%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET196+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 13:13:15 EDT 2022
% Result : Theorem 1.97s 2.16s
% Output : Refutation 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 10 ( 7 unt; 1 nHn; 8 RR)
% Number of literals : 13 ( 1 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 9 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ member(A,intersection(B,C))
| member(A,C) ),
file('SET196+3.p',unknown),
[] ).
cnf(5,axiom,
( subset(A,B)
| ~ member(dollar_f1(A,B),B) ),
file('SET196+3.p',unknown),
[] ).
cnf(9,axiom,
~ subset(intersection(dollar_c2,dollar_c1),dollar_c2),
file('SET196+3.p',unknown),
[] ).
cnf(13,axiom,
( subset(A,B)
| member(dollar_f1(A,B),A) ),
file('SET196+3.p',unknown),
[] ).
cnf(14,axiom,
intersection(A,B) = intersection(B,A),
file('SET196+3.p',unknown),
[] ).
cnf(18,plain,
~ subset(intersection(dollar_c1,dollar_c2),dollar_c2),
inference(para_from,[status(thm),theory(equality)],[14,9]),
[iquote('para_from,14.1.1,9.1.1')] ).
cnf(23,plain,
member(dollar_f1(intersection(dollar_c1,dollar_c2),dollar_c2),intersection(dollar_c1,dollar_c2)),
inference(hyper,[status(thm)],[13,18]),
[iquote('hyper,13,18')] ).
cnf(68,plain,
member(dollar_f1(intersection(dollar_c1,dollar_c2),dollar_c2),dollar_c2),
inference(hyper,[status(thm)],[23,2]),
[iquote('hyper,23,2')] ).
cnf(88,plain,
subset(intersection(dollar_c1,dollar_c2),dollar_c2),
inference(hyper,[status(thm)],[68,5]),
[iquote('hyper,68,5')] ).
cnf(89,plain,
$false,
inference(binary,[status(thm)],[88,18]),
[iquote('binary,88.1,18.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET196+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % 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 10:51:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.97/2.16 ----- Otter 3.3f, August 2004 -----
% 1.97/2.16 The process was started by sandbox2 on n006.cluster.edu,
% 1.97/2.16 Wed Jul 27 10:51:02 2022
% 1.97/2.16 The command was "./otter". The process ID is 6949.
% 1.97/2.16
% 1.97/2.16 set(prolog_style_variables).
% 1.97/2.16 set(auto).
% 1.97/2.16 dependent: set(auto1).
% 1.97/2.16 dependent: set(process_input).
% 1.97/2.16 dependent: clear(print_kept).
% 1.97/2.16 dependent: clear(print_new_demod).
% 1.97/2.16 dependent: clear(print_back_demod).
% 1.97/2.16 dependent: clear(print_back_sub).
% 1.97/2.16 dependent: set(control_memory).
% 1.97/2.16 dependent: assign(max_mem, 12000).
% 1.97/2.16 dependent: assign(pick_given_ratio, 4).
% 1.97/2.16 dependent: assign(stats_level, 1).
% 1.97/2.16 dependent: assign(max_seconds, 10800).
% 1.97/2.16 clear(print_given).
% 1.97/2.16
% 1.97/2.16 formula_list(usable).
% 1.97/2.16 all A (A=A).
% 1.97/2.16 all B C D (member(D,intersection(B,C))<->member(D,B)&member(D,C)).
% 1.97/2.16 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.97/2.16 all B C (intersection(B,C)=intersection(C,B)).
% 1.97/2.16 all B subset(B,B).
% 1.97/2.16 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 1.97/2.16 -(all B C subset(intersection(B,C),B)).
% 1.97/2.16 end_of_list.
% 1.97/2.16
% 1.97/2.16 -------> usable clausifies to:
% 1.97/2.16
% 1.97/2.16 list(usable).
% 1.97/2.16 0 [] A=A.
% 1.97/2.16 0 [] -member(D,intersection(B,C))|member(D,B).
% 1.97/2.16 0 [] -member(D,intersection(B,C))|member(D,C).
% 1.97/2.16 0 [] member(D,intersection(B,C))| -member(D,B)| -member(D,C).
% 1.97/2.16 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.97/2.16 0 [] subset(B,C)|member($f1(B,C),B).
% 1.97/2.16 0 [] subset(B,C)| -member($f1(B,C),C).
% 1.97/2.16 0 [] intersection(B,C)=intersection(C,B).
% 1.97/2.16 0 [] subset(B,B).
% 1.97/2.16 0 [] B!=C| -member(D,B)|member(D,C).
% 1.97/2.16 0 [] B!=C|member(D,B)| -member(D,C).
% 1.97/2.16 0 [] B=C|member($f2(B,C),B)|member($f2(B,C),C).
% 1.97/2.16 0 [] B=C| -member($f2(B,C),B)| -member($f2(B,C),C).
% 1.97/2.16 0 [] -subset(intersection($c2,$c1),$c2).
% 1.97/2.16 end_of_list.
