,plain,
~ equal(apply(k,s),k_projection2),
inference(spt,[spt(split,[position(sa)])],[39,31]),
[iquote('1:Spt:39.0,30.0,31.0')] ).
cnf(41,plain,
equal(s,projection2),
inference(spt,[spt(split,[position(s2)])],[30]),
[iquote('1:Spt:39.0,30.1')] ).
cnf(44,plain,
equal(apply(eq,pair(k_projection2,k_projection2)),projection2),
inference(rew,[status(thm),theory(equality)],[10,14,41]),
[iquote('1:Rew:10.0,14.0,41.0,14.0')] ).
cnf(45,plain,
equal(projection2,projection1),
inference(rew,[status(thm),theory(equality)],[5,44]),
[iquote('1:Rew:5.0,44.0')] ).
cnf(46,plain,
$false,
inference(mrr,[status(thm)],[45,8]),
[iquote('1:MRR:45.0,8.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COL074-3 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % 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 : Tue May 31 06:30:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.41
% 0.19/0.41 SPASS V 3.9
% 0.19/0.41 SPASS beiseite: Proof found.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.41 SPASS derived 21 clauses, backtracked 5 clauses, performed 1 splits and kept 27 clauses.
% 0.19/0.41 SPASS allocated 63120 KBytes.
% 0.19/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.19/0.41 0:00:00.03 for the input.
% 0.19/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.41 0:00:00.00 for inferences.
% 0.19/0.41 0:00:00.00 for the backtracking.
% 0.19/0.41 0:00:00.00 for the reduction.
% 0.19/0.41
% 0.19/0.41
% 0.19/0.41 Here is a proof with depth 2, length 24 :
% 0.19/0.41 % SZS output start Refutation
% See solution above
% 0.19/0.41 Formulae used in the proof : equality extensionality1 different_projections k_projection1 k_projection2 self_referential k_definition
% 0.19/0.41
%------------------------------------------------------------------------------