TSTP Solution File: SET925+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET925+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 13:14:32 EDT 2022
% Result : Theorem 1.81s 2.00s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 5 unt; 1 nHn; 8 RR)
% Number of literals : 13 ( 6 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 5 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( set_difference(singleton(dollar_c4),dollar_c3) != empty_set
| ~ in(dollar_c4,dollar_c3) ),
file('SET925+1.p',unknown),
[] ).
cnf(4,axiom,
( set_difference(singleton(A),B) != empty_set
| in(A,B) ),
file('SET925+1.p',unknown),
[] ).
cnf(5,axiom,
( set_difference(singleton(A),B) = empty_set
| ~ in(A,B) ),
file('SET925+1.p',unknown),
[] ).
cnf(7,axiom,
A = A,
file('SET925+1.p',unknown),
[] ).
cnf(10,axiom,
( set_difference(singleton(dollar_c4),dollar_c3) = empty_set
| in(dollar_c4,dollar_c3) ),
file('SET925+1.p',unknown),
[] ).
cnf(12,plain,
set_difference(singleton(dollar_c4),dollar_c3) = empty_set,
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[10,5])]),
[iquote('hyper,10,5,factor_simp')] ).
cnf(13,plain,
~ in(dollar_c4,dollar_c3),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3]),12]),7]),
[iquote('back_demod,3,demod,12,unit_del,7')] ).
cnf(14,plain,
in(dollar_c4,dollar_c3),
inference(hyper,[status(thm)],[12,4]),
[iquote('hyper,11,4')] ).
cnf(15,plain,
$false,
inference(binary,[status(thm)],[14,13]),
[iquote('binary,14.1,13.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET925+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : otter-tptp-script %s
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Jul 27 10:50:56 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.81/2.00 ----- Otter 3.3f, August 2004 -----
% 1.81/2.00 The process was started by sandbox2 on n003.cluster.edu,
% 1.81/2.00 Wed Jul 27 10:50:57 2022
% 1.81/2.00 The command was "./otter". The process ID is 9754.
% 1.81/2.00
% 1.81/2.00 set(prolog_style_variables).
% 1.81/2.00 set(auto).
% 1.81/2.00 dependent: set(auto1).
% 1.81/2.00 dependent: set(process_input).
% 1.81/2.00 dependent: clear(print_kept).
% 1.81/2.00 dependent: clear(print_new_demod).
% 1.81/2.00 dependent: clear(print_back_demod).
% 1.81/2.00 dependent: clear(print_back_sub).
% 1.81/2.00 dependent: set(control_memory).
% 1.81/2.00 dependent: assign(max_mem, 12000).
% 1.81/2.00 dependent: assign(pick_given_ratio, 4).
% 1.81/2.00 dependent: assign(stats_level, 1).
% 1.81/2.00 dependent: assign(max_seconds, 10800).
% 1.81/2.00 clear(print_given).
% 1.81/2.00
% 1.81/2.00 formula_list(usable).
% 1.81/2.00 all A (A=A).
% 1.81/2.00 all A B (in(A,B)-> -in(B,A)).
% 1.81/2.00 empty(empty_set).
% 1.81/2.00 exists A empty(A).
% 1.81/2.00 exists A (-empty(A)).
% 1.81/2.00 -(all A B (set_difference(singleton(A),B)=empty_set<->in(A,B))).
% 1.81/2.00 all A B (set_difference(singleton(A),B)=empty_set<->in(A,B)).
% 1.81/2.00 end_of_list.
% 1.81/2.00
% 1.81/2.00 -------> usable clausifies to:
% 1.81/2.00
% 1.81/2.00 list(usable).
% 1.81/2.00 0 [] A=A.
% 1.81/2.00 0 [] -in(A,B)| -in(B,A).
% 1.81/2.00 0 [] empty(empty_set).
% 1.81/2.00 0 [] empty($c1).
% 1.81/2.00 0 [] -empty($c2).
% 1.81/2.00 0 [] set_difference(singleton($c4),$c3)=empty_set|in($c4,$c3).
% 1.81/2.00 0 [] set_difference(singleton($c4),$c3)!=empty_set| -in($c4,$c3).
% 1.81/2.00 0 [] set_difference(singleton(A),B)!=empty_set|in(A,B).
% 1.81/2.00 0 [] set_difference(singleton(A),B)=empty_set| -in(A,B).
