%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU170+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 14:34:40 EDT 2022
% Result : Theorem 25.60s 25.78s
% Output : Refutation 25.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 20
% Syntax : Number of clauses : 68 ( 22 unt; 18 nHn; 68 RR)
% Number of literals : 130 ( 0 equ; 54 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
empty(empty_set),
file('SEU170+1.p',unknown),
[] ).
cnf(6,axiom,
element(skc7,powerset(skc5)),
file('SEU170+1.p',unknown),
[] ).
cnf(7,axiom,
element(skc6,powerset(skc5)),
file('SEU170+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ disjoint(u,v)
| disjoint(v,u) ),
file('SEU170+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ empty(u)
| ~ in(v,u) ),
file('SEU170+1.p',unknown),
[] ).
cnf(18,axiom,
( disjoint(skc6,skc7)
| subset(skc6,subset_complement(skc5,skc7)) ),
file('SEU170+1.p',unknown),
[] ).
cnf(20,axiom,
( subset(u,v)
| in(skf6(v,u),u) ),
file('SEU170+1.p',unknown),
[] ).
cnf(21,axiom,
( disjoint(u,v)
| in(skf11(v,u),u) ),
file('SEU170+1.p',unknown),
[] ).
cnf(22,axiom,
( disjoint(u,v)
| in(skf11(v,w),v) ),
file('SEU170+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ in(skf6(u,v),u)
| subset(w,u) ),
file('SEU170+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ disjoint(skc6,skc7)
| ~ subset(skc6,subset_complement(skc5,skc7)) ),
file('SEU170+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ in(u,v)
| ~ subset(v,w)
| in(u,w) ),
file('SEU170+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ element(u,powerset(v))
| element(subset_complement(v,u),powerset(v)) ),
file('SEU170+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ element(u,powerset(v))
| equal(subset_complement(v,u),set_difference(v,u)) ),
file('SEU170+1.p',unknown),
[] ).
cnf(29,axiom,
( ~ element(u,powerset(v))
| equal(subset_complement(v,subset_complement(v,u)),u) ),
file('SEU170+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ in(u,v)
| ~ element(v,powerset(w))
| in(u,w) ),
file('SEU170+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ disjoint(u,v)
| ~ in(w,v)
| ~ in(w,u) ),
file('SEU170+1.p',unknown),
[] ).
cnf(33,axiom,
( ~ in(u,v)
| ~ in(u,w)
| ~ equal(v,set_difference(x,w)) ),
file('SEU170+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ in(u,v)
| ~ equal(w,set_difference(v,x))
| in(u,w)
| in(u,x) ),
file('SEU170+1.p',unknown),
[] ).
cnf(35,axiom,
( equal(u,set_difference(v,w))
| in(skf7(w,v,u),u)
| in(skf7(w,v,u),v) ),
file('SEU170+1.p',unknown),
[] ).
cnf(38,plain,
( ~ element(u,powerset(v))
| element(set_difference(v,u),powerset(v)) ),
inference(rew,[status(thm),theory(equality)],[28,27]),
[iquote('0:Rew:28.1,27.1')] ).
cnf(39,plain,
( ~ element(u,powerset(v))
| equal(subset_complement(v,set_difference(v,u)),u) ),
inference(rew,[status(thm),theory(equality)],[28,29]),
[iquote('0:Rew:28.1,29.1')] ).
cnf(43,plain,
( ~ in(u,skc6)
| in(u,skc5) ),
inference(res,[status(thm),theory(equality)],[7,30]),
[iquote('0:Res:7.0,30.0')] ).
cnf(44,plain,
equal(subset_complement(skc5,set_difference(skc5,skc7)),skc7),
inference(res,[status(thm),theory(equality)],[6,39]),
[iquote('0:Res:6.0,39.0')] ).
cnf(45,plain,
element(set_difference(skc5,skc7),powerset(skc5)),
inference(res,[status(thm),theory(equality)],[6,38]),
[iquote('0:Res:6.0,38.0')] ).
cnf(46,plain,
equal(subset_complement(skc5,skc7),set_difference(skc5,skc7)),
inference(res,[status(thm),theory(equality)],[6,28]),
[iquote('0:Res:6.0,28.0')] ).
cnf(48,plain,
( ~ disjoint(skc6,skc7)
| ~ subset(skc6,set_difference(skc5,skc7)) ),
inference(rew,[status(thm),theory(equality)],[46,25]),
[iquote('0:Rew:46.0,25.1')] ).
cnf(49,plain,
( disjoint(skc6,skc7)
| subset(skc6,set_difference(skc5,skc7)) ),
inference(rew,[status(thm),theory(equality)],[46,18]),
[iquote('0:Rew:46.0,18.1')] ).
cnf(65,plain,
disjoint(skc6,skc7),
inference(spt,[spt(split,[position(s1)])],[49]),
[iquote('1:Spt:49.0')] ).
cnf(66,plain,
~ subset(skc6,set_difference(skc5,skc7)),
inference(mrr,[status(thm)],[48,65]),
[iquote('1:MRR:48.0,65.0')] ).
