TSTP Solution File: SET005-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET005-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n006.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 : 300s
% DateTime : Wed Jul 27 13:12:45 EDT 2022
% Result : Unsatisfiable 5.04s 5.30s
% Output : Refutation 5.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of clauses : 45 ( 15 unt; 25 nHn; 22 RR)
% Number of literals : 96 ( 0 equ; 13 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-3 aty)
% Number of variables : 55 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
( ~ intersection(A,B,C)
| ~ member(D,C)
| member(D,A) ),
file('SET005-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ intersection(A,B,C)
| ~ member(D,C)
| member(D,B) ),
file('SET005-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ intersection(A,B,C)
| ~ member(D,B)
| ~ member(D,A)
| member(D,C) ),
file('SET005-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ member(h(A,B,C),C)
| ~ member(h(A,B,C),B)
| ~ member(h(A,B,C),A)
| intersection(A,B,C) ),
file('SET005-1.p',unknown),
[] ).
cnf(10,axiom,
~ intersection(aIb,c,aIbIc),
file('SET005-1.p',unknown),
[] ).
cnf(13,plain,
( ~ member(h(A,B,B),B)
| ~ member(h(A,B,B),A)
| intersection(A,B,B) ),
inference(factor,[status(thm)],[9]),
[iquote('factor,9.1.2')] ).
cnf(18,axiom,
( member(h(A,B,C),C)
| intersection(A,B,C)
| member(h(A,B,C),A) ),
file('SET005-1.p',unknown),
[] ).
cnf(19,axiom,
( member(h(A,B,C),C)
| intersection(A,B,C)
| member(h(A,B,C),B) ),
file('SET005-1.p',unknown),
[] ).
cnf(20,axiom,
intersection(a,b,aIb),
file('SET005-1.p',unknown),
[] ).
cnf(21,axiom,
intersection(b,c,bIc),
file('SET005-1.p',unknown),
[] ).
cnf(22,axiom,
intersection(a,bIc,aIbIc),
file('SET005-1.p',unknown),
[] ).
cnf(24,plain,
( member(h(A,B,B),B)
| intersection(A,B,B) ),
inference(factor,[status(thm)],[19]),
[iquote('factor,19.1.3')] ).
cnf(35,plain,
( intersection(A,B,aIbIc)
| member(h(A,B,aIbIc),A)
| member(h(A,B,aIbIc),bIc) ),
inference(hyper,[status(thm)],[18,7,22]),
[iquote('hyper,18,7,22')] ).
cnf(37,plain,
( intersection(A,B,aIb)
| member(h(A,B,aIb),A)
| member(h(A,B,aIb),b) ),
inference(hyper,[status(thm)],[18,7,20]),
[iquote('hyper,18,7,20')] ).
cnf(38,plain,
( intersection(A,B,aIbIc)
| member(h(A,B,aIbIc),A)
| member(h(A,B,aIbIc),a) ),
inference(hyper,[status(thm)],[18,6,22]),
[iquote('hyper,18,6,22')] ).
cnf(44,plain,
( member(h(aIb,A,B),B)
| intersection(aIb,A,B)
| member(h(aIb,A,B),b) ),
inference(hyper,[status(thm)],[18,7,20]),
[iquote('hyper,18,7,20')] ).
cnf(47,plain,
( member(h(aIb,A,B),B)
| intersection(aIb,A,B)
| member(h(aIb,A,B),a) ),
inference(hyper,[status(thm)],[18,6,20]),
[iquote('hyper,18,6,20')] ).
cnf(49,plain,
( intersection(bIc,A,aIbIc)
| member(h(bIc,A,aIbIc),bIc) ),
inference(factor,[status(thm)],[35]),
[iquote('factor,35.2.3')] ).
cnf(51,plain,
( intersection(b,A,aIb)
| member(h(b,A,aIb),b) ),
inference(factor,[status(thm)],[37]),
[iquote('factor,37.2.3')] ).
cnf(76,plain,
( intersection(A,B,aIbIc)
| member(h(A,B,aIbIc),B)
| member(h(A,B,aIbIc),a) ),
inference(hyper,[status(thm)],[19,6,22]),
[iquote('hyper,19,6,22')] ).
cnf(78,plain,
( intersection(A,B,aIb)
| member(h(A,B,aIb),B)
| member(h(A,B,aIb),a) ),
inference(hyper,[status(thm)],[19,6,20]),
[iquote('hyper,19,6,20')] ).
