TSTP Solution File: SET008-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET008-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.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 1.72s 1.97s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of clauses : 8 ( 4 unt; 3 nHn; 5 RR)
% Number of literals : 15 ( 0 equ; 5 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 13 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(11,axiom,
( ~ member(A,B)
| ~ member(A,C)
| ~ difference(D,B,C) ),
file('SET008-1.p',unknown),
[] ).
cnf(15,axiom,
~ intersection(a,bDa,aI_bDa),
file('SET008-1.p',unknown),
[] ).
cnf(16,axiom,
~ member(A,aI_bDa),
file('SET008-1.p',unknown),
[] ).
cnf(27,axiom,
( member(h(A,B,C),C)
| intersection(A,B,C)
| member(h(A,B,C),A) ),
file('SET008-1.p',unknown),
[] ).
cnf(28,axiom,
( member(h(A,B,C),C)
| intersection(A,B,C)
| member(h(A,B,C),B) ),
file('SET008-1.p',unknown),
[] ).
cnf(30,axiom,
difference(b,a,bDa),
file('SET008-1.p',unknown),
[] ).
cnf(42,plain,
( intersection(A,B,aI_bDa)
| member(h(A,B,aI_bDa),A) ),
inference(hyper,[status(thm)],[27,16]),
[iquote('hyper,27,16')] ).
cnf(111,plain,
$false,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[42,11,28,30]),15,16,15]),
[iquote('hyper,42,11,28,30,unit_del,15,16,15')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET008-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n027.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 10:59:36 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.72/1.94 ----- Otter 3.3f, August 2004 -----
% 1.72/1.94 The process was started by sandbox on n027.cluster.edu,
% 1.72/1.94 Wed Jul 27 10:59:37 2022
% 1.72/1.94 The command was "./otter". The process ID is 4736.
% 1.72/1.94
% 1.72/1.94 set(prolog_style_variables).
% 1.72/1.94 set(auto).
% 1.72/1.94 dependent: set(auto1).
% 1.72/1.94 dependent: set(process_input).
% 1.72/1.94 dependent: clear(print_kept).
% 1.72/1.94 dependent: clear(print_new_demod).
% 1.72/1.94 dependent: clear(print_back_demod).
% 1.72/1.94 dependent: clear(print_back_sub).
% 1.72/1.94 dependent: set(control_memory).
% 1.72/1.94 dependent: assign(max_mem, 12000).
% 1.72/1.94 dependent: assign(pick_given_ratio, 4).
% 1.72/1.94 dependent: assign(stats_level, 1).
% 1.72/1.94 dependent: assign(max_seconds, 10800).
% 1.72/1.94 clear(print_given).
% 1.72/1.94
% 1.72/1.94 list(usable).
% 1.72/1.94 0 [] -member(Element,Subset)| -subset(Subset,Superset)|member(Element,Superset).
% 1.72/1.94 0 [] subset(Subset,Superset)|member(member_of_1_not_of_2(Subset,Superset),Subset).
% 1.72/1.94 0 [] -member(member_of_1_not_of_2(Subset,Superset),Superset)|subset(Subset,Superset).
% 1.72/1.94 0 [] -e_qual_sets(Subset,Superset)|subset(Subset,Superset).
% 1.72/1.94 0 [] -e_qual_sets(Superset,Subset)|subset(Subset,Superset).
% 1.72/1.94 0 [] -subset(Set1,Set2)| -subset(Set2,Set1)|e_qual_sets(Set2,Set1).
% 1.72/1.94 0 [] -intersection(Set1,Set2,Intersection)| -member(Element,Intersection)|member(Element,Set1).
% 1.72/1.94 0 [] -intersection(Set1,Set2,Intersection)| -member(Element,Intersection)|member(Element,Set2).
% 1.72/1.94 0 [] -intersection(Set1,Set2,Intersection)| -member(Element,Set2)| -member(Element,Set1)|member(Element,Intersection).
% 1.72/1.94 0 [] member(h(Set1,Set2,Intersection),Intersection)|intersection(Set1,Set2,Intersection)|member(h(Set1,Set2,Intersection),Set1).
% 1.72/1.94 0 [] member(h(Set1,Set2,Intersection),Intersection)|intersection(Set1,Set2,Intersection)|member(h(Set1,Set2,Intersection),Set2).
% 1.72/1.94 0 [] -member(h(Set1,Set2,Intersection),Intersection)| -member(h(Set1,Set2,Intersection),Set2)| -member(h(Set1,Set2,Intersection),Set1)|intersection(Set1,Set2,Intersection).
% 1.72/1.94 0 [] -difference(Set1,Set2,Difference)| -member(Element,Difference)|member(Element,Set1).
% 1.72/1.94 0 [] -member(Element,Set1)| -member(Element,Set2)| -difference(A_set,Set1,Set2).
% 1.72/1.94 0 [] -member(Element,Set1)| -difference(Set1,Set2,Difference)|member(Element,Difference)|member(Element,Set2).
% 1.72/1.94 0 [] difference(Set1,Set2,Difference)|member(k(Set1,Set2,Difference),Set1)|member(k(Set1,Set2,Difference),Difference).
% 1.72/1.94 0 [] -member(k(Set1,Set2,Difference),Set2)|member(k(Set1,Set2,Difference),Difference)|difference(Set1,Set2,Difference).
% 1.72/1.94 0 [] -member(k(Set1,Set2,Difference),Difference)| -member(k(Set1,Set2,Difference),Set1)|member(k(Set1,Set2,Difference),Set2)|difference(Set1,Set2,Difference).
% 1.72/1.94 0 [] difference(b,a,bDa).
% 1.72/1.94 0 [] -intersection(a,bDa,aI_bDa).
