%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET960+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n012.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 13:14:36 EDT 2022
% Result : Theorem 2.04s 2.25s
% Output : Refutation 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 22 ( 7 unt; 9 nHn; 13 RR)
% Number of literals : 45 ( 32 equ; 16 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 24 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( A != empty_set
| ~ in(B,A) ),
file('SET960+1.p',unknown),
[] ).
cnf(7,axiom,
( A != cartesian_product2(B,C)
| in(D,A)
| ~ in(E,B)
| ~ in(F,C)
| D != ordered_pair(E,F) ),
file('SET960+1.p',unknown),
[] ).
cnf(11,axiom,
( cartesian_product2(dollar_c4,dollar_c3) != empty_set
| dollar_c4 != empty_set ),
file('SET960+1.p',unknown),
[] ).
cnf(12,plain,
( cartesian_product2(dollar_c4,dollar_c3) != empty_set
| empty_set != dollar_c4 ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[11])]),
[iquote('copy,11,flip.2')] ).
cnf(13,axiom,
( cartesian_product2(dollar_c4,dollar_c3) != empty_set
| dollar_c3 != empty_set ),
file('SET960+1.p',unknown),
[] ).
cnf(14,plain,
( cartesian_product2(dollar_c4,dollar_c3) != empty_set
| empty_set != dollar_c3 ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13])]),
[iquote('copy,13,flip.2')] ).
cnf(21,axiom,
A = A,
file('SET960+1.p',unknown),
[] ).
cnf(23,axiom,
( A = empty_set
| in(dollar_f1(A),A) ),
file('SET960+1.p',unknown),
[] ).
cnf(24,axiom,
( A = cartesian_product2(B,C)
| in(dollar_f6(B,C,A),A)
| in(dollar_f5(B,C,A),B) ),
file('SET960+1.p',unknown),
[] ).
cnf(25,axiom,
( A = cartesian_product2(B,C)
| in(dollar_f6(B,C,A),A)
| in(dollar_f4(B,C,A),C) ),
file('SET960+1.p',unknown),
[] ).
cnf(33,axiom,
( cartesian_product2(dollar_c4,dollar_c3) = empty_set
| dollar_c4 = empty_set
| dollar_c3 = empty_set ),
file('SET960+1.p',unknown),
[] ).
cnf(34,plain,
( cartesian_product2(dollar_c4,dollar_c3) = empty_set
| empty_set = dollar_c4
| empty_set = dollar_c3 ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[33])])]),
[iquote('copy,33,flip.2,flip.3')] ).
cnf(51,plain,
( A = empty_set
| in(ordered_pair(dollar_f1(B),dollar_f1(A)),cartesian_product2(B,A))
| B = empty_set ),
inference(hyper,[status(thm)],[23,7,21,23,21]),
[iquote('hyper,23,7,21,23,21')] ).
cnf(108,plain,
( cartesian_product2(A,B) = empty_set
| in(dollar_f5(A,B,empty_set),A) ),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[24,2,21])]),
[iquote('hyper,24,2,21,flip.1')] ).
cnf(391,plain,
( cartesian_product2(A,B) = empty_set
| in(dollar_f4(A,B,empty_set),B) ),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[25,2,21])]),
[iquote('hyper,25,2,21,flip.1')] ).
cnf(528,plain,
cartesian_product2(empty_set,A) = empty_set,
inference(hyper,[status(thm)],[108,2,21]),
[iquote('hyper,108,2,21')] ).
cnf(540,plain,
( cartesian_product2(dollar_c4,dollar_c3) = empty_set
| empty_set = dollar_c3 ),
inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[528,34])]),
[iquote('para_into,527.1.1.1,34.2.1,factor_simp')] ).
cnf(608,plain,
cartesian_product2(A,empty_set) = empty_set,
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[391,2,528]),528]),
[iquote('hyper,391,2,527,demod,528')] ).
cnf(621,plain,
cartesian_product2(dollar_c4,dollar_c3) = empty_set,
inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[608,540])]),
[iquote('para_into,608.1.1.2,540.2.1,factor_simp')] ).
cnf(626,plain,
empty_set != dollar_c3,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[14]),621]),21]),
[iquote('back_demod,14,demod,621,unit_del,21')] ).
cnf(627,plain,
empty_set != dollar_c4,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[12]),621]),21]),
[iquote('back_demod,12,demod,621,unit_del,21')] ).
cnf(646,plain,
$false,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[51,2,621]),626,627]),
[iquote('hyper,51,2,620,unit_del,626,627')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET960+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n012.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 10:34:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.67/1.89 ----- Otter 3.3f, August 2004 -----
% 1.67/1.89 The process was started by sandbox on n012.cluster.edu,
% 1.67/1.89 Wed Jul 27 10:34:35 2022
% 1.67/1.89 The command was "./otter". The process ID is 12602.
