%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC039-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 22:01:17 EDT 2022
% Result : Unsatisfiable 0.55s 0.74s
% Output : Refutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of clauses : 32 ( 14 unt; 6 nHn; 32 RR)
% Number of literals : 59 ( 0 equ; 26 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(sk1),
file('SWC039-1.p',unknown),
[] ).
cnf(5,axiom,
equal(nil,sk2),
file('SWC039-1.p',unknown),
[] ).
cnf(6,axiom,
equal(sk4,sk2),
file('SWC039-1.p',unknown),
[] ).
cnf(7,axiom,
equal(sk3,sk1),
file('SWC039-1.p',unknown),
[] ).
cnf(8,axiom,
~ equal(nil,sk1),
file('SWC039-1.p',unknown),
[] ).
cnf(17,axiom,
( ssList(sk6)
| equal(nil,sk3) ),
file('SWC039-1.p',unknown),
[] ).
cnf(18,axiom,
( ssList(sk7)
| equal(nil,sk3) ),
file('SWC039-1.p',unknown),
[] ).
cnf(20,axiom,
( equal(app(app(sk6,sk3),sk7),sk4)
| equal(nil,sk3) ),
file('SWC039-1.p',unknown),
[] ).
cnf(95,axiom,
( ~ ssList(u)
| equal(app(u,nil),u) ),
file('SWC039-1.p',unknown),
[] ).
cnf(107,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC039-1.p',unknown),
[] ).
cnf(141,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(v,u),nil)
| equal(nil,u) ),
file('SWC039-1.p',unknown),
[] ).
cnf(219,plain,
~ equal(sk2,sk1),
inference(rew,[status(thm),theory(equality)],[5,8]),
[iquote('0:Rew:5.0,8.0')] ).
cnf(220,plain,
( ssList(sk7)
| equal(sk2,sk1) ),
inference(rew,[status(thm),theory(equality)],[5,18,7]),
[iquote('0:Rew:5.0,18.1,7.0,18.1')] ).
cnf(221,plain,
ssList(sk7),
inference(mrr,[status(thm)],[220,219]),
[iquote('0:MRR:220.1,219.0')] ).
cnf(222,plain,
( ssList(sk6)
| equal(sk2,sk1) ),
inference(rew,[status(thm),theory(equality)],[5,17,7]),
[iquote('0:Rew:5.0,17.1,7.0,17.1')] ).
cnf(223,plain,
ssList(sk6),
inference(mrr,[status(thm)],[222,219]),
[iquote('0:MRR:222.1,219.0')] ).
cnf(238,plain,
( ~ ssList(u)
| equal(app(u,sk2),u) ),
inference(rew,[status(thm),theory(equality)],[5,95]),
[iquote('0:Rew:5.0,95.1')] ).
cnf(252,plain,
( equal(app(app(sk6,sk1),sk7),sk2)
| equal(sk2,sk1) ),
inference(rew,[status(thm),theory(equality)],[5,20,7,6]),
[iquote('0:Rew:5.0,20.1,7.0,20.1,7.0,20.0,6.0,20.0')] ).
cnf(253,plain,
equal(app(app(sk6,sk1),sk7),sk2),
inference(mrr,[status(thm)],[252,219]),
[iquote('0:MRR:252.1,219.0')] ).
cnf(267,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(u,v),sk2)
| equal(sk2,v) ),
inference(rew,[status(thm),theory(equality)],[5,141]),
[iquote('0:Rew:5.0,141.3,5.0,141.2')] ).
cnf(507,plain,
( ~ ssList(u)
| ~ equal(app(u,sk1),sk2)
| equal(sk2,sk1) ),
inference(res,[status(thm),theory(equality)],[1,267]),
[iquote('0:Res:1.0,267.0')] ).
cnf(528,plain,
( ~ ssList(u)
| ssList(app(u,sk1)) ),
inference(res,[status(thm),theory(equality)],[1,107]),
[iquote('0:Res:1.0,107.0')] ).
cnf(641,plain,
( ~ ssList(u)
| ~ equal(app(u,sk1),sk2) ),
inference(mrr,[status(thm)],[507,219]),
[iquote('0:MRR:507.2,219.0')] ).
cnf(1521,plain,
( ~ ssList(app(sk6,sk1))
| ~ ssList(sk7)
| ~ equal(sk2,sk2)
| equal(sk7,sk2) ),
inference(spl,[status(thm),theory(equality)],[253,267]),
[iquote('0:SpL:253.0,267.2')] ).
cnf(1525,plain,
( ~ ssList(app(sk6,sk1))
| ~ ssList(sk7)
| equal(sk7,sk2) ),
inference(obv,[status(thm),theory(equality)],[1521]),
[iquote('0:Obv:1521.2')] ).
cnf(1526,plain,
equal(sk7,sk2),
inference(ssi,[status(thm)],[1525,221,528,223]),
[iquote('0:SSi:1525.1,1525.0,221.0,528.1,223.0')] ).
cnf(1528,plain,
equal(app(app(sk6,sk1),sk2),sk2),
inference(rew,[status(thm),theory(equality)],[1526,253]),
[iquote('0:Rew:1526.0,253.0')] ).
cnf(1542,plain,
( ~ ssList(app(sk6,sk1))
| equal(app(sk6,sk1),sk2) ),
inference(spr,[status(thm),theory(equality)],[1528,238]),
[iquote('0:SpR:1528.0,238.1')] ).
cnf(1548,plain,
equal(app(sk6,sk1),sk2),
inference(ssi,[status(thm)],[1542,528,223]),
[iquote('0:SSi:1542.0,528.0,223.1')] ).
cnf(1555,plain,
( ~ ssList(sk6)
| ~ equal(sk2,sk2) ),
inference(spl,[status(thm),theory(equality)],[1548,641]),
[iquote('0:SpL:1548.0,641.1')] ).
cnf(1557,plain,
~ ssList(sk6),
inference(obv,[status(thm),theory(equality)],[1555]),
[iquote('0:Obv:1555.1')] ).
cnf(1558,plain,
$false,
inference(ssi,[status(thm)],[1557,223]),
[iquote('0:SSi:1557.0,223.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWC039-1 : TPTP v8.1.0. Released v2.4.0.
% 0.08/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jun 12 02:32:41 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.55/0.74
% 0.55/0.74 SPASS V 3.9
% 0.55/0.74 SPASS beiseite: Proof found.
% 0.55/0.74 % SZS status Theorem
% 0.55/0.74 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.55/0.74 SPASS derived 1072 clauses, backtracked 0 clauses, performed 6 splits and kept 813 clauses.
% 0.55/0.74 SPASS allocated 77167 KBytes.
% 0.55/0.74 SPASS spent 0:00:00.37 on the problem.
% 0.55/0.74 0:00:00.04 for the input.
% 0.55/0.74 0:00:00.00 for the FLOTTER CNF translation.
% 0.55/0.74 0:00:00.01 for inferences.
% 0.55/0.74 0:00:00.01 for the backtracking.
% 0.55/0.74 0:00:00.17 for the reduction.
% 0.55/0.74
% 0.55/0.74
% 0.55/0.74 Here is a proof with depth 2, length 32 :
% 0.55/0.74 % SZS output start Refutation
% See solution above
% 0.55/0.74 Formulae used in the proof : co1_1 co1_5 co1_6 co1_7 co1_8 co1_17 co1_18 co1_20 clause73 clause85 clause119
% 0.55/0.74
%------------------------------------------------------------------------------