TSTP Solution File: SET908+1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET908+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n025.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 13:14:30 EDT 2022
% Result : Theorem 1.96s 2.12s
% Output : Refutation 1.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 8 ( 5 unt; 0 nHn; 5 RR)
% Number of literals : 13 ( 6 equ; 6 neg)
% Maximal clause size : 3 ( 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 : 13 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( A != singleton(B)
| in(C,A)
| C != B ),
file('SET908+1.p',unknown),
[] ).
cnf(5,axiom,
( A != empty_set
| ~ in(B,A) ),
file('SET908+1.p',unknown),
[] ).
cnf(7,axiom,
( A != set_union2(B,C)
| in(D,A)
| ~ in(D,B) ),
file('SET908+1.p',unknown),
[] ).
cnf(18,axiom,
A = A,
file('SET908+1.p',unknown),
[] ).
cnf(27,axiom,
set_union2(singleton(dollar_c4),dollar_c3) = empty_set,
file('SET908+1.p',unknown),
[] ).
cnf(33,plain,
in(A,singleton(A)),
inference(hyper,[status(thm)],[18,3,18]),
[iquote('hyper,18,3,18')] ).
cnf(47,plain,
in(A,set_union2(singleton(A),B)),
inference(hyper,[status(thm)],[33,7,18]),
[iquote('hyper,33,7,18')] ).
cnf(167,plain,
$false,
inference(hyper,[status(thm)],[47,5,27]),
[iquote('hyper,47,5,27')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET908+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 10:53:15 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.92/2.11 ----- Otter 3.3f, August 2004 -----
% 1.92/2.11 The process was started by sandbox2 on n025.cluster.edu,
% 1.92/2.11 Wed Jul 27 10:53:15 2022
% 1.92/2.11 The command was "./otter". The process ID is 20296.
% 1.92/2.11
% 1.92/2.11 set(prolog_style_variables).
% 1.92/2.11 set(auto).
% 1.92/2.11 dependent: set(auto1).
% 1.92/2.11 dependent: set(process_input).
% 1.92/2.11 dependent: clear(print_kept).
% 1.92/2.11 dependent: clear(print_new_demod).
% 1.92/2.11 dependent: clear(print_back_demod).
% 1.92/2.11 dependent: clear(print_back_sub).
% 1.92/2.11 dependent: set(control_memory).
% 1.92/2.11 dependent: assign(max_mem, 12000).
% 1.92/2.11 dependent: assign(pick_given_ratio, 4).
% 1.92/2.11 dependent: assign(stats_level, 1).
% 1.92/2.11 dependent: assign(max_seconds, 10800).
% 1.92/2.11 clear(print_given).
% 1.92/2.11
% 1.92/2.11 formula_list(usable).
% 1.92/2.11 all A (A=A).
% 1.92/2.11 all A B (in(A,B)-> -in(B,A)).
% 1.92/2.11 all A B (set_union2(A,B)=set_union2(B,A)).
% 1.92/2.11 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 1.92/2.11 all A (A=empty_set<-> (all B (-in(B,A)))).
% 1.92/2.11 all A B C (C=set_union2(A,B)<-> (all D (in(D,C)<->in(D,A)|in(D,B)))).
% 1.92/2.11 empty(empty_set).
% 1.92/2.11 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 1.92/2.11 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 1.92/2.11 all A B (set_union2(A,A)=A).
% 1.92/2.11 exists A empty(A).
% 1.92/2.11 exists A (-empty(A)).
% 1.92/2.11 -(all A B (set_union2(singleton(A),B)!=empty_set)).
% 1.92/2.11 end_of_list.
% 1.92/2.11
% 1.92/2.11 -------> usable clausifies to:
% 1.92/2.11
% 1.92/2.11 list(usable).
% 1.92/2.11 0 [] A=A.
% 1.92/2.11 0 [] -in(A,B)| -in(B,A).
% 1.92/2.11 0 [] set_union2(A,B)=set_union2(B,A).
% 1.92/2.11 0 [] B!=singleton(A)| -in(C,B)|C=A.
% 1.92/2.11 0 [] B!=singleton(A)|in(C,B)|C!=A.
