%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET625+3 : TPTP v8.1.0. Released v2.2.0.
% 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 13:13:54 EDT 2022
% Result : Theorem 1.91s 2.08s
% Output : Refutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 12 ( 8 unt; 0 nHn; 12 RR)
% Number of literals : 18 ( 0 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ intersect(A,B)
| member(dollar_f1(A,B),A) ),
file('SET625+3.p',unknown),
[] ).
cnf(2,axiom,
( ~ intersect(A,B)
| member(dollar_f1(A,B),B) ),
file('SET625+3.p',unknown),
[] ).
cnf(3,axiom,
( intersect(A,B)
| ~ member(C,A)
| ~ member(C,B) ),
file('SET625+3.p',unknown),
[] ).
cnf(4,axiom,
( ~ subset(A,B)
| ~ member(C,A)
| member(C,B) ),
file('SET625+3.p',unknown),
[] ).
cnf(7,axiom,
~ intersect(dollar_c3,dollar_c1),
file('SET625+3.p',unknown),
[] ).
cnf(11,axiom,
intersect(dollar_c3,dollar_c2),
file('SET625+3.p',unknown),
[] ).
cnf(12,axiom,
subset(dollar_c2,dollar_c1),
file('SET625+3.p',unknown),
[] ).
cnf(14,plain,
member(dollar_f1(dollar_c3,dollar_c2),dollar_c2),
inference(hyper,[status(thm)],[11,2]),
[iquote('hyper,11,2')] ).
cnf(15,plain,
member(dollar_f1(dollar_c3,dollar_c2),dollar_c3),
inference(hyper,[status(thm)],[11,1]),
[iquote('hyper,11,1')] ).
cnf(19,plain,
member(dollar_f1(dollar_c3,dollar_c2),dollar_c1),
inference(hyper,[status(thm)],[14,4,12]),
[iquote('hyper,14,4,12')] ).
cnf(30,plain,
intersect(dollar_c3,dollar_c1),
inference(hyper,[status(thm)],[19,3,15]),
[iquote('hyper,19,3,15')] ).
cnf(31,plain,
$false,
inference(binary,[status(thm)],[30,7]),
[iquote('binary,30.1,7.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET625+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 10:38:16 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.91/2.08 ----- Otter 3.3f, August 2004 -----
% 1.91/2.08 The process was started by sandbox2 on n006.cluster.edu,
% 1.91/2.08 Wed Jul 27 10:38:17 2022
% 1.91/2.08 The command was "./otter". The process ID is 25002.
% 1.91/2.08
% 1.91/2.08 set(prolog_style_variables).
% 1.91/2.08 set(auto).
% 1.91/2.08 dependent: set(auto1).
% 1.91/2.08 dependent: set(process_input).
% 1.91/2.08 dependent: clear(print_kept).
% 1.91/2.08 dependent: clear(print_new_demod).
% 1.91/2.08 dependent: clear(print_back_demod).
% 1.91/2.08 dependent: clear(print_back_sub).
% 1.91/2.08 dependent: set(control_memory).
% 1.91/2.08 dependent: assign(max_mem, 12000).
% 1.91/2.08 dependent: assign(pick_given_ratio, 4).
% 1.91/2.08 dependent: assign(stats_level, 1).
% 1.91/2.08 dependent: assign(max_seconds, 10800).
% 1.91/2.08 clear(print_given).
% 1.91/2.08
% 1.91/2.08 formula_list(usable).
% 1.91/2.08 all B C (intersect(B,C)<-> (exists D (member(D,B)&member(D,C)))).
% 1.91/2.08 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.91/2.08 all B C (intersect(B,C)->intersect(C,B)).
% 1.91/2.08 all B subset(B,B).
% 1.91/2.08 -(all B C D (intersect(B,C)&subset(C,D)->intersect(B,D))).
% 1.91/2.08 end_of_list.
% 1.91/2.08
% 1.91/2.08 -------> usable clausifies to:
% 1.91/2.08
% 1.91/2.08 list(usable).
% 1.91/2.08 0 [] -intersect(B,C)|member($f1(B,C),B).
% 1.91/2.08 0 [] -intersect(B,C)|member($f1(B,C),C).
% 1.91/2.08 0 [] intersect(B,C)| -member(D,B)| -member(D,C).
