TSTP Solution File: PUZ021-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : PUZ021-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 : Mon Jul 18 18:27:18 EDT 2022
% Result : Unsatisfiable 0.18s 0.43s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of clauses : 39 ( 9 unt; 17 nHn; 39 RR)
% Number of literals : 78 ( 0 equ; 29 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( a_truth(knave(u),v)
| a_truth(knight(u),v) ),
file('PUZ021-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ a_truth(poor(u),v)
| ~ a_truth(rich(u),v) ),
file('PUZ021-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ says(u,v)
| ~ a_truth(knight(u),w)
| a_truth(v,w) ),
file('PUZ021-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ a_truth(u,v)
| ~ says(w,u)
| ~ a_truth(knave(w),v) ),
file('PUZ021-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ a_truth(knave(u),v)
| a_truth(w,v)
| says(u,w) ),
file('PUZ021-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ a_truth(and__dfg(u,v),w)
| a_truth(u,w) ),
file('PUZ021-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ a_truth(and__dfg(u,v),w)
| a_truth(v,w) ),
file('PUZ021-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ a_truth(u,v)
| ~ a_truth(w,v)
| a_truth(and__dfg(w,u),v) ),
file('PUZ021-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ says(me,u)
| ~ a_truth(and__dfg(knave(me),rich(me)),u) ),
file('PUZ021-1.p',unknown),
[] ).
cnf(13,axiom,
( says(me,u)
| a_truth(and__dfg(knave(me),rich(me)),u) ),
file('PUZ021-1.p',unknown),
[] ).
cnf(14,plain,
( says(me,u)
| a_truth(knave(me),u) ),
inference(res,[status(thm),theory(equality)],[13,9]),
[iquote('0:Res:13.1,9.0')] ).
cnf(15,plain,
( says(me,u)
| a_truth(rich(me),u) ),
inference(res,[status(thm),theory(equality)],[13,10]),
[iquote('0:Res:13.1,10.0')] ).
cnf(17,plain,
( ~ a_truth(poor(me),u)
| says(me,u) ),
inference(res,[status(thm),theory(equality)],[15,3]),
[iquote('0:Res:15.1,3.1')] ).
cnf(19,plain,
( says(me,u)
| a_truth(v,u)
| says(me,v) ),
inference(res,[status(thm),theory(equality)],[14,8]),
[iquote('0:Res:14.1,8.0')] ).
cnf(20,plain,
( a_truth(u,u)
| says(me,u) ),
inference(fac,[status(thm)],[19]),
[iquote('0:Fac:19.0,19.2')] ).
cnf(32,plain,
( says(me,and__dfg(u,v))
| a_truth(u,and__dfg(u,v)) ),
inference(res,[status(thm),theory(equality)],[20,9]),
[iquote('0:Res:20.0,9.0')] ).
cnf(33,plain,
( says(me,and__dfg(u,v))
| a_truth(v,and__dfg(u,v)) ),
inference(res,[status(thm),theory(equality)],[20,10]),
[iquote('0:Res:20.0,10.0')] ).
cnf(55,plain,
( says(me,and__dfg(poor(me),u))
| says(me,and__dfg(poor(me),u)) ),
inference(res,[status(thm),theory(equality)],[32,17]),
[iquote('0:Res:32.1,17.0')] ).
cnf(56,plain,
says(me,and__dfg(poor(me),u)),
inference(obv,[status(thm),theory(equality)],[55]),
[iquote('0:Obv:55.0')] ).
cnf(64,plain,
( says(me,and__dfg(u,poor(me)))
| says(me,and__dfg(u,poor(me))) ),
inference(res,[status(thm),theory(equality)],[33,17]),
[iquote('0:Res:33.1,17.0')] ).
cnf(65,plain,
says(me,and__dfg(u,poor(me))),
inference(obv,[status(thm),theory(equality)],[64]),
[iquote('0:Obv:64.0')] ).
cnf(66,plain,
( ~ says(u,v)
| a_truth(knave(u),w)
| a_truth(v,w) ),
inference(res,[status(thm),theory(equality)],[2,5]),
[iquote('0:Res:2.1,5.1')] ).
cnf(87,plain,
( ~ a_truth(u,v)
| ~ says(me,u)
| says(me,v) ),
inference(res,[status(thm),theory(equality)],[14,7]),
[iquote('0:Res:14.1,7.2')] ).
