%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU172+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n019.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 13:15:02 EDT 2022
% Result : Theorem 1.75s 1.98s
% Output : Refutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of clauses : 9 ( 7 unt; 0 nHn; 8 RR)
% Number of literals : 12 ( 4 equ; 4 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 7 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(10,axiom,
( ~ element(A,powerset(B))
| subset_complement(B,A) = set_difference(B,A) ),
file('SEU172+1.p',unknown),
[] ).
cnf(12,axiom,
( A != set_difference(B,C)
| ~ in(D,A)
| ~ in(D,C) ),
file('SEU172+1.p',unknown),
[] ).
cnf(21,axiom,
A = A,
file('SEU172+1.p',unknown),
[] ).
cnf(32,axiom,
element(dollar_c3,powerset(dollar_c5)),
file('SEU172+1.p',unknown),
[] ).
cnf(33,axiom,
in(dollar_c4,subset_complement(dollar_c5,dollar_c3)),
file('SEU172+1.p',unknown),
[] ).
cnf(34,axiom,
in(dollar_c4,dollar_c3),
file('SEU172+1.p',unknown),
[] ).
cnf(85,plain,
subset_complement(dollar_c5,dollar_c3) = set_difference(dollar_c5,dollar_c3),
inference(hyper,[status(thm)],[32,10]),
[iquote('hyper,32,10')] ).
cnf(89,plain,
in(dollar_c4,set_difference(dollar_c5,dollar_c3)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[33]),85]),
[iquote('back_demod,33,demod,85')] ).
cnf(319,plain,
$false,
inference(hyper,[status(thm)],[89,12,21,34]),
[iquote('hyper,89,12,21,34')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU172+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n019.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 07:57:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.75/1.96 ----- Otter 3.3f, August 2004 -----
% 1.75/1.96 The process was started by sandbox on n019.cluster.edu,
% 1.75/1.96 Wed Jul 27 07:57:22 2022
% 1.75/1.96 The command was "./otter". The process ID is 26011.
% 1.75/1.96
% 1.75/1.96 set(prolog_style_variables).
% 1.75/1.96 set(auto).
% 1.75/1.96 dependent: set(auto1).
% 1.75/1.96 dependent: set(process_input).
% 1.75/1.96 dependent: clear(print_kept).
% 1.75/1.96 dependent: clear(print_new_demod).
% 1.75/1.96 dependent: clear(print_back_demod).
% 1.75/1.96 dependent: clear(print_back_sub).
% 1.75/1.96 dependent: set(control_memory).
% 1.75/1.96 dependent: assign(max_mem, 12000).
% 1.75/1.96 dependent: assign(pick_given_ratio, 4).
% 1.75/1.96 dependent: assign(stats_level, 1).
% 1.75/1.96 dependent: assign(max_seconds, 10800).
% 1.75/1.96 clear(print_given).
% 1.75/1.96
% 1.75/1.96 formula_list(usable).
% 1.75/1.96 all A (A=A).
% 1.75/1.96 $T.
% 1.75/1.96 empty(empty_set).
% 1.75/1.96 all A (set_difference(A,empty_set)=A).
% 1.75/1.96 all A (set_difference(empty_set,A)=empty_set).
% 1.75/1.96 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 1.75/1.96 all A exists B (element(B,powerset(A))&empty(B)).
% 1.75/1.96 exists A empty(A).
% 1.75/1.96 exists A (-empty(A)).
% 1.75/1.96 all A (empty(A)->A=empty_set).
% 1.75/1.96 all A B (-(empty(A)&A!=B&empty(B))).
% 1.75/1.96 all A B (element(B,powerset(A))->subset_complement(A,subset_complement(A,B))=B).
% 1.75/1.96 all A B (in(A,B)-> -in(B,A)).
% 1.75/1.96 all A exists B element(B,A).
% 1.75/1.96 $T.
% 1.75/1.96 all A B (element(B,powerset(A))->element(subset_complement(A,B),powerset(A))).
% 1.75/1.96 $T.
% 1.75/1.96 $T.
% 1.75/1.96 all A (-empty(powerset(A))).
% 1.75/1.96 all A B (-(in(A,B)&empty(B))).
% 1.75/1.96 all A B (element(B,powerset(A))->subset_complement(A,B)=set_difference(A,B)).
% 1.75/1.96 -(all A B C (element(C,powerset(A))-> -(in(B,subset_complement(A,C))&in(B,C)))).
% 1.75/1.96 all A B C (C=set_difference(A,B)<-> (all D (in(D,C)<->in(D,A)& -in(D,B)))).
% 1.75/1.96 end_of_list.
% 1.75/1.96
% 1.75/1.96 -------> usable clausifies to:
% 1.75/1.96
% 1.75/1.96 list(usable).
% 1.75/1.96 0 [] A=A.
% 1.75/1.96 0 [] $T.
% 1.75/1.96 0 [] empty(empty_set).
% 1.75/1.96 0 [] set_difference(A,empty_set)=A.
