TSTP Solution File: SET979+1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET979+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 13:14:37 EDT 2022
% Result : Theorem 1.85s 1.99s
% Output : Refutation 1.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 21 ( 16 unt; 0 nHn; 6 RR)
% Number of literals : 26 ( 25 equ; 10 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
( cartesian_product2(unordered_pair(dollar_c5,dollar_c4),dollar_c3) != set_union2(cartesian_product2(singleton(dollar_c5),dollar_c3),cartesian_product2(singleton(dollar_c4),dollar_c3))
| cartesian_product2(dollar_c3,unordered_pair(dollar_c5,dollar_c4)) != set_union2(cartesian_product2(dollar_c3,singleton(dollar_c5)),cartesian_product2(dollar_c3,singleton(dollar_c4))) ),
file('SET979+1.p',unknown),
[] ).
cnf(5,plain,
( set_union2(cartesian_product2(singleton(dollar_c5),dollar_c3),cartesian_product2(singleton(dollar_c4),dollar_c3)) != cartesian_product2(unordered_pair(dollar_c5,dollar_c4),dollar_c3)
| set_union2(cartesian_product2(dollar_c3,singleton(dollar_c5)),cartesian_product2(dollar_c3,singleton(dollar_c4))) != cartesian_product2(dollar_c3,unordered_pair(dollar_c5,dollar_c4)) ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[4])])]),
[iquote('copy,4,flip.1,flip.2')] ).
cnf(6,axiom,
A = A,
file('SET979+1.p',unknown),
[] ).
cnf(8,axiom,
set_union2(A,B) = set_union2(B,A),
file('SET979+1.p',unknown),
[] ).
cnf(9,axiom,
set_union2(A,A) = A,
file('SET979+1.p',unknown),
[] ).
cnf(12,axiom,
cartesian_product2(set_union2(A,B),C) = set_union2(cartesian_product2(A,C),cartesian_product2(B,C)),
file('SET979+1.p',unknown),
[] ).
cnf(14,plain,
set_union2(cartesian_product2(A,B),cartesian_product2(C,B)) = cartesian_product2(set_union2(A,C),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[12])]),
[iquote('copy,12,flip.1')] ).
cnf(15,axiom,
cartesian_product2(A,set_union2(B,C)) = set_union2(cartesian_product2(A,B),cartesian_product2(A,C)),
file('SET979+1.p',unknown),
[] ).
cnf(17,plain,
set_union2(cartesian_product2(A,B),cartesian_product2(A,C)) = cartesian_product2(A,set_union2(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
[iquote('copy,15,flip.1')] ).
cnf(18,axiom,
unordered_pair(A,B) = set_union2(singleton(A),singleton(B)),
file('SET979+1.p',unknown),
[] ).
cnf(19,plain,
( cartesian_product2(set_union2(singleton(dollar_c5),singleton(dollar_c4)),dollar_c3) != cartesian_product2(unordered_pair(dollar_c5,dollar_c4),dollar_c3)
| cartesian_product2(dollar_c3,set_union2(singleton(dollar_c5),singleton(dollar_c4))) != cartesian_product2(dollar_c3,unordered_pair(dollar_c5,dollar_c4)) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[5]),14,17]),
[iquote('back_demod,5,demod,14,17')] ).
cnf(20,plain,
set_union2(singleton(A),singleton(B)) = unordered_pair(A,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[18])]),
[iquote('copy,18,flip.1')] ).
cnf(21,plain,
cartesian_product2(set_union2(A,B),C) = cartesian_product2(set_union2(B,A),C),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[14,8]),14]),
[iquote('para_into,13.1.1,8.1.1,demod,14')] ).
cnf(27,plain,
singleton(A) = unordered_pair(A,A),
inference(para_into,[status(thm),theory(equality)],[20,9]),
[iquote('para_into,20.1.1,9.1.1')] ).
cnf(28,plain,
set_union2(unordered_pair(A,A),unordered_pair(B,B)) = unordered_pair(B,A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[20,8]),27,27]),
[iquote('para_into,20.1.1,8.1.1,demod,27,27')] ).
cnf(30,plain,
set_union2(unordered_pair(A,A),unordered_pair(B,B)) = unordered_pair(A,B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[20]),27,27]),
[iquote('back_demod,20,demod,27,27')] ).