cnf(80,plain,
( member(h(bIc,a,A),A)
| intersection(bIc,a,A)
| member(h(bIc,a,A),aIbIc) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[19,8,22,18])])]),
[iquote('hyper,19,8,22,18,factor_simp,factor_simp')] ).
cnf(82,plain,
( member(h(b,a,A),A)
| intersection(b,a,A)
| member(h(b,a,A),aIb) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[19,8,20,18])])]),
[iquote('hyper,19,8,20,18,factor_simp,factor_simp')] ).
cnf(96,plain,
( intersection(A,a,aIbIc)
| member(h(A,a,aIbIc),a) ),
inference(factor,[status(thm)],[76]),
[iquote('factor,76.2.3')] ).
cnf(98,plain,
( intersection(A,a,aIb)
| member(h(A,a,aIb),a) ),
inference(factor,[status(thm)],[78]),
[iquote('factor,78.2.3')] ).
cnf(100,plain,
( member(h(bIc,a,aIbIc),aIbIc)
| intersection(bIc,a,aIbIc) ),
inference(factor,[status(thm)],[80]),
[iquote('factor,80.1.3')] ).
cnf(102,plain,
( member(h(b,a,aIb),aIb)
| intersection(b,a,aIb) ),
inference(factor,[status(thm)],[82]),
[iquote('factor,82.1.3')] ).
cnf(142,plain,
( intersection(A,B,aIbIc)
| member(h(A,B,aIbIc),A)
| member(h(A,B,aIbIc),c) ),
inference(hyper,[status(thm)],[35,7,21]),
[iquote('hyper,35,7,21')] ).
cnf(143,plain,
( intersection(A,B,aIbIc)
| member(h(A,B,aIbIc),A)
| member(h(A,B,aIbIc),b) ),
inference(hyper,[status(thm)],[35,6,21]),
[iquote('hyper,35,6,21')] ).
cnf(146,plain,
( intersection(c,A,aIbIc)
| member(h(c,A,aIbIc),c) ),
inference(factor,[status(thm)],[142]),
[iquote('factor,142.2.3')] ).
cnf(147,plain,
( intersection(b,A,aIbIc)
| member(h(b,A,aIbIc),b) ),
inference(factor,[status(thm)],[143]),
[iquote('factor,143.2.3')] ).
cnf(319,plain,
intersection(bIc,a,aIbIc),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[100,9,96,49])])])]),
[iquote('hyper,100,9,96,49,factor_simp,factor_simp,factor_simp')] ).
cnf(323,plain,
intersection(b,a,aIb),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[102,9,98,51])])])]),
[iquote('hyper,102,9,98,51,factor_simp,factor_simp,factor_simp')] ).
cnf(362,plain,
intersection(c,aIbIc,aIbIc),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[146,13,24])])]),
[iquote('hyper,146,13,24,factor_simp,factor_simp')] ).
cnf(374,plain,
( member(h(A,B,aIbIc),c)
| intersection(A,B,aIbIc)
| member(h(A,B,aIbIc),B) ),
inference(hyper,[status(thm)],[362,6,19]),
[iquote('hyper,362,6,19')] ).
cnf(379,plain,
( member(h(A,c,aIbIc),c)
| intersection(A,c,aIbIc) ),
inference(factor,[status(thm)],[374]),
[iquote('factor,374.1.3')] ).
cnf(474,plain,
intersection(b,aIbIc,aIbIc),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[147,13,24])])]),
[iquote('hyper,147,13,24,factor_simp,factor_simp')] ).
cnf(482,plain,
( member(h(aIb,A,aIbIc),b)
| intersection(aIb,A,aIbIc) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[474,6,44])]),
[iquote('hyper,474,6,44,factor_simp')] ).
cnf(1750,plain,
member(h(aIb,c,aIbIc),a),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[379,9,47,38]),10,10,10,10])]),
[iquote('hyper,379,9,47,38,unit_del,10,10,10,10,factor_simp')] ).
cnf(1799,plain,
member(h(aIb,c,aIbIc),aIb),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[482,8,323,1750]),10]),
[iquote('hyper,482,8,323,1750,unit_del,10')] ).
cnf(1801,plain,
member(h(aIb,c,aIbIc),bIc),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[482,8,21,379]),10,10]),
[iquote('hyper,482,8,21,379,unit_del,10,10')] ).
cnf(1809,plain,
member(h(aIb,c,aIbIc),c),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[1799,9,19,379]),10,10,10]),
[iquote('hyper,1799,9,19,379,unit_del,10,10,10')] ).
