TSTP Solution File: SET904+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET904+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.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 13:14:29 EDT 2022
% Result : Theorem 1.67s 1.89s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of clauses : 5 ( 4 unt; 0 nHn; 5 RR)
% Number of literals : 6 ( 0 equ; 2 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 2 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
~ in(dollar_c4,dollar_c3),
file('SET904+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ subset(set_union2(singleton(A),B),B)
| in(A,B) ),
file('SET904+1.p',unknown),
[] ).
cnf(13,axiom,
subset(set_union2(singleton(dollar_c4),dollar_c3),dollar_c3),
file('SET904+1.p',unknown),
[] ).
cnf(15,plain,
in(dollar_c4,dollar_c3),
inference(hyper,[status(thm)],[13,6]),
[iquote('hyper,13,6')] ).
cnf(16,plain,
$false,
inference(binary,[status(thm)],[15,5]),
[iquote('binary,15.1,5.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET904+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.11/0.33 % Computer : n027.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Jul 27 10:51:21 EDT 2022
% 0.11/0.33 % CPUTime :
% 1.67/1.89 ----- Otter 3.3f, August 2004 -----
% 1.67/1.89 The process was started by sandbox on n027.cluster.edu,
% 1.67/1.89 Wed Jul 27 10:51:22 2022
% 1.67/1.89 The command was "./otter". The process ID is 24046.
% 1.67/1.89
% 1.67/1.89 set(prolog_style_variables).
% 1.67/1.89 set(auto).
% 1.67/1.89 dependent: set(auto1).
% 1.67/1.89 dependent: set(process_input).
% 1.67/1.89 dependent: clear(print_kept).
% 1.67/1.89 dependent: clear(print_new_demod).
% 1.67/1.89 dependent: clear(print_back_demod).
% 1.67/1.89 dependent: clear(print_back_sub).
% 1.67/1.89 dependent: set(control_memory).
% 1.67/1.89 dependent: assign(max_mem, 12000).
% 1.67/1.89 dependent: assign(pick_given_ratio, 4).
% 1.67/1.89 dependent: assign(stats_level, 1).
% 1.67/1.89 dependent: assign(max_seconds, 10800).
% 1.67/1.89 clear(print_given).
% 1.67/1.89
% 1.67/1.89 formula_list(usable).
% 1.67/1.89 all A (A=A).
% 1.67/1.89 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 1.67/1.89 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 1.67/1.89 all A B (set_union2(A,B)=set_union2(B,A)).
% 1.67/1.89 all A B (set_union2(A,A)=A).
% 1.67/1.89 all A B subset(A,A).
% 1.67/1.89 all A B (in(A,B)-> -in(B,A)).
% 1.67/1.89 exists A empty(A).
% 1.67/1.89 exists A (-empty(A)).
% 1.67/1.89 -(all A B (subset(set_union2(singleton(A),B),B)->in(A,B))).
% 1.67/1.89 all A B (subset(set_union2(singleton(A),B),B)->in(A,B)).
% 1.67/1.89 end_of_list.
% 1.67/1.89
% 1.67/1.89 -------> usable clausifies to:
% 1.67/1.89
% 1.67/1.89 list(usable).
% 1.67/1.89 0 [] A=A.
% 1.67/1.89 0 [] empty(A)| -empty(set_union2(A,B)).
% 1.67/1.89 0 [] empty(A)| -empty(set_union2(B,A)).
% 1.67/1.89 0 [] set_union2(A,B)=set_union2(B,A).
% 1.67/1.89 0 [] set_union2(A,A)=A.
% 1.67/1.89 0 [] subset(A,A).
% 1.67/1.89 0 [] -in(A,B)| -in(B,A).
% 1.67/1.89 0 [] empty($c1).
% 1.67/1.89 0 [] -empty($c2).
% 1.67/1.89 0 [] subset(set_union2(singleton($c4),$c3),$c3).
% 1.67/1.89 0 [] -in($c4,$c3).
% 1.67/1.89 0 [] -subset(set_union2(singleton(A),B),B)|in(A,B).
% 1.67/1.89 end_of_list.
% 1.67/1.89
% 1.67/1.89 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.67/1.89
% 1.67/1.89 This is a Horn set with equality. The strategy will be
% 1.67/1.89 Knuth-Bendix and hyper_res, with positive clauses in
% 1.67/1.89 sos and nonpositive clauses in usable.
% 1.67/1.89
% 1.67/1.89 dependent: set(knuth_bendix).
% 1.67/1.89 dependent: set(anl_eq).