cnf(31,plain,
( cartesian_product2(set_union2(unordered_pair(dollar_c5,dollar_c5),unordered_pair(dollar_c4,dollar_c4)),dollar_c3) != cartesian_product2(unordered_pair(dollar_c5,dollar_c4),dollar_c3)
| cartesian_product2(dollar_c3,set_union2(unordered_pair(dollar_c5,dollar_c5),unordered_pair(dollar_c4,dollar_c4))) != cartesian_product2(dollar_c3,unordered_pair(dollar_c5,dollar_c4)) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[19]),27,27,27,27]),
[iquote('back_demod,19,demod,27,27,27,27')] ).
cnf(59,plain,
cartesian_product2(unordered_pair(A,B),C) = cartesian_product2(set_union2(unordered_pair(A,A),unordered_pair(B,B)),C),
inference(para_from,[status(thm),theory(equality)],[28,21]),
[iquote('para_from,28.1.1,21.1.1.1')] ).
cnf(61,plain,
cartesian_product2(set_union2(unordered_pair(A,A),unordered_pair(B,B)),C) = cartesian_product2(unordered_pair(A,B),C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[59])]),
[iquote('copy,59,flip.1')] ).
cnf(67,plain,
( cartesian_product2(set_union2(unordered_pair(dollar_c5,dollar_c5),unordered_pair(dollar_c4,dollar_c4)),dollar_c3) != cartesian_product2(unordered_pair(dollar_c5,dollar_c4),dollar_c3)
| cartesian_product2(dollar_c3,unordered_pair(dollar_c5,dollar_c4)) != cartesian_product2(dollar_c3,unordered_pair(dollar_c5,dollar_c4)) ),
inference(para_into,[status(thm),theory(equality)],[31,30]),
[iquote('para_into,31.2.1.2,30.1.1')] ).
cnf(798,plain,
$false,
inference(hyper,[status(thm)],[67,61,6]),
[iquote('hyper,67,61,6')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET979+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Jul 27 10:29:50 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.80/1.96 ----- Otter 3.3f, August 2004 -----
% 1.80/1.96 The process was started by sandbox on n022.cluster.edu,
% 1.80/1.96 Wed Jul 27 10:29:50 2022
% 1.80/1.96 The command was "./otter". The process ID is 6891.
% 1.80/1.96
% 1.80/1.96 set(prolog_style_variables).
% 1.80/1.96 set(auto).
% 1.80/1.96 dependent: set(auto1).
% 1.80/1.96 dependent: set(process_input).
% 1.80/1.96 dependent: clear(print_kept).
% 1.80/1.96 dependent: clear(print_new_demod).
% 1.80/1.96 dependent: clear(print_back_demod).
% 1.80/1.96 dependent: clear(print_back_sub).
% 1.80/1.96 dependent: set(control_memory).
% 1.80/1.96 dependent: assign(max_mem, 12000).
% 1.80/1.96 dependent: assign(pick_given_ratio, 4).
% 1.80/1.96 dependent: assign(stats_level, 1).
% 1.80/1.96 dependent: assign(max_seconds, 10800).
% 1.80/1.96 clear(print_given).
% 1.80/1.96
% 1.80/1.96 formula_list(usable).
% 1.80/1.96 all A (A=A).
% 1.80/1.96 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.80/1.96 all A B (set_union2(A,B)=set_union2(B,A)).
% 1.80/1.96 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 1.80/1.96 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 1.80/1.96 all A B (set_union2(A,A)=A).
% 1.80/1.96 exists A empty(A).
% 1.80/1.96 exists A (-empty(A)).
% 1.80/1.96 all A B C (cartesian_product2(set_union2(A,B),C)=set_union2(cartesian_product2(A,C),cartesian_product2(B,C))&cartesian_product2(C,set_union2(A,B))=set_union2(cartesian_product2(C,A),cartesian_product2(C,B))).
% 1.80/1.96 -(all A B C (cartesian_product2(unordered_pair(A,B),C)=set_union2(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),C))&cartesian_product2(C,unordered_pair(A,B))=set_union2(cartesian_product2(C,singleton(A)),cartesian_product2(C,singleton(B))))).
