TSTP Solution File: SET010-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET010-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n021.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 13:12:46 EDT 2022
% Result : Unsatisfiable 126.48s 126.70s
% Output : Refutation 126.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of clauses : 39 ( 17 unt; 15 nHn; 31 RR)
% Number of literals : 80 ( 0 equ; 22 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-3 aty)
% Number of variables : 50 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(9,axiom,
( ~ member(g(A,B,C),A)
| ~ member(g(A,B,C),C)
| union(A,B,C) ),
file('SET010-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ member(g(A,B,C),B)
| ~ member(g(A,B,C),C)
| union(A,B,C) ),
file('SET010-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ intersection(A,B,C)
| ~ member(D,C)
| member(D,A) ),
file('SET010-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ intersection(A,B,C)
| ~ member(D,C)
| member(D,B) ),
file('SET010-1.p',unknown),
[] ).
cnf(13,axiom,
( ~ intersection(A,B,C)
| ~ member(D,B)
| ~ member(D,A)
| member(D,C) ),
file('SET010-1.p',unknown),
[] ).
cnf(15,axiom,
( ~ difference(A,B,C)
| ~ member(D,C)
| member(D,A) ),
file('SET010-1.p',unknown),
[] ).
cnf(16,axiom,
( ~ member(A,B)
| ~ member(A,C)
| ~ difference(D,B,C) ),
file('SET010-1.p',unknown),
[] ).
cnf(17,axiom,
( ~ member(A,B)
| ~ difference(B,C,D)
| member(A,D)
| member(A,C) ),
file('SET010-1.p',unknown),
[] ).
cnf(19,axiom,
( ~ member(k(A,B,C),C)
| ~ member(k(A,B,C),A)
| member(k(A,B,C),B)
| difference(A,B,C) ),
file('SET010-1.p',unknown),
[] ).
cnf(20,axiom,
~ union(cDa,cDb,cD_aIb),
file('SET010-1.p',unknown),
[] ).
cnf(31,plain,
( ~ member(k(A,B,A),A)
| member(k(A,B,A),B)
| difference(A,B,A) ),
inference(factor,[status(thm)],[19]),
[iquote('factor,19.1.2')] ).
cnf(34,axiom,
( union(A,B,C)
| member(g(A,B,C),A)
| member(g(A,B,C),B)
| member(g(A,B,C),C) ),
file('SET010-1.p',unknown),
[] ).
cnf(37,axiom,
( difference(A,B,C)
| member(k(A,B,C),A)
| member(k(A,B,C),C) ),
file('SET010-1.p',unknown),
[] ).
cnf(38,axiom,
intersection(a,b,aIb),
file('SET010-1.p',unknown),
[] ).
cnf(39,axiom,
difference(c,a,cDa),
file('SET010-1.p',unknown),
[] ).
cnf(40,axiom,
difference(c,b,cDb),
file('SET010-1.p',unknown),
[] ).
cnf(41,axiom,
difference(c,aIb,cD_aIb),
file('SET010-1.p',unknown),
[] ).
cnf(47,plain,
( difference(A,B,A)
| member(k(A,B,A),A) ),
inference(factor,[status(thm)],[37]),
[iquote('factor,37.2.3')] ).
cnf(56,plain,
( union(cDa,A,B)
| member(g(cDa,A,B),A)
| member(g(cDa,A,B),B)
| member(g(cDa,A,B),c) ),
inference(hyper,[status(thm)],[34,15,39]),
[iquote('hyper,34,15,39')] ).
cnf(304,plain,
( difference(A,B,A)
| member(k(A,B,A),B) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[47,31])]),
[iquote('hyper,47,31,factor_simp')] ).
cnf(311,plain,
( difference(aIb,A,aIb)
| member(k(aIb,A,aIb),b) ),
inference(hyper,[status(thm)],[47,12,38]),
[iquote('hyper,47,12,38')] ).
cnf(312,plain,
( difference(aIb,A,aIb)
| member(k(aIb,A,aIb),a) ),
inference(hyper,[status(thm)],[47,11,38]),
[iquote('hyper,47,11,38')] ).
