%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET935+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 05:29:56 EDT 2022
% Result : Theorem 0.38s 0.60s
% Output : Refutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of clauses : 41 ( 21 unt; 6 nHn; 41 RR)
% Number of literals : 69 ( 0 equ; 26 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
subset(u,u),
file('SET935+1.p',unknown),
[] ).
cnf(5,axiom,
~ inclusion_comparable(skc4,skc5),
file('SET935+1.p',unknown),
[] ).
cnf(7,axiom,
subset(u,set_union2(u,v)),
file('SET935+1.p',unknown),
[] ).
cnf(8,axiom,
equal(set_union2(u,v),set_union2(v,u)),
file('SET935+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ subset(u,v)
| inclusion_comparable(u,v) ),
file('SET935+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ subset(u,v)
| inclusion_comparable(v,u) ),
file('SET935+1.p',unknown),
[] ).
cnf(17,axiom,
equal(set_union2(powerset(skc4),powerset(skc5)),powerset(set_union2(skc4,skc5))),
file('SET935+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| equal(v,u) ),
file('SET935+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ in(u,v)
| ~ equal(v,powerset(w))
| subset(u,w) ),
file('SET935+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ subset(u,v)
| ~ equal(w,powerset(v))
| in(u,w) ),
file('SET935+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ in(u,v)
| ~ equal(w,set_union2(x,v))
| in(u,w) ),
file('SET935+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ in(u,v)
| ~ equal(v,set_union2(w,x))
| in(u,x)
| in(u,w) ),
file('SET935+1.p',unknown),
[] ).
cnf(30,plain,
~ subset(skc4,skc5),
inference(res,[status(thm),theory(equality)],[11,5]),
[iquote('0:Res:11.1,5.0')] ).
cnf(31,plain,
~ subset(skc5,skc4),
inference(res,[status(thm),theory(equality)],[12,5]),
[iquote('0:Res:12.1,5.0')] ).
cnf(37,plain,
( ~ in(u,powerset(skc5))
| in(u,powerset(set_union2(skc4,skc5))) ),
inference(res,[status(thm),theory(equality)],[17,24]),
[iquote('0:Res:17.0,24.1')] ).
cnf(39,plain,
( ~ in(u,powerset(set_union2(skc4,skc5)))
| in(u,powerset(skc5))
| in(u,powerset(skc4)) ),
inference(res,[status(thm),theory(equality)],[17,26]),
[iquote('0:Res:17.0,26.1')] ).
cnf(49,plain,
subset(u,set_union2(v,u)),
inference(spr,[status(thm),theory(equality)],[8,7]),
[iquote('0:SpR:8.0,7.0')] ).
cnf(85,plain,
( ~ subset(set_union2(u,v),u)
| equal(set_union2(u,v),u) ),
inference(res,[status(thm),theory(equality)],[7,20]),
[iquote('0:Res:7.0,20.0')] ).
cnf(86,plain,
( ~ subset(set_union2(u,v),v)
| equal(set_union2(u,v),v) ),
inference(res,[status(thm),theory(equality)],[49,20]),
[iquote('0:Res:49.0,20.0')] ).
cnf(92,plain,
( ~ subset(set_union2(u,v),v)
| equal(set_union2(v,u),v) ),
inference(spl,[status(thm),theory(equality)],[8,85]),
[iquote('0:SpL:8.0,85.0')] ).
cnf(98,plain,
( ~ subset(set_union2(u,v),u)
| equal(set_union2(v,u),u) ),
inference(spl,[status(thm),theory(equality)],[8,86]),
[iquote('0:SpL:8.0,86.0')] ).
cnf(109,plain,
( ~ in(u,powerset(v))
| subset(u,v) ),
inference(eqr,[status(thm),theory(equality)],[21]),
[iquote('0:EqR:21.1')] ).
cnf(129,plain,
( ~ subset(u,v)
| in(u,powerset(v)) ),
inference(eqr,[status(thm),theory(equality)],[22]),
[iquote('0:EqR:22.1')] ).
cnf(390,plain,
( ~ subset(u,set_union2(skc4,skc5))
| in(u,powerset(skc5))
| in(u,powerset(skc4)) ),
inference(res,[status(thm),theory(equality)],[129,39]),
[iquote('0:Res:129.1,39.0')] ).
cnf(852,plain,
( in(set_union2(skc4,skc5),powerset(skc5))
| in(set_union2(skc4,skc5),powerset(skc4)) ),
inference(res,[status(thm),theory(equality)],[3,390]),
[iquote('0:Res:3.0,390.0')] ).