% 1.80/1.96 all A B (unordered_pair(A,B)=set_union2(singleton(A),singleton(B))).
% 1.80/1.96 end_of_list.
% 1.80/1.96
% 1.80/1.96 -------> usable clausifies to:
% 1.80/1.96
% 1.80/1.96 list(usable).
% 1.80/1.96 0 [] A=A.
% 1.80/1.96 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.80/1.96 0 [] set_union2(A,B)=set_union2(B,A).
% 1.80/1.96 0 [] empty(A)| -empty(set_union2(A,B)).
% 1.80/1.96 0 [] empty(A)| -empty(set_union2(B,A)).
% 1.80/1.96 0 [] set_union2(A,A)=A.
% 1.80/1.96 0 [] empty($c1).
% 1.80/1.96 0 [] -empty($c2).
% 1.80/1.96 0 [] cartesian_product2(set_union2(A,B),C)=set_union2(cartesian_product2(A,C),cartesian_product2(B,C)).
% 1.80/1.96 0 [] cartesian_product2(C,set_union2(A,B))=set_union2(cartesian_product2(C,A),cartesian_product2(C,B)).
% 1.80/1.96 0 [] cartesian_product2(unordered_pair($c5,$c4),$c3)!=set_union2(cartesian_product2(singleton($c5),$c3),cartesian_product2(singleton($c4),$c3))|cartesian_product2($c3,unordered_pair($c5,$c4))!=set_union2(cartesian_product2($c3,singleton($c5)),cartesian_product2($c3,singleton($c4))).
% 1.80/1.96 0 [] unordered_pair(A,B)=set_union2(singleton(A),singleton(B)).
% 1.80/1.96 end_of_list.
% 1.80/1.96
% 1.80/1.96 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.80/1.96
% 1.80/1.96 This is a Horn set with equality. The strategy will be
% 1.80/1.96 Knuth-Bendix and hyper_res, with positive clauses in
% 1.80/1.96 sos and nonpositive clauses in usable.
% 1.80/1.96
% 1.80/1.96 dependent: set(knuth_bendix).
% 1.80/1.96 dependent: set(anl_eq).
% 1.80/1.96 dependent: set(para_from).
% 1.80/1.96 dependent: set(para_into).
% 1.80/1.96 dependent: clear(para_from_right).
% 1.80/1.96 dependent: clear(para_into_right).
% 1.80/1.96 dependent: set(para_from_vars).
% 1.80/1.96 dependent: set(eq_units_both_ways).
% 1.80/1.96 dependent: set(dynamic_demod_all).
% 1.80/1.96 dependent: set(dynamic_demod).
% 1.80/1.96 dependent: set(order_eq).
% 1.80/1.96 dependent: set(back_demod).
% 1.80/1.96 dependent: set(lrpo).
% 1.80/1.96 dependent: set(hyper_res).
% 1.80/1.96 dependent: clear(order_hyper).
% 1.80/1.96
% 1.80/1.96 ------------> process usable:
% 1.80/1.96 ** KEPT (pick-wt=6): 1 [] empty(A)| -empty(set_union2(A,B)).
% 1.80/1.96 ** KEPT (pick-wt=6): 2 [] empty(A)| -empty(set_union2(B,A)).
% 1.80/1.96 ** KEPT (pick-wt=2): 3 [] -empty($c2).
% 1.80/1.96 ** KEPT (pick-wt=30): 5 [copy,4,flip.1,flip.2] set_union2(cartesian_product2(singleton($c5),$c3),cartesian_product2(singleton($c4),$c3))!=cartesian_product2(unordered_pair($c5,$c4),$c3)|set_union2(cartesian_product2($c3,singleton($c5)),cartesian_product2($c3,singleton($c4)))!=cartesian_product2($c3,unordered_pair($c5,$c4)).
% 1.80/1.96
% 1.80/1.96 ------------> process sos:
% 1.80/1.96 ** KEPT (pick-wt=3): 6 [] A=A.
% 1.80/1.96 ** KEPT (pick-wt=7): 7 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.80/1.96 ** KEPT (pick-wt=7): 8 [] set_union2(A,B)=set_union2(B,A).
% 1.80/1.96 ** KEPT (pick-wt=5): 9 [] set_union2(A,A)=A.
