%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU145+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 14:34:19 EDT 2022
% Result : Theorem 9.13s 9.38s
% Output : Refutation 9.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of clauses : 92 ( 14 unt; 42 nHn; 92 RR)
% Number of literals : 214 ( 0 equ; 81 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
subset(skc3,skc5),
file('SEU145+1.p',unknown),
[] ).
cnf(3,axiom,
~ in(skc4,skc3),
file('SEU145+1.p',unknown),
[] ).
cnf(4,axiom,
~ subset(skc3,set_difference(skc5,singleton(skc4))),
file('SEU145+1.p',unknown),
[] ).
cnf(6,axiom,
( subset(u,v)
| in(skf4(v,u),u) ),
file('SEU145+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ in(skf4(u,v),u)
| subset(w,u) ),
file('SEU145+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ in(u,v)
| ~ subset(v,w)
| in(u,w) ),
file('SEU145+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ in(u,v)
| ~ equal(v,singleton(w))
| equal(u,w) ),
file('SEU145+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ equal(u,v)
| ~ equal(w,singleton(v))
| in(u,w) ),
file('SEU145+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ in(u,v)
| ~ equal(v,set_difference(w,x))
| in(u,w) ),
file('SEU145+1.p',unknown),
[] ).
cnf(12,axiom,
( equal(u,singleton(v))
| equal(skf3(v,u),v)
| in(skf3(v,u),u) ),
file('SEU145+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ in(u,v)
| ~ in(u,w)
| ~ equal(v,set_difference(x,w)) ),
file('SEU145+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ equal(skf3(u,v),u)
| ~ in(skf3(u,v),v)
| equal(v,singleton(u)) ),
file('SEU145+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ in(u,v)
| ~ equal(w,set_difference(v,x))
| in(u,w)
| in(u,x) ),
file('SEU145+1.p',unknown),
[] ).
cnf(16,axiom,
( equal(u,set_difference(v,w))
| in(skf5(w,v,u),u)
| in(skf5(w,v,u),v) ),
file('SEU145+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ in(skf5(u,v,w),u)
| equal(w,set_difference(v,u))
| in(skf5(u,v,w),w) ),
file('SEU145+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ in(skf5(u,v,w),v)
| ~ in(skf5(u,v,w),w)
| equal(w,set_difference(v,u))
| in(skf5(u,v,w),u) ),
file('SEU145+1.p',unknown),
[] ).
cnf(19,plain,
( ~ in(u,skc3)
| in(u,skc5) ),
inference(res,[status(thm),theory(equality)],[1,8]),
[iquote('0:Res:1.0,8.0')] ).
cnf(20,plain,
( ~ subset(u,skc3)
| ~ in(skc4,u) ),
inference(res,[status(thm),theory(equality)],[8,3]),
[iquote('0:Res:8.2,3.0')] ).
cnf(33,plain,
( ~ in(skf4(skc5,u),skc3)
| subset(v,skc5) ),
inference(res,[status(thm),theory(equality)],[19,7]),
[iquote('0:Res:19.1,7.0')] ).
cnf(42,plain,
( ~ equal(u,v)
| in(u,singleton(v)) ),
inference(eqr,[status(thm),theory(equality)],[10]),
[iquote('0:EqR:10.1')] ).
cnf(43,plain,
( ~ equal(u,v)
| ~ subset(singleton(v),w)
| in(u,w) ),
inference(res,[status(thm),theory(equality)],[42,8]),
[iquote('0:Res:42.1,8.0')] ).
cnf(49,plain,
( ~ in(u,singleton(v))
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[9]),
[iquote('0:EqR:9.1')] ).
cnf(51,plain,
( subset(singleton(u),v)
| equal(skf4(v,singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[6,49]),
[iquote('0:Res:6.1,49.0')] ).
cnf(52,plain,
( subset(singleton(u),v)
| subset(singleton(u),v)
| in(u,singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[51,6]),
[iquote('0:SpR:51.1,6.1')] ).
cnf(55,plain,
( ~ in(u,skc3)
| subset(singleton(u),skc5)
| subset(v,skc5) ),
inference(spl,[status(thm),theory(equality)],[51,33]),
[iquote('0:SpL:51.1,33.0')] ).
cnf(56,plain,
( ~ in(u,v)
| subset(singleton(u),v)
| subset(w,v) ),
inference(spl,[status(thm),theory(equality)],[51,7]),
[iquote('0:SpL:51.1,7.0')] ).
