TSTP Solution File: SEU147+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU147+1 : TPTP v8.1.0. Released v3.3.0.
% 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 13:14:54 EDT 2022
% Result : Theorem 2.06s 2.23s
% Output : Refutation 2.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of clauses : 14 ( 7 unt; 3 nHn; 8 RR)
% Number of literals : 27 ( 16 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
( A = singleton(B)
| ~ in(dollar_f1(B,A),A)
| dollar_f1(B,A) != B ),
file('SEU147+1.p',unknown),
[] ).
cnf(5,axiom,
( A != powerset(B)
| ~ in(C,A)
| subset(C,B) ),
file('SEU147+1.p',unknown),
[] ).
cnf(6,axiom,
( A != powerset(B)
| in(C,A)
| ~ subset(C,B) ),
file('SEU147+1.p',unknown),
[] ).
cnf(9,axiom,
powerset(empty_set) != singleton(empty_set),
file('SEU147+1.p',unknown),
[] ).
cnf(10,plain,
singleton(empty_set) != powerset(empty_set),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[9])]),
[iquote('copy,9,flip.1')] ).
cnf(12,axiom,
( ~ subset(A,empty_set)
| A = empty_set ),
file('SEU147+1.p',unknown),
[] ).
cnf(15,axiom,
A = A,
file('SEU147+1.p',unknown),
[] ).
cnf(16,axiom,
( A = singleton(B)
| in(dollar_f1(B,A),A)
| dollar_f1(B,A) = B ),
file('SEU147+1.p',unknown),
[] ).
cnf(20,axiom,
subset(A,A),
file('SEU147+1.p',unknown),
[] ).
cnf(31,plain,
in(A,powerset(A)),
inference(hyper,[status(thm)],[20,6,15]),
[iquote('hyper,20,6,15')] ).
cnf(37,plain,
( powerset(A) = singleton(B)
| dollar_f1(B,powerset(A)) = B
| subset(dollar_f1(B,powerset(A)),A) ),
inference(hyper,[status(thm)],[16,5,15]),
[iquote('hyper,16,5,15')] ).
cnf(2089,plain,
( singleton(A) = powerset(empty_set)
| dollar_f1(A,powerset(empty_set)) = A
| dollar_f1(A,powerset(empty_set)) = empty_set ),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[37,12])]),
[iquote('hyper,37,12,flip.1')] ).
cnf(2091,plain,
dollar_f1(empty_set,powerset(empty_set)) = empty_set,
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[2089]),10]),
[iquote('factor,2089.2.3,unit_del,10')] ).
cnf(2174,plain,
$false,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[2091,4]),2091]),10,31,15]),
[iquote('para_from,2090.1.1,4.3.1,demod,2091,unit_del,10,31,15')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU147+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 07:56:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.06/2.22 ----- Otter 3.3f, August 2004 -----
% 2.06/2.22 The process was started by sandbox on n022.cluster.edu,
% 2.06/2.22 Wed Jul 27 07:56:05 2022
% 2.06/2.22 The command was "./otter". The process ID is 14689.
% 2.06/2.22
% 2.06/2.22 set(prolog_style_variables).
% 2.06/2.22 set(auto).
% 2.06/2.22 dependent: set(auto1).
% 2.06/2.22 dependent: set(process_input).
% 2.06/2.22 dependent: clear(print_kept).
% 2.06/2.22 dependent: clear(print_new_demod).
% 2.06/2.22 dependent: clear(print_back_demod).
% 2.06/2.22 dependent: clear(print_back_sub).
% 2.06/2.22 dependent: set(control_memory).
% 2.06/2.22 dependent: assign(max_mem, 12000).
% 2.06/2.22 dependent: assign(pick_given_ratio, 4).
% 2.06/2.22 dependent: assign(stats_level, 1).
% 2.06/2.22 dependent: assign(max_seconds, 10800).
% 2.06/2.22 clear(print_given).
% 2.06/2.22
% 2.06/2.22 formula_list(usable).
% 2.06/2.22 all A (A=A).
% 2.06/2.22 all A B (in(A,B)-> -in(B,A)).
% 2.06/2.22 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 2.06/2.22 all A B (B=powerset(A)<-> (all C (in(C,B)<->subset(C,A)))).
% 2.06/2.22 $T.
% 2.06/2.22 $T.
% 2.06/2.22 $T.
% 2.06/2.22 empty(empty_set).
% 2.06/2.22 exists A empty(A).
% 2.06/2.22 exists A (-empty(A)).
% 2.06/2.22 all A B subset(A,A).
% 2.06/2.22 powerset(empty_set)!=singleton(empty_set).
% 2.06/2.22 all A B ((all C (in(C,A)<->in(C,B)))->A=B).