cnf(814,plain,
( union(cDa,cDb,A)
| member(g(cDa,cDb,A),A)
| member(g(cDa,cDb,A),c) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[56,15,40])]),
[iquote('hyper,56,15,40,factor_simp')] ).
cnf(1262,plain,
difference(aIb,cD_aIb,aIb),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[304,16,47,41])]),
[iquote('hyper,304,16,47,41,factor_simp')] ).
cnf(1263,plain,
difference(b,cDb,b),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[304,16,47,40])]),
[iquote('hyper,304,16,47,40,factor_simp')] ).
cnf(1264,plain,
difference(a,cDa,a),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[304,16,47,39])]),
[iquote('hyper,304,16,47,39,factor_simp')] ).
cnf(1389,plain,
difference(aIb,cDb,aIb),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[311,16,304,1263])]),
[iquote('hyper,311,16,304,1263,factor_simp')] ).
cnf(1463,plain,
difference(aIb,cDa,aIb),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[312,16,304,1264])]),
[iquote('hyper,312,16,304,1264,factor_simp')] ).
cnf(1467,plain,
difference(cDa,aIb,cDa),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[1463,16,47,304])]),
[iquote('hyper,1463,16,47,304,factor_simp')] ).
cnf(8204,plain,
member(g(cDa,cDb,cD_aIb),c),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[814,15,41]),20])]),
[iquote('hyper,814,15,41,unit_del,20,factor_simp')] ).
cnf(8205,plain,
( member(g(cDa,cDb,cD_aIb),cD_aIb)
| member(g(cDa,cDb,cD_aIb),aIb) ),
inference(hyper,[status(thm)],[8204,17,41]),
[iquote('hyper,8204,17,41')] ).
cnf(8206,plain,
( member(g(cDa,cDb,cD_aIb),cDb)
| member(g(cDa,cDb,cD_aIb),b) ),
inference(hyper,[status(thm)],[8204,17,40]),
[iquote('hyper,8204,17,40')] ).
cnf(8207,plain,
( member(g(cDa,cDb,cD_aIb),cDa)
| member(g(cDa,cDb,cD_aIb),a) ),
inference(hyper,[status(thm)],[8204,17,39]),
[iquote('hyper,8204,17,39')] ).
cnf(8280,plain,
( member(g(cDa,cDb,cD_aIb),cD_aIb)
| member(g(cDa,cDb,cD_aIb),cDa) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[8205,16,34,1389]),20])]),
[iquote('hyper,8205,16,34,1389,unit_del,20,factor_simp')] ).
cnf(9264,plain,
member(g(cDa,cDb,cD_aIb),cD_aIb),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[8280,16,8205,1467])]),
[iquote('hyper,8280,16,8205,1467,factor_simp')] ).
cnf(9265,plain,
member(g(cDa,cDb,cD_aIb),b),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[9264,10,8206]),20]),
[iquote('hyper,9264,10,8206,unit_del,20')] ).
cnf(9266,plain,
member(g(cDa,cDb,cD_aIb),a),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[9264,9,8207]),20]),
[iquote('hyper,9264,9,8207,unit_del,20')] ).
cnf(9271,plain,
member(g(cDa,cDb,cD_aIb),aIb),
inference(hyper,[status(thm)],[9266,13,38,9265]),
[iquote('hyper,9266,13,38,9265')] ).
cnf(9273,plain,
$false,
inference(hyper,[status(thm)],[9271,16,9264,1262]),
[iquote('hyper,9271,16,9264,1262')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET010-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n021.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 : 300
% 0.13/0.34 % DateTime : Wed Jul 27 10:37:38 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.79/1.95 ----- Otter 3.3f, August 2004 -----
% 1.79/1.95 The process was started by sandbox2 on n021.cluster.edu,
% 1.79/1.95 Wed Jul 27 10:37:38 2022
% 1.79/1.95 The command was "./otter". The process ID is 3919.
% 1.79/1.95
% 1.79/1.95 set(prolog_style_variables).
% 1.79/1.95 set(auto).
% 1.79/1.95 dependent: set(auto1).
% 1.79/1.95 dependent: set(process_input).
% 1.79/1.95 dependent: clear(print_kept).
% 1.79/1.95 dependent: clear(print_new_demod).
