TSTP Solution File: SWC030-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC030-1 : 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 22:01:13 EDT 2022
% Result : Unsatisfiable 2.73s 2.95s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of clauses : 50 ( 33 unt; 2 nHn; 50 RR)
% Number of literals : 83 ( 0 equ; 38 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 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(5,axiom,
equal(sk2,sk4),
file('SWC030-1.p',unknown),
[] ).
cnf(6,axiom,
equal(sk1,sk3),
file('SWC030-1.p',unknown),
[] ).
cnf(7,axiom,
ssList(sk5),
file('SWC030-1.p',unknown),
[] ).
cnf(8,axiom,
ssList(sk6),
file('SWC030-1.p',unknown),
[] ).
cnf(9,axiom,
equal(app(sk5,sk6),sk4),
file('SWC030-1.p',unknown),
[] ).
cnf(10,axiom,
equal(app(sk6,sk5),sk3),
file('SWC030-1.p',unknown),
[] ).
cnf(11,axiom,
( equal(nil,sk2)
| equal(nil,sk1) ),
file('SWC030-1.p',unknown),
[] ).
cnf(14,axiom,
( ~ equal(nil,sk1)
| ~ equal(nil,sk2) ),
file('SWC030-1.p',unknown),
[] ).
cnf(87,axiom,
( ~ ssList(u)
| equal(app(u,nil),u) ),
file('SWC030-1.p',unknown),
[] ).
cnf(88,axiom,
( ~ ssList(u)
| equal(app(nil,u),u) ),
file('SWC030-1.p',unknown),
[] ).
cnf(132,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(u,v),nil)
| equal(nil,u) ),
file('SWC030-1.p',unknown),
[] ).
cnf(133,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(u,v),nil)
| equal(nil,v) ),
file('SWC030-1.p',unknown),
[] ).
cnf(202,plain,
( equal(nil,sk3)
| equal(nil,sk4) ),
inference(rew,[status(thm),theory(equality)],[6,11,5]),
[iquote('0:Rew:6.0,11.1,5.0,11.0')] ).
cnf(203,plain,
( ~ equal(nil,sk4)
| ~ equal(nil,sk3) ),
inference(rew,[status(thm),theory(equality)],[5,14,6]),
[iquote('0:Rew:5.0,14.1,6.0,14.0')] ).
cnf(458,plain,
equal(app(sk5,nil),sk5),
inference(res,[status(thm),theory(equality)],[7,87]),
[iquote('0:Res:7.0,87.0')] ).
cnf(459,plain,
equal(app(nil,sk5),sk5),
inference(res,[status(thm),theory(equality)],[7,88]),
[iquote('0:Res:7.0,88.0')] ).
cnf(758,plain,
equal(nil,sk3),
inference(spt,[spt(split,[position(s1)])],[202]),
[iquote('1:Spt:202.0')] ).
cnf(759,plain,
( ~ equal(sk4,sk3)
| ~ equal(nil,sk3) ),
inference(rew,[status(thm),theory(equality)],[758,203]),
[iquote('1:Rew:758.0,203.0')] ).
cnf(776,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(u,v),nil)
| equal(sk3,u) ),
inference(rew,[status(thm),theory(equality)],[758,132]),
[iquote('1:Rew:758.0,132.3')] ).
cnf(844,plain,
equal(app(sk3,sk5),sk5),
inference(rew,[status(thm),theory(equality)],[758,459]),
[iquote('1:Rew:758.0,459.0')] ).
cnf(845,plain,
equal(app(sk5,sk3),sk5),
inference(rew,[status(thm),theory(equality)],[758,458]),
[iquote('1:Rew:758.0,458.0')] ).
cnf(885,plain,
( ~ equal(sk4,sk3)
| ~ equal(sk3,sk3) ),
inference(rew,[status(thm),theory(equality)],[758,759]),
[iquote('1:Rew:758.0,759.1')] ).
cnf(886,plain,
~ equal(sk4,sk3),
inference(obv,[status(thm),theory(equality)],[885]),
[iquote('1:Obv:885.1')] ).
cnf(901,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(u,v),sk3)
| equal(sk3,u) ),
inference(rew,[status(thm),theory(equality)],[758,776]),
[iquote('1:Rew:758.0,776.2')] ).
cnf(4437,plain,
( ~ ssList(sk6)
| ~ ssList(sk5)
| ~ equal(sk3,sk3)
| equal(sk6,sk3) ),
inference(spl,[status(thm),theory(equality)],[10,901]),
[iquote('1:SpL:10.0,901.2')] ).
cnf(4445,plain,
( ~ ssList(sk6)
| ~ ssList(sk5)
| equal(sk6,sk3) ),
inference(obv,[status(thm),theory(equality)],[4437]),
[iquote('1:Obv:4437.2')] ).
cnf(4918,plain,
equal(sk6,sk3),
inference(mrr,[status(thm)],[4445,8,7]),
[iquote('1:MRR:4445.0,4445.1,8.0,7.0')] ).
cnf(4938,plain,
equal(app(sk5,sk3),sk4),
inference(rew,[status(thm),theory(equality)],[4918,9]),
[iquote('1:Rew:4918.0,9.0')] ).
cnf(4939,plain,
equal(app(sk3,sk5),sk3),
inference(rew,[status(thm),theory(equality)],[4918,10]),
[iquote('1:Rew:4918.0,10.0')] ).
cnf(4950,plain,
equal(sk5,sk4),
inference(rew,[status(thm),theory(equality)],[845,4938]),
[iquote('1:Rew:845.0,4938.0')] ).