cnf(57,plain,
( ~ in(u,skc3)
| subset(singleton(u),skc5) ),
inference(con,[status(thm)],[55]),
[iquote('0:Con:55.2')] ).
cnf(58,plain,
( ~ in(u,v)
| subset(singleton(u),v) ),
inference(con,[status(thm)],[56]),
[iquote('0:Con:56.2')] ).
cnf(59,plain,
( subset(singleton(u),v)
| in(u,singleton(u)) ),
inference(obv,[status(thm),theory(equality)],[52]),
[iquote('0:Obv:52.0')] ).
cnf(61,plain,
( ~ in(u,set_difference(v,w))
| in(u,v) ),
inference(eqr,[status(thm),theory(equality)],[11]),
[iquote('0:EqR:11.1')] ).
cnf(62,plain,
( ~ in(u,skc3)
| ~ in(skc4,singleton(u)) ),
inference(res,[status(thm),theory(equality)],[58,20]),
[iquote('0:Res:58.1,20.0')] ).
cnf(68,plain,
( ~ equal(skc4,u)
| ~ in(u,skc3) ),
inference(res,[status(thm),theory(equality)],[42,62]),
[iquote('0:Res:42.1,62.1')] ).
cnf(70,plain,
( ~ in(u,set_difference(v,w))
| ~ in(u,w) ),
inference(eqr,[status(thm),theory(equality)],[13]),
[iquote('0:EqR:13.2')] ).
cnf(90,plain,
( equal(singleton(u),singleton(v))
| equal(skf3(v,singleton(u)),v)
| equal(skf3(v,singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[12,49]),
[iquote('0:Res:12.2,49.0')] ).
cnf(99,plain,
( ~ equal(skf3(u,singleton(v)),v)
| ~ equal(skf3(u,singleton(v)),u)
| equal(singleton(v),singleton(u)) ),
inference(res,[status(thm),theory(equality)],[42,14]),
[iquote('0:Res:42.1,14.1')] ).
cnf(106,plain,
( ~ in(u,v)
| in(u,set_difference(v,w))
| in(u,w) ),
inference(eqr,[status(thm),theory(equality)],[15]),
[iquote('0:EqR:15.1')] ).
cnf(107,plain,
( ~ in(skf4(u,set_difference(v,w)),w)
| subset(set_difference(v,w),u) ),
inference(res,[status(thm),theory(equality)],[6,70]),
[iquote('0:Res:6.1,70.0')] ).
cnf(125,plain,
( equal(set_difference(u,v),u)
| in(skf5(v,u,u),u) ),
inference(fac,[status(thm)],[16]),
[iquote('0:Fac:16.1,16.2')] ).
cnf(141,plain,
( equal(u,set_difference(set_difference(v,w),x))
| in(skf5(x,set_difference(v,w),u),u)
| in(skf5(x,set_difference(v,w),u),v) ),
inference(res,[status(thm),theory(equality)],[16,61]),
[iquote('0:Res:16.2,61.0')] ).
cnf(148,plain,
( equal(set_difference(singleton(u),v),singleton(u))
| equal(skf5(v,singleton(u),singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[125,49]),
[iquote('0:Res:125.1,49.0')] ).
cnf(155,plain,
( equal(u,set_difference(v,v))
| in(skf5(v,v,u),u)
| equal(u,set_difference(v,v))
| in(skf5(v,v,u),u) ),
inference(res,[status(thm),theory(equality)],[16,17]),
[iquote('0:Res:16.2,17.0')] ).
cnf(157,plain,
( equal(u,set_difference(v,v))
| in(skf5(v,v,u),u) ),
inference(obv,[status(thm),theory(equality)],[155]),
[iquote('0:Obv:155.1')] ).
cnf(165,plain,
( ~ in(skf5(u,u,set_difference(v,w)),w)
| equal(set_difference(v,w),set_difference(u,u)) ),
inference(res,[status(thm),theory(equality)],[157,70]),
[iquote('0:Res:157.1,70.0')] ).
cnf(166,plain,
( equal(set_difference(u,v),set_difference(w,w))
| in(skf5(w,w,set_difference(u,v)),u) ),
inference(res,[status(thm),theory(equality)],[157,61]),
[iquote('0:Res:157.1,61.0')] ).
