%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC242-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 22:02:45 EDT 2022
% Result : Unsatisfiable 24.95s 25.16s
% Output : Refutation 24.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of clauses : 45 ( 14 unt; 7 nHn; 45 RR)
% Number of literals : 123 ( 0 equ; 85 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(sk1),
file('SWC242-1.p',unknown),
[] ).
cnf(6,axiom,
equal(sk3,sk1),
file('SWC242-1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(nil,sk1),
file('SWC242-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ equal(app(app(v,cons(w,nil)),u),sk1)
| lt(w,sk5(u,v,w)) ),
file('SWC242-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ leq(w,sk5(u,v,w))
| ~ equal(app(app(v,cons(w,nil)),u),sk1) ),
file('SWC242-1.p',unknown),
[] ).
cnf(14,axiom,
( equal(sk3,nil)
| ssList(sk7) ),
file('SWC242-1.p',unknown),
[] ).
cnf(15,axiom,
( equal(sk3,nil)
| ssList(sk8) ),
file('SWC242-1.p',unknown),
[] ).
cnf(16,axiom,
( equal(sk3,nil)
| equal(app(app(sk7,cons(sk6,nil)),sk8),sk3) ),
file('SWC242-1.p',unknown),
[] ).
cnf(64,axiom,
ssItem(skaf44(u)),
file('SWC242-1.p',unknown),
[] ).
cnf(89,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC242-1.p',unknown),
[] ).
cnf(102,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC242-1.p',unknown),
[] ).
cnf(103,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC242-1.p',unknown),
[] ).
cnf(120,axiom,
( ~ ssItem(u)
| ~ ssItem(v)
| ~ lt(u,v)
| leq(u,v) ),
file('SWC242-1.p',unknown),
[] ).
cnf(174,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC242-1.p',unknown),
[] ).
cnf(196,axiom,
( ~ ssList(u)
| ~ duplicatefreeP(u)
| ~ ssItem(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ ssList(y)
| ~ equal(app(app(w,cons(v,x)),cons(v,y)),u) ),
file('SWC242-1.p',unknown),
[] ).
cnf(205,plain,
( equal(nil,sk1)
| ssList(sk8) ),
inference(rew,[status(thm),theory(equality)],[6,15]),
[iquote('0:Rew:6.0,15.0')] ).
cnf(206,plain,
ssList(sk8),
inference(mrr,[status(thm)],[205,7]),
[iquote('0:MRR:205.0,7.0')] ).
cnf(207,plain,
( equal(nil,sk1)
| ssList(sk7) ),
inference(rew,[status(thm),theory(equality)],[6,14]),
[iquote('0:Rew:6.0,14.0')] ).
cnf(208,plain,
ssList(sk7),
inference(mrr,[status(thm)],[207,7]),
[iquote('0:MRR:207.0,7.0')] ).
cnf(211,plain,
( equal(nil,sk1)
| equal(app(app(sk7,cons(sk6,nil)),sk8),sk1) ),
inference(rew,[status(thm),theory(equality)],[6,16]),
[iquote('0:Rew:6.0,16.1,6.0,16.0')] ).
cnf(212,plain,
equal(app(app(sk7,cons(sk6,nil)),sk8),sk1),
inference(mrr,[status(thm)],[211,7]),
[iquote('0:MRR:211.0,7.0')] ).
cnf(542,plain,
( ~ ssItem(u)
| ssList(cons(u,sk1)) ),
inference(res,[status(thm),theory(equality)],[1,103]),
[iquote('0:Res:1.0,103.1')] ).
cnf(599,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[89]),
[iquote('1:Spt:89.1')] ).
cnf(638,plain,
( ~ lt(u,v)
| leq(u,v) ),
inference(mrr,[status(thm)],[120,599]),
[iquote('1:MRR:120.1,120.0,599.0')] ).
cnf(810,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(app(v,cons(w,nil)),u),sk1)
| lt(w,sk5(u,v,w)) ),
inference(mrr,[status(thm)],[11,599]),
[iquote('1:MRR:11.2,599.0')] ).
cnf(813,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ leq(w,sk5(u,v,w))
| ~ equal(app(app(v,cons(w,nil)),u),sk1) ),
inference(mrr,[status(thm)],[12,599]),
[iquote('1:MRR:12.2,599.0')] ).
cnf(9088,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| ~ equal(sk1,sk1)
| lt(sk6,sk5(sk8,sk7,sk6)) ),
inference(spl,[status(thm),theory(equality)],[212,810]),
[iquote('1:SpL:212.0,810.2')] ).