cnf(1828,plain,
member(h(aIb,c,aIbIc),aIbIc),
inference(hyper,[status(thm)],[1801,8,319,1750]),
[iquote('hyper,1801,8,319,1750')] ).
cnf(1836,plain,
intersection(aIb,c,aIbIc),
inference(hyper,[status(thm)],[1828,9,1809,1799]),
[iquote('hyper,1828,9,1809,1799')] ).
cnf(1837,plain,
$false,
inference(binary,[status(thm)],[1836,10]),
[iquote('binary,1836.1,10.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET005-1 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n006.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 : 300
% 0.12/0.33 % DateTime : Wed Jul 27 10:38:46 EDT 2022
% 0.12/0.33 % CPUTime :
% 5.04/5.30 ----- Otter 3.3f, August 2004 -----
% 5.04/5.30 The process was started by sandbox2 on n006.cluster.edu,
% 5.04/5.30 Wed Jul 27 10:38:47 2022
% 5.04/5.30 The command was "./otter". The process ID is 26810.
% 5.04/5.30
% 5.04/5.30 set(prolog_style_variables).
% 5.04/5.30 set(auto).
% 5.04/5.30 dependent: set(auto1).
% 5.04/5.30 dependent: set(process_input).
% 5.04/5.30 dependent: clear(print_kept).
% 5.04/5.30 dependent: clear(print_new_demod).
% 5.04/5.30 dependent: clear(print_back_demod).
% 5.04/5.30 dependent: clear(print_back_sub).
% 5.04/5.30 dependent: set(control_memory).
% 5.04/5.30 dependent: assign(max_mem, 12000).
% 5.04/5.30 dependent: assign(pick_given_ratio, 4).
% 5.04/5.30 dependent: assign(stats_level, 1).
% 5.04/5.30 dependent: assign(max_seconds, 10800).
% 5.04/5.30 clear(print_given).
% 5.04/5.30
% 5.04/5.30 list(usable).
% 5.04/5.30 0 [] -member(Element,Subset)| -subset(Subset,Superset)|member(Element,Superset).
% 5.04/5.30 0 [] subset(Subset,Superset)|member(member_of_1_not_of_2(Subset,Superset),Subset).
% 5.04/5.30 0 [] -member(member_of_1_not_of_2(Subset,Superset),Superset)|subset(Subset,Superset).
% 5.04/5.30 0 [] -e_qual_sets(Subset,Superset)|subset(Subset,Superset).
% 5.04/5.30 0 [] -e_qual_sets(Superset,Subset)|subset(Subset,Superset).
% 5.04/5.30 0 [] -subset(Set1,Set2)| -subset(Set2,Set1)|e_qual_sets(Set2,Set1).
% 5.04/5.30 0 [] -intersection(Set1,Set2,Intersection)| -member(Element,Intersection)|member(Element,Set1).
% 5.04/5.30 0 [] -intersection(Set1,Set2,Intersection)| -member(Element,Intersection)|member(Element,Set2).
% 5.04/5.30 0 [] -intersection(Set1,Set2,Intersection)| -member(Element,Set2)| -member(Element,Set1)|member(Element,Intersection).
% 5.04/5.30 0 [] member(h(Set1,Set2,Intersection),Intersection)|intersection(Set1,Set2,Intersection)|member(h(Set1,Set2,Intersection),Set1).
% 5.04/5.30 0 [] member(h(Set1,Set2,Intersection),Intersection)|intersection(Set1,Set2,Intersection)|member(h(Set1,Set2,Intersection),Set2).
% 5.04/5.30 0 [] -member(h(Set1,Set2,Intersection),Intersection)| -member(h(Set1,Set2,Intersection),Set2)| -member(h(Set1,Set2,Intersection),Set1)|intersection(Set1,Set2,Intersection).
% 5.04/5.30 0 [] intersection(a,b,aIb).
% 5.04/5.30 0 [] intersection(b,c,bIc).
% 5.04/5.30 0 [] intersection(a,bIc,aIbIc).
% 5.04/5.30 0 [] -intersection(aIb,c,aIbIc).
% 5.04/5.30 end_of_list.
% 5.04/5.30
% 5.04/5.30 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=4.
% 5.04/5.30
% 5.04/5.30 This is a non-Horn set without equality. The strategy will
% 5.04/5.30 be ordered hyper_res, unit deletion, and factoring, with
% 5.04/5.30 satellites in sos and with nuclei in usable.
% 5.04/5.30
% 5.04/5.30 dependent: set(hyper_res).
% 5.04/5.30 dependent: set(factor).
% 5.04/5.30 dependent: set(unit_deletion).
