TSTP Solution File: SET016-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET016-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n023.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 13:12:48 EDT 2022
% Result : Unsatisfiable 5.15s 5.31s
% Output : Refutation 5.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of clauses : 22 ( 15 unt; 4 nHn; 17 RR)
% Number of literals : 31 ( 19 equ; 7 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 19 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ member(A,singleton_set(B))
| A = B ),
file('SET016-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ member(A,unordered_pair(B,C))
| A = B
| A = C ),
file('SET016-1.p',unknown),
[] ).
cnf(3,axiom,
m1 != m2,
file('SET016-1.p',unknown),
[] ).
cnf(4,plain,
m2 != m1,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[3])]),
[iquote('copy,3,flip.1')] ).
cnf(7,axiom,
member(A,singleton_set(A)),
file('SET016-1.p',unknown),
[] ).
cnf(8,axiom,
member(A,unordered_pair(A,B)),
file('SET016-1.p',unknown),
[] ).
cnf(10,axiom,
ordered_pair(A,B) = unordered_pair(singleton_set(A),unordered_pair(A,B)),
file('SET016-1.p',unknown),
[] ).
cnf(11,plain,
unordered_pair(singleton_set(A),unordered_pair(A,B)) = ordered_pair(A,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[10])]),
[iquote('copy,10,flip.1')] ).
cnf(13,axiom,
ordered_pair(m1,r1) = ordered_pair(m2,r2),
file('SET016-1.p',unknown),
[] ).
cnf(14,plain,
ordered_pair(m2,r2) = ordered_pair(m1,r1),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13])]),
[iquote('copy,13,flip.1')] ).
cnf(55,plain,
member(singleton_set(A),ordered_pair(A,B)),
inference(para_from,[status(thm),theory(equality)],[11,8]),
[iquote('para_from,11.1.1,8.1.2')] ).
cnf(56,plain,
( ~ member(A,ordered_pair(B,C))
| A = singleton_set(B)
| A = unordered_pair(B,C) ),
inference(para_from,[status(thm),theory(equality)],[11,2]),
[iquote('para_from,11.1.1,2.1.2')] ).
cnf(61,plain,
member(singleton_set(m2),ordered_pair(m1,r1)),
inference(para_into,[status(thm),theory(equality)],[55,14]),
[iquote('para_into,55.1.2,14.1.1')] ).
cnf(4006,plain,
( singleton_set(m2) = singleton_set(m1)
| singleton_set(m2) = unordered_pair(m1,r1) ),
inference(hyper,[status(thm)],[56,61]),
[iquote('hyper,56,61')] ).
cnf(4018,plain,
( member(m2,singleton_set(m1))
| singleton_set(m2) = unordered_pair(m1,r1) ),
inference(para_from,[status(thm),theory(equality)],[4006,7]),
[iquote('para_from,4006.1.1,7.1.2')] ).
cnf(4036,plain,
singleton_set(m2) = unordered_pair(m1,r1),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4018,1]),4]),
[iquote('hyper,4018,1,unit_del,4')] ).
cnf(4154,plain,
member(m2,unordered_pair(m1,r1)),
inference(para_from,[status(thm),theory(equality)],[4036,7]),
[iquote('para_from,4036.1.1,7.1.2')] ).
cnf(4181,plain,
( ~ member(A,unordered_pair(m1,r1))
| A = m2 ),
inference(para_from,[status(thm),theory(equality)],[4036,1]),
[iquote('para_from,4036.1.1,1.1.2')] ).
cnf(4186,plain,
r1 = m2,
inference(flip,[status(thm),theory(equality)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4154,2]),4])]),
[iquote('hyper,4154,2,unit_del,4,flip.1')] ).
cnf(4187,plain,
( ~ member(A,unordered_pair(m1,m2))
| A = m2 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4181]),4186]),
[iquote('back_demod,4181,demod,4186')] ).
cnf(4563,plain,
m2 = m1,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[4187,8])]),
[iquote('hyper,4187,8,flip.1')] ).
cnf(4565,plain,
$false,
inference(binary,[status(thm)],[4563,4]),
[iquote('binary,4563.1,4.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET016-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n023.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 11:05:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 5.15/5.31 ----- Otter 3.3f, August 2004 -----
% 5.15/5.31 The process was started by sandbox on n023.cluster.edu,
% 5.15/5.31 Wed Jul 27 11:05:33 2022
% 5.15/5.31 The command was "./otter". The process ID is 30856.
