TSTP Solution File: COM007+2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COM007+2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 01:44:14 EDT 2022
% Result : Theorem 0.20s 0.44s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of clauses : 34 ( 20 unt; 6 nHn; 34 RR)
% Number of literals : 55 ( 0 equ; 25 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ goal,
file('COM007+2.p',unknown),
[] ).
cnf(2,axiom,
reflexive_rewrite(a,b),
file('COM007+2.p',unknown),
[] ).
cnf(3,axiom,
reflexive_rewrite(a,c),
file('COM007+2.p',unknown),
[] ).
cnf(4,axiom,
reflexive_rewrite(u,u),
file('COM007+2.p',unknown),
[] ).
cnf(5,axiom,
( ~ rewrite(u,v)
| reflexive_rewrite(u,v) ),
file('COM007+2.p',unknown),
[] ).
cnf(6,axiom,
( ~ reflexive_rewrite(b,u)
| ~ reflexive_rewrite(c,u)
| goal ),
file('COM007+2.p',unknown),
[] ).
cnf(7,axiom,
( ~ rewrite(u,v)
| rewrite(v,skf1(v,w)) ),
file('COM007+2.p',unknown),
[] ).
cnf(8,axiom,
( ~ reflexive_rewrite(u,v)
| rewrite(u,v)
| equal(u,v) ),
file('COM007+2.p',unknown),
[] ).
cnf(9,axiom,
( ~ rewrite(u,v)
| ~ rewrite(u,w)
| rewrite(w,skf1(v,w)) ),
file('COM007+2.p',unknown),
[] ).
cnf(10,plain,
( ~ reflexive_rewrite(c,u)
| ~ reflexive_rewrite(b,u) ),
inference(mrr,[status(thm)],[6,1]),
[iquote('0:MRR:6.2,1.0')] ).
cnf(11,plain,
~ reflexive_rewrite(c,b),
inference(res,[status(thm),theory(equality)],[4,10]),
[iquote('0:Res:4.0,10.0')] ).
cnf(12,plain,
~ reflexive_rewrite(b,c),
inference(res,[status(thm),theory(equality)],[4,10]),
[iquote('0:Res:4.0,10.1')] ).
cnf(14,plain,
( ~ reflexive_rewrite(u,v)
| equal(u,v)
| rewrite(v,skf1(v,w)) ),
inference(res,[status(thm),theory(equality)],[8,7]),
[iquote('0:Res:8.1,7.0')] ).
cnf(16,plain,
( equal(c,a)
| rewrite(c,skf1(c,u)) ),
inference(res,[status(thm),theory(equality)],[3,14]),
[iquote('0:Res:3.0,14.0')] ).
cnf(17,plain,
( equal(b,a)
| rewrite(b,skf1(b,u)) ),
inference(res,[status(thm),theory(equality)],[2,14]),
[iquote('0:Res:2.0,14.0')] ).
cnf(19,plain,
equal(c,a),
inference(spt,[spt(split,[position(s1)])],[16]),
[iquote('1:Spt:16.0')] ).
cnf(22,plain,
~ reflexive_rewrite(a,b),
inference(rew,[status(thm),theory(equality)],[19,11]),
[iquote('1:Rew:19.0,11.0')] ).
cnf(24,plain,
$false,
inference(mrr,[status(thm)],[22,2]),
[iquote('1:MRR:22.0,2.0')] ).
cnf(25,plain,
~ equal(c,a),
inference(spt,[spt(split,[position(sa)])],[24,19]),
[iquote('1:Spt:24.0,16.0,19.0')] ).
cnf(26,plain,
rewrite(c,skf1(c,u)),
inference(spt,[spt(split,[position(s2)])],[16]),
[iquote('1:Spt:24.0,16.1')] ).
cnf(28,plain,
reflexive_rewrite(c,skf1(c,u)),
inference(res,[status(thm),theory(equality)],[26,5]),
[iquote('1:Res:26.0,5.0')] ).