% 1.81/2.00 end_of_list.
% 1.81/2.00
% 1.81/2.00 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=2.
% 1.81/2.00
% 1.81/2.00 This ia a non-Horn set with equality. The strategy will be
% 1.81/2.00 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.81/2.00 deletion, with positive clauses in sos and nonpositive
% 1.81/2.00 clauses in usable.
% 1.81/2.00
% 1.81/2.00 dependent: set(knuth_bendix).
% 1.81/2.00 dependent: set(anl_eq).
% 1.81/2.00 dependent: set(para_from).
% 1.81/2.00 dependent: set(para_into).
% 1.81/2.00 dependent: clear(para_from_right).
% 1.81/2.00 dependent: clear(para_into_right).
% 1.81/2.00 dependent: set(para_from_vars).
% 1.81/2.00 dependent: set(eq_units_both_ways).
% 1.81/2.00 dependent: set(dynamic_demod_all).
% 1.81/2.00 dependent: set(dynamic_demod).
% 1.81/2.00 dependent: set(order_eq).
% 1.81/2.00 dependent: set(back_demod).
% 1.81/2.00 dependent: set(lrpo).
% 1.81/2.00 dependent: set(hyper_res).
% 1.81/2.00 dependent: set(unit_deletion).
% 1.81/2.00 dependent: set(factor).
% 1.81/2.00
% 1.81/2.00 ------------> process usable:
% 1.81/2.00 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.81/2.00 ** KEPT (pick-wt=2): 2 [] -empty($c2).
% 1.81/2.00 ** KEPT (pick-wt=9): 3 [] set_difference(singleton($c4),$c3)!=empty_set| -in($c4,$c3).
% 1.81/2.00 ** KEPT (pick-wt=9): 4 [] set_difference(singleton(A),B)!=empty_set|in(A,B).
% 1.81/2.00 ** KEPT (pick-wt=9): 5 [] set_difference(singleton(A),B)=empty_set| -in(A,B).
% 1.81/2.00
% 1.81/2.00 ------------> process sos:
% 1.81/2.00 ** KEPT (pick-wt=3): 7 [] A=A.
% 1.81/2.00 ** KEPT (pick-wt=2): 8 [] empty(empty_set).
% 1.81/2.00 ** KEPT (pick-wt=2): 9 [] empty($c1).
% 1.81/2.00 ** KEPT (pick-wt=9): 10 [] set_difference(singleton($c4),$c3)=empty_set|in($c4,$c3).
% 1.81/2.00 Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] A=A.
% 1.81/2.00
% 1.81/2.00 ======= end of input processing =======
% 1.81/2.00
% 1.81/2.00 =========== start of search ===========
% 1.81/2.00
% 1.81/2.00 -------- PROOF --------
% 1.81/2.00
% 1.81/2.00 ----> UNIT CONFLICT at 0.00 sec ----> 15 [binary,14.1,13.1] $F.
% 1.81/2.00
% 1.81/2.00 Length of proof is 3. Level of proof is 2.
% 1.81/2.00
% 1.81/2.00 ---------------- PROOF ----------------
% 1.81/2.00 % SZS status Theorem
% 1.81/2.00 % SZS output start Refutation
% See solution above
% 1.81/2.00 ------------ end of proof -------------
% 1.81/2.00
% 1.81/2.00
% 1.81/2.00 Search stopped by max_proofs option.
% 1.81/2.00
% 1.81/2.00
% 1.81/2.00 Search stopped by max_proofs option.
% 1.81/2.00
% 1.81/2.00 ============ end of search ============
% 1.81/2.00
% 1.81/2.00 -------------- statistics -------------
% 1.81/2.00 clauses given 6
% 1.81/2.00 clauses generated 3
% 1.81/2.00 clauses kept 13
% 1.81/2.00 clauses forward subsumed 2
% 1.81/2.00 clauses back subsumed 0
% 1.81/2.00 Kbytes malloced 976
% 1.81/2.00
% 1.81/2.00 ----------- times (seconds) -----------
% 1.81/2.00 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.81/2.00 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.81/2.00 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.81/2.00
% 1.81/2.00 That finishes the proof of the theorem.
% 1.81/2.00
% 1.81/2.00 Process 9754 finished Wed Jul 27 10:50:58 2022
% 1.81/2.00 Otter interrupted
% 1.81/2.00 PROOF FOUND
%------------------------------------------------------------------------------