TSTP Solution File: SET935+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET935+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n011.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 13:14:34 EDT 2022
% Result : Theorem 2.66s 2.84s
% Output : Refutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 26 ( 16 unt; 3 nHn; 18 RR)
% Number of literals : 43 ( 10 equ; 15 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 35 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
( A = B
| ~ subset(A,B)
| ~ subset(B,A) ),
file('SET935+1.p',unknown),
[] ).
cnf(5,axiom,
( A != powerset(B)
| ~ in(C,A)
| subset(C,B) ),
file('SET935+1.p',unknown),
[] ).
cnf(6,axiom,
( A != powerset(B)
| in(C,A)
| ~ subset(C,B) ),
file('SET935+1.p',unknown),
[] ).
cnf(8,axiom,
( A != set_union2(B,C)
| ~ in(D,A)
| in(D,B)
| in(D,C) ),
file('SET935+1.p',unknown),
[] ).
cnf(14,axiom,
( inclusion_comparable(A,B)
| ~ subset(A,B) ),
file('SET935+1.p',unknown),
[] ).
cnf(15,axiom,
( inclusion_comparable(A,B)
| ~ subset(B,A) ),
file('SET935+1.p',unknown),
[] ).
cnf(20,axiom,
~ inclusion_comparable(dollar_c4,dollar_c3),
file('SET935+1.p',unknown),
[] ).
cnf(27,axiom,
A = A,
file('SET935+1.p',unknown),
[] ).
cnf(28,axiom,
set_union2(A,B) = set_union2(B,A),
file('SET935+1.p',unknown),
[] ).
cnf(34,axiom,
subset(A,A),
file('SET935+1.p',unknown),
[] ).
cnf(36,axiom,
subset(A,set_union2(A,B)),
file('SET935+1.p',unknown),
[] ).
cnf(37,axiom,
set_union2(powerset(dollar_c4),powerset(dollar_c3)) = powerset(set_union2(dollar_c4,dollar_c3)),
file('SET935+1.p',unknown),
[] ).
cnf(38,plain,
powerset(set_union2(dollar_c4,dollar_c3)) = set_union2(powerset(dollar_c4),powerset(dollar_c3)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[37])]),
[iquote('copy,37,flip.1')] ).
cnf(50,plain,
in(A,powerset(A)),
inference(hyper,[status(thm)],[34,6,27]),
[iquote('hyper,34,6,27')] ).
cnf(63,plain,
( A = set_union2(B,C)
| ~ subset(set_union2(C,B),A)
| ~ subset(A,set_union2(C,B)) ),
inference(para_into,[status(thm),theory(equality)],[28,4]),
[iquote('para_into,28.1.1,4.1.1')] ).
cnf(69,plain,
inclusion_comparable(set_union2(A,B),A),
inference(hyper,[status(thm)],[36,15]),
[iquote('hyper,36,15')] ).
cnf(70,plain,
inclusion_comparable(A,set_union2(A,B)),
inference(hyper,[status(thm)],[36,14]),
[iquote('hyper,36,14')] ).
cnf(72,plain,
subset(A,set_union2(B,A)),
inference(para_into,[status(thm),theory(equality)],[36,28]),
[iquote('para_into,36.1.2,28.1.1')] ).
cnf(93,plain,
( inclusion_comparable(A,B)
| ~ subset(set_union2(A,C),B)
| ~ subset(B,set_union2(A,C)) ),
inference(para_into,[status(thm),theory(equality)],[70,4]),
[iquote('para_into,70.1.2,4.1.1')] ).
cnf(498,plain,
( in(set_union2(dollar_c4,dollar_c3),powerset(dollar_c4))
| in(set_union2(dollar_c4,dollar_c3),powerset(dollar_c3)) ),
inference(hyper,[status(thm)],[38,8,50]),
[iquote('hyper,38,8,50')] ).
