TSTP Solution File: SYN986+1.003 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SYN986+1.003 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 : Thu Jul 21 12:32:32 EDT 2022
% Result : Theorem 0.20s 0.43s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of clauses : 20 ( 3 unt; 0 nHn; 20 RR)
% Number of literals : 49 ( 0 equ; 36 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 16 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
r(u,zero,succ(u)),
file('SYN986+1.003.p',unknown),
[] ).
cnf(2,axiom,
( ~ r(u,v,w)
| ~ r(x,v,u)
| r(x,succ(v),w) ),
file('SYN986+1.003.p',unknown),
[] ).
cnf(3,axiom,
( ~ r(zero,u,v)
| ~ r(zero,w,u)
| ~ r(zero,v,x)
| ~ r(zero,zero,w) ),
file('SYN986+1.003.p',unknown),
[] ).
cnf(5,plain,
( ~ r(zero,u,v)
| ~ r(zero,v,w)
| ~ r(zero,succ(zero),u) ),
inference(res,[status(thm),theory(equality)],[1,3]),
[iquote('0:Res:1.0,3.1')] ).
cnf(9,plain,
( ~ r(u,zero,v)
| r(u,succ(zero),succ(v)) ),
inference(res,[status(thm),theory(equality)],[1,2]),
[iquote('0:Res:1.0,2.0')] ).
cnf(11,plain,
( ~ r(u,zero,v)
| ~ r(w,succ(zero),u)
| r(w,succ(succ(zero)),succ(v)) ),
inference(res,[status(thm),theory(equality)],[9,2]),
[iquote('0:Res:9.1,2.0')] ).
cnf(18,plain,
( ~ r(zero,zero,u)
| ~ r(zero,succ(u),v)
| ~ r(zero,v,w) ),
inference(res,[status(thm),theory(equality)],[9,5]),
[iquote('0:Res:9.1,5.2')] ).
cnf(23,plain,
( ~ r(u,zero,v)
| ~ r(succ(v),zero,w)
| r(u,succ(succ(zero)),succ(w)) ),
inference(res,[status(thm),theory(equality)],[9,11]),
[iquote('0:Res:9.1,11.1')] ).
cnf(24,plain,
( ~ r(u,zero,v)
| r(u,succ(succ(zero)),succ(succ(succ(v)))) ),
inference(res,[status(thm),theory(equality)],[1,23]),
[iquote('0:Res:1.0,23.1')] ).
cnf(25,plain,
( ~ r(u,zero,v)
| ~ r(w,succ(succ(zero)),u)
| r(w,succ(succ(succ(zero))),succ(succ(succ(v)))) ),
inference(res,[status(thm),theory(equality)],[24,2]),
[iquote('0:Res:24.1,2.0')] ).
cnf(28,plain,
( ~ r(zero,zero,u)
| ~ r(zero,zero,succ(zero))
| ~ r(zero,succ(succ(succ(u))),v) ),
inference(res,[status(thm),theory(equality)],[24,18]),
[iquote('0:Res:24.1,18.1')] ).
cnf(29,plain,
( ~ r(zero,zero,u)
| ~ r(zero,succ(succ(succ(u))),v) ),
inference(mrr,[status(thm)],[28,1]),
[iquote('0:MRR:28.1,1.0')] ).
cnf(32,plain,
( ~ r(u,zero,v)
| ~ r(succ(succ(succ(v))),zero,w)
| r(u,succ(succ(succ(zero))),succ(succ(succ(w)))) ),
inference(res,[status(thm),theory(equality)],[24,25]),
[iquote('0:Res:24.1,25.1')] ).
cnf(33,plain,
( ~ r(u,zero,v)
| r(u,succ(succ(succ(zero))),succ(succ(succ(succ(succ(succ(succ(v)))))))) ),
inference(res,[status(thm),theory(equality)],[1,32]),
[iquote('0:Res:1.0,32.1')] ).
cnf(34,plain,
( ~ r(u,zero,v)
| ~ r(w,succ(succ(succ(zero))),u)
| r(w,succ(succ(succ(succ(zero)))),succ(succ(succ(succ(succ(succ(succ(v)))))))) ),
inference(res,[status(thm),theory(equality)],[33,2]),
[iquote('0:Res:33.1,2.0')] ).
cnf(40,plain,
( ~ r(u,zero,v)
| ~ r(succ(succ(succ(succ(succ(succ(succ(v))))))),zero,w)
| r(u,succ(succ(succ(succ(zero)))),succ(succ(succ(succ(succ(succ(succ(w)))))))) ),
inference(res,[status(thm),theory(equality)],[33,34]),
[iquote('0:Res:33.1,34.1')] ).
cnf(41,plain,
( ~ r(u,zero,v)
| r(u,succ(succ(succ(succ(zero)))),succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(v)))))))))))))))) ),
inference(res,[status(thm),theory(equality)],[1,40]),
[iquote('0:Res:1.0,40.1')] ).
cnf(46,plain,
( ~ r(zero,zero,u)
| ~ r(zero,zero,succ(zero)) ),
inference(res,[status(thm),theory(equality)],[41,29]),
[iquote('0:Res:41.1,29.1')] ).
cnf(47,plain,
~ r(zero,zero,succ(zero)),
inference(con,[status(thm)],[46]),
[iquote('0:Con:46.0')] ).
cnf(48,plain,
$false,
inference(mrr,[status(thm)],[47,1]),
[iquote('0:MRR:47.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN986+1.003 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n022.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 : Mon Jul 11 15:47:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.43
% 0.20/0.43 SPASS V 3.9
% 0.20/0.43 SPASS beiseite: Proof found.
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.43 SPASS derived 37 clauses, backtracked 0 clauses, performed 0 splits and kept 33 clauses.
% 0.20/0.43 SPASS allocated 85121 KBytes.
% 0.20/0.43 SPASS spent 0:00:00.08 on the problem.
% 0.20/0.43 0:00:00.03 for the input.
% 0.20/0.43 0:00:00.02 for the FLOTTER CNF translation.
% 0.20/0.43 0:00:00.00 for inferences.
% 0.20/0.43 0:00:00.00 for the backtracking.
% 0.20/0.43 0:00:00.00 for the reduction.
% 0.20/0.43
% 0.20/0.43
% 0.20/0.43 Here is a proof with depth 11, length 20 :
% 0.20/0.43 % SZS output start Refutation
% See solution above
% 0.20/0.43 Formulae used in the proof : hyp1 hyp2 ck
% 0.20/0.43
%------------------------------------------------------------------------------