% 1.67/1.89 dependent: set(para_from).
% 1.67/1.89 dependent: set(para_into).
% 1.67/1.89 dependent: clear(para_from_right).
% 1.67/1.89 dependent: clear(para_into_right).
% 1.67/1.89 dependent: set(para_from_vars).
% 1.67/1.89 dependent: set(eq_units_both_ways).
% 1.67/1.89 dependent: set(dynamic_demod_all).
% 1.67/1.89 dependent: set(dynamic_demod).
% 1.67/1.89 dependent: set(order_eq).
% 1.67/1.89 dependent: set(back_demod).
% 1.67/1.89 dependent: set(lrpo).
% 1.67/1.89 dependent: set(hyper_res).
% 1.67/1.89 dependent: clear(order_hyper).
% 1.67/1.89
% 1.67/1.89 ------------> process usable:
% 1.67/1.89 ** KEPT (pick-wt=6): 1 [] empty(A)| -empty(set_union2(A,B)).
% 1.67/1.89 ** KEPT (pick-wt=6): 2 [] empty(A)| -empty(set_union2(B,A)).
% 1.67/1.89 ** KEPT (pick-wt=6): 3 [] -in(A,B)| -in(B,A).
% 1.67/1.89 ** KEPT (pick-wt=2): 4 [] -empty($c2).
% 1.67/1.89 ** KEPT (pick-wt=3): 5 [] -in($c4,$c3).
% 1.67/1.89 ** KEPT (pick-wt=9): 6 [] -subset(set_union2(singleton(A),B),B)|in(A,B).
% 1.67/1.89
% 1.67/1.89 ------------> process sos:
% 1.67/1.89 ** KEPT (pick-wt=3): 7 [] A=A.
% 1.67/1.89 ** KEPT (pick-wt=7): 8 [] set_union2(A,B)=set_union2(B,A).
% 1.67/1.89 ** KEPT (pick-wt=5): 9 [] set_union2(A,A)=A.
% 1.67/1.89 ---> New Demodulator: 10 [new_demod,9] set_union2(A,A)=A.
% 1.67/1.89 ** KEPT (pick-wt=3): 11 [] subset(A,A).
% 1.67/1.89 ** KEPT (pick-wt=2): 12 [] empty($c1).
% 1.67/1.89 ** KEPT (pick-wt=6): 13 [] subset(set_union2(singleton($c4),$c3),$c3).
% 1.67/1.89 Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] A=A.
% 1.67/1.89 Following clause subsumed by 8 during input processing: 0 [copy,8,flip.1] set_union2(A,B)=set_union2(B,A).
% 1.67/1.89 >>>> Starting back demodulation with 10.
% 1.67/1.89
% 1.67/1.89 ======= end of input processing =======
% 1.67/1.89
% 1.67/1.89 =========== start of search ===========
% 1.67/1.89
% 1.67/1.89 -------- PROOF --------
% 1.67/1.89
% 1.67/1.89 ----> UNIT CONFLICT at 0.00 sec ----> 16 [binary,15.1,5.1] $F.
% 1.67/1.89
% 1.67/1.89 Length of proof is 1. Level of proof is 1.
% 1.67/1.89
% 1.67/1.89 ---------------- PROOF ----------------
% 1.67/1.89 % SZS status Theorem
% 1.67/1.89 % SZS output start Refutation
% See solution above
% 1.67/1.89 ------------ end of proof -------------
% 1.67/1.89
% 1.67/1.89
% 1.67/1.89 Search stopped by max_proofs option.
% 1.67/1.89
% 1.67/1.89
% 1.67/1.89 Search stopped by max_proofs option.
% 1.67/1.89
% 1.67/1.89 ============ end of search ============
% 1.67/1.89
% 1.67/1.89 -------------- statistics -------------
% 1.67/1.89 clauses given 5
% 1.67/1.89 clauses generated 6
% 1.67/1.89 clauses kept 14
% 1.67/1.89 clauses forward subsumed 4
% 1.67/1.89 clauses back subsumed 0
% 1.67/1.89 Kbytes malloced 976
% 1.67/1.89
% 1.67/1.89 ----------- times (seconds) -----------
% 1.67/1.89 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.89 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.89 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.67/1.89
% 1.67/1.89 That finishes the proof of the theorem.
% 1.67/1.89
% 1.67/1.89 Process 24046 finished Wed Jul 27 10:51:23 2022
% 1.67/1.89 Otter interrupted
% 1.67/1.89 PROOF FOUND
%------------------------------------------------------------------------------