% 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 (in(A,B)-> -in(B,A)).
% 1.67/1.89 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.67/1.89 all A (A=empty_set<-> (all B (-in(B,A)))).
% 1.67/1.89 all A B C (C=cartesian_product2(A,B)<-> (all D (in(D,C)<-> (exists E F (in(E,A)&in(F,B)&D=ordered_pair(E,F)))))).
% 1.67/1.89 all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 1.67/1.89 empty(empty_set).
% 1.67/1.89 all A B (-empty(ordered_pair(A,B))).
% 1.67/1.89 exists A empty(A).
% 1.67/1.89 exists A (-empty(A)).
% 1.67/1.89 -(all A B (cartesian_product2(A,B)=empty_set<->A=empty_set|B=empty_set)).
% 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 [] -in(A,B)| -in(B,A).
% 1.67/1.89 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.67/1.89 0 [] A!=empty_set| -in(B,A).
% 1.67/1.89 0 [] A=empty_set|in($f1(A),A).
% 1.67/1.89 0 [] C!=cartesian_product2(A,B)| -in(D,C)|in($f3(A,B,C,D),A).
% 1.67/1.89 0 [] C!=cartesian_product2(A,B)| -in(D,C)|in($f2(A,B,C,D),B).
% 1.67/1.89 0 [] C!=cartesian_product2(A,B)| -in(D,C)|D=ordered_pair($f3(A,B,C,D),$f2(A,B,C,D)).
% 1.67/1.89 0 [] C!=cartesian_product2(A,B)|in(D,C)| -in(E,A)| -in(F,B)|D!=ordered_pair(E,F).
% 1.67/1.89 0 [] C=cartesian_product2(A,B)|in($f6(A,B,C),C)|in($f5(A,B,C),A).
% 1.67/1.89 0 [] C=cartesian_product2(A,B)|in($f6(A,B,C),C)|in($f4(A,B,C),B).
% 1.67/1.89 0 [] C=cartesian_product2(A,B)|in($f6(A,B,C),C)|$f6(A,B,C)=ordered_pair($f5(A,B,C),$f4(A,B,C)).
% 1.67/1.89 0 [] C=cartesian_product2(A,B)| -in($f6(A,B,C),C)| -in(X1,A)| -in(X2,B)|$f6(A,B,C)!=ordered_pair(X1,X2).
% 1.67/1.89 0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 1.67/1.89 0 [] empty(empty_set).
% 1.67/1.89 0 [] -empty(ordered_pair(A,B)).
% 1.67/1.89 0 [] empty($c1).
% 1.67/1.89 0 [] -empty($c2).
% 1.67/1.89 0 [] cartesian_product2($c4,$c3)=empty_set|$c4=empty_set|$c3=empty_set.
% 1.67/1.89 0 [] cartesian_product2($c4,$c3)!=empty_set|$c4!=empty_set.
% 1.67/1.89 0 [] cartesian_product2($c4,$c3)!=empty_set|$c3!=empty_set.
% 1.67/1.89 end_of_list.
% 1.67/1.89
% 1.67/1.89 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 1.67/1.89
% 1.67/1.89 This ia a non-Horn set with equality. The strategy will be
% 1.67/1.89 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.67/1.89 deletion, with positive clauses in sos and nonpositive
% 1.67/1.89 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: set(unit_deletion).
% 1.67/1.89 dependent: set(factor).
% 1.67/1.89
% 1.67/1.89 ------------> process usable:
% 1.67/1.89 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.67/1.89 ** KEPT (pick-wt=6): 2 [] A!=empty_set| -in(B,A).
% 1.67/1.89 ** KEPT (pick-wt=15): 3 [] A!=cartesian_product2(B,C)| -in(D,A)|in($f3(B,C,A,D),B).
% 1.67/1.89 ** KEPT (pick-wt=15): 4 [] A!=cartesian_product2(B,C)| -in(D,A)|in($f2(B,C,A,D),C).
% 1.67/1.89 ** KEPT (pick-wt=21): 6 [copy,5,flip.3] A!=cartesian_product2(B,C)| -in(D,A)|ordered_pair($f3(B,C,A,D),$f2(B,C,A,D))=D.
% 1.67/1.89 ** KEPT (pick-wt=19): 7 [] A!=cartesian_product2(B,C)|in(D,A)| -in(E,B)| -in(F,C)|D!=ordered_pair(E,F).
% 1.67/1.89 ** KEPT (pick-wt=25): 8 [] A=cartesian_product2(B,C)| -in($f6(B,C,A),A)| -in(D,B)| -in(E,C)|$f6(B,C,A)!=ordered_pair(D,E).
% 1.67/1.89 ** KEPT (pick-wt=4): 9 [] -empty(ordered_pair(A,B)).
% 1.67/1.89 ** KEPT (pick-wt=2): 10 [] -empty($c2).