% 1.92/2.11 0 [] B=singleton(A)|in($f1(A,B),B)|$f1(A,B)=A.
% 1.92/2.11 0 [] B=singleton(A)| -in($f1(A,B),B)|$f1(A,B)!=A.
% 1.92/2.11 0 [] A!=empty_set| -in(B,A).
% 1.92/2.11 0 [] A=empty_set|in($f2(A),A).
% 1.92/2.11 0 [] C!=set_union2(A,B)| -in(D,C)|in(D,A)|in(D,B).
% 1.92/2.11 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,A).
% 1.92/2.11 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,B).
% 1.92/2.11 0 [] C=set_union2(A,B)|in($f3(A,B,C),C)|in($f3(A,B,C),A)|in($f3(A,B,C),B).
% 1.92/2.11 0 [] C=set_union2(A,B)| -in($f3(A,B,C),C)| -in($f3(A,B,C),A).
% 1.92/2.11 0 [] C=set_union2(A,B)| -in($f3(A,B,C),C)| -in($f3(A,B,C),B).
% 1.92/2.11 0 [] empty(empty_set).
% 1.92/2.11 0 [] empty(A)| -empty(set_union2(A,B)).
% 1.92/2.11 0 [] empty(A)| -empty(set_union2(B,A)).
% 1.92/2.11 0 [] set_union2(A,A)=A.
% 1.92/2.11 0 [] empty($c1).
% 1.92/2.11 0 [] -empty($c2).
% 1.92/2.11 0 [] set_union2(singleton($c4),$c3)=empty_set.
% 1.92/2.11 end_of_list.
% 1.92/2.11
% 1.92/2.11 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.92/2.11
% 1.92/2.11 This ia a non-Horn set with equality. The strategy will be
% 1.92/2.11 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.92/2.11 deletion, with positive clauses in sos and nonpositive
% 1.92/2.11 clauses in usable.
% 1.92/2.11
% 1.92/2.11 dependent: set(knuth_bendix).
% 1.92/2.11 dependent: set(anl_eq).
% 1.92/2.11 dependent: set(para_from).
% 1.92/2.11 dependent: set(para_into).
% 1.92/2.11 dependent: clear(para_from_right).
% 1.92/2.11 dependent: clear(para_into_right).
% 1.92/2.11 dependent: set(para_from_vars).
% 1.92/2.11 dependent: set(eq_units_both_ways).
% 1.92/2.11 dependent: set(dynamic_demod_all).
% 1.92/2.11 dependent: set(dynamic_demod).
% 1.92/2.11 dependent: set(order_eq).
% 1.92/2.11 dependent: set(back_demod).
% 1.92/2.11 dependent: set(lrpo).
% 1.92/2.11 dependent: set(hyper_res).
% 1.92/2.11 dependent: set(unit_deletion).
% 1.92/2.11 dependent: set(factor).
% 1.92/2.11
% 1.92/2.11 ------------> process usable:
% 1.92/2.11 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.92/2.11 ** KEPT (pick-wt=10): 2 [] A!=singleton(B)| -in(C,A)|C=B.
% 1.92/2.11 ** KEPT (pick-wt=10): 3 [] A!=singleton(B)|in(C,A)|C!=B.
% 1.92/2.11 ** KEPT (pick-wt=14): 4 [] A=singleton(B)| -in($f1(B,A),A)|$f1(B,A)!=B.
% 1.92/2.11 ** KEPT (pick-wt=6): 5 [] A!=empty_set| -in(B,A).
% 1.92/2.11 ** KEPT (pick-wt=14): 6 [] A!=set_union2(B,C)| -in(D,A)|in(D,B)|in(D,C).
% 1.92/2.11 ** KEPT (pick-wt=11): 7 [] A!=set_union2(B,C)|in(D,A)| -in(D,B).
% 1.92/2.11 ** KEPT (pick-wt=11): 8 [] A!=set_union2(B,C)|in(D,A)| -in(D,C).
% 1.92/2.11 ** KEPT (pick-wt=17): 9 [] A=set_union2(B,C)| -in($f3(B,C,A),A)| -in($f3(B,C,A),B).
% 1.92/2.11 ** KEPT (pick-wt=17): 10 [] A=set_union2(B,C)| -in($f3(B,C,A),A)| -in($f3(B,C,A),C).