cnf(178,plain,
( ~ in(skf5(u,v,v),v)
| equal(set_difference(v,u),v)
| equal(set_difference(v,u),v)
| in(skf5(u,v,v),u) ),
inference(res,[status(thm),theory(equality)],[125,18]),
[iquote('0:Res:125.1,18.0')] ).
cnf(181,plain,
( ~ in(skf5(u,v,v),v)
| equal(set_difference(v,u),v)
| in(skf5(u,v,v),u) ),
inference(obv,[status(thm),theory(equality)],[178]),
[iquote('0:Obv:178.1')] ).
cnf(182,plain,
( equal(set_difference(u,v),u)
| in(skf5(v,u,u),v) ),
inference(mrr,[status(thm)],[181,125]),
[iquote('0:MRR:181.0,125.1')] ).
cnf(185,plain,
( ~ equal(skf5(skc3,u,u),skc4)
| equal(set_difference(u,skc3),u) ),
inference(res,[status(thm),theory(equality)],[182,68]),
[iquote('0:Res:182.1,68.1')] ).
cnf(188,plain,
( equal(set_difference(u,singleton(v)),u)
| equal(skf5(singleton(v),u,u),v) ),
inference(res,[status(thm),theory(equality)],[182,49]),
[iquote('0:Res:182.1,49.0')] ).
cnf(189,plain,
( ~ in(skf5(set_difference(u,v),w,w),v)
| equal(set_difference(w,set_difference(u,v)),w) ),
inference(res,[status(thm),theory(equality)],[182,70]),
[iquote('0:Res:182.1,70.0')] ).
cnf(195,plain,
( ~ equal(u,v)
| in(v,singleton(v))
| in(u,w) ),
inference(res,[status(thm),theory(equality)],[59,43]),
[iquote('0:Res:59.0,43.1')] ).
cnf(197,plain,
( ~ in(u,skc3)
| ~ equal(v,u)
| in(v,skc5) ),
inference(res,[status(thm),theory(equality)],[57,43]),
[iquote('0:Res:57.1,43.1')] ).
cnf(220,plain,
( ~ equal(u,skf4(v,skc3))
| subset(skc3,v)
| in(u,skc5) ),
inference(res,[status(thm),theory(equality)],[6,197]),
[iquote('0:Res:6.1,197.0')] ).
cnf(229,plain,
( in(u,singleton(u))
| in(u,v) ),
inference(eqr,[status(thm),theory(equality)],[195]),
[iquote('0:EqR:195.0')] ).
cnf(230,plain,
in(u,singleton(u)),
inference(con,[status(thm)],[229]),
[iquote('0:Con:229.1')] ).
cnf(235,plain,
( ~ in(skf4(set_difference(u,v),w),u)
| in(skf4(set_difference(u,v),w),v)
| subset(x,set_difference(u,v)) ),
inference(res,[status(thm),theory(equality)],[106,7]),
[iquote('0:Res:106.1,7.0')] ).
cnf(271,plain,
( subset(skc3,u)
| in(skf4(u,skc3),skc5) ),
inference(eqr,[status(thm),theory(equality)],[220]),
[iquote('0:EqR:220.0')] ).
cnf(486,plain,
( equal(set_difference(u,singleton(v)),u)
| equal(set_difference(u,singleton(v)),u)
| in(v,u) ),
inference(spr,[status(thm),theory(equality)],[188,125]),
[iquote('0:SpR:188.1,125.1')] ).
cnf(500,plain,
( equal(set_difference(u,singleton(v)),u)
| in(v,u) ),
inference(obv,[status(thm),theory(equality)],[486]),
[iquote('0:Obv:486.0')] ).
cnf(528,plain,
( ~ in(u,v)
| ~ equal(v,w)
| in(x,w)
| in(u,w) ),
inference(spl,[status(thm),theory(equality)],[500,11]),
[iquote('0:SpL:500.0,11.1')] ).
cnf(538,plain,
( ~ in(u,v)
| ~ equal(v,w)
| in(u,w) ),
inference(con,[status(thm)],[528]),
[iquote('0:Con:528.2')] ).
cnf(727,plain,
( ~ equal(u,skc4)
| equal(set_difference(singleton(u),skc3),singleton(u))
| equal(set_difference(singleton(u),skc3),singleton(u)) ),
inference(spl,[status(thm),theory(equality)],[148,185]),
[iquote('0:SpL:148.1,185.0')] ).