% 1.67/1.89 ** KEPT (pick-wt=8): 12 [copy,11,flip.2] cartesian_product2($c4,$c3)!=empty_set|empty_set!=$c4.
% 1.67/1.89 ** KEPT (pick-wt=8): 14 [copy,13,flip.2] cartesian_product2($c4,$c3)!=empty_set|empty_set!=$c3.
% 1.67/1.89
% 1.67/1.89 ------------> process sos:
% 1.67/1.89 ** KEPT (pick-wt=3): 21 [] A=A.
% 2.04/2.25 ** KEPT (pick-wt=7): 22 [] unordered_pair(A,B)=unordered_pair(B,A).
% 2.04/2.25 ** KEPT (pick-wt=7): 23 [] A=empty_set|in($f1(A),A).
% 2.04/2.25 ** KEPT (pick-wt=17): 24 [] A=cartesian_product2(B,C)|in($f6(B,C,A),A)|in($f5(B,C,A),B).
% 2.04/2.25 ** KEPT (pick-wt=17): 25 [] A=cartesian_product2(B,C)|in($f6(B,C,A),A)|in($f4(B,C,A),C).
% 2.04/2.25 ** KEPT (pick-wt=25): 27 [copy,26,flip.3] A=cartesian_product2(B,C)|in($f6(B,C,A),A)|ordered_pair($f5(B,C,A),$f4(B,C,A))=$f6(B,C,A).
% 2.04/2.25 ** KEPT (pick-wt=10): 29 [copy,28,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 2.04/2.25 ---> New Demodulator: 30 [new_demod,29] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 2.04/2.25 ** KEPT (pick-wt=2): 31 [] empty(empty_set).
% 2.04/2.25 ** KEPT (pick-wt=2): 32 [] empty($c1).
% 2.04/2.25 ** KEPT (pick-wt=11): 34 [copy,33,flip.2,flip.3] cartesian_product2($c4,$c3)=empty_set|empty_set=$c4|empty_set=$c3.
% 2.04/2.25 Following clause subsumed by 21 during input processing: 0 [copy,21,flip.1] A=A.
% 2.04/2.25 Following clause subsumed by 22 during input processing: 0 [copy,22,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 2.04/2.25 >>>> Starting back demodulation with 30.
% 2.04/2.25
% 2.04/2.25 ======= end of input processing =======
% 2.04/2.25
% 2.04/2.25 =========== start of search ===========
% 2.04/2.25
% 2.04/2.25
% 2.04/2.25 Resetting weight limit to 14.
% 2.04/2.25
% 2.04/2.25
% 2.04/2.25 Resetting weight limit to 14.
% 2.04/2.25
% 2.04/2.25 sos_size=457
% 2.04/2.25
% 2.04/2.25
% 2.04/2.25 Resetting weight limit to 13.
% 2.04/2.25
% 2.04/2.25
% 2.04/2.25 Resetting weight limit to 13.
% 2.04/2.25
% 2.04/2.25 sos_size=463
% 2.04/2.25
% 2.04/2.25 -------- PROOF --------
% 2.04/2.25
% 2.04/2.25 -----> EMPTY CLAUSE at 0.36 sec ----> 646 [hyper,51,2,620,unit_del,626,627] $F.
% 2.04/2.25
% 2.04/2.25 Length of proof is 12. Level of proof is 5.
% 2.04/2.25
% 2.04/2.25 ---------------- PROOF ----------------
% 2.04/2.25 % SZS status Theorem
% 2.04/2.25 % SZS output start Refutation
% See solution above
% 2.04/2.25 ------------ end of proof -------------
% 2.04/2.25
% 2.04/2.25
% 2.04/2.25 Search stopped by max_proofs option.
% 2.04/2.25
% 2.04/2.25
% 2.04/2.25 Search stopped by max_proofs option.
% 2.04/2.25
% 2.04/2.25 ============ end of search ============
% 2.04/2.25
% 2.04/2.25 -------------- statistics -------------
% 2.04/2.25 clauses given 86
% 2.04/2.25 clauses generated 13372
% 2.04/2.25 clauses kept 628
% 2.04/2.25 clauses forward subsumed 949
% 2.04/2.25 clauses back subsumed 85
% 2.04/2.25 Kbytes malloced 5859
% 2.04/2.25
% 2.04/2.25 ----------- times (seconds) -----------
% 2.04/2.25 user CPU time 0.36 (0 hr, 0 min, 0 sec)
% 2.04/2.25 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.04/2.25 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.04/2.25
% 2.04/2.25 That finishes the proof of the theorem.
% 2.04/2.25
% 2.04/2.25 Process 12602 finished Wed Jul 27 10:34:37 2022
% 2.04/2.25 Otter interrupted
% 2.04/2.25 PROOF FOUND
%------------------------------------------------------------------------------