cnf(2032,plain,
( in(set_union2(dollar_c4,dollar_c3),powerset(dollar_c4))
| subset(set_union2(dollar_c4,dollar_c3),dollar_c3) ),
inference(hyper,[status(thm)],[498,5,27]),
[iquote('hyper,498,5,27')] ).
cnf(2039,plain,
in(set_union2(dollar_c4,dollar_c3),powerset(dollar_c4)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[2032,93,72]),20]),
[iquote('hyper,2032,93,72,unit_del,20')] ).
cnf(2042,plain,
subset(set_union2(dollar_c4,dollar_c3),dollar_c4),
inference(hyper,[status(thm)],[2039,5,27]),
[iquote('hyper,2039,5,27')] ).
cnf(2049,plain,
set_union2(dollar_c3,dollar_c4) = dollar_c4,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[2042,63,36])]),
[iquote('hyper,2042,63,36,flip.1')] ).
cnf(2087,plain,
inclusion_comparable(dollar_c4,dollar_c3),
inference(para_from,[status(thm),theory(equality)],[2049,69]),
[iquote('para_from,2049.1.1,69.1.1')] ).
cnf(2088,plain,
$false,
inference(binary,[status(thm)],[2087,20]),
[iquote('binary,2087.1,20.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET935+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : otter-tptp-script %s
% 0.13/0.32 % Computer : n011.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Wed Jul 27 10:26:55 EDT 2022
% 0.13/0.32 % CPUTime :
% 1.97/2.14 ----- Otter 3.3f, August 2004 -----
% 1.97/2.14 The process was started by sandbox2 on n011.cluster.edu,
% 1.97/2.14 Wed Jul 27 10:26:56 2022
% 1.97/2.14 The command was "./otter". The process ID is 28884.
% 1.97/2.14
% 1.97/2.14 set(prolog_style_variables).
% 1.97/2.14 set(auto).
% 1.97/2.14 dependent: set(auto1).
% 1.97/2.14 dependent: set(process_input).
% 1.97/2.14 dependent: clear(print_kept).
% 1.97/2.14 dependent: clear(print_new_demod).
% 1.97/2.14 dependent: clear(print_back_demod).
% 1.97/2.14 dependent: clear(print_back_sub).
% 1.97/2.14 dependent: set(control_memory).
% 1.97/2.14 dependent: assign(max_mem, 12000).
% 1.97/2.14 dependent: assign(pick_given_ratio, 4).
% 1.97/2.14 dependent: assign(stats_level, 1).
% 1.97/2.14 dependent: assign(max_seconds, 10800).
% 1.97/2.14 clear(print_given).
% 1.97/2.14
% 1.97/2.14 formula_list(usable).
% 1.97/2.14 all A (A=A).
% 1.97/2.14 all A B (in(A,B)-> -in(B,A)).
% 1.97/2.14 all A B (set_union2(A,B)=set_union2(B,A)).
% 1.97/2.14 all A B (A=B<->subset(A,B)&subset(B,A)).
% 1.97/2.14 all A B (B=powerset(A)<-> (all C (in(C,B)<->subset(C,A)))).
% 1.97/2.14 all A B C (C=set_union2(A,B)<-> (all D (in(D,C)<->in(D,A)|in(D,B)))).
% 1.97/2.14 all A B (inclusion_comparable(A,B)<->subset(A,B)|subset(B,A)).
% 1.97/2.14 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 1.97/2.14 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 1.97/2.14 all A B (set_union2(A,A)=A).
% 1.97/2.14 exists A empty(A).
% 1.97/2.14 exists A (-empty(A)).
% 1.97/2.14 all A B subset(A,A).
% 1.97/2.14 all A B inclusion_comparable(A,A).
% 1.97/2.14 all A B (inclusion_comparable(A,B)->inclusion_comparable(B,A)).
% 1.97/2.14 all A B subset(A,set_union2(A,B)).
% 1.97/2.14 -(all A B (set_union2(powerset(A),powerset(B))=powerset(set_union2(A,B))->inclusion_comparable(A,B))).
% 1.97/2.14 end_of_list.
