%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET575+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 1.65s 1.84s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 4 unt; 0 nHn; 7 RR)
% Number of literals : 10 ( 0 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 5 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ intersect(A,B)
| member(dollar_f1(A,B),A) ),
file('SET575+3.p',unknown),
[] ).
cnf(2,axiom,
( ~ intersect(A,B)
| member(dollar_f1(A,B),B) ),
file('SET575+3.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(A,dollar_c2)
| ~ member(A,dollar_c1) ),
file('SET575+3.p',unknown),
[] ).
cnf(6,axiom,
intersect(dollar_c2,dollar_c1),
file('SET575+3.p',unknown),
[] ).
cnf(8,plain,
member(dollar_f1(dollar_c2,dollar_c1),dollar_c1),
inference(hyper,[status(thm)],[6,2]),
[iquote('hyper,6,2')] ).
cnf(9,plain,
member(dollar_f1(dollar_c2,dollar_c1),dollar_c2),
inference(hyper,[status(thm)],[6,1]),
[iquote('hyper,6,1')] ).
cnf(14,plain,
$false,
inference(hyper,[status(thm)],[9,5,8]),
[iquote('hyper,9,5,8')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET575+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : otter-tptp-script %s
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Jul 27 10:42:20 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.65/1.84 ----- Otter 3.3f, August 2004 -----
% 1.65/1.84 The process was started by sandbox2 on n022.cluster.edu,
% 1.65/1.84 Wed Jul 27 10:42:20 2022
% 1.65/1.84 The command was "./otter". The process ID is 24630.
% 1.65/1.84
% 1.65/1.84 set(prolog_style_variables).
% 1.65/1.84 set(auto).
% 1.65/1.84 dependent: set(auto1).
% 1.65/1.84 dependent: set(process_input).
% 1.65/1.84 dependent: clear(print_kept).
% 1.65/1.84 dependent: clear(print_new_demod).
% 1.65/1.84 dependent: clear(print_back_demod).
% 1.65/1.84 dependent: clear(print_back_sub).
% 1.65/1.84 dependent: set(control_memory).
% 1.65/1.84 dependent: assign(max_mem, 12000).
% 1.65/1.84 dependent: assign(pick_given_ratio, 4).
% 1.65/1.84 dependent: assign(stats_level, 1).
% 1.65/1.84 dependent: assign(max_seconds, 10800).
% 1.65/1.84 clear(print_given).
% 1.65/1.84
% 1.65/1.84 formula_list(usable).
% 1.65/1.84 all B C (intersect(B,C)<-> (exists D (member(D,B)&member(D,C)))).
% 1.65/1.84 all B C (intersect(B,C)->intersect(C,B)).
% 1.65/1.84 -(all B C (intersect(B,C)-> (exists D (member(D,B)&member(D,C))))).
% 1.65/1.84 end_of_list.
% 1.65/1.84
% 1.65/1.84 -------> usable clausifies to:
% 1.65/1.84
% 1.65/1.84 list(usable).
% 1.65/1.84 0 [] -intersect(B,C)|member($f1(B,C),B).
% 1.65/1.84 0 [] -intersect(B,C)|member($f1(B,C),C).
% 1.65/1.84 0 [] intersect(B,C)| -member(D,B)| -member(D,C).
% 1.65/1.84 0 [] -intersect(B,C)|intersect(C,B).
% 1.65/1.84 0 [] intersect($c2,$c1).
% 1.65/1.84 0 [] -member(D,$c2)| -member(D,$c1).
% 1.65/1.84 end_of_list.
% 1.65/1.84
% 1.65/1.84 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=3.
% 1.65/1.84
% 1.65/1.84 This is a Horn set without equality. The strategy will
% 1.65/1.84 be hyperresolution, with satellites in sos and nuclei
% 1.65/1.84 in usable.
% 1.65/1.84
% 1.65/1.84 dependent: set(hyper_res).
% 1.65/1.84 dependent: clear(order_hyper).
% 1.65/1.84
% 1.65/1.84 ------------> process usable:
% 1.65/1.84 ** KEPT (pick-wt=8): 1 [] -intersect(A,B)|member($f1(A,B),A).
% 1.65/1.84 ** KEPT (pick-wt=8): 2 [] -intersect(A,B)|member($f1(A,B),B).
% 1.65/1.84 ** KEPT (pick-wt=9): 3 [] intersect(A,B)| -member(C,A)| -member(C,B).
% 1.65/1.84 ** KEPT (pick-wt=6): 4 [] -intersect(A,B)|intersect(B,A).
% 1.65/1.84 ** KEPT (pick-wt=6): 5 [] -member(A,$c2)| -member(A,$c1).
% 1.65/1.84
% 1.65/1.84 ------------> process sos:
% 1.65/1.84 ** KEPT (pick-wt=3): 6 [] intersect($c2,$c1).
% 1.65/1.84
% 1.65/1.84 ======= end of input processing =======
% 1.65/1.84
% 1.65/1.84 =========== start of search ===========
% 1.65/1.84
% 1.65/1.84 -------- PROOF --------
% 1.65/1.84
% 1.65/1.84 -----> EMPTY CLAUSE at 0.00 sec ----> 14 [hyper,9,5,8] $F.
% 1.65/1.84
% 1.65/1.84 Length of proof is 2. Level of proof is 1.
% 1.65/1.84
% 1.65/1.84 ---------------- PROOF ----------------
% 1.65/1.84 % SZS status Theorem
% 1.65/1.84 % SZS output start Refutation
% See solution above
% 1.65/1.84 ------------ end of proof -------------
% 1.65/1.84
% 1.65/1.84
% 1.65/1.84 Search stopped by max_proofs option.
% 1.65/1.84
% 1.65/1.84
% 1.65/1.84 Search stopped by max_proofs option.
% 1.65/1.84
% 1.65/1.84 ============ end of search ============
% 1.65/1.84
% 1.65/1.84 -------------- statistics -------------
% 1.65/1.84 clauses given 5
% 1.65/1.84 clauses generated 12
% 1.65/1.84 clauses kept 13
% 1.65/1.84 clauses forward subsumed 4
% 1.65/1.84 clauses back subsumed 0
% 1.65/1.84 Kbytes malloced 976
% 1.65/1.84
% 1.65/1.84 ----------- times (seconds) -----------
% 1.65/1.84 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.65/1.84 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.65/1.84 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.65/1.84
% 1.65/1.84 That finishes the proof of the theorem.
% 1.65/1.84
% 1.65/1.84 Process 24630 finished Wed Jul 27 10:42:22 2022
% 1.65/1.84 Otter interrupted
% 1.65/1.84 PROOF FOUND
%------------------------------------------------------------------------------