% 1.75/1.96 0 [] set_difference(empty_set,A)=empty_set.
% 1.75/1.96 0 [] empty(A)|element($f1(A),powerset(A)).
% 1.75/1.96 0 [] empty(A)| -empty($f1(A)).
% 1.75/1.96 0 [] element($f2(A),powerset(A)).
% 1.75/1.96 0 [] empty($f2(A)).
% 1.75/1.96 0 [] empty($c1).
% 1.75/1.96 0 [] -empty($c2).
% 1.75/1.96 0 [] -empty(A)|A=empty_set.
% 1.75/1.96 0 [] -empty(A)|A=B| -empty(B).
% 1.75/1.96 0 [] -element(B,powerset(A))|subset_complement(A,subset_complement(A,B))=B.
% 1.75/1.96 0 [] -in(A,B)| -in(B,A).
% 1.75/1.96 0 [] element($f3(A),A).
% 1.75/1.96 0 [] $T.
% 1.75/1.96 0 [] -element(B,powerset(A))|element(subset_complement(A,B),powerset(A)).
% 1.75/1.96 0 [] $T.
% 1.75/1.96 0 [] $T.
% 1.75/1.96 0 [] -empty(powerset(A)).
% 1.75/1.96 0 [] -in(A,B)| -empty(B).
% 1.75/1.96 0 [] -element(B,powerset(A))|subset_complement(A,B)=set_difference(A,B).
% 1.75/1.96 0 [] element($c3,powerset($c5)).
% 1.75/1.96 0 [] in($c4,subset_complement($c5,$c3)).
% 1.75/1.96 0 [] in($c4,$c3).
% 1.75/1.96 0 [] C!=set_difference(A,B)| -in(D,C)|in(D,A).
% 1.75/1.96 0 [] C!=set_difference(A,B)| -in(D,C)| -in(D,B).
% 1.75/1.96 0 [] C!=set_difference(A,B)|in(D,C)| -in(D,A)|in(D,B).
% 1.75/1.96 0 [] C=set_difference(A,B)|in($f4(A,B,C),C)|in($f4(A,B,C),A).
% 1.75/1.96 0 [] C=set_difference(A,B)|in($f4(A,B,C),C)| -in($f4(A,B,C),B).
% 1.75/1.96 0 [] C=set_difference(A,B)| -in($f4(A,B,C),C)| -in($f4(A,B,C),A)|in($f4(A,B,C),B).
% 1.75/1.96 end_of_list.
% 1.75/1.96
% 1.75/1.96 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.75/1.96
% 1.75/1.96 This ia a non-Horn set with equality. The strategy will be
% 1.75/1.96 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.75/1.96 deletion, with positive clauses in sos and nonpositive
% 1.75/1.96 clauses in usable.
% 1.75/1.96
% 1.75/1.96 dependent: set(knuth_bendix).
% 1.75/1.96 dependent: set(anl_eq).
% 1.75/1.96 dependent: set(para_from).
% 1.75/1.96 dependent: set(para_into).
% 1.75/1.96 dependent: clear(para_from_right).
% 1.75/1.96 dependent: clear(para_into_right).
% 1.75/1.96 dependent: set(para_from_vars).
% 1.75/1.96 dependent: set(eq_units_both_ways).
% 1.75/1.96 dependent: set(dynamic_demod_all).
% 1.75/1.96 dependent: set(dynamic_demod).
% 1.75/1.96 dependent: set(order_eq).
% 1.75/1.96 dependent: set(back_demod).
% 1.75/1.96 dependent: set(lrpo).
% 1.75/1.96 dependent: set(hyper_res).
% 1.75/1.96 dependent: set(unit_deletion).
% 1.75/1.96 dependent: set(factor).
% 1.75/1.96
% 1.75/1.96 ------------> process usable:
% 1.75/1.96 ** KEPT (pick-wt=5): 1 [] empty(A)| -empty($f1(A)).
% 1.75/1.96 ** KEPT (pick-wt=2): 2 [] -empty($c2).
% 1.75/1.96 ** KEPT (pick-wt=5): 3 [] -empty(A)|A=empty_set.
% 1.75/1.96 ** KEPT (pick-wt=7): 4 [] -empty(A)|A=B| -empty(B).
% 1.75/1.96 ** KEPT (pick-wt=11): 5 [] -element(A,powerset(B))|subset_complement(B,subset_complement(B,A))=A.
% 1.75/1.96 ** KEPT (pick-wt=6): 6 [] -in(A,B)| -in(B,A).
% 1.75/1.96 ** KEPT (pick-wt=10): 7 [] -element(A,powerset(B))|element(subset_complement(B,A),powerset(B)).
% 1.75/1.96 ** KEPT (pick-wt=3): 8 [] -empty(powerset(A)).
% 1.75/1.96 ** KEPT (pick-wt=5): 9 [] -in(A,B)| -empty(B).