% 1.97/2.14
% 1.97/2.14 -------> usable clausifies to:
% 1.97/2.14
% 1.97/2.14 list(usable).
% 1.97/2.14 0 [] A=A.
% 1.97/2.14 0 [] -in(A,B)| -in(B,A).
% 1.97/2.14 0 [] set_union2(A,B)=set_union2(B,A).
% 1.97/2.14 0 [] A!=B|subset(A,B).
% 1.97/2.14 0 [] A!=B|subset(B,A).
% 1.97/2.14 0 [] A=B| -subset(A,B)| -subset(B,A).
% 1.97/2.14 0 [] B!=powerset(A)| -in(C,B)|subset(C,A).
% 1.97/2.14 0 [] B!=powerset(A)|in(C,B)| -subset(C,A).
% 1.97/2.14 0 [] B=powerset(A)|in($f1(A,B),B)|subset($f1(A,B),A).
% 1.97/2.14 0 [] B=powerset(A)| -in($f1(A,B),B)| -subset($f1(A,B),A).
% 1.97/2.14 0 [] C!=set_union2(A,B)| -in(D,C)|in(D,A)|in(D,B).
% 1.97/2.14 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,A).
% 1.97/2.14 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,B).
% 1.97/2.14 0 [] C=set_union2(A,B)|in($f2(A,B,C),C)|in($f2(A,B,C),A)|in($f2(A,B,C),B).
% 1.97/2.14 0 [] C=set_union2(A,B)| -in($f2(A,B,C),C)| -in($f2(A,B,C),A).
% 1.97/2.14 0 [] C=set_union2(A,B)| -in($f2(A,B,C),C)| -in($f2(A,B,C),B).
% 1.97/2.14 0 [] -inclusion_comparable(A,B)|subset(A,B)|subset(B,A).
% 1.97/2.14 0 [] inclusion_comparable(A,B)| -subset(A,B).
% 1.97/2.14 0 [] inclusion_comparable(A,B)| -subset(B,A).
% 1.97/2.14 0 [] empty(A)| -empty(set_union2(A,B)).
% 1.97/2.14 0 [] empty(A)| -empty(set_union2(B,A)).
% 1.97/2.14 0 [] set_union2(A,A)=A.
% 1.97/2.14 0 [] empty($c1).
% 1.97/2.14 0 [] -empty($c2).
% 1.97/2.14 0 [] subset(A,A).
% 1.97/2.14 0 [] inclusion_comparable(A,A).
% 1.97/2.14 0 [] -inclusion_comparable(A,B)|inclusion_comparable(B,A).
% 1.97/2.14 0 [] subset(A,set_union2(A,B)).
% 1.97/2.14 0 [] set_union2(powerset($c4),powerset($c3))=powerset(set_union2($c4,$c3)).
% 1.97/2.14 0 [] -inclusion_comparable($c4,$c3).
% 1.97/2.14 end_of_list.
% 1.97/2.14
% 1.97/2.14 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.97/2.14
% 1.97/2.14 This ia a non-Horn set with equality. The strategy will be
% 1.97/2.14 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.97/2.14 deletion, with positive clauses in sos and nonpositive
% 1.97/2.14 clauses in usable.
% 1.97/2.14
% 1.97/2.14 dependent: set(knuth_bendix).
% 1.97/2.14 dependent: set(anl_eq).
% 1.97/2.14 dependent: set(para_from).
% 1.97/2.14 dependent: set(para_into).
% 1.97/2.14 dependent: clear(para_from_right).
% 1.97/2.14 dependent: clear(para_into_right).
% 1.97/2.14 dependent: set(para_from_vars).
% 1.97/2.14 dependent: set(eq_units_both_ways).
% 1.97/2.14 dependent: set(dynamic_demod_all).
% 1.97/2.14 dependent: set(dynamic_demod).
% 1.97/2.14 dependent: set(order_eq).
% 1.97/2.14 dependent: set(back_demod).
% 1.97/2.14 dependent: set(lrpo).