% 1.79/1.95 dependent: clear(print_back_demod).
% 1.79/1.95 dependent: clear(print_back_sub).
% 1.79/1.95 dependent: set(control_memory).
% 1.79/1.95 dependent: assign(max_mem, 12000).
% 1.79/1.95 dependent: assign(pick_given_ratio, 4).
% 1.79/1.95 dependent: assign(stats_level, 1).
% 1.79/1.95 dependent: assign(max_seconds, 10800).
% 1.79/1.95 clear(print_given).
% 1.79/1.95
% 1.79/1.95 list(usable).
% 1.79/1.95 0 [] -member(Element,Subset)| -subset(Subset,Superset)|member(Element,Superset).
% 1.79/1.95 0 [] subset(Subset,Superset)|member(member_of_1_not_of_2(Subset,Superset),Subset).
% 1.79/1.95 0 [] -member(member_of_1_not_of_2(Subset,Superset),Superset)|subset(Subset,Superset).
% 1.79/1.95 0 [] -e_qual_sets(Subset,Superset)|subset(Subset,Superset).
% 1.79/1.95 0 [] -e_qual_sets(Superset,Subset)|subset(Subset,Superset).
% 1.79/1.95 0 [] -subset(Set1,Set2)| -subset(Set2,Set1)|e_qual_sets(Set2,Set1).
% 1.79/1.95 0 [] -union(Set1,Set2,Union)| -member(Element,Union)|member(Element,Set1)|member(Element,Set2).
% 1.79/1.95 0 [] -union(Set1,Set2,Union)| -member(Element,Set1)|member(Element,Union).
% 1.79/1.95 0 [] -union(Set1,Set2,Union)| -member(Element,Set2)|member(Element,Union).
% 1.79/1.95 0 [] union(Set1,Set2,Union)|member(g(Set1,Set2,Union),Set1)|member(g(Set1,Set2,Union),Set2)|member(g(Set1,Set2,Union),Union).
% 1.79/1.95 0 [] -member(g(Set1,Set2,Union),Set1)| -member(g(Set1,Set2,Union),Union)|union(Set1,Set2,Union).
% 1.79/1.95 0 [] -member(g(Set1,Set2,Union),Set2)| -member(g(Set1,Set2,Union),Union)|union(Set1,Set2,Union).
% 1.79/1.95 0 [] -intersection(Set1,Set2,Intersection)| -member(Element,Intersection)|member(Element,Set1).
% 1.79/1.95 0 [] -intersection(Set1,Set2,Intersection)| -member(Element,Intersection)|member(Element,Set2).
% 1.79/1.95 0 [] -intersection(Set1,Set2,Intersection)| -member(Element,Set2)| -member(Element,Set1)|member(Element,Intersection).
% 1.79/1.95 0 [] member(h(Set1,Set2,Intersection),Intersection)|intersection(Set1,Set2,Intersection)|member(h(Set1,Set2,Intersection),Set1).
% 1.79/1.95 0 [] member(h(Set1,Set2,Intersection),Intersection)|intersection(Set1,Set2,Intersection)|member(h(Set1,Set2,Intersection),Set2).
% 1.79/1.95 0 [] -member(h(Set1,Set2,Intersection),Intersection)| -member(h(Set1,Set2,Intersection),Set2)| -member(h(Set1,Set2,Intersection),Set1)|intersection(Set1,Set2,Intersection).
% 1.79/1.95 0 [] -difference(Set1,Set2,Difference)| -member(Element,Difference)|member(Element,Set1).
% 1.79/1.95 0 [] -member(Element,Set1)| -member(Element,Set2)| -difference(A_set,Set1,Set2).
% 1.79/1.95 0 [] -member(Element,Set1)| -difference(Set1,Set2,Difference)|member(Element,Difference)|member(Element,Set2).
% 1.79/1.95 0 [] difference(Set1,Set2,Difference)|member(k(Set1,Set2,Difference),Set1)|member(k(Set1,Set2,Difference),Difference).
% 1.79/1.95 0 [] -member(k(Set1,Set2,Difference),Set2)|member(k(Set1,Set2,Difference),Difference)|difference(Set1,Set2,Difference).