cnf(31,plain,
equal(b,a),
inference(spt,[spt(split,[position(s2s1)])],[17]),
[iquote('2:Spt:17.0')] ).
cnf(34,plain,
~ reflexive_rewrite(a,c),
inference(rew,[status(thm),theory(equality)],[31,12]),
[iquote('2:Rew:31.0,12.0')] ).
cnf(36,plain,
$false,
inference(mrr,[status(thm)],[34,3]),
[iquote('2:MRR:34.0,3.0')] ).
cnf(37,plain,
~ equal(b,a),
inference(spt,[spt(split,[position(s2sa)])],[36,31]),
[iquote('2:Spt:36.0,17.0,31.0')] ).
cnf(38,plain,
rewrite(b,skf1(b,u)),
inference(spt,[spt(split,[position(s2s2)])],[17]),
[iquote('2:Spt:36.0,17.1')] ).
cnf(44,plain,
~ reflexive_rewrite(b,skf1(c,u)),
inference(res,[status(thm),theory(equality)],[28,10]),
[iquote('1:Res:28.0,10.0')] ).
cnf(45,plain,
( ~ reflexive_rewrite(u,v)
| ~ rewrite(u,w)
| equal(u,v)
| rewrite(w,skf1(v,w)) ),
inference(res,[status(thm),theory(equality)],[8,9]),
[iquote('0:Res:8.1,9.0')] ).
cnf(55,plain,
( ~ rewrite(a,u)
| equal(c,a)
| rewrite(u,skf1(c,u)) ),
inference(res,[status(thm),theory(equality)],[3,45]),
[iquote('0:Res:3.0,45.0')] ).
cnf(61,plain,
( ~ rewrite(a,u)
| rewrite(u,skf1(c,u)) ),
inference(mrr,[status(thm)],[55,25]),
[iquote('1:MRR:55.1,25.0')] ).
cnf(67,plain,
( ~ rewrite(a,u)
| reflexive_rewrite(u,skf1(c,u)) ),
inference(res,[status(thm),theory(equality)],[61,5]),
[iquote('1:Res:61.1,5.0')] ).
cnf(74,plain,
~ rewrite(a,b),
inference(res,[status(thm),theory(equality)],[67,44]),
[iquote('1:Res:67.1,44.0')] ).
cnf(79,plain,
( ~ reflexive_rewrite(a,b)
| equal(b,a) ),
inference(res,[status(thm),theory(equality)],[8,74]),
[iquote('1:Res:8.1,74.0')] ).
cnf(80,plain,
$false,
inference(mrr,[status(thm)],[79,2,37]),
[iquote('2:MRR:79.0,79.1,2.0,37.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COM007+2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n019.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 : Thu Jun 16 18:16:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.44
% 0.20/0.44 SPASS V 3.9
% 0.20/0.44 SPASS beiseite: Proof found.
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.44 SPASS derived 60 clauses, backtracked 12 clauses, performed 2 splits and kept 57 clauses.
% 0.20/0.44 SPASS allocated 85124 KBytes.
% 0.20/0.44 SPASS spent 0:00:00.08 on the problem.
% 0.20/0.44 0:00:00.04 for the input.
% 0.20/0.44 0:00:00.02 for the FLOTTER CNF translation.
% 0.20/0.44 0:00:00.00 for inferences.
% 0.20/0.44 0:00:00.00 for the backtracking.
% 0.20/0.44 0:00:00.00 for the reduction.
% 0.20/0.44
% 0.20/0.44
% 0.20/0.44 Here is a proof with depth 7, length 34 :
% 0.20/0.44 % SZS output start Refutation
% See solution above
% 0.20/0.44 Formulae used in the proof : goal_to_be_proved assumption equal_in_reflexive_rewrite rewrite_in_reflexive_rewrite goal_ax rewrite_diamond equal_or_rewrite
% 0.20/0.44
%------------------------------------------------------------------------------