cnf(67,plain,
disjoint(skc7,skc6),
inference(res,[status(thm),theory(equality)],[65,16]),
[iquote('1:Res:65.0,16.0')] ).
cnf(71,plain,
( subset(skc6,u)
| in(skf6(u,skc6),skc5) ),
inference(res,[status(thm),theory(equality)],[20,43]),
[iquote('0:Res:20.1,43.0')] ).
cnf(74,plain,
( ~ empty(u)
| disjoint(u,v) ),
inference(res,[status(thm),theory(equality)],[21,17]),
[iquote('0:Res:21.1,17.1')] ).
cnf(116,plain,
( ~ subset(u,v)
| disjoint(w,u)
| in(skf11(u,x),v) ),
inference(res,[status(thm),theory(equality)],[22,26]),
[iquote('0:Res:22.1,26.0')] ).
cnf(148,plain,
equal(subset_complement(skc5,set_difference(skc5,skc7)),set_difference(skc5,set_difference(skc5,skc7))),
inference(res,[status(thm),theory(equality)],[45,28]),
[iquote('0:Res:45.0,28.0')] ).
cnf(157,plain,
equal(set_difference(skc5,set_difference(skc5,skc7)),skc7),
inference(rew,[status(thm),theory(equality)],[44,148]),
[iquote('0:Rew:44.0,148.0')] ).
cnf(200,plain,
( ~ in(u,v)
| ~ in(u,w)
| in(skf11(v,x),v) ),
inference(res,[status(thm),theory(equality)],[22,31]),
[iquote('0:Res:22.0,31.0')] ).
cnf(214,plain,
( ~ in(u,v)
| in(skf11(v,w),v) ),
inference(con,[status(thm)],[200]),
[iquote('0:Con:200.1')] ).
cnf(247,plain,
( ~ in(u,set_difference(v,w))
| ~ in(u,w) ),
inference(eqr,[status(thm),theory(equality)],[33]),
[iquote('0:EqR:33.2')] ).
cnf(270,plain,
( ~ in(u,v)
| in(u,set_difference(v,w))
| in(u,w) ),
inference(eqr,[status(thm),theory(equality)],[34]),
[iquote('0:EqR:34.1')] ).
cnf(284,plain,
( equal(set_difference(u,v),u)
| in(skf7(v,u,u),u) ),
inference(fac,[status(thm)],[35]),
[iquote('0:Fac:35.1,35.2')] ).
cnf(292,plain,
( ~ empty(u)
| equal(v,set_difference(u,w))
| in(skf7(w,u,v),v) ),
inference(res,[status(thm),theory(equality)],[35,17]),
[iquote('0:Res:35.2,17.1')] ).
cnf(389,plain,
( ~ in(u,skc6)
| ~ in(u,skc7) ),
inference(res,[status(thm),theory(equality)],[67,31]),
[iquote('1:Res:67.0,31.0')] ).
cnf(599,plain,
( ~ in(skf11(u,set_difference(v,w)),w)
| disjoint(set_difference(v,w),u) ),
inference(res,[status(thm),theory(equality)],[21,247]),
[iquote('0:Res:21.1,247.0')] ).
cnf(805,plain,
( ~ empty(u)
| equal(set_difference(u,v),u) ),
inference(res,[status(thm),theory(equality)],[284,17]),
[iquote('0:Res:284.1,17.1')] ).
cnf(820,plain,
( ~ empty(u)
| equal(v,u)
| in(skf7(w,u,v),v) ),
inference(rew,[status(thm),theory(equality)],[805,292]),
[iquote('0:Rew:805.1,292.1')] ).
cnf(1054,plain,
( ~ in(skf6(set_difference(u,v),w),u)
| in(skf6(set_difference(u,v),w),v)
| subset(x,set_difference(u,v)) ),
inference(res,[status(thm),theory(equality)],[270,23]),
[iquote('0:Res:270.1,23.0')] ).
cnf(1088,plain,
( ~ empty(u)
| equal(v,u)
| in(skf11(v,w),v) ),
inference(res,[status(thm),theory(equality)],[820,214]),
[iquote('0:Res:820.2,214.0')] ).
cnf(4926,plain,
( ~ in(skf11(u,skc7),set_difference(skc5,skc7))
| disjoint(set_difference(skc5,set_difference(skc5,skc7)),u) ),
inference(spl,[status(thm),theory(equality)],[157,599]),
[iquote('0:SpL:157.0,599.0')] ).
cnf(4986,plain,
( ~ in(skf11(u,skc7),set_difference(skc5,skc7))
| disjoint(skc7,u) ),
inference(rew,[status(thm),theory(equality)],[157,4926]),
[iquote('0:Rew:157.0,4926.1')] ).
cnf(14215,plain,
( subset(skc6,set_difference(skc5,u))
| in(skf6(set_difference(skc5,u),skc6),u)
| subset(v,set_difference(skc5,u)) ),
inference(res,[status(thm),theory(equality)],[71,1054]),
[iquote('0:Res:71.1,1054.0')] ).