cnf(97,plain,
( ~ says(me,rich(me))
| says(me,u)
| says(me,u) ),
inference(res,[status(thm),theory(equality)],[15,87]),
[iquote('0:Res:15.1,87.0')] ).
cnf(104,plain,
( ~ says(me,rich(me))
| says(me,u) ),
inference(obv,[status(thm),theory(equality)],[97]),
[iquote('0:Obv:97.1')] ).
cnf(134,plain,
( ~ a_truth(rich(me),u)
| ~ a_truth(knave(me),u)
| ~ says(me,u) ),
inference(res,[status(thm),theory(equality)],[11,12]),
[iquote('0:Res:11.2,12.1')] ).
cnf(177,plain,
( a_truth(knave(me),u)
| a_truth(and__dfg(v,poor(me)),u) ),
inference(res,[status(thm),theory(equality)],[65,66]),
[iquote('0:Res:65.0,66.0')] ).
cnf(217,plain,
( a_truth(knave(me),u)
| a_truth(v,u) ),
inference(res,[status(thm),theory(equality)],[177,9]),
[iquote('0:Res:177.1,9.0')] ).
cnf(219,plain,
a_truth(knave(me),u),
inference(con,[status(thm)],[217]),
[iquote('0:Con:217.1')] ).
cnf(220,plain,
( ~ a_truth(rich(me),u)
| ~ says(me,u) ),
inference(mrr,[status(thm)],[134,219]),
[iquote('0:MRR:134.1,219.0')] ).
cnf(221,plain,
( a_truth(u,v)
| says(me,u) ),
inference(res,[status(thm),theory(equality)],[219,8]),
[iquote('0:Res:219.0,8.0')] ).
cnf(222,plain,
( ~ a_truth(u,v)
| ~ says(me,u) ),
inference(res,[status(thm),theory(equality)],[219,7]),
[iquote('0:Res:219.0,7.2')] ).
cnf(245,plain,
( a_truth(rich(me),u)
| says(me,v) ),
inference(res,[status(thm),theory(equality)],[221,104]),
[iquote('0:Res:221.1,104.0')] ).
cnf(252,plain,
says(me,u),
inference(spt,[spt(split,[position(s1)])],[245]),
[iquote('1:Spt:245.1')] ).
cnf(257,plain,
~ a_truth(u,v),
inference(mrr,[status(thm)],[222,252]),
[iquote('1:MRR:222.1,252.0')] ).
cnf(258,plain,
$false,
inference(unc,[status(thm)],[257,219]),
[iquote('1:UnC:257.0,219.0')] ).
cnf(259,plain,
a_truth(rich(me),u),
inference(spt,[spt(split,[position(s2)])],[245]),
[iquote('1:Spt:258.0,245.0')] ).
cnf(260,plain,
~ says(me,u),
inference(mrr,[status(thm)],[220,259]),
[iquote('1:MRR:220.0,259.0')] ).
cnf(261,plain,
$false,
inference(unc,[status(thm)],[260,56]),
[iquote('1:UnC:260.0,56.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : PUZ021-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n017.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat May 28 21:07:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.43
% 0.18/0.43 SPASS V 3.9
% 0.18/0.43 SPASS beiseite: Proof found.
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 SPASS derived 216 clauses, backtracked 65 clauses, performed 1 splits and kept 222 clauses.
% 0.18/0.43 SPASS allocated 63283 KBytes.
% 0.18/0.43 SPASS spent 0:00:00.08 on the problem.
% 0.18/0.43 0:00:00.03 for the input.
% 0.18/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.43 0:00:00.00 for inferences.
% 0.18/0.43 0:00:00.00 for the backtracking.
% 0.18/0.43 0:00:00.03 for the reduction.
% 0.18/0.43
% 0.18/0.43
% 0.18/0.43 Here is a proof with depth 10, length 39 :
% 0.18/0.43 % SZS output start Refutation
% See solution above
% 0.18/0.43 Formulae used in the proof : knight_or_knave not_rich_and_poor knights_tell_truth1 knaves_lie1 knaves_lie2 conjunction1 conjunction2 conjunction3 prove_statement_exists1 prove_statement_exists2
% 0.18/0.43
%------------------------------------------------------------------------------