% 1.97/2.14 dependent: set(hyper_res).
% 1.97/2.14 dependent: set(unit_deletion).
% 1.97/2.14 dependent: set(factor).
% 1.97/2.14
% 1.97/2.14 ------------> process usable:
% 1.97/2.14 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.97/2.14 ** KEPT (pick-wt=6): 2 [] A!=B|subset(A,B).
% 1.97/2.14 ** KEPT (pick-wt=6): 3 [] A!=B|subset(B,A).
% 1.97/2.14 ** KEPT (pick-wt=9): 4 [] A=B| -subset(A,B)| -subset(B,A).
% 1.97/2.14 ** KEPT (pick-wt=10): 5 [] A!=powerset(B)| -in(C,A)|subset(C,B).
% 1.97/2.14 ** KEPT (pick-wt=10): 6 [] A!=powerset(B)|in(C,A)| -subset(C,B).
% 1.97/2.14 ** KEPT (pick-wt=14): 7 [] A=powerset(B)| -in($f1(B,A),A)| -subset($f1(B,A),B).
% 1.97/2.14 ** KEPT (pick-wt=14): 8 [] A!=set_union2(B,C)| -in(D,A)|in(D,B)|in(D,C).
% 1.97/2.14 ** KEPT (pick-wt=11): 9 [] A!=set_union2(B,C)|in(D,A)| -in(D,B).
% 1.97/2.14 ** KEPT (pick-wt=11): 10 [] A!=set_union2(B,C)|in(D,A)| -in(D,C).
% 2.66/2.84 ** KEPT (pick-wt=17): 11 [] A=set_union2(B,C)| -in($f2(B,C,A),A)| -in($f2(B,C,A),B).
% 2.66/2.84 ** KEPT (pick-wt=17): 12 [] A=set_union2(B,C)| -in($f2(B,C,A),A)| -in($f2(B,C,A),C).
% 2.66/2.84 ** KEPT (pick-wt=9): 13 [] -inclusion_comparable(A,B)|subset(A,B)|subset(B,A).
% 2.66/2.84 ** KEPT (pick-wt=6): 14 [] inclusion_comparable(A,B)| -subset(A,B).
% 2.66/2.84 ** KEPT (pick-wt=6): 15 [] inclusion_comparable(A,B)| -subset(B,A).
% 2.66/2.84 ** KEPT (pick-wt=6): 16 [] empty(A)| -empty(set_union2(A,B)).
% 2.66/2.84 ** KEPT (pick-wt=6): 17 [] empty(A)| -empty(set_union2(B,A)).
% 2.66/2.84 ** KEPT (pick-wt=2): 18 [] -empty($c2).
% 2.66/2.84 ** KEPT (pick-wt=6): 19 [] -inclusion_comparable(A,B)|inclusion_comparable(B,A).
% 2.66/2.84 ** KEPT (pick-wt=3): 20 [] -inclusion_comparable($c4,$c3).
% 2.66/2.84
% 2.66/2.84 ------------> process sos:
% 2.66/2.84 ** KEPT (pick-wt=3): 27 [] A=A.
% 2.66/2.84 ** KEPT (pick-wt=7): 28 [] set_union2(A,B)=set_union2(B,A).
% 2.66/2.84 ** KEPT (pick-wt=14): 29 [] A=powerset(B)|in($f1(B,A),A)|subset($f1(B,A),B).
% 2.66/2.84 ** KEPT (pick-wt=23): 30 [] A=set_union2(B,C)|in($f2(B,C,A),A)|in($f2(B,C,A),B)|in($f2(B,C,A),C).
% 2.66/2.84 ** KEPT (pick-wt=5): 31 [] set_union2(A,A)=A.
% 2.66/2.84 ---> New Demodulator: 32 [new_demod,31] set_union2(A,A)=A.
% 2.66/2.84 ** KEPT (pick-wt=2): 33 [] empty($c1).
% 2.66/2.84 ** KEPT (pick-wt=3): 34 [] subset(A,A).