cnf(854,plain,
( in(skc5,powerset(skc5))
| in(skc5,powerset(skc4)) ),
inference(res,[status(thm),theory(equality)],[49,390]),
[iquote('0:Res:49.0,390.0')] ).
cnf(900,plain,
( in(set_union2(skc4,skc5),powerset(skc4))
| subset(set_union2(skc4,skc5),skc5) ),
inference(res,[status(thm),theory(equality)],[852,109]),
[iquote('0:Res:852.0,109.0')] ).
cnf(920,plain,
in(set_union2(skc4,skc5),powerset(skc4)),
inference(spt,[spt(split,[position(s1)])],[900]),
[iquote('1:Spt:900.0')] ).
cnf(925,plain,
subset(set_union2(skc4,skc5),skc4),
inference(res,[status(thm),theory(equality)],[920,109]),
[iquote('1:Res:920.0,109.0')] ).
cnf(927,plain,
equal(set_union2(skc5,skc4),skc4),
inference(res,[status(thm),theory(equality)],[925,98]),
[iquote('1:Res:925.0,98.0')] ).
cnf(931,plain,
equal(set_union2(skc4,skc5),skc4),
inference(rew,[status(thm),theory(equality)],[8,927]),
[iquote('1:Rew:8.0,927.0')] ).
cnf(938,plain,
( ~ in(u,powerset(skc5))
| in(u,powerset(skc4)) ),
inference(rew,[status(thm),theory(equality)],[931,37]),
[iquote('1:Rew:931.0,37.1')] ).
cnf(1057,plain,
in(skc5,powerset(skc4)),
inference(mrr,[status(thm)],[854,938]),
[iquote('1:MRR:854.0,938.0')] ).
cnf(1153,plain,
subset(skc5,skc4),
inference(res,[status(thm),theory(equality)],[1057,109]),
[iquote('1:Res:1057.0,109.0')] ).
cnf(1154,plain,
$false,
inference(mrr,[status(thm)],[1153,31]),
[iquote('1:MRR:1153.0,31.0')] ).
cnf(1155,plain,
~ in(set_union2(skc4,skc5),powerset(skc4)),
inference(spt,[spt(split,[position(sa)])],[1154,920]),
[iquote('1:Spt:1154.0,900.0,920.0')] ).
cnf(1156,plain,
subset(set_union2(skc4,skc5),skc5),
inference(spt,[spt(split,[position(s2)])],[900]),
[iquote('1:Spt:1154.0,900.1')] ).
cnf(1163,plain,
equal(set_union2(skc5,skc4),skc5),
inference(res,[status(thm),theory(equality)],[1156,92]),
[iquote('1:Res:1156.0,92.0')] ).
cnf(1165,plain,
equal(set_union2(skc4,skc5),skc5),
inference(rew,[status(thm),theory(equality)],[8,1163]),
[iquote('1:Rew:8.0,1163.0')] ).
cnf(1335,plain,
subset(skc4,skc5),
inference(spr,[status(thm),theory(equality)],[1165,7]),
[iquote('1:SpR:1165.0,7.0')] ).
cnf(1372,plain,
$false,
inference(mrr,[status(thm)],[1335,30]),
[iquote('1:MRR:1335.0,30.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET935+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n007.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 : Sat Jul 9 23:08:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.38/0.60
% 0.38/0.60 SPASS V 3.9
% 0.38/0.60 SPASS beiseite: Proof found.
% 0.38/0.60 % SZS status Theorem
% 0.38/0.60 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.38/0.60 SPASS derived 1224 clauses, backtracked 130 clauses, performed 1 splits and kept 627 clauses.
% 0.38/0.60 SPASS allocated 86187 KBytes.
% 0.38/0.60 SPASS spent 0:00:00.25 on the problem.
% 0.38/0.60 0:00:00.03 for the input.
% 0.38/0.60 0:00:00.03 for the FLOTTER CNF translation.
% 0.38/0.60 0:00:00.02 for inferences.
% 0.38/0.60 0:00:00.00 for the backtracking.
% 0.38/0.60 0:00:00.14 for the reduction.
% 0.38/0.60
% 0.38/0.60
% 0.38/0.60 Here is a proof with depth 7, length 41 :
% 0.38/0.60 % SZS output start Refutation
% See solution above
% 0.38/0.60 Formulae used in the proof : reflexivity_r1_tarski t82_zfmisc_1 t7_xboole_1 commutativity_k2_xboole_0 d9_xboole_0 d10_xboole_0 d1_zfmisc_1 d2_xboole_0
% 0.38/0.60
%------------------------------------------------------------------------------