% 1.72/1.94 0 [] -member(A,aI_bDa).
% 1.72/1.94 end_of_list.
% 1.72/1.94
% 1.72/1.94 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=4.
% 1.72/1.94
% 1.72/1.94 This is a non-Horn set without equality. The strategy will
% 1.72/1.94 be ordered hyper_res, unit deletion, and factoring, with
% 1.72/1.94 satellites in sos and with nuclei in usable.
% 1.72/1.94
% 1.72/1.94 dependent: set(hyper_res).
% 1.72/1.94 dependent: set(factor).
% 1.72/1.94 dependent: set(unit_deletion).
% 1.72/1.94
% 1.72/1.94 ------------> process usable:
% 1.72/1.94 ** KEPT (pick-wt=9): 1 [] -member(A,B)| -subset(B,C)|member(A,C).
% 1.72/1.94 ** KEPT (pick-wt=8): 2 [] -member(member_of_1_not_of_2(A,B),B)|subset(A,B).
% 1.72/1.94 ** KEPT (pick-wt=6): 3 [] -e_qual_sets(A,B)|subset(A,B).
% 1.72/1.94 ** KEPT (pick-wt=6): 4 [] -e_qual_sets(A,B)|subset(B,A).
% 1.72/1.94 ** KEPT (pick-wt=9): 5 [] -subset(A,B)| -subset(B,A)|e_qual_sets(B,A).
% 1.72/1.94 ** KEPT (pick-wt=10): 6 [] -intersection(A,B,C)| -member(D,C)|member(D,A).
% 1.72/1.94 ** KEPT (pick-wt=10): 7 [] -intersection(A,B,C)| -member(D,C)|member(D,B).
% 1.72/1.94 ** KEPT (pick-wt=13): 8 [] -intersection(A,B,C)| -member(D,B)| -member(D,A)|member(D,C).
% 1.72/1.94 ** 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).
% 1.72/1.94 ** KEPT (pick-wt=10): 10 [] -difference(A,B,C)| -member(D,C)|member(D,A).
% 1.72/1.94 ** KEPT (pick-wt=10): 11 [] -member(A,B)| -member(A,C)| -difference(D,B,C).
% 1.72/1.94 ** KEPT (pick-wt=13): 12 [] -member(A,B)| -difference(B,C,D)|member(A,D)|member(A,C).
% 1.72/1.94 ** KEPT (pick-wt=16): 13 [] -member(k(A,B,C),B)|member(k(A,B,C),C)|difference(A,B,C).
% 1.72/1.94 ** KEPT (pick-wt=22): 14 [] -member(k(A,B,C),C)| -member(k(A,B,C),A)|member(k(A,B,C),B)|difference(A,B,C).
% 1.72/1.94 ** KEPT (pick-wt=4): 15 [] -intersection(a,bDa,aI_bDa).
% 1.72/1.97 ** KEPT (pick-wt=3): 16 [] -member(A,aI_bDa).
% 1.72/1.97
% 1.72/1.97 ------------> process sos:
% 1.72/1.97 ** KEPT (pick-wt=8): 26 [] subset(A,B)|member(member_of_1_not_of_2(A,B),A).
% 1.72/1.97 ** KEPT (pick-wt=16): 27 [] member(h(A,B,C),C)|intersection(A,B,C)|member(h(A,B,C),A).
% 1.72/1.97 ** KEPT (pick-wt=16): 28 [] member(h(A,B,C),C)|intersection(A,B,C)|member(h(A,B,C),B).
% 1.72/1.97 ** KEPT (pick-wt=16): 29 [] difference(A,B,C)|member(k(A,B,C),A)|member(k(A,B,C),C).
% 1.72/1.97 ** KEPT (pick-wt=4): 30 [] difference(b,a,bDa).
% 1.72/1.97
% 1.72/1.97 ======= end of input processing =======
% 1.72/1.97
% 1.72/1.97 =========== start of search ===========
% 1.72/1.97
% 1.72/1.97 -------- PROOF --------
% 1.72/1.97
% 1.72/1.97 -----> EMPTY CLAUSE at 0.03 sec ----> 111 [hyper,42,11,28,30,unit_del,15,16,15] $F.
% 1.72/1.97
% 1.72/1.97 Length of proof is 1. Level of proof is 1.
% 1.72/1.97
% 1.72/1.97 ---------------- PROOF ----------------
% 1.72/1.97 % SZS status Unsatisfiable
% 1.72/1.97 % SZS output start Refutation
% See solution above
% 1.72/1.97 ------------ end of proof -------------
% 1.72/1.97
% 1.72/1.97
% 1.72/1.97 Search stopped by max_proofs option.
% 1.72/1.97
% 1.72/1.97
% 1.72/1.97 Search stopped by max_proofs option.
% 1.72/1.97
% 1.72/1.97 ============ end of search ============
% 1.72/1.97
% 1.72/1.97 -------------- statistics -------------
% 1.72/1.97 clauses given 19
% 1.72/1.97 clauses generated 988
% 1.72/1.97 clauses kept 110
% 1.72/1.97 clauses forward subsumed 898
% 1.72/1.97 clauses back subsumed 10
% 1.72/1.97 Kbytes malloced 976
% 1.72/1.97
% 1.72/1.97 ----------- times (seconds) -----------
% 1.72/1.97 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.72/1.97 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.72/1.97 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.72/1.97
% 1.72/1.97 That finishes the proof of the theorem.
% 1.72/1.97
% 1.72/1.97 Process 4736 finished Wed Jul 27 10:59:38 2022
% 1.72/1.97 Otter interrupted
% 1.72/1.97 PROOF FOUND
%------------------------------------------------------------------------------