% 1.80/1.96 ---> New Demodulator: 10 [new_demod,9] set_union2(A,A)=A.
% 1.80/1.96 ** KEPT (pick-wt=2): 11 [] empty($c1).
% 1.80/1.96 ** KEPT (pick-wt=13): 13 [copy,12,flip.1] set_union2(cartesian_product2(A,B),cartesian_product2(C,B))=cartesian_product2(set_union2(A,C),B).
% 1.80/1.96 ---> New Demodulator: 14 [new_demod,13] set_union2(cartesian_product2(A,B),cartesian_product2(C,B))=cartesian_product2(set_union2(A,C),B).
% 1.85/1.99 ** KEPT (pick-wt=13): 16 [copy,15,flip.1] set_union2(cartesian_product2(A,B),cartesian_product2(A,C))=cartesian_product2(A,set_union2(B,C)).
% 1.85/1.99 ---> New Demodulator: 17 [new_demod,16] set_union2(cartesian_product2(A,B),cartesian_product2(A,C))=cartesian_product2(A,set_union2(B,C)).
% 1.85/1.99 ** KEPT (pick-wt=9): 18 [] unordered_pair(A,B)=set_union2(singleton(A),singleton(B)).
% 1.85/1.99 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] A=A.
% 1.85/1.99 Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.85/1.99 Following clause subsumed by 8 during input processing: 0 [copy,8,flip.1] set_union2(A,B)=set_union2(B,A).
% 1.85/1.99 >>>> Starting back demodulation with 10.
% 1.85/1.99 >>>> Starting back demodulation with 14.
% 1.85/1.99 >> back demodulating 5 with 14.
% 1.85/1.99 >>>> Starting back demodulation with 17.
% 1.85/1.99 ** KEPT (pick-wt=9): 20 [copy,18,flip.1] set_union2(singleton(A),singleton(B))=unordered_pair(A,B).
% 1.85/1.99 Following clause subsumed by 18 during input processing: 0 [copy,20,flip.1] unordered_pair(A,B)=set_union2(singleton(A),singleton(B)).
% 1.85/1.99
% 1.85/1.99 ======= end of input processing =======
% 1.85/1.99
% 1.85/1.99 =========== start of search ===========
% 1.85/1.99
% 1.85/1.99
% 1.85/1.99 Resetting weight limit to 16.
% 1.85/1.99
% 1.85/1.99
% 1.85/1.99 Resetting weight limit to 16.
% 1.85/1.99
% 1.85/1.99 sos_size=668
% 1.85/1.99
% 1.85/1.99 -------- PROOF --------
% 1.85/1.99
% 1.85/1.99 -----> EMPTY CLAUSE at 0.03 sec ----> 798 [hyper,67,61,6] $F.
% 1.85/1.99
% 1.85/1.99 Length of proof is 13. Level of proof is 5.
% 1.85/1.99
% 1.85/1.99 ---------------- PROOF ----------------
% 1.85/1.99 % SZS status Theorem
% 1.85/1.99 % SZS output start Refutation
% See solution above
% 1.85/1.99 ------------ end of proof -------------
% 1.85/1.99
% 1.85/1.99
% 1.85/1.99 Search stopped by max_proofs option.
% 1.85/1.99
% 1.85/1.99
% 1.85/1.99 Search stopped by max_proofs option.
% 1.85/1.99
% 1.85/1.99 ============ end of search ============
% 1.85/1.99
% 1.85/1.99 -------------- statistics -------------
% 1.85/1.99 clauses given 76
% 1.85/1.99 clauses generated 2156
% 1.85/1.99 clauses kept 769
% 1.85/1.99 clauses forward subsumed 1313
% 1.85/1.99 clauses back subsumed 12
% 1.85/1.99 Kbytes malloced 4882
% 1.85/1.99
% 1.85/1.99 ----------- times (seconds) -----------
% 1.85/1.99 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.85/1.99 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.85/1.99 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.85/1.99
% 1.85/1.99 That finishes the proof of the theorem.
% 1.85/1.99
% 1.85/1.99 Process 6891 finished Wed Jul 27 10:29:52 2022
% 1.85/1.99 Otter interrupted
% 1.85/1.99 PROOF FOUND
%------------------------------------------------------------------------------