% 1.97/2.16
% 1.97/2.16 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.97/2.16
% 1.97/2.16 This ia a non-Horn set with equality. The strategy will be
% 1.97/2.16 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.97/2.16 deletion, with positive clauses in sos and nonpositive
% 1.97/2.16 clauses in usable.
% 1.97/2.16
% 1.97/2.16 dependent: set(knuth_bendix).
% 1.97/2.16 dependent: set(anl_eq).
% 1.97/2.16 dependent: set(para_from).
% 1.97/2.16 dependent: set(para_into).
% 1.97/2.16 dependent: clear(para_from_right).
% 1.97/2.16 dependent: clear(para_into_right).
% 1.97/2.16 dependent: set(para_from_vars).
% 1.97/2.16 dependent: set(eq_units_both_ways).
% 1.97/2.16 dependent: set(dynamic_demod_all).
% 1.97/2.16 dependent: set(dynamic_demod).
% 1.97/2.16 dependent: set(order_eq).
% 1.97/2.16 dependent: set(back_demod).
% 1.97/2.16 dependent: set(lrpo).
% 1.97/2.16 dependent: set(hyper_res).
% 1.97/2.16 dependent: set(unit_deletion).
% 1.97/2.16 dependent: set(factor).
% 1.97/2.16
% 1.97/2.16 ------------> process usable:
% 1.97/2.16 ** KEPT (pick-wt=8): 1 [] -member(A,intersection(B,C))|member(A,B).
% 1.97/2.16 ** KEPT (pick-wt=8): 2 [] -member(A,intersection(B,C))|member(A,C).
% 1.97/2.16 ** KEPT (pick-wt=11): 3 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 1.97/2.16 ** KEPT (pick-wt=9): 4 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.97/2.16 ** KEPT (pick-wt=8): 5 [] subset(A,B)| -member($f1(A,B),B).
% 1.97/2.16 ** KEPT (pick-wt=9): 6 [] A!=B| -member(C,A)|member(C,B).
% 1.97/2.16 ** KEPT (pick-wt=9): 7 [] A!=B|member(C,A)| -member(C,B).
% 1.97/2.16 ** KEPT (pick-wt=13): 8 [] A=B| -member($f2(A,B),A)| -member($f2(A,B),B).
% 1.97/2.16 ** KEPT (pick-wt=5): 9 [] -subset(intersection($c2,$c1),$c2).
% 1.97/2.16
% 1.97/2.16 ------------> process sos:
% 1.97/2.16 ** KEPT (pick-wt=3): 12 [] A=A.
% 1.97/2.16 ** KEPT (pick-wt=8): 13 [] subset(A,B)|member($f1(A,B),A).
% 1.97/2.16 ** KEPT (pick-wt=7): 14 [] intersection(A,B)=intersection(B,A).
% 1.97/2.16 ** KEPT (pick-wt=3): 15 [] subset(A,A).
% 1.97/2.16 ** KEPT (pick-wt=13): 16 [] A=B|member($f2(A,B),A)|member($f2(A,B),B).
% 1.97/2.16 Following clause subsumed by 12 during input processing: 0 [copy,12,flip.1] A=A.
% 1.97/2.16 12 back subsumes 11.
% 1.97/2.16 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] intersection(A,B)=intersection(B,A).
% 1.97/2.16
% 1.97/2.16 ======= end of input processing =======
% 1.97/2.16
% 1.97/2.16 =========== start of search ===========
% 1.97/2.16
% 1.97/2.16 -------- PROOF --------
% 1.97/2.16
% 1.97/2.16 ----> UNIT CONFLICT at 0.00 sec ----> 89 [binary,88.1,18.1] $F.
% 1.97/2.16
% 1.97/2.16 Length of proof is 4. Level of proof is 4.
% 1.97/2.16
% 1.97/2.16 ---------------- PROOF ----------------
% 1.97/2.16 % SZS status Theorem
% 1.97/2.16 % SZS output start Refutation
% See solution above
% 1.97/2.16 ------------ end of proof -------------
% 1.97/2.16
% 1.97/2.16
% 1.97/2.16 Search stopped by max_proofs option.
% 1.97/2.16
% 1.97/2.16
% 1.97/2.16 Search stopped by max_proofs option.
% 1.97/2.16
% 1.97/2.16 ============ end of search ============
% 1.97/2.16
% 1.97/2.16 -------------- statistics -------------
% 1.97/2.16 clauses given 8
% 1.97/2.16 clauses generated 175
% 1.97/2.16 clauses kept 88
% 1.97/2.16 clauses forward subsumed 101
% 1.97/2.16 clauses back subsumed 1
% 1.97/2.16 Kbytes malloced 976
% 1.97/2.16
% 1.97/2.16 ----------- times (seconds) -----------
% 1.97/2.16 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.97/2.16 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.97/2.16 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.97/2.16
% 1.97/2.16 That finishes the proof of the theorem.
% 1.97/2.16
% 1.97/2.16 Process 6949 finished Wed Jul 27 10:51:03 2022
% 1.97/2.16 Otter interrupted
% 1.97/2.16 PROOF FOUND
%------------------------------------------------------------------------------