% 5.04/5.30
% 5.04/5.30 ------------> process usable:
% 5.04/5.30 ** KEPT (pick-wt=9): 1 [] -member(A,B)| -subset(B,C)|member(A,C).
% 5.04/5.30 ** KEPT (pick-wt=8): 2 [] -member(member_of_1_not_of_2(A,B),B)|subset(A,B).
% 5.04/5.30 ** KEPT (pick-wt=6): 3 [] -e_qual_sets(A,B)|subset(A,B).
% 5.04/5.30 ** KEPT (pick-wt=6): 4 [] -e_qual_sets(A,B)|subset(B,A).
% 5.04/5.30 ** KEPT (pick-wt=9): 5 [] -subset(A,B)| -subset(B,A)|e_qual_sets(B,A).
% 5.04/5.30 ** KEPT (pick-wt=10): 6 [] -intersection(A,B,C)| -member(D,C)|member(D,A).
% 5.04/5.30 ** KEPT (pick-wt=10): 7 [] -intersection(A,B,C)| -member(D,C)|member(D,B).
% 5.04/5.30 ** KEPT (pick-wt=13): 8 [] -intersection(A,B,C)| -member(D,B)| -member(D,A)|member(D,C).
% 5.04/5.30 ** KEPT (pick-wt=22): 9 [] -member(h(A,B,C),C)| -member(h(A,B,C),B)| -member(h(A,B,C),A)|intersection(A,B,C).
% 5.04/5.30 ** KEPT (pick-wt=4): 10 [] -intersection(aIb,c,aIbIc).
% 5.04/5.30
% 5.04/5.30 ------------> process sos:
% 5.04/5.30 ** KEPT (pick-wt=8): 17 [] subset(A,B)|member(member_of_1_not_of_2(A,B),A).
% 5.04/5.30 ** KEPT (pick-wt=16): 18 [] member(h(A,B,C),C)|intersection(A,B,C)|member(h(A,B,C),A).
% 5.04/5.30 ** KEPT (pick-wt=16): 19 [] member(h(A,B,C),C)|intersection(A,B,C)|member(h(A,B,C),B).
% 5.04/5.30 ** KEPT (pick-wt=4): 20 [] intersection(a,b,aIb).
% 5.04/5.30 ** KEPT (pick-wt=4): 21 [] intersection(b,c,bIc).
% 5.04/5.30 ** KEPT (pick-wt=4): 22 [] intersection(a,bIc,aIbIc).
% 5.04/5.30
% 5.04/5.30 ======= end of input processing =======
% 5.04/5.30
% 5.04/5.30 =========== start of search ===========
% 5.04/5.30
% 5.04/5.30 -------- PROOF --------
% 5.04/5.30
% 5.04/5.30 ----> UNIT CONFLICT at 3.18 sec ----> 1837 [binary,1836.1,10.1] $F.
% 5.04/5.30
% 5.04/5.30 Length of proof is 34. Level of proof is 10.
% 5.04/5.30
% 5.04/5.30 ---------------- PROOF ----------------
% 5.04/5.30 % SZS status Unsatisfiable
% 5.04/5.30 % SZS output start Refutation
% See solution above
% 5.04/5.30 ------------ end of proof -------------
% 5.04/5.30
% 5.04/5.30
% 5.04/5.30 Search stopped by max_proofs option.
% 5.04/5.30
% 5.04/5.30
% 5.04/5.30 Search stopped by max_proofs option.
% 5.04/5.30
% 5.04/5.30 ============ end of search ============
% 5.04/5.30
% 5.04/5.30 -------------- statistics -------------
% 5.04/5.30 clauses given 253
% 5.04/5.30 clauses generated 173241
% 5.04/5.30 clauses kept 1836
% 5.04/5.30 clauses forward subsumed 171421
% 5.04/5.30 clauses back subsumed 515
% 5.04/5.30 Kbytes malloced 1953
% 5.04/5.30
% 5.04/5.30 ----------- times (seconds) -----------
% 5.04/5.30 user CPU time 3.18 (0 hr, 0 min, 3 sec)
% 5.04/5.30 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 5.04/5.30 wall-clock time 4 (0 hr, 0 min, 4 sec)
% 5.04/5.30
% 5.04/5.30 That finishes the proof of the theorem.
% 5.04/5.30
% 5.04/5.30 Process 26810 finished Wed Jul 27 10:38:51 2022
% 5.04/5.30 Otter interrupted
% 5.04/5.30 PROOF FOUND
%------------------------------------------------------------------------------