%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET792+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 8.13s 8.36s
% Output : Refutation 8.13s
% 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('SET792+4.p',unknown),
[] ).
cnf(2,axiom,
least(skc5,skc3,skc4),
file('SET792+4.p',unknown),
[] ).
cnf(3,axiom,
~ min(skc5,skc3,skc4),
file('SET792+4.p',unknown),
[] ).
cnf(5,axiom,
( ~ order(u,v)
| skP1(u,v) ),
file('SET792+4.p',unknown),
[] ).
cnf(11,axiom,
( ~ least(u,v,w)
| member(u,w) ),
file('SET792+4.p',unknown),
[] ).
cnf(32,axiom,
( ~ member(u,v)
| ~ least(w,x,v)
| apply(x,w,u) ),
file('SET792+4.p',unknown),
[] ).
cnf(36,axiom,
( ~ member(u,v)
| member(skf29(u,v,w),v)
| min(u,x,v) ),
file('SET792+4.p',unknown),
[] ).
cnf(39,axiom,
( ~ member(u,v)
| min(u,w,v)
| apply(w,skf29(u,v,w),u) ),
file('SET792+4.p',unknown),
[] ).
cnf(40,axiom,
( ~ member(u,v)
| ~ equal(skf29(u,w,x),u)
| min(u,y,v) ),
file('SET792+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('SET792+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)],[2,11]),
[iquote('0:Res:2.0,11.0')] ).
cnf(72,plain,
( ~ member(u,skc4)
| apply(skc3,skc5,u) ),
inference(res,[status(thm),theory(equality)],[2,32]),
[iquote('0:Res:2.0,32.1')] ).
cnf(73,plain,
( ~ member(skc5,skc4)
| member(skf29(skc5,skc4,u),skc4) ),
inference(res,[status(thm),theory(equality)],[36,3]),
[iquote('0:Res:36.2,3.0')] ).
cnf(74,plain,
( ~ member(skc5,skc4)
| apply(skc3,skf29(skc5,skc4,skc3),skc5) ),
inference(res,[status(thm),theory(equality)],[39,3]),
[iquote('0:Res:39.2,3.0')] ).
cnf(75,plain,
( ~ equal(skf29(skc5,u,v),skc5)
| ~ member(skc5,skc4) ),
inference(res,[status(thm),theory(equality)],[40,3]),
[iquote('0:Res:40.2,3.0')] ).
cnf(76,plain,
member(skf29(skc5,skc4,u),skc4),
inference(mrr,[status(thm)],[73,71]),
[iquote('0:MRR:73.0,71.0')] ).
cnf(77,plain,
apply(skc3,skf29(skc5,skc4,skc3),skc5),
inference(mrr,[status(thm)],[74,71]),
[iquote('0:MRR:74.0,71.0')] ).
cnf(78,plain,
~ equal(skf29(skc5,u,v),skc5),
inference(mrr,[status(thm)],[75,71]),
[iquote('0:MRR:75.1,71.0')] ).
cnf(11616,plain,
( ~ member(skf29(skc5,skc4,skc3),u)
| ~ member(skc5,u)
| ~ skP1(skc3,u)
| ~ apply(skc3,skc5,skf29(skc5,skc4,skc3))
| equal(skf29(skc5,skc4,skc3),skc5) ),
inference(res,[status(thm),theory(equality)],[77,62]),
[iquote('0:Res:77.0,62.3')] ).
cnf(11617,plain,
( ~ member(skf29(skc5,skc4,skc3),u)
| ~ member(skc5,u)
| ~ skP1(skc3,u)
| ~ apply(skc3,skc5,skf29(skc5,skc4,skc3)) ),
inference(mrr,[status(thm)],[11616,78]),
[iquote('0:MRR:11616.4,78.0')] ).
cnf(18108,plain,
( ~ member(skf29(skc5,skc4,skc3),skc4)
| ~ member(skf29(skc5,skc4,skc3),u)
| ~ member(skc5,u)
| ~ skP1(skc3,u) ),
inference(res,[status(thm),theory(equality)],[72,11617]),
[iquote('0:Res:72.1,11617.3')] ).
cnf(18109,plain,
( ~ member(skf29(skc5,skc4,skc3),u)
| ~ member(skc5,u)
| ~ skP1(skc3,u) ),
inference(mrr,[status(thm)],[18108,76]),
[iquote('0:MRR:18108.0,76.0')] ).
cnf(18110,plain,
( ~ member(skc5,skc4)
| ~ skP1(skc3,skc4) ),
inference(res,[status(thm),theory(equality)],[76,18109]),
[iquote('0:Res:76.0,18109.0')] ).
cnf(18113,plain,
~ skP1(skc3,skc4),
inference(mrr,[status(thm)],[18110,71]),
[iquote('0:MRR:18110.0,71.0')] ).
cnf(18114,plain,
$false,
inference(mrr,[status(thm)],[18113,69]),
[iquote('0:MRR:18113.0,69.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET792+4 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % 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 : Sun Jul 10 05:37:16 EDT 2022
% 0.12/0.34 % CPUTime :
% 8.13/8.36
% 8.13/8.36 SPASS V 3.9
% 8.13/8.36 SPASS beiseite: Proof found.
% 8.13/8.36 % SZS status Theorem
% 8.13/8.36 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.13/8.36 SPASS derived 16237 clauses, backtracked 4557 clauses, performed 229 splits and kept 9257 clauses.
% 8.13/8.36 SPASS allocated 98545 KBytes.
% 8.13/8.36 SPASS spent 0:00:07.86 on the problem.
% 8.13/8.36 0:00:00.04 for the input.
% 8.13/8.36 0:00:00.18 for the FLOTTER CNF translation.
% 8.13/8.36 0:00:00.28 for inferences.
% 8.13/8.36 0:00:00.45 for the backtracking.
% 8.13/8.36 0:00:06.80 for the reduction.
% 8.13/8.36
% 8.13/8.36
% 8.13/8.36 Here is a proof with depth 4, length 26 :
% 8.13/8.36 % SZS output start Refutation
% See solution above
% 8.13/8.36 Formulae used in the proof : thIV4 order least min
% 8.13/8.36
%------------------------------------------------------------------------------