% 1.92/2.11 ** KEPT (pick-wt=6): 11 [] empty(A)| -empty(set_union2(A,B)).
% 1.92/2.11 ** KEPT (pick-wt=6): 12 [] empty(A)| -empty(set_union2(B,A)).
% 1.92/2.11 ** KEPT (pick-wt=2): 13 [] -empty($c2).
% 1.92/2.11
% 1.92/2.11 ------------> process sos:
% 1.92/2.11 ** KEPT (pick-wt=3): 18 [] A=A.
% 1.92/2.11 ** KEPT (pick-wt=7): 19 [] set_union2(A,B)=set_union2(B,A).
% 1.92/2.11 ** KEPT (pick-wt=14): 20 [] A=singleton(B)|in($f1(B,A),A)|$f1(B,A)=B.
% 1.92/2.11 ** KEPT (pick-wt=7): 21 [] A=empty_set|in($f2(A),A).
% 1.92/2.11 ** KEPT (pick-wt=23): 22 [] A=set_union2(B,C)|in($f3(B,C,A),A)|in($f3(B,C,A),B)|in($f3(B,C,A),C).
% 1.92/2.11 ** KEPT (pick-wt=2): 23 [] empty(empty_set).
% 1.92/2.11 ** KEPT (pick-wt=5): 24 [] set_union2(A,A)=A.
% 1.96/2.12 ---> New Demodulator: 25 [new_demod,24] set_union2(A,A)=A.
% 1.96/2.12 ** KEPT (pick-wt=2): 26 [] empty($c1).
% 1.96/2.12 ** KEPT (pick-wt=6): 27 [] set_union2(singleton($c4),$c3)=empty_set.
% 1.96/2.12 ---> New Demodulator: 28 [new_demod,27] set_union2(singleton($c4),$c3)=empty_set.
% 1.96/2.12 Following clause subsumed by 18 during input processing: 0 [copy,18,flip.1] A=A.
% 1.96/2.12 Following clause subsumed by 19 during input processing: 0 [copy,19,flip.1] set_union2(A,B)=set_union2(B,A).
% 1.96/2.12 >>>> Starting back demodulation with 25.
% 1.96/2.12 >> back demodulating 15 with 25.
% 1.96/2.12 >>>> Starting back demodulation with 28.
% 1.96/2.12
% 1.96/2.12 ======= end of input processing =======
% 1.96/2.12
% 1.96/2.12 =========== start of search ===========
% 1.96/2.12
% 1.96/2.12 -------- PROOF --------
% 1.96/2.12
% 1.96/2.12 -----> EMPTY CLAUSE at 0.01 sec ----> 167 [hyper,47,5,27] $F.
% 1.96/2.12
% 1.96/2.12 Length of proof is 2. Level of proof is 2.
% 1.96/2.12
% 1.96/2.12 ---------------- PROOF ----------------
% 1.96/2.12 % SZS status Theorem
% 1.96/2.12 % SZS output start Refutation
% See solution above
% 1.96/2.12 ------------ end of proof -------------
% 1.96/2.12
% 1.96/2.12
% 1.96/2.12 Search stopped by max_proofs option.
% 1.96/2.12
% 1.96/2.12
% 1.96/2.12 Search stopped by max_proofs option.
% 1.96/2.12
% 1.96/2.12 ============ end of search ============
% 1.96/2.12
% 1.96/2.12 -------------- statistics -------------
% 1.96/2.12 clauses given 12
% 1.96/2.12 clauses generated 224
% 1.96/2.12 clauses kept 163
% 1.96/2.12 clauses forward subsumed 82
% 1.96/2.12 clauses back subsumed 0
% 1.96/2.12 Kbytes malloced 1953
% 1.96/2.12
% 1.96/2.12 ----------- times (seconds) -----------
% 1.96/2.12 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.96/2.12 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.96/2.12 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.96/2.12
% 1.96/2.12 That finishes the proof of the theorem.
% 1.96/2.12
% 1.96/2.12 Process 20296 finished Wed Jul 27 10:53:17 2022
% 1.96/2.12 Otter interrupted
% 1.96/2.12 PROOF FOUND
%------------------------------------------------------------------------------