cnf(735,plain,
( ~ equal(u,skc4)
| equal(set_difference(singleton(u),skc3),singleton(u)) ),
inference(obv,[status(thm),theory(equality)],[727]),
[iquote('0:Obv:727.1')] ).
cnf(955,plain,
( ~ equal(singleton(u),v)
| in(u,v) ),
inference(res,[status(thm),theory(equality)],[230,538]),
[iquote('0:Res:230.0,538.0')] ).
cnf(1200,plain,
( equal(set_difference(u,u),set_difference(v,v))
| equal(set_difference(u,u),set_difference(v,v)) ),
inference(res,[status(thm),theory(equality)],[166,165]),
[iquote('0:Res:166.1,165.0')] ).
cnf(1204,plain,
equal(set_difference(u,u),set_difference(v,v)),
inference(obv,[status(thm),theory(equality)],[1200]),
[iquote('0:Obv:1200.0')] ).
cnf(1272,plain,
( ~ in(u,set_difference(v,v))
| ~ in(u,w) ),
inference(spl,[status(thm),theory(equality)],[1204,70]),
[iquote('0:SpL:1204.0,70.0')] ).
cnf(1311,plain,
~ in(u,set_difference(v,v)),
inference(con,[status(thm)],[1272]),
[iquote('0:Con:1272.1')] ).
cnf(1323,plain,
~ equal(singleton(u),set_difference(v,v)),
inference(res,[status(thm),theory(equality)],[955,1311]),
[iquote('0:Res:955.1,1311.0')] ).
cnf(1764,plain,
( ~ equal(u,v)
| equal(singleton(v),singleton(u))
| equal(skf3(u,singleton(v)),v) ),
inference(eqf,[status(thm),theory(equality)],[90]),
[iquote('0:EqF:90.1,90.2')] ).
cnf(4396,plain,
( subset(skc3,set_difference(skc5,u))
| in(skf4(set_difference(skc5,u),skc3),u)
| subset(v,set_difference(skc5,u)) ),
inference(res,[status(thm),theory(equality)],[271,235]),
[iquote('0:Res:271.1,235.0')] ).
cnf(4398,plain,
( subset(skc3,set_difference(skc5,u))
| in(skf4(set_difference(skc5,u),skc3),u) ),
inference(con,[status(thm)],[4396]),
[iquote('0:Con:4396.2')] ).
cnf(5134,plain,
( equal(u,set_difference(set_difference(v,w),v))
| in(skf5(v,set_difference(v,w),u),u)
| equal(u,set_difference(set_difference(v,w),v))
| in(skf5(v,set_difference(v,w),u),u) ),
inference(res,[status(thm),theory(equality)],[141,17]),
[iquote('0:Res:141.2,17.0')] ).
cnf(5188,plain,
( equal(u,set_difference(set_difference(v,w),v))
| in(skf5(v,set_difference(v,w),u),u) ),
inference(obv,[status(thm),theory(equality)],[5134]),
[iquote('0:Obv:5134.1')] ).
cnf(10120,plain,
( ~ equal(u,v)
| ~ equal(v,v)
| ~ equal(skf3(u,singleton(v)),u)
| equal(singleton(v),singleton(u))
| equal(singleton(v),singleton(u)) ),
inference(spl,[status(thm),theory(equality)],[1764,99]),
[iquote('0:SpL:1764.2,99.0')] ).
cnf(10123,plain,
( ~ equal(u,v)
| ~ equal(skf3(u,singleton(v)),u)
| equal(singleton(v),singleton(u)) ),
inference(obv,[status(thm),theory(equality)],[10120]),
[iquote('0:Obv:10120.3')] ).
cnf(10124,plain,
( ~ equal(u,v)
| ~ equal(v,u)
| equal(singleton(v),singleton(u)) ),
inference(rew,[status(thm),theory(equality)],[1764,10123]),
[iquote('0:Rew:1764.2,10123.1')] ).
cnf(10125,plain,
( ~ equal(u,v)
| equal(singleton(u),singleton(v)) ),
inference(obv,[status(thm),theory(equality)],[10124]),
[iquote('0:Obv:10124.0')] ).
cnf(10234,plain,
( ~ equal(skc4,u)
| ~ subset(skc3,set_difference(skc5,singleton(u))) ),
inference(spl,[status(thm),theory(equality)],[10125,4]),
[iquote('0:SpL:10125.1,4.0')] ).
