TSTP Solution File: COM007+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COM007+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 0.21s 0.45s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of clauses : 43 ( 21 unt; 8 nHn; 43 RR)
% Number of literals : 73 ( 0 equ; 30 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+1.p',unknown),
[] ).
cnf(2,axiom,
reflexive_rewrite(a,b),
file('COM007+1.p',unknown),
[] ).
cnf(3,axiom,
reflexive_rewrite(a,c),
file('COM007+1.p',unknown),
[] ).
cnf(4,axiom,
equalish(u,u),
file('COM007+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ equalish(u,v)
| equalish(v,u) ),
file('COM007+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ equalish(u,v)
| reflexive_rewrite(u,v) ),
file('COM007+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ rewrite(u,v)
| reflexive_rewrite(u,v) ),
file('COM007+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ reflexive_rewrite(b,u)
| ~ reflexive_rewrite(c,u)
| goal ),
file('COM007+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ rewrite(u,v)
| rewrite(v,skf1(v,w)) ),
file('COM007+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ reflexive_rewrite(u,v)
| rewrite(u,v)
| equalish(u,v) ),
file('COM007+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ reflexive_rewrite(u,v)
| ~ equalish(w,u)
| reflexive_rewrite(w,v) ),
file('COM007+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ rewrite(u,v)
| ~ rewrite(u,w)
| rewrite(w,skf1(v,w)) ),
file('COM007+1.p',unknown),
[] ).
cnf(13,plain,
( ~ reflexive_rewrite(c,u)
| ~ reflexive_rewrite(b,u) ),
inference(mrr,[status(thm)],[8,1]),
[iquote('0:MRR:8.2,1.0')] ).
cnf(15,plain,
reflexive_rewrite(u,u),
inference(res,[status(thm),theory(equality)],[4,6]),
[iquote('0:Res:4.0,6.0')] ).
cnf(16,plain,
~ reflexive_rewrite(c,b),
inference(res,[status(thm),theory(equality)],[15,13]),
[iquote('0:Res:15.0,13.1')] ).
cnf(17,plain,
( ~ reflexive_rewrite(u,v)
| equalish(u,v)
| rewrite(v,skf1(v,w)) ),
inference(res,[status(thm),theory(equality)],[10,9]),
[iquote('0:Res:10.1,9.0')] ).
cnf(19,plain,
( ~ equalish(u,a)
| reflexive_rewrite(u,c) ),
inference(res,[status(thm),theory(equality)],[3,11]),
[iquote('0:Res:3.0,11.0')] ).
cnf(20,plain,
( ~ equalish(u,a)
| reflexive_rewrite(u,b) ),
inference(res,[status(thm),theory(equality)],[2,11]),
[iquote('0:Res:2.0,11.0')] ).
cnf(23,plain,
( ~ reflexive_rewrite(u,v)
| ~ rewrite(u,w)
| equalish(u,v)
| rewrite(w,skf1(v,w)) ),
inference(res,[status(thm),theory(equality)],[10,12]),
[iquote('0:Res:10.1,12.0')] ).
cnf(25,plain,
( equalish(a,c)
| rewrite(c,skf1(c,u)) ),
inference(res,[status(thm),theory(equality)],[3,17]),
[iquote('0:Res:3.0,17.0')] ).
cnf(26,plain,
( equalish(a,b)
| rewrite(b,skf1(b,u)) ),
inference(res,[status(thm),theory(equality)],[2,17]),
[iquote('0:Res:2.0,17.0')] ).
cnf(30,plain,
( equalish(a,c)
| reflexive_rewrite(c,skf1(c,u)) ),
inference(res,[status(thm),theory(equality)],[25,7]),
[iquote('0:Res:25.1,7.0')] ).
cnf(33,plain,
( equalish(a,b)
| reflexive_rewrite(b,skf1(b,u)) ),
inference(res,[status(thm),theory(equality)],[26,7]),
[iquote('0:Res:26.1,7.0')] ).
cnf(34,plain,
( ~ rewrite(a,u)
| equalish(a,c)
| rewrite(u,skf1(c,u)) ),
inference(res,[status(thm),theory(equality)],[3,23]),
[iquote('0:Res:3.0,23.0')] ).
cnf(37,plain,
equalish(a,c),
inference(spt,[spt(split,[position(s1)])],[30]),
[iquote('1:Spt:30.0')] ).
cnf(39,plain,
equalish(c,a),
inference(res,[status(thm),theory(equality)],[37,5]),
[iquote('1:Res:37.0,5.0')] ).
