TSTP Solution File: SET791+4 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET791+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 : Tue Jul 19 05:28:42 EDT 2022
% Result : Theorem 10.67s 10.84s
% Output : Refutation 10.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 26 ( 10 unt; 2 nHn; 26 RR)
% Number of literals : 58 ( 0 equ; 38 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
order(skc3,skc4),
file('SET791+4.p',unknown),
[] ).
cnf(2,axiom,
greatest(skc5,skc3,skc4),
file('SET791+4.p',unknown),
[] ).
cnf(3,axiom,
~ max(skc5,skc3,skc4),
file('SET791+4.p',unknown),
[] ).
cnf(5,axiom,
( ~ order(u,v)
| skP1(u,v) ),
file('SET791+4.p',unknown),
[] ).
cnf(10,axiom,
( ~ greatest(u,v,w)
| member(u,w) ),
file('SET791+4.p',unknown),
[] ).
cnf(31,axiom,
( ~ member(u,v)
| ~ greatest(w,x,v)
| apply(x,u,w) ),
file('SET791+4.p',unknown),
[] ).
cnf(35,axiom,
( ~ member(u,v)
| member(skf28(u,v,w),v)
| max(u,x,v) ),
file('SET791+4.p',unknown),
[] ).
cnf(37,axiom,
( ~ member(u,v)
| max(u,w,v)
| apply(w,u,skf28(u,v,w)) ),
file('SET791+4.p',unknown),
[] ).
cnf(38,axiom,
( ~ member(u,v)
| ~ equal(skf28(u,w,x),u)
| max(u,y,v) ),
file('SET791+4.p',unknown),
[] ).
cnf(62,axiom,
( ~ member(u,v)
| ~ member(w,v)
| ~ skP1(x,v)
| ~ apply(x,u,w)
| ~ apply(x,w,u)
| equal(w,u) ),
file('SET791+4.p',unknown),
[] ).
cnf(69,plain,
skP1(skc3,skc4),
inference(res,[status(thm),theory(equality)],[1,5]),
[iquote('0:Res:1.0,5.0')] ).
cnf(71,plain,
member(skc5,skc4),
inference(res,[status(thm),theory(equality)],[2,10]),
[iquote('0:Res:2.0,10.0')] ).
cnf(72,plain,
( ~ member(u,skc4)
| apply(skc3,u,skc5) ),
inference(res,[status(thm),theory(equality)],[2,31]),
[iquote('0:Res:2.0,31.1')] ).
cnf(73,plain,
( ~ member(skc5,skc4)
| member(skf28(skc5,skc4,u),skc4) ),
inference(res,[status(thm),theory(equality)],[35,3]),
[iquote('0:Res:35.2,3.0')] ).
cnf(74,plain,
( ~ member(skc5,skc4)
| apply(skc3,skc5,skf28(skc5,skc4,skc3)) ),
inference(res,[status(thm),theory(equality)],[37,3]),
[iquote('0:Res:37.2,3.0')] ).
cnf(75,plain,
( ~ equal(skf28(skc5,u,v),skc5)
| ~ member(skc5,skc4) ),
inference(res,[status(thm),theory(equality)],[38,3]),
[iquote('0:Res:38.2,3.0')] ).
cnf(76,plain,
member(skf28(skc5,skc4,u),skc4),
inference(mrr,[status(thm)],[73,71]),
[iquote('0:MRR:73.0,71.0')] ).
cnf(77,plain,
apply(skc3,skc5,skf28(skc5,skc4,skc3)),
inference(mrr,[status(thm)],[74,71]),
[iquote('0:MRR:74.0,71.0')] ).
cnf(78,plain,
~ equal(skf28(skc5,u,v),skc5),
inference(mrr,[status(thm)],[75,71]),
[iquote('0:MRR:75.1,71.0')] ).
cnf(16143,plain,
( ~ member(skc5,u)
| ~ member(skf28(skc5,skc4,skc3),u)
| ~ skP1(skc3,u)
| ~ apply(skc3,skf28(skc5,skc4,skc3),skc5)
| equal(skf28(skc5,skc4,skc3),skc5) ),
inference(res,[status(thm),theory(equality)],[77,62]),
[iquote('0:Res:77.0,62.3')] ).
cnf(16144,plain,
( ~ member(skc5,u)
| ~ member(skf28(skc5,skc4,skc3),u)
| ~ skP1(skc3,u)
| ~ apply(skc3,skf28(skc5,skc4,skc3),skc5) ),
inference(mrr,[status(thm)],[16143,78]),
[iquote('0:MRR:16143.4,78.0')] ).
cnf(22440,plain,
( ~ member(skf28(skc5,skc4,skc3),skc4)
| ~ member(skc5,u)
| ~ member(skf28(skc5,skc4,skc3),u)
| ~ skP1(skc3,u) ),
inference(res,[status(thm),theory(equality)],[72,16144]),
[iquote('0:Res:72.1,16144.3')] ).
cnf(22441,plain,
( ~ member(skc5,u)
| ~ member(skf28(skc5,skc4,skc3),u)
| ~ skP1(skc3,u) ),
inference(mrr,[status(thm)],[22440,76]),
[iquote('0:MRR:22440.0,76.0')] ).
cnf(22442,plain,
( ~ member(skc5,skc4)
| ~ skP1(skc3,skc4) ),
inference(res,[status(thm),theory(equality)],[76,22441]),
[iquote('0:Res:76.0,22441.1')] ).
cnf(22445,plain,
~ skP1(skc3,skc4),
inference(mrr,[status(thm)],[22442,71]),
[iquote('0:MRR:22442.0,71.0')] ).
cnf(22446,plain,
$false,
inference(mrr,[status(thm)],[22445,69]),
[iquote('0:MRR:22445.0,69.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET791+4 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n009.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 : Sun Jul 10 11:52:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 10.67/10.84
% 10.67/10.84 SPASS V 3.9
% 10.67/10.84 SPASS beiseite: Proof found.
% 10.67/10.84 % SZS status Theorem
% 10.67/10.84 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.67/10.84 SPASS derived 20292 clauses, backtracked 5253 clauses, performed 229 splits and kept 10612 clauses.
% 10.67/10.84 SPASS allocated 101198 KBytes.
% 10.67/10.84 SPASS spent 0:0:10.30 on the problem.
% 10.67/10.84 0:00:00.04 for the input.
% 10.67/10.84 0:00:00.18 for the FLOTTER CNF translation.
% 10.67/10.84 0:00:00.34 for inferences.
% 10.67/10.84 0:00:00.53 for the backtracking.
% 10.67/10.84 0:00:09.06 for the reduction.
% 10.67/10.84
% 10.67/10.84
% 10.67/10.84 Here is a proof with depth 4, length 26 :
% 10.67/10.84 % SZS output start Refutation
% See solution above
% 10.67/10.84 Formulae used in the proof : thIV3 order greatest max
% 10.67/10.84
%------------------------------------------------------------------------------