cnf(11753,plain,
( equal(singleton(u),set_difference(set_difference(v,w),v))
| equal(skf5(v,set_difference(v,w),singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[5188,49]),
[iquote('0:Res:5188.1,49.0')] ).
cnf(11756,plain,
equal(set_difference(u,u),set_difference(set_difference(v,w),v)),
inference(res,[status(thm),theory(equality)],[5188,1311]),
[iquote('0:Res:5188.1,1311.0')] ).
cnf(11982,plain,
~ equal(singleton(u),set_difference(set_difference(v,w),v)),
inference(spl,[status(thm),theory(equality)],[11756,1323]),
[iquote('0:SpL:11756.0,1323.0')] ).
cnf(12051,plain,
equal(skf5(u,set_difference(u,v),singleton(w)),w),
inference(mrr,[status(thm)],[11753,11982]),
[iquote('0:MRR:11753.0,11982.0')] ).
cnf(14456,plain,
( equal(set_difference(u,set_difference(v,u)),u)
| equal(set_difference(u,set_difference(v,u)),u) ),
inference(res,[status(thm),theory(equality)],[125,189]),
[iquote('0:Res:125.1,189.0')] ).
cnf(14470,plain,
equal(set_difference(u,set_difference(v,u)),u),
inference(obv,[status(thm),theory(equality)],[14456]),
[iquote('0:Obv:14456.0')] ).
cnf(14623,plain,
( ~ in(skf4(u,v),set_difference(w,v))
| subset(set_difference(v,set_difference(w,v)),u) ),
inference(spl,[status(thm),theory(equality)],[14470,107]),
[iquote('0:SpL:14470.0,107.0')] ).
cnf(14689,plain,
( ~ in(skf4(u,v),set_difference(w,v))
| subset(v,u) ),
inference(rew,[status(thm),theory(equality)],[14470,14623]),
[iquote('0:Rew:14470.0,14623.1')] ).
cnf(23831,plain,
( subset(skc3,set_difference(skc5,set_difference(u,skc3)))
| subset(skc3,set_difference(skc5,set_difference(u,skc3))) ),
inference(res,[status(thm),theory(equality)],[4398,14689]),
[iquote('0:Res:4398.1,14689.0')] ).
cnf(23844,plain,
subset(skc3,set_difference(skc5,set_difference(u,skc3))),
inference(obv,[status(thm),theory(equality)],[23831]),
[iquote('0:Obv:23831.0')] ).
cnf(23868,plain,
( ~ equal(u,skc4)
| subset(skc3,set_difference(skc5,singleton(u))) ),
inference(spr,[status(thm),theory(equality)],[735,23844]),
[iquote('0:SpR:735.1,23844.0')] ).
cnf(23897,plain,
~ equal(u,skc4),
inference(mrr,[status(thm)],[23868,10234]),
[iquote('0:MRR:23868.1,10234.1')] ).
cnf(23898,plain,
$false,
inference(unc,[status(thm)],[23897,12051]),
[iquote('0:UnC:23897.0,12051.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU145+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n008.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 19 08:05:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 9.13/9.38
% 9.13/9.38 SPASS V 3.9
% 9.13/9.38 SPASS beiseite: Proof found.
% 9.13/9.38 % SZS status Theorem
% 9.13/9.38 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.13/9.38 SPASS derived 19501 clauses, backtracked 323 clauses, performed 2 splits and kept 5457 clauses.
% 9.13/9.38 SPASS allocated 102894 KBytes.
% 9.13/9.38 SPASS spent 0:00:09.03 on the problem.
% 9.13/9.38 0:00:00.03 for the input.
% 9.13/9.38 0:00:00.04 for the FLOTTER CNF translation.
% 9.13/9.38 0:00:00.23 for inferences.
% 9.13/9.38 0:00:00.33 for the backtracking.
% 9.13/9.38 0:00:08.32 for the reduction.
% 9.13/9.38
% 9.13/9.38
% 9.13/9.38 Here is a proof with depth 9, length 92 :
% 9.13/9.38 % SZS output start Refutation
% See solution above
% 9.35/9.52 Formulae used in the proof : l3_zfmisc_1 d3_tarski d1_tarski d4_xboole_0
% 9.35/9.52
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