cnf(14223,plain,
( subset(skc6,set_difference(skc5,u))
| in(skf6(set_difference(skc5,u),skc6),u) ),
inference(con,[status(thm)],[14215]),
[iquote('0:Con:14215.2')] ).
cnf(39448,plain,
( ~ in(skf6(set_difference(skc5,skc7),skc6),skc6)
| subset(skc6,set_difference(skc5,skc7)) ),
inference(res,[status(thm),theory(equality)],[14223,389]),
[iquote('1:Res:14223.1,389.1')] ).
cnf(39465,plain,
$false,
inference(mrr,[status(thm)],[39448,20,66]),
[iquote('1:MRR:39448.0,39448.1,20.1,66.0')] ).
cnf(39476,plain,
~ disjoint(skc6,skc7),
inference(spt,[spt(split,[position(sa)])],[39465,65]),
[iquote('1:Spt:39465.0,49.0,65.0')] ).
cnf(39477,plain,
subset(skc6,set_difference(skc5,skc7)),
inference(spt,[spt(split,[position(s2)])],[49]),
[iquote('1:Spt:39465.0,49.1')] ).
cnf(42075,plain,
( disjoint(u,skc6)
| in(skf11(skc6,v),set_difference(skc5,skc7)) ),
inference(res,[status(thm),theory(equality)],[39477,116]),
[iquote('1:Res:39477.0,116.0')] ).
cnf(42091,plain,
( ~ empty(u)
| ~ disjoint(u,skc7)
| in(skf11(skc6,v),skc6) ),
inference(spl,[status(thm),theory(equality)],[1088,39476]),
[iquote('1:SpL:1088.1,39476.0')] ).
cnf(42127,plain,
( ~ empty(u)
| in(skf11(skc6,v),skc6) ),
inference(mrr,[status(thm)],[42091,74]),
[iquote('1:MRR:42091.1,74.1')] ).
cnf(42230,plain,
disjoint(u,skc6),
inference(spt,[spt(split,[position(s2s1)])],[42075]),
[iquote('2:Spt:42075.0')] ).
cnf(42232,plain,
( ~ in(u,skc6)
| ~ in(u,v) ),
inference(res,[status(thm),theory(equality)],[42230,31]),
[iquote('2:Res:42230.0,31.0')] ).
cnf(42235,plain,
~ in(u,skc6),
inference(con,[status(thm)],[42232]),
[iquote('2:Con:42232.1')] ).
cnf(42237,plain,
~ empty(u),
inference(mrr,[status(thm)],[42127,42235]),
[iquote('2:MRR:42127.1,42235.0')] ).
cnf(42238,plain,
$false,
inference(unc,[status(thm)],[42237,1]),
[iquote('2:UnC:42237.0,1.0')] ).
cnf(42239,plain,
in(skf11(skc6,u),set_difference(skc5,skc7)),
inference(spt,[spt(split,[position(s2s2)])],[42075]),
[iquote('2:Spt:42238.0,42075.1')] ).
cnf(42263,plain,
disjoint(skc7,skc6),
inference(res,[status(thm),theory(equality)],[42239,4986]),
[iquote('2:Res:42239.0,4986.0')] ).
cnf(42270,plain,
disjoint(skc6,skc7),
inference(res,[status(thm),theory(equality)],[42263,16]),
[iquote('2:Res:42263.0,16.0')] ).
cnf(42271,plain,
$false,
inference(mrr,[status(thm)],[42270,39476]),
[iquote('2:MRR:42270.0,39476.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU170+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 19 05:37:55 EDT 2022
% 0.13/0.35 % CPUTime :
% 25.60/25.78
% 25.60/25.78 SPASS V 3.9
% 25.60/25.78 SPASS beiseite: Proof found.
% 25.60/25.78 % SZS status Theorem
% 25.60/25.78 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.60/25.78 SPASS derived 31918 clauses, backtracked 3612 clauses, performed 10 splits and kept 11507 clauses.
% 25.60/25.78 SPASS allocated 124859 KBytes.
% 25.60/25.78 SPASS spent 0:0:24.57 on the problem.
% 25.60/25.78 0:00:00.03 for the input.
% 25.60/25.78 0:00:00.04 for the FLOTTER CNF translation.
% 25.60/25.78 0:00:00.36 for inferences.
% 25.60/25.78 0:00:01.09 for the backtracking.
% 25.60/25.78 0:0:22.81 for the reduction.
% 25.60/25.78
% 25.60/25.78
% 25.60/25.78 Here is a proof with depth 5, length 68 :
% 25.60/25.78 % SZS output start Refutation
% See solution above
% 25.60/25.78 Formulae used in the proof : fc1_xboole_0 t43_subset_1 symmetry_r1_xboole_0 t7_boole d3_tarski t3_xboole_0 dt_k3_subset_1 d5_subset_1 involutiveness_k3_subset_1 l3_subset_1 d4_xboole_0
% 25.60/25.78
%------------------------------------------------------------------------------