cnf(9090,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| lt(sk6,sk5(sk8,sk7,sk6)) ),
inference(obv,[status(thm),theory(equality)],[9088]),
[iquote('1:Obv:9088.2')] ).
cnf(9091,plain,
lt(sk6,sk5(sk8,sk7,sk6)),
inference(ssi,[status(thm)],[9090,208,206]),
[iquote('1:SSi:9090.1,9090.0,208.0,206.0')] ).
cnf(9272,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| ~ leq(sk6,sk5(sk8,sk7,sk6))
| ~ equal(sk1,sk1) ),
inference(spl,[status(thm),theory(equality)],[212,813]),
[iquote('1:SpL:212.0,813.3')] ).
cnf(9274,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| ~ leq(sk6,sk5(sk8,sk7,sk6)) ),
inference(obv,[status(thm),theory(equality)],[9272]),
[iquote('1:Obv:9272.3')] ).
cnf(9275,plain,
~ leq(sk6,sk5(sk8,sk7,sk6)),
inference(ssi,[status(thm)],[9274,208,206]),
[iquote('1:SSi:9274.1,9274.0,208.0,206.0')] ).
cnf(9702,plain,
~ lt(sk6,sk5(sk8,sk7,sk6)),
inference(res,[status(thm),theory(equality)],[638,9275]),
[iquote('1:Res:638.1,9275.0')] ).
cnf(9703,plain,
$false,
inference(mrr,[status(thm)],[9702,9091]),
[iquote('1:MRR:9702.0,9091.0')] ).
cnf(9704,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[89]),
[iquote('1:Spt:9703.0,89.0,89.2')] ).
cnf(9733,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ ssList(y)
| ~ equal(app(app(w,cons(v,x)),cons(v,y)),u) ),
inference(mrr,[status(thm)],[196,9704]),
[iquote('1:MRR:196.1,9704.1')] ).
cnf(40961,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ ssList(cons(w,v))
| ~ ssList(u)
| ssList(cons(w,app(v,u))) ),
inference(spr,[status(thm),theory(equality)],[174,102]),
[iquote('0:SpR:174.3,102.2')] ).
cnf(41003,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[40961]),
[iquote('0:Obv:40961.0')] ).
cnf(41004,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[41003,103]),
[iquote('0:SSi:41003.2,103.2')] ).
cnf(43076,plain,
( ~ ssList(app(app(u,cons(v,w)),cons(v,x)))
| ~ ssItem(v)
| ~ ssList(u)
| ~ ssList(w)
| ~ ssList(x) ),
inference(eqr,[status(thm),theory(equality)],[9733]),
[iquote('1:EqR:9733.5')] ).
cnf(43109,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[43076,102,103]),
[iquote('1:SSi:43076.0,102.2,102.2,103.2,103.2')] ).
cnf(43111,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[41004,43109]),
[iquote('1:MRR:41004.3,43109.1')] ).
cnf(43114,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[43111]),
[iquote('1:Con:43111.2')] ).
cnf(43116,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[542,43114]),
[iquote('1:MRR:542.1,43114.0')] ).
cnf(43120,plain,
$false,
inference(unc,[status(thm)],[43116,64]),
[iquote('1:UnC:43116.0,64.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC242-1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n023.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 Jun 12 06:17:06 EDT 2022
% 0.12/0.34 % CPUTime :
% 24.95/25.16
% 24.95/25.16 SPASS V 3.9
% 24.95/25.16 SPASS beiseite: Proof found.
% 24.95/25.16 % SZS status Theorem
% 24.95/25.16 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.95/25.16 SPASS derived 31093 clauses, backtracked 6425 clauses, performed 88 splits and kept 18023 clauses.
% 24.95/25.16 SPASS allocated 105618 KBytes.
% 24.95/25.16 SPASS spent 0:0:18.05 on the problem.
% 24.95/25.16 0:00:00.04 for the input.
% 24.95/25.16 0:00:00.00 for the FLOTTER CNF translation.
% 24.95/25.16 0:00:00.30 for inferences.
% 24.95/25.16 0:00:00.66 for the backtracking.
% 24.95/25.16 0:0:16.67 for the reduction.
% 24.95/25.16
% 24.95/25.16
% 24.95/25.16 Here is a proof with depth 2, length 45 :
% 24.95/25.16 % SZS output start Refutation
% See solution above
% 24.95/25.16 Formulae used in the proof : co1_1 co1_6 co1_7 co1_11 co1_12 co1_14 co1_15 co1_16 clause47 clause72 clause85 clause86 clause103 clause157 clause179
% 24.95/25.16
%------------------------------------------------------------------------------