% 1.79/1.95 0 [] -member(k(Set1,Set2,Difference),Difference)| -member(k(Set1,Set2,Difference),Set1)|member(k(Set1,Set2,Difference),Set2)|difference(Set1,Set2,Difference).
% 1.79/1.95 0 [] intersection(a,b,aIb).
% 1.79/1.95 0 [] difference(c,a,cDa).
% 1.79/1.95 0 [] difference(c,b,cDb).
% 1.79/1.95 0 [] difference(c,aIb,cD_aIb).
% 1.79/1.95 0 [] -union(cDa,cDb,cD_aIb).
% 1.79/1.95 end_of_list.
% 1.79/1.95
% 1.79/1.95 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=4.
% 1.79/1.95
% 1.79/1.95 This is a non-Horn set without equality. The strategy will
% 1.79/1.95 be ordered hyper_res, unit deletion, and factoring, with
% 1.79/1.95 satellites in sos and with nuclei in usable.
% 1.79/1.95
% 1.79/1.95 dependent: set(hyper_res).
% 1.79/1.95 dependent: set(factor).
% 1.79/1.95 dependent: set(unit_deletion).
% 1.79/1.95
% 1.79/1.95 ------------> process usable:
% 1.79/1.95 ** KEPT (pick-wt=9): 1 [] -member(A,B)| -subset(B,C)|member(A,C).
% 1.79/1.95 ** KEPT (pick-wt=8): 2 [] -member(member_of_1_not_of_2(A,B),B)|subset(A,B).
% 1.79/1.95 ** KEPT (pick-wt=6): 3 [] -e_qual_sets(A,B)|subset(A,B).
% 1.79/1.95 ** KEPT (pick-wt=6): 4 [] -e_qual_sets(A,B)|subset(B,A).
% 1.79/1.95 ** KEPT (pick-wt=9): 5 [] -subset(A,B)| -subset(B,A)|e_qual_sets(B,A).
% 1.79/1.95 ** KEPT (pick-wt=13): 6 [] -union(A,B,C)| -member(D,C)|member(D,A)|member(D,B).
% 1.79/1.95 ** KEPT (pick-wt=10): 7 [] -union(A,B,C)| -member(D,A)|member(D,C).
% 1.79/1.95 ** KEPT (pick-wt=10): 8 [] -union(A,B,C)| -member(D,B)|member(D,C).
% 126.48/126.70 ** KEPT (pick-wt=16): 9 [] -member(g(A,B,C),A)| -member(g(A,B,C),C)|union(A,B,C).
% 126.48/126.70 ** KEPT (pick-wt=16): 10 [] -member(g(A,B,C),B)| -member(g(A,B,C),C)|union(A,B,C).
% 126.48/126.70 ** KEPT (pick-wt=10): 11 [] -intersection(A,B,C)| -member(D,C)|member(D,A).
% 126.48/126.70 ** KEPT (pick-wt=10): 12 [] -intersection(A,B,C)| -member(D,C)|member(D,B).
% 126.48/126.70 ** KEPT (pick-wt=13): 13 [] -intersection(A,B,C)| -member(D,B)| -member(D,A)|member(D,C).
% 126.48/126.70 ** KEPT (pick-wt=22): 14 [] -member(h(A,B,C),C)| -member(h(A,B,C),B)| -member(h(A,B,C),A)|intersection(A,B,C).
% 126.48/126.70 ** KEPT (pick-wt=10): 15 [] -difference(A,B,C)| -member(D,C)|member(D,A).
% 126.48/126.70 ** KEPT (pick-wt=10): 16 [] -member(A,B)| -member(A,C)| -difference(D,B,C).
% 126.48/126.70 ** KEPT (pick-wt=13): 17 [] -member(A,B)| -difference(B,C,D)|member(A,D)|member(A,C).
% 126.48/126.70 ** KEPT (pick-wt=16): 18 [] -member(k(A,B,C),B)|member(k(A,B,C),C)|difference(A,B,C).
% 126.48/126.70 ** KEPT (pick-wt=22): 19 [] -member(k(A,B,C),C)| -member(k(A,B,C),A)|member(k(A,B,C),B)|difference(A,B,C).
