%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KRS013-1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 : Sun Jul 17 03:30:16 EDT 2022
% Result : Unsatisfiable 0.18s 0.40s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 16
% Syntax : Number of clauses : 34 ( 8 unt; 8 nHn; 34 RR)
% Number of literals : 78 ( 0 equ; 41 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c(u)
| t2least(u) ),
file('KRS013-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ t2least(u)
| ~ equalish(u1r2(u),u1r1(u)) ),
file('KRS013-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ t2least(u)
| t(u,u1r1(u)) ),
file('KRS013-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ t2least(u)
| t(u,u1r2(u)) ),
file('KRS013-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ d(u)
| t1most(u) ),
file('KRS013-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ t1most(u)
| ~ t(u,v)
| ~ t(u,w)
| equalish(w,v) ),
file('KRS013-1.p',unknown),
[] ).
cnf(13,axiom,
( ~ e(u)
| ~ r(u,v)
| d(v) ),
file('KRS013-1.p',unknown),
[] ).
cnf(14,axiom,
( ~ s2least(u)
| ~ e(v)
| ~ r(v,u)
| c(u) ),
file('KRS013-1.p',unknown),
[] ).
cnf(24,axiom,
( ~ s(u,v)
| ~ s(u,w)
| s2least(u)
| equalish(w,v) ),
file('KRS013-1.p',unknown),
[] ).
cnf(26,axiom,
( ~ s1most(u6r1(u))
| f(u) ),
file('KRS013-1.p',unknown),
[] ).
cnf(27,axiom,
( f(u)
| r(u,u6r1(u)) ),
file('KRS013-1.p',unknown),
[] ).
cnf(29,axiom,
( ~ equalish(u7r2(u),u7r1(u))
| s1most(u) ),
file('KRS013-1.p',unknown),
[] ).
cnf(30,axiom,
( s1most(u)
| s(u,u7r1(u)) ),
file('KRS013-1.p',unknown),
[] ).
cnf(31,axiom,
( s1most(u)
| s(u,u7r2(u)) ),
file('KRS013-1.p',unknown),
[] ).
cnf(32,axiom,
e(exist),
file('KRS013-1.p',unknown),
[] ).
cnf(33,axiom,
~ f(exist),
file('KRS013-1.p',unknown),
[] ).
cnf(34,plain,
( ~ s2least(u)
| ~ r(exist,u)
| c(u) ),
inference(res,[status(thm),theory(equality)],[32,14]),
[iquote('0:Res:32.0,14.0')] ).
cnf(35,plain,
( ~ r(exist,u)
| d(u) ),
inference(res,[status(thm),theory(equality)],[32,13]),
[iquote('0:Res:32.0,13.0')] ).
cnf(36,plain,
~ s1most(u6r1(exist)),
inference(res,[status(thm),theory(equality)],[26,33]),
[iquote('0:Res:26.1,33.0')] ).
cnf(37,plain,
r(exist,u6r1(exist)),
inference(res,[status(thm),theory(equality)],[27,33]),
[iquote('0:Res:27.0,33.0')] ).
cnf(66,plain,
d(u6r1(exist)),
inference(res,[status(thm),theory(equality)],[37,35]),
[iquote('0:Res:37.0,35.0')] ).
cnf(68,plain,
( ~ s2least(u6r1(exist))
| c(u6r1(exist)) ),
inference(res,[status(thm),theory(equality)],[37,34]),
[iquote('0:Res:37.0,34.1')] ).
cnf(115,plain,
( ~ s(u,v)
| s1most(u)
| s2least(u)
| equalish(v,u7r1(u)) ),
inference(res,[status(thm),theory(equality)],[30,24]),
[iquote('0:Res:30.1,24.0')] ).
cnf(124,plain,
( ~ t2least(u)
| ~ t1most(u)
| ~ t(u,v)
| equalish(v,u1r1(u)) ),
inference(res,[status(thm),theory(equality)],[4,9]),
[iquote('0:Res:4.1,9.1')] ).
cnf(125,plain,
( ~ s(u,u7r2(u))
| s1most(u)
| s2least(u)
| s1most(u) ),
inference(res,[status(thm),theory(equality)],[115,29]),
[iquote('0:Res:115.3,29.0')] ).
cnf(126,plain,
( ~ s(u,u7r2(u))
| s2least(u)
| s1most(u) ),
inference(obv,[status(thm),theory(equality)],[125]),
[iquote('0:Obv:125.1')] ).
cnf(127,plain,
( s2least(u)
| s1most(u) ),
inference(mrr,[status(thm)],[126,31]),
[iquote('0:MRR:126.0,31.1')] ).
cnf(128,plain,
s2least(u6r1(exist)),
inference(res,[status(thm),theory(equality)],[127,36]),
[iquote('0:Res:127.1,36.0')] ).
cnf(130,plain,
c(u6r1(exist)),
inference(mrr,[status(thm)],[68,128]),
[iquote('0:MRR:68.0,128.0')] ).
cnf(136,plain,
( ~ t2least(u)
| ~ t1most(u)
| ~ t2least(u)
| ~ t(u,u1r2(u)) ),
inference(res,[status(thm),theory(equality)],[124,3]),
[iquote('0:Res:124.3,3.1')] ).
cnf(137,plain,
( ~ t1most(u)
| ~ t2least(u)
| ~ t(u,u1r2(u)) ),
inference(obv,[status(thm),theory(equality)],[136]),
[iquote('0:Obv:136.0')] ).
cnf(138,plain,
( ~ t1most(u)
| ~ t2least(u) ),
inference(mrr,[status(thm)],[137,5]),
[iquote('0:MRR:137.2,5.1')] ).
cnf(139,plain,
( ~ d(u)
| ~ c(u) ),
inference(ems,[status(thm)],[138,7,1]),
[iquote('0:EmS:138.0,138.1,7.1,1.1')] ).
cnf(145,plain,
$false,
inference(ems,[status(thm)],[139,66,130]),
[iquote('0:EmS:139.0,139.1,66.0,130.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KRS013-1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n025.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 : Tue Jun 7 17:23:34 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.40
% 0.18/0.40 SPASS V 3.9
% 0.18/0.40 SPASS beiseite: Proof found.
% 0.18/0.40 % SZS status Theorem
% 0.18/0.40 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.40 SPASS derived 80 clauses, backtracked 0 clauses, performed 0 splits and kept 75 clauses.
% 0.18/0.40 SPASS allocated 75683 KBytes.
% 0.18/0.40 SPASS spent 0:00:00.06 on the problem.
% 0.18/0.40 0:00:00.03 for the input.
% 0.18/0.40 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.40 0:00:00.00 for inferences.
% 0.18/0.40 0:00:00.00 for the backtracking.
% 0.18/0.40 0:00:00.00 for the reduction.
% 0.18/0.40
% 0.18/0.40
% 0.18/0.40 Here is a proof with depth 4, length 34 :
% 0.18/0.40 % SZS output start Refutation
% See solution above
% 0.18/0.40 Formulae used in the proof : clause_3 clause_5 clause_6 clause_7 clause_9 clause_11 clause_15 clause_16 clause_26 clause_28 clause_29 clause_31 clause_32 clause_33 clause_1 clause_2
% 0.18/0.40
%------------------------------------------------------------------------------