% 5.15/5.31
% 5.15/5.31 set(prolog_style_variables).
% 5.15/5.31 set(auto).
% 5.15/5.31 dependent: set(auto1).
% 5.15/5.31 dependent: set(process_input).
% 5.15/5.31 dependent: clear(print_kept).
% 5.15/5.31 dependent: clear(print_new_demod).
% 5.15/5.31 dependent: clear(print_back_demod).
% 5.15/5.31 dependent: clear(print_back_sub).
% 5.15/5.31 dependent: set(control_memory).
% 5.15/5.31 dependent: assign(max_mem, 12000).
% 5.15/5.31 dependent: assign(pick_given_ratio, 4).
% 5.15/5.31 dependent: assign(stats_level, 1).
% 5.15/5.31 dependent: assign(max_seconds, 10800).
% 5.15/5.31 clear(print_given).
% 5.15/5.31
% 5.15/5.31 list(usable).
% 5.15/5.31 0 [] A=A.
% 5.15/5.31 0 [] member(X,singleton_set(X)).
% 5.15/5.31 0 [] -member(X,singleton_set(Y))|X=Y.
% 5.15/5.31 0 [] member(X,unordered_pair(X,Y)).
% 5.15/5.31 0 [] member(Y,unordered_pair(X,Y)).
% 5.15/5.31 0 [] -member(X,unordered_pair(Y,Z))|X=Y|X=Z.
% 5.15/5.31 0 [] ordered_pair(X,Y)=unordered_pair(singleton_set(X),unordered_pair(X,Y)).
% 5.15/5.31 0 [] ordered_pair(m1,r1)=ordered_pair(m2,r2).
% 5.15/5.31 0 [] m1!=m2.
% 5.15/5.31 end_of_list.
% 5.15/5.31
% 5.15/5.31 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 5.15/5.31
% 5.15/5.31 This ia a non-Horn set with equality. The strategy will be
% 5.15/5.31 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 5.15/5.31 deletion, with positive clauses in sos and nonpositive
% 5.15/5.31 clauses in usable.
% 5.15/5.31
% 5.15/5.31 dependent: set(knuth_bendix).
% 5.15/5.31 dependent: set(anl_eq).
% 5.15/5.31 dependent: set(para_from).
% 5.15/5.31 dependent: set(para_into).
% 5.15/5.31 dependent: clear(para_from_right).
% 5.15/5.31 dependent: clear(para_into_right).
% 5.15/5.31 dependent: set(para_from_vars).
% 5.15/5.31 dependent: set(eq_units_both_ways).
% 5.15/5.31 dependent: set(dynamic_demod_all).
% 5.15/5.31 dependent: set(dynamic_demod).
% 5.15/5.31 dependent: set(order_eq).
% 5.15/5.31 dependent: set(back_demod).
% 5.15/5.31 dependent: set(lrpo).
% 5.15/5.31 dependent: set(hyper_res).
% 5.15/5.31 dependent: set(unit_deletion).
% 5.15/5.31 dependent: set(factor).
% 5.15/5.31
% 5.15/5.31 ------------> process usable:
% 5.15/5.31 ** KEPT (pick-wt=7): 1 [] -member(A,singleton_set(B))|A=B.
% 5.15/5.31 ** KEPT (pick-wt=11): 2 [] -member(A,unordered_pair(B,C))|A=B|A=C.