% 2.66/2.84 ** KEPT (pick-wt=3): 35 [] inclusion_comparable(A,A).
% 2.66/2.84 ** KEPT (pick-wt=5): 36 [] subset(A,set_union2(A,B)).
% 2.66/2.84 ** KEPT (pick-wt=10): 38 [copy,37,flip.1] powerset(set_union2($c4,$c3))=set_union2(powerset($c4),powerset($c3)).
% 2.66/2.84 ---> New Demodulator: 39 [new_demod,38] powerset(set_union2($c4,$c3))=set_union2(powerset($c4),powerset($c3)).
% 2.66/2.84 Following clause subsumed by 27 during input processing: 0 [copy,27,flip.1] A=A.
% 2.66/2.84 27 back subsumes 22.
% 2.66/2.84 Following clause subsumed by 28 during input processing: 0 [copy,28,flip.1] set_union2(A,B)=set_union2(B,A).
% 2.66/2.84 >>>> Starting back demodulation with 32.
% 2.66/2.84 >> back demodulating 23 with 32.
% 2.66/2.84 34 back subsumes 26.
% 2.66/2.84 >>>> Starting back demodulation with 39.
% 2.66/2.84
% 2.66/2.84 ======= end of input processing =======
% 2.66/2.84
% 2.66/2.84 =========== start of search ===========
% 2.66/2.84
% 2.66/2.84
% 2.66/2.84 Resetting weight limit to 14.
% 2.66/2.84
% 2.66/2.84
% 2.66/2.84 Resetting weight limit to 14.
% 2.66/2.84
% 2.66/2.84 sos_size=1612
% 2.66/2.84
% 2.66/2.84
% 2.66/2.84 Resetting weight limit to 13.
% 2.66/2.84
% 2.66/2.84
% 2.66/2.84 Resetting weight limit to 13.
% 2.66/2.84
% 2.66/2.84 sos_size=1663
% 2.66/2.84
% 2.66/2.84
% 2.66/2.84 Resetting weight limit to 12.
% 2.66/2.84
% 2.66/2.84
% 2.66/2.84 Resetting weight limit to 12.
% 2.66/2.84
% 2.66/2.84 sos_size=1677
% 2.66/2.84
% 2.66/2.84 -------- PROOF --------
% 2.66/2.84
% 2.66/2.84 ----> UNIT CONFLICT at 0.69 sec ----> 2088 [binary,2087.1,20.1] $F.
% 2.66/2.84
% 2.66/2.84 Length of proof is 13. Level of proof is 7.
% 2.66/2.84
% 2.66/2.84 ---------------- PROOF ----------------
% 2.66/2.84 % SZS status Theorem
% 2.66/2.84 % SZS output start Refutation
% See solution above
% 2.66/2.84 ------------ end of proof -------------
% 2.66/2.84
% 2.66/2.84
% 2.66/2.84 Search stopped by max_proofs option.
% 2.66/2.84
% 2.66/2.84
% 2.66/2.84 Search stopped by max_proofs option.
% 2.66/2.84
% 2.66/2.84 ============ end of search ============
% 2.66/2.84
% 2.66/2.84 -------------- statistics -------------
% 2.66/2.84 clauses given 224
% 2.66/2.84 clauses generated 22980
% 2.66/2.84 clauses kept 2080
% 2.66/2.84 clauses forward subsumed 4564
% 2.66/2.84 clauses back subsumed 92
% 2.66/2.84 Kbytes malloced 5859
% 2.66/2.84
% 2.66/2.84 ----------- times (seconds) -----------
% 2.66/2.84 user CPU time 0.69 (0 hr, 0 min, 0 sec)
% 2.66/2.84 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.66/2.84 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.66/2.84
% 2.66/2.84 That finishes the proof of the theorem.
% 2.66/2.84
% 2.66/2.84 Process 28884 finished Wed Jul 27 10:26:58 2022
% 2.66/2.84 Otter interrupted
% 2.66/2.84 PROOF FOUND
%------------------------------------------------------------------------------