% 1.75/1.96 ** KEPT (pick-wt=11): 10 [] -element(A,powerset(B))|subset_complement(B,A)=set_difference(B,A).
% 1.75/1.98 ** KEPT (pick-wt=11): 11 [] A!=set_difference(B,C)| -in(D,A)|in(D,B).
% 1.75/1.98 ** KEPT (pick-wt=11): 12 [] A!=set_difference(B,C)| -in(D,A)| -in(D,C).
% 1.75/1.98 ** KEPT (pick-wt=14): 13 [] A!=set_difference(B,C)|in(D,A)| -in(D,B)|in(D,C).
% 1.75/1.98 ** KEPT (pick-wt=17): 14 [] A=set_difference(B,C)|in($f4(B,C,A),A)| -in($f4(B,C,A),C).
% 1.75/1.98 ** KEPT (pick-wt=23): 15 [] A=set_difference(B,C)| -in($f4(B,C,A),A)| -in($f4(B,C,A),B)|in($f4(B,C,A),C).
% 1.75/1.98
% 1.75/1.98 ------------> process sos:
% 1.75/1.98 ** KEPT (pick-wt=3): 21 [] A=A.
% 1.75/1.98 ** KEPT (pick-wt=2): 22 [] empty(empty_set).
% 1.75/1.98 ** KEPT (pick-wt=5): 23 [] set_difference(A,empty_set)=A.
% 1.75/1.98 ---> New Demodulator: 24 [new_demod,23] set_difference(A,empty_set)=A.
% 1.75/1.98 ** KEPT (pick-wt=5): 25 [] set_difference(empty_set,A)=empty_set.
% 1.75/1.98 ---> New Demodulator: 26 [new_demod,25] set_difference(empty_set,A)=empty_set.
% 1.75/1.98 ** KEPT (pick-wt=7): 27 [] empty(A)|element($f1(A),powerset(A)).
% 1.75/1.98 ** KEPT (pick-wt=5): 28 [] element($f2(A),powerset(A)).
% 1.75/1.98 ** KEPT (pick-wt=3): 29 [] empty($f2(A)).
% 1.75/1.98 ** KEPT (pick-wt=2): 30 [] empty($c1).
% 1.75/1.98 ** KEPT (pick-wt=4): 31 [] element($f3(A),A).
% 1.75/1.98 ** KEPT (pick-wt=4): 32 [] element($c3,powerset($c5)).
% 1.75/1.98 ** KEPT (pick-wt=5): 33 [] in($c4,subset_complement($c5,$c3)).
% 1.75/1.98 ** KEPT (pick-wt=3): 34 [] in($c4,$c3).
% 1.75/1.98 ** KEPT (pick-wt=17): 35 [] A=set_difference(B,C)|in($f4(B,C,A),A)|in($f4(B,C,A),B).
% 1.75/1.98 Following clause subsumed by 21 during input processing: 0 [copy,21,flip.1] A=A.
% 1.75/1.98 21 back subsumes 16.
% 1.75/1.98 >>>> Starting back demodulation with 24.
% 1.75/1.98 >>>> Starting back demodulation with 26.
% 1.75/1.98
% 1.75/1.98 ======= end of input processing =======
% 1.75/1.98
% 1.75/1.98 =========== start of search ===========
% 1.75/1.98
% 1.75/1.98 -------- PROOF --------
% 1.75/1.98
% 1.75/1.98 -----> EMPTY CLAUSE at 0.02 sec ----> 319 [hyper,89,12,21,34] $F.
% 1.75/1.98
% 1.75/1.98 Length of proof is 2. Level of proof is 2.
% 1.75/1.98
% 1.75/1.98 ---------------- PROOF ----------------
% 1.75/1.98 % SZS status Theorem
% 1.75/1.98 % SZS output start Refutation
% See solution above
% 1.75/1.98 ------------ end of proof -------------
% 1.75/1.98
% 1.75/1.98
% 1.75/1.98 Search stopped by max_proofs option.
% 1.75/1.98
% 1.75/1.98
% 1.75/1.98 Search stopped by max_proofs option.
% 1.75/1.98
% 1.75/1.98 ============ end of search ============
% 1.75/1.98
% 1.75/1.98 -------------- statistics -------------
% 1.75/1.98 clauses given 20
% 1.75/1.98 clauses generated 431
% 1.75/1.98 clauses kept 301
% 1.75/1.98 clauses forward subsumed 165
% 1.75/1.98 clauses back subsumed 9
% 1.75/1.98 Kbytes malloced 1953
% 1.75/1.98
% 1.75/1.98 ----------- times (seconds) -----------
% 1.75/1.98 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.75/1.98 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.75/1.98 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.75/1.98
% 1.75/1.98 That finishes the proof of the theorem.
% 1.75/1.98
% 1.75/1.98 Process 26011 finished Wed Jul 27 07:57:23 2022
% 1.75/1.98 Otter interrupted
% 1.75/1.98 PROOF FOUND
%------------------------------------------------------------------------------