% 5.15/5.31 ** KEPT (pick-wt=3): 4 [copy,3,flip.1] m2!=m1.
% 5.15/5.31
% 5.15/5.31 ------------> process sos:
% 5.15/5.31 ** KEPT (pick-wt=3): 6 [] A=A.
% 5.15/5.31 ** KEPT (pick-wt=4): 7 [] member(A,singleton_set(A)).
% 5.15/5.31 ** KEPT (pick-wt=5): 8 [] member(A,unordered_pair(A,B)).
% 5.15/5.31 ** KEPT (pick-wt=5): 9 [] member(A,unordered_pair(B,A)).
% 5.15/5.31 ** KEPT (pick-wt=10): 11 [copy,10,flip.1] unordered_pair(singleton_set(A),unordered_pair(A,B))=ordered_pair(A,B).
% 5.15/5.31 ---> New Demodulator: 12 [new_demod,11] unordered_pair(singleton_set(A),unordered_pair(A,B))=ordered_pair(A,B).
% 5.15/5.31 ** KEPT (pick-wt=7): 14 [copy,13,flip.1] ordered_pair(m2,r2)=ordered_pair(m1,r1).
% 5.15/5.31 ---> New Demodulator: 15 [new_demod,14] ordered_pair(m2,r2)=ordered_pair(m1,r1).
% 5.15/5.31 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] A=A.
% 5.15/5.31 >>>> Starting back demodulation with 12.
% 5.15/5.31 >>>> Starting back demodulation with 15.
% 5.15/5.31
% 5.15/5.31 ======= end of input processing =======
% 5.15/5.31
% 5.15/5.31 =========== start of search ===========
% 5.15/5.31
% 5.15/5.31
% 5.15/5.31 Resetting weight limit to 15.
% 5.15/5.31
% 5.15/5.31
% 5.15/5.31 Resetting weight limit to 15.
% 5.15/5.31
% 5.15/5.31 sos_size=3882
% 5.15/5.31
% 5.15/5.31 -------- PROOF --------
% 5.15/5.31
% 5.15/5.31 ----> UNIT CONFLICT at 3.23 sec ----> 4565 [binary,4563.1,4.1] $F.
% 5.15/5.31
% 5.15/5.31 Length of proof is 14. Level of proof is 10.
% 5.15/5.31
% 5.15/5.31 ---------------- PROOF ----------------
% 5.15/5.31 % SZS status Unsatisfiable
% 5.15/5.31 % SZS output start Refutation
% See solution above
% 5.15/5.31 ------------ end of proof -------------
% 5.15/5.31
% 5.15/5.31
% 5.15/5.31 Search stopped by max_proofs option.
% 5.15/5.31
% 5.15/5.31
% 5.15/5.31 Search stopped by max_proofs option.
% 5.15/5.31
% 5.15/5.31 ============ end of search ============
% 5.15/5.31
% 5.15/5.31 -------------- statistics -------------
% 5.15/5.31 clauses given 140
% 5.15/5.31 clauses generated 12236
% 5.15/5.31 clauses kept 4549
% 5.15/5.31 clauses forward subsumed 1858
% 5.15/5.31 clauses back subsumed 25
% 5.15/5.31 Kbytes malloced 4882
% 5.15/5.31
% 5.15/5.31 ----------- times (seconds) -----------
% 5.15/5.31 user CPU time 3.23 (0 hr, 0 min, 3 sec)
% 5.15/5.31 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 5.15/5.31 wall-clock time 5 (0 hr, 0 min, 5 sec)
% 5.15/5.31
% 5.15/5.31 That finishes the proof of the theorem.
% 5.15/5.31
% 5.15/5.31 Process 30856 finished Wed Jul 27 11:05:38 2022
% 5.15/5.31 Otter interrupted
% 5.15/5.31 PROOF FOUND
%------------------------------------------------------------------------------