% 126.48/126.70 ** KEPT (pick-wt=4): 20 [] -union(cDa,cDb,cD_aIb).
% 126.48/126.70
% 126.48/126.70 ------------> process sos:
% 126.48/126.70 ** KEPT (pick-wt=8): 33 [] subset(A,B)|member(member_of_1_not_of_2(A,B),A).
% 126.48/126.70 ** KEPT (pick-wt=22): 34 [] union(A,B,C)|member(g(A,B,C),A)|member(g(A,B,C),B)|member(g(A,B,C),C).
% 126.48/126.70 ** KEPT (pick-wt=16): 35 [] member(h(A,B,C),C)|intersection(A,B,C)|member(h(A,B,C),A).
% 126.48/126.70 ** KEPT (pick-wt=16): 36 [] member(h(A,B,C),C)|intersection(A,B,C)|member(h(A,B,C),B).
% 126.48/126.70 ** KEPT (pick-wt=16): 37 [] difference(A,B,C)|member(k(A,B,C),A)|member(k(A,B,C),C).
% 126.48/126.70 ** KEPT (pick-wt=4): 38 [] intersection(a,b,aIb).
% 126.48/126.70 ** KEPT (pick-wt=4): 39 [] difference(c,a,cDa).
% 126.48/126.70 ** KEPT (pick-wt=4): 40 [] difference(c,b,cDb).
% 126.48/126.70 ** KEPT (pick-wt=4): 41 [] difference(c,aIb,cD_aIb).
% 126.48/126.70
% 126.48/126.70 ======= end of input processing =======
% 126.48/126.70
% 126.48/126.70 =========== start of search ===========
% 126.48/126.70
% 126.48/126.70
% 126.48/126.70 Resetting weight limit to 15.
% 126.48/126.70
% 126.48/126.70
% 126.48/126.70 Resetting weight limit to 15.
% 126.48/126.70
% 126.48/126.70 sos_size=4878
% 126.48/126.70
% 126.48/126.70
% 126.48/126.70 Resetting weight limit to 13.
% 126.48/126.70
% 126.48/126.70
% 126.48/126.70 Resetting weight limit to 13.
% 126.48/126.70
% 126.48/126.70 sos_size=3495
% 126.48/126.70
% 126.48/126.70 -- HEY sandbox2, WE HAVE A PROOF!! --
% 126.48/126.70
% 126.48/126.70 -----> EMPTY CLAUSE at 124.72 sec ----> 9273 [hyper,9271,16,9264,1262] $F.
% 126.48/126.70
% 126.48/126.70 Length of proof is 22. Level of proof is 8.
% 126.48/126.70
% 126.48/126.70 ---------------- PROOF ----------------
% 126.48/126.70 % SZS status Unsatisfiable
% 126.48/126.70 % SZS output start Refutation
% See solution above
% 126.48/126.70 ------------ end of proof -------------
% 126.48/126.70
% 126.48/126.70
% 126.48/126.70 Search stopped by max_proofs option.
% 126.48/126.70
% 126.48/126.70
% 126.48/126.70 Search stopped by max_proofs option.
% 126.48/126.70
% 126.48/126.70 ============ end of search ============
% 126.48/126.70
% 126.48/126.70 -------------- statistics -------------
% 126.48/126.70 clauses given 3660
% 126.48/126.70 clauses generated 7529707
% 126.48/126.70 clauses kept 9272
% 126.48/126.70 clauses forward subsumed 372432
% 126.48/126.70 clauses back subsumed 6221
% 126.48/126.70 Kbytes malloced 5859
% 126.48/126.70
% 126.48/126.70 ----------- times (seconds) -----------
% 126.48/126.70 user CPU time 124.72 (0 hr, 2 min, 4 sec)
% 126.48/126.70 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 126.48/126.70 wall-clock time 126 (0 hr, 2 min, 6 sec)
% 126.48/126.70
% 126.48/126.70 That finishes the proof of the theorem.
% 126.48/126.70
% 126.48/126.70 Process 3919 finished Wed Jul 27 10:39:44 2022
% 126.48/126.70 Otter interrupted
% 126.48/126.70 PROOF FOUND
%------------------------------------------------------------------------------