% 1.91/2.08 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.91/2.08 0 [] subset(B,C)|member($f2(B,C),B).
% 1.91/2.08 0 [] subset(B,C)| -member($f2(B,C),C).
% 1.91/2.08 0 [] -intersect(B,C)|intersect(C,B).
% 1.91/2.08 0 [] subset(B,B).
% 1.91/2.08 0 [] intersect($c3,$c2).
% 1.91/2.08 0 [] subset($c2,$c1).
% 1.91/2.08 0 [] -intersect($c3,$c1).
% 1.91/2.08 end_of_list.
% 1.91/2.08
% 1.91/2.08 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=3.
% 1.91/2.08
% 1.91/2.08 This is a non-Horn set without equality. The strategy will
% 1.91/2.08 be ordered hyper_res, unit deletion, and factoring, with
% 1.91/2.08 satellites in sos and with nuclei in usable.
% 1.91/2.08
% 1.91/2.08 dependent: set(hyper_res).
% 1.91/2.08 dependent: set(factor).
% 1.91/2.08 dependent: set(unit_deletion).
% 1.91/2.08
% 1.91/2.08 ------------> process usable:
% 1.91/2.08 ** KEPT (pick-wt=8): 1 [] -intersect(A,B)|member($f1(A,B),A).
% 1.91/2.08 ** KEPT (pick-wt=8): 2 [] -intersect(A,B)|member($f1(A,B),B).
% 1.91/2.08 ** KEPT (pick-wt=9): 3 [] intersect(A,B)| -member(C,A)| -member(C,B).
% 1.91/2.08 ** KEPT (pick-wt=9): 4 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.91/2.08 ** KEPT (pick-wt=8): 5 [] subset(A,B)| -member($f2(A,B),B).
% 1.91/2.08 ** KEPT (pick-wt=6): 6 [] -intersect(A,B)|intersect(B,A).
% 1.91/2.08 ** KEPT (pick-wt=3): 7 [] -intersect($c3,$c1).
% 1.91/2.08
% 1.91/2.08 ------------> process sos:
% 1.91/2.08 ** KEPT (pick-wt=8): 9 [] subset(A,B)|member($f2(A,B),A).
% 1.91/2.08 ** KEPT (pick-wt=3): 10 [] subset(A,A).
% 1.91/2.08 ** KEPT (pick-wt=3): 11 [] intersect($c3,$c2).
% 1.91/2.08 ** KEPT (pick-wt=3): 12 [] subset($c2,$c1).
% 1.91/2.08
% 1.91/2.08 ======= end of input processing =======
% 1.91/2.08
% 1.91/2.08 =========== start of search ===========
% 1.91/2.08
% 1.91/2.08 -------- PROOF --------
% 1.91/2.08
% 1.91/2.08 ----> UNIT CONFLICT at 0.00 sec ----> 31 [binary,30.1,7.1] $F.
% 1.91/2.08
% 1.91/2.08 Length of proof is 4. Level of proof is 3.
% 1.91/2.08
% 1.91/2.08 ---------------- PROOF ----------------
% 1.91/2.08 % SZS status Theorem
% 1.91/2.08 % SZS output start Refutation
% See solution above
% 1.91/2.08 ------------ end of proof -------------
% 1.91/2.08
% 1.91/2.08
% 1.91/2.08 Search stopped by max_proofs option.
% 1.91/2.08
% 1.91/2.08
% 1.91/2.08 Search stopped by max_proofs option.
% 1.91/2.08
% 1.91/2.08 ============ end of search ============
% 1.91/2.08
% 1.91/2.08 -------------- statistics -------------
% 1.91/2.08 clauses given 12
% 1.91/2.08 clauses generated 44
% 1.91/2.08 clauses kept 30
% 1.91/2.08 clauses forward subsumed 25
% 1.91/2.08 clauses back subsumed 0
% 1.91/2.08 Kbytes malloced 976
% 1.91/2.08
% 1.91/2.08 ----------- times (seconds) -----------
% 1.91/2.08 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.91/2.08 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.91/2.08 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.91/2.08
% 1.91/2.08 That finishes the proof of the theorem.
% 1.91/2.08
% 1.91/2.08 Process 25002 finished Wed Jul 27 10:38:18 2022
% 1.91/2.08 Otter interrupted
% 1.91/2.08 PROOF FOUND
%------------------------------------------------------------------------------