cnf(4969,plain,
equal(app(sk3,sk4),sk4),
inference(rew,[status(thm),theory(equality)],[4950,844]),
[iquote('1:Rew:4950.0,844.0')] ).
cnf(4988,plain,
equal(app(sk3,sk4),sk3),
inference(rew,[status(thm),theory(equality)],[4950,4939]),
[iquote('1:Rew:4950.0,4939.0')] ).
cnf(4989,plain,
equal(sk4,sk3),
inference(rew,[status(thm),theory(equality)],[4988,4969]),
[iquote('1:Rew:4988.0,4969.0')] ).
cnf(4990,plain,
$false,
inference(mrr,[status(thm)],[4989,886]),
[iquote('1:MRR:4989.0,886.0')] ).
cnf(5291,plain,
~ equal(nil,sk3),
inference(spt,[spt(split,[position(sa)])],[4990,758]),
[iquote('1:Spt:4990.0,202.0,758.0')] ).
cnf(5292,plain,
equal(nil,sk4),
inference(spt,[spt(split,[position(s2)])],[202]),
[iquote('1:Spt:4990.0,202.1')] ).
cnf(5316,plain,
~ equal(sk4,sk3),
inference(rew,[status(thm),theory(equality)],[5292,5291]),
[iquote('1:Rew:5292.0,5291.0')] ).
cnf(5319,plain,
equal(app(sk5,sk4),sk5),
inference(rew,[status(thm),theory(equality)],[5292,458]),
[iquote('1:Rew:5292.0,458.0')] ).
cnf(5320,plain,
equal(app(sk4,sk5),sk5),
inference(rew,[status(thm),theory(equality)],[5292,459]),
[iquote('1:Rew:5292.0,459.0')] ).
cnf(5405,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(u,v),sk4)
| equal(sk4,v) ),
inference(rew,[status(thm),theory(equality)],[5292,133]),
[iquote('1:Rew:5292.0,133.3,5292.0,133.2')] ).
cnf(7150,plain,
( ~ ssList(sk5)
| ~ ssList(sk6)
| ~ equal(sk4,sk4)
| equal(sk6,sk4) ),
inference(spl,[status(thm),theory(equality)],[9,5405]),
[iquote('1:SpL:9.0,5405.2')] ).
cnf(7155,plain,
( ~ ssList(sk5)
| ~ ssList(sk6)
| equal(sk6,sk4) ),
inference(obv,[status(thm),theory(equality)],[7150]),
[iquote('1:Obv:7150.2')] ).
cnf(7643,plain,
equal(sk6,sk4),
inference(mrr,[status(thm)],[7155,7,8]),
[iquote('1:MRR:7155.0,7155.1,7.0,8.0')] ).
cnf(7663,plain,
equal(app(sk4,sk5),sk3),
inference(rew,[status(thm),theory(equality)],[7643,10]),
[iquote('1:Rew:7643.0,10.0')] ).
cnf(7664,plain,
equal(app(sk5,sk4),sk4),
inference(rew,[status(thm),theory(equality)],[7643,9]),
[iquote('1:Rew:7643.0,9.0')] ).
cnf(7681,plain,
equal(sk5,sk3),
inference(rew,[status(thm),theory(equality)],[5320,7663]),
[iquote('1:Rew:5320.0,7663.0')] ).
cnf(7698,plain,
equal(app(sk3,sk4),sk3),
inference(rew,[status(thm),theory(equality)],[7681,5319]),
[iquote('1:Rew:7681.0,5319.0')] ).
cnf(7715,plain,
equal(app(sk3,sk4),sk4),
inference(rew,[status(thm),theory(equality)],[7681,7664]),
[iquote('1:Rew:7681.0,7664.0')] ).
cnf(7717,plain,
equal(sk4,sk3),
inference(rew,[status(thm),theory(equality)],[7715,7698]),
[iquote('1:Rew:7715.0,7698.0')] ).
cnf(7718,plain,
$false,
inference(mrr,[status(thm)],[7717,5316]),
[iquote('1:MRR:7717.0,5316.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWC030-1 : TPTP v8.1.0. Released v2.4.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.31 % Computer : n018.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 600
% 0.12/0.31 % DateTime : Sun Jun 12 13:22:41 EDT 2022
% 0.16/0.31 % CPUTime :
% 2.73/2.95
% 2.73/2.95 SPASS V 3.9
% 2.73/2.95 SPASS beiseite: Proof found.
% 2.73/2.95 % SZS status Theorem
% 2.73/2.95 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.73/2.95 SPASS derived 4904 clauses, backtracked 3948 clauses, performed 43 splits and kept 6845 clauses.
% 2.73/2.95 SPASS allocated 80864 KBytes.
% 2.73/2.95 SPASS spent 0:00:02.40 on the problem.
% 2.73/2.95 0:00:00.04 for the input.
% 2.73/2.95 0:00:00.00 for the FLOTTER CNF translation.
% 2.73/2.95 0:00:00.02 for inferences.
% 2.73/2.95 0:00:00.05 for the backtracking.
% 2.73/2.95 0:00:02.10 for the reduction.
% 2.73/2.95
% 2.73/2.95
% 2.73/2.95 Here is a proof with depth 1, length 50 :
% 2.73/2.95 % SZS output start Refutation
% See solution above
% 2.73/2.95 Formulae used in the proof : co1_5 co1_6 co1_7 co1_8 co1_9 co1_10 co1_11 co1_14 clause73 clause74 clause118 clause119
% 2.73/2.95
%------------------------------------------------------------------------------