cnf(42,plain,
reflexive_rewrite(c,b),
inference(res,[status(thm),theory(equality)],[39,20]),
[iquote('1:Res:39.0,20.0')] ).
cnf(44,plain,
$false,
inference(mrr,[status(thm)],[42,16]),
[iquote('1:MRR:42.0,16.0')] ).
cnf(45,plain,
~ equalish(a,c),
inference(spt,[spt(split,[position(sa)])],[44,37]),
[iquote('1:Spt:44.0,30.0,37.0')] ).
cnf(46,plain,
reflexive_rewrite(c,skf1(c,u)),
inference(spt,[spt(split,[position(s2)])],[30]),
[iquote('1:Spt:44.0,30.1')] ).
cnf(49,plain,
( ~ rewrite(a,u)
| rewrite(u,skf1(c,u)) ),
inference(mrr,[status(thm)],[34,45]),
[iquote('1:MRR:34.1,45.0')] ).
cnf(59,plain,
( ~ rewrite(a,u)
| reflexive_rewrite(u,skf1(c,u)) ),
inference(res,[status(thm),theory(equality)],[49,7]),
[iquote('1:Res:49.1,7.0')] ).
cnf(60,plain,
equalish(a,b),
inference(spt,[spt(split,[position(s2s1)])],[33]),
[iquote('2:Spt:33.0')] ).
cnf(62,plain,
equalish(b,a),
inference(res,[status(thm),theory(equality)],[60,5]),
[iquote('2:Res:60.0,5.0')] ).
cnf(66,plain,
reflexive_rewrite(b,c),
inference(res,[status(thm),theory(equality)],[62,19]),
[iquote('2:Res:62.0,19.0')] ).
cnf(74,plain,
~ reflexive_rewrite(c,c),
inference(res,[status(thm),theory(equality)],[66,13]),
[iquote('2:Res:66.0,13.1')] ).
cnf(75,plain,
$false,
inference(mrr,[status(thm)],[74,15]),
[iquote('2:MRR:74.0,15.0')] ).
cnf(76,plain,
~ equalish(a,b),
inference(spt,[spt(split,[position(s2sa)])],[75,60]),
[iquote('2:Spt:75.0,33.0,60.0')] ).
cnf(77,plain,
reflexive_rewrite(b,skf1(b,u)),
inference(spt,[spt(split,[position(s2s2)])],[33]),
[iquote('2:Spt:75.0,33.1')] ).
cnf(103,plain,
( ~ rewrite(a,b)
| ~ reflexive_rewrite(c,skf1(c,b)) ),
inference(res,[status(thm),theory(equality)],[59,13]),
[iquote('1:Res:59.1,13.1')] ).
cnf(104,plain,
~ rewrite(a,b),
inference(mrr,[status(thm)],[103,46]),
[iquote('1:MRR:103.1,46.0')] ).
cnf(105,plain,
( ~ reflexive_rewrite(a,b)
| equalish(a,b) ),
inference(res,[status(thm),theory(equality)],[10,104]),
[iquote('1:Res:10.1,104.0')] ).
cnf(106,plain,
$false,
inference(mrr,[status(thm)],[105,2,76]),
[iquote('2:MRR:105.0,105.1,2.0,76.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : COM007+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jun 16 20:05:51 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.45
% 0.21/0.45 SPASS V 3.9
% 0.21/0.45 SPASS beiseite: Proof found.
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.45 SPASS derived 76 clauses, backtracked 12 clauses, performed 2 splits and kept 69 clauses.
% 0.21/0.45 SPASS allocated 85194 KBytes.
% 0.21/0.45 SPASS spent 0:00:00.09 on the problem.
% 0.21/0.45 0:00:00.03 for the input.
% 0.21/0.45 0:00:00.03 for the FLOTTER CNF translation.
% 0.21/0.45 0:00:00.00 for inferences.
% 0.21/0.45 0:00:00.00 for the backtracking.
% 0.21/0.45 0:00:00.00 for the reduction.
% 0.21/0.45
% 0.21/0.45
% 0.21/0.45 Here is a proof with depth 7, length 43 :
% 0.21/0.45 % SZS output start Refutation
% See solution above
% 0.21/0.45 Formulae used in the proof : goal_to_be_proved assumption reflexivity symmtery equalish_in_reflexive_rewrite rewrite_in_reflexive_rewrite goal_ax rewrite_diamond equalish_or_rewrite substitution
% 0.21/0.45
%------------------------------------------------------------------------------