%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET576+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n015.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 13:13:43 EDT 2022
% Result : Theorem 1.92s 2.12s
% Output : Refutation 1.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 5
% Syntax : Number of clauses : 8 ( 2 unt; 3 nHn; 5 RR)
% Number of literals : 14 ( 0 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ intersect(A,B)
| member(dollar_f1(A,B),A) ),
file('SET576+3.p',unknown),
[] ).
cnf(2,axiom,
( ~ intersect(A,B)
| member(dollar_f1(A,B),B) ),
file('SET576+3.p',unknown),
[] ).
cnf(6,axiom,
( ~ member(A,dollar_c2)
| ~ member(A,dollar_c1) ),
file('SET576+3.p',unknown),
[] ).
cnf(7,axiom,
~ disjoint(dollar_c2,dollar_c1),
file('SET576+3.p',unknown),
[] ).
cnf(9,axiom,
( disjoint(A,B)
| intersect(A,B) ),
file('SET576+3.p',unknown),
[] ).
cnf(11,plain,
( disjoint(A,B)
| member(dollar_f1(A,B),B) ),
inference(hyper,[status(thm)],[9,2]),
[iquote('hyper,9,2')] ).
cnf(12,plain,
( disjoint(A,B)
| member(dollar_f1(A,B),A) ),
inference(hyper,[status(thm)],[9,1]),
[iquote('hyper,9,1')] ).
cnf(19,plain,
$false,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[12,6,11]),7,7]),
[iquote('hyper,12,6,11,unit_del,7,7')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET576+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n015.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 10:49:57 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.92/2.12 ----- Otter 3.3f, August 2004 -----
% 1.92/2.12 The process was started by sandbox2 on n015.cluster.edu,
% 1.92/2.12 Wed Jul 27 10:49:57 2022
% 1.92/2.12 The command was "./otter". The process ID is 20918.
% 1.92/2.12
% 1.92/2.12 set(prolog_style_variables).
% 1.92/2.12 set(auto).
% 1.92/2.12 dependent: set(auto1).
% 1.92/2.12 dependent: set(process_input).
% 1.92/2.12 dependent: clear(print_kept).
% 1.92/2.12 dependent: clear(print_new_demod).
% 1.92/2.12 dependent: clear(print_back_demod).
% 1.92/2.12 dependent: clear(print_back_sub).
% 1.92/2.12 dependent: set(control_memory).
% 1.92/2.12 dependent: assign(max_mem, 12000).
% 1.92/2.12 dependent: assign(pick_given_ratio, 4).
% 1.92/2.12 dependent: assign(stats_level, 1).
% 1.92/2.12 dependent: assign(max_seconds, 10800).
% 1.92/2.12 clear(print_given).
% 1.92/2.12
% 1.92/2.12 formula_list(usable).
% 1.92/2.12 all B C (intersect(B,C)<-> (exists D (member(D,B)&member(D,C)))).
% 1.92/2.12 all B C (disjoint(B,C)<-> -intersect(B,C)).
% 1.92/2.12 all B C (intersect(B,C)->intersect(C,B)).
% 1.92/2.12 -(all B C ((all D (member(D,B)-> -member(D,C)))->disjoint(B,C))).
% 1.92/2.12 end_of_list.
% 1.92/2.12
% 1.92/2.12 -------> usable clausifies to:
% 1.92/2.12
% 1.92/2.12 list(usable).
% 1.92/2.12 0 [] -intersect(B,C)|member($f1(B,C),B).
% 1.92/2.12 0 [] -intersect(B,C)|member($f1(B,C),C).
% 1.92/2.12 0 [] intersect(B,C)| -member(D,B)| -member(D,C).
% 1.92/2.12 0 [] -disjoint(B,C)| -intersect(B,C).
% 1.92/2.12 0 [] disjoint(B,C)|intersect(B,C).
% 1.92/2.12 0 [] -intersect(B,C)|intersect(C,B).
% 1.92/2.12 0 [] -member(D,$c2)| -member(D,$c1).
% 1.92/2.12 0 [] -disjoint($c2,$c1).
% 1.92/2.12 end_of_list.
% 1.92/2.12
% 1.92/2.12 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=3.
% 1.92/2.12
% 1.92/2.12 This is a non-Horn set without equality. The strategy will
% 1.92/2.12 be ordered hyper_res, unit deletion, and factoring, with
% 1.92/2.12 satellites in sos and with nuclei in usable.
% 1.92/2.12
% 1.92/2.12 dependent: set(hyper_res).
% 1.92/2.12 dependent: set(factor).
% 1.92/2.12 dependent: set(unit_deletion).
% 1.92/2.12
% 1.92/2.12 ------------> process usable:
% 1.92/2.12 ** KEPT (pick-wt=8): 1 [] -intersect(A,B)|member($f1(A,B),A).
% 1.92/2.12 ** KEPT (pick-wt=8): 2 [] -intersect(A,B)|member($f1(A,B),B).
% 1.92/2.12 ** KEPT (pick-wt=9): 3 [] intersect(A,B)| -member(C,A)| -member(C,B).
% 1.92/2.12 ** KEPT (pick-wt=6): 4 [] -disjoint(A,B)| -intersect(A,B).
% 1.92/2.12 ** KEPT (pick-wt=6): 5 [] -intersect(A,B)|intersect(B,A).
% 1.92/2.12 ** KEPT (pick-wt=6): 6 [] -member(A,$c2)| -member(A,$c1).
% 1.92/2.12 ** KEPT (pick-wt=3): 7 [] -disjoint($c2,$c1).
% 1.92/2.12
% 1.92/2.12 ------------> process sos:
% 1.92/2.12 ** KEPT (pick-wt=6): 9 [] disjoint(A,B)|intersect(A,B).
% 1.92/2.12
% 1.92/2.12 ======= end of input processing =======
% 1.92/2.12
% 1.92/2.12 =========== start of search ===========
% 1.92/2.12
% 1.92/2.12 -------- PROOF --------
% 1.92/2.12
% 1.92/2.12 -----> EMPTY CLAUSE at 0.00 sec ----> 19 [hyper,12,6,11,unit_del,7,7] $F.
% 1.92/2.12
% 1.92/2.12 Length of proof is 2. Level of proof is 1.
% 1.92/2.12
% 1.92/2.12 ---------------- PROOF ----------------
% 1.92/2.12 % SZS status Theorem
% 1.92/2.12 % SZS output start Refutation
% See solution above
% 1.92/2.12 ------------ end of proof -------------
% 1.92/2.12
% 1.92/2.12
% 1.92/2.12 Search stopped by max_proofs option.
% 1.92/2.12
% 1.92/2.12
% 1.92/2.12 Search stopped by max_proofs option.
% 1.92/2.12
% 1.92/2.12 ============ end of search ============
% 1.92/2.12
% 1.92/2.12 -------------- statistics -------------
% 1.92/2.12 clauses given 5
% 1.92/2.12 clauses generated 16
% 1.92/2.12 clauses kept 18
% 1.92/2.12 clauses forward subsumed 5
% 1.92/2.12 clauses back subsumed 0
% 1.92/2.12 Kbytes malloced 976
% 1.92/2.12
% 1.92/2.12 ----------- times (seconds) -----------
% 1.92/2.12 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.92/2.12 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.92/2.12 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.92/2.12
% 1.92/2.12 That finishes the proof of the theorem.
% 1.92/2.12
% 1.92/2.12 Process 20918 finished Wed Jul 27 10:49:58 2022
% 1.92/2.12 Otter interrupted
% 1.92/2.12 PROOF FOUND
%------------------------------------------------------------------------------