% 2.06/2.22 all A (subset(A,empty_set)->A=empty_set).
% 2.06/2.23 end_of_list.
% 2.06/2.23
% 2.06/2.23 -------> usable clausifies to:
% 2.06/2.23
% 2.06/2.23 list(usable).
% 2.06/2.23 0 [] A=A.
% 2.06/2.23 0 [] -in(A,B)| -in(B,A).
% 2.06/2.23 0 [] B!=singleton(A)| -in(C,B)|C=A.
% 2.06/2.23 0 [] B!=singleton(A)|in(C,B)|C!=A.
% 2.06/2.23 0 [] B=singleton(A)|in($f1(A,B),B)|$f1(A,B)=A.
% 2.06/2.23 0 [] B=singleton(A)| -in($f1(A,B),B)|$f1(A,B)!=A.
% 2.06/2.23 0 [] B!=powerset(A)| -in(C,B)|subset(C,A).
% 2.06/2.23 0 [] B!=powerset(A)|in(C,B)| -subset(C,A).
% 2.06/2.23 0 [] B=powerset(A)|in($f2(A,B),B)|subset($f2(A,B),A).
% 2.06/2.23 0 [] B=powerset(A)| -in($f2(A,B),B)| -subset($f2(A,B),A).
% 2.06/2.23 0 [] $T.
% 2.06/2.23 0 [] $T.
% 2.06/2.23 0 [] $T.
% 2.06/2.23 0 [] empty(empty_set).
% 2.06/2.23 0 [] empty($c1).
% 2.06/2.23 0 [] -empty($c2).
% 2.06/2.23 0 [] subset(A,A).
% 2.06/2.23 0 [] powerset(empty_set)!=singleton(empty_set).
% 2.06/2.23 0 [] in($f3(A,B),A)|in($f3(A,B),B)|A=B.
% 2.06/2.23 0 [] -in($f3(A,B),A)| -in($f3(A,B),B)|A=B.
% 2.06/2.23 0 [] -subset(A,empty_set)|A=empty_set.
% 2.06/2.23 end_of_list.
% 2.06/2.23
% 2.06/2.23 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 2.06/2.23
% 2.06/2.23 This ia a non-Horn set with equality. The strategy will be
% 2.06/2.23 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.06/2.23 deletion, with positive clauses in sos and nonpositive
% 2.06/2.23 clauses in usable.
% 2.06/2.23
% 2.06/2.23 dependent: set(knuth_bendix).
% 2.06/2.23 dependent: set(anl_eq).
% 2.06/2.23 dependent: set(para_from).
% 2.06/2.23 dependent: set(para_into).
% 2.06/2.23 dependent: clear(para_from_right).
% 2.06/2.23 dependent: clear(para_into_right).
% 2.06/2.23 dependent: set(para_from_vars).
% 2.06/2.23 dependent: set(eq_units_both_ways).
% 2.06/2.23 dependent: set(dynamic_demod_all).
% 2.06/2.23 dependent: set(dynamic_demod).
% 2.06/2.23 dependent: set(order_eq).
% 2.06/2.23 dependent: set(back_demod).
% 2.06/2.23 dependent: set(lrpo).
% 2.06/2.23 dependent: set(hyper_res).
% 2.06/2.23 dependent: set(unit_deletion).
% 2.06/2.23 dependent: set(factor).
% 2.06/2.23
% 2.06/2.23 ------------> process usable:
% 2.06/2.23 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 2.06/2.23 ** KEPT (pick-wt=10): 2 [] A!=singleton(B)| -in(C,A)|C=B.
% 2.06/2.23 ** KEPT (pick-wt=10): 3 [] A!=singleton(B)|in(C,A)|C!=B.
% 2.06/2.23 ** KEPT (pick-wt=14): 4 [] A=singleton(B)| -in($f1(B,A),A)|$f1(B,A)!=B.
% 2.06/2.23 ** KEPT (pick-wt=10): 5 [] A!=powerset(B)| -in(C,A)|subset(C,B).
% 2.06/2.23 ** KEPT (pick-wt=10): 6 [] A!=powerset(B)|in(C,A)| -subset(C,B).
% 2.06/2.23 ** KEPT (pick-wt=14): 7 [] A=powerset(B)| -in($f2(B,A),A)| -subset($f2(B,A),B).
% 2.06/2.23 ** KEPT (pick-wt=2): 8 [] -empty($c2).
% 2.06/2.23 ** KEPT (pick-wt=5): 10 [copy,9,flip.1] singleton(empty_set)!=powerset(empty_set).
% 2.06/2.23 ** KEPT (pick-wt=13): 11 [] -in($f3(A,B),A)| -in($f3(A,B),B)|A=B.
% 2.06/2.23 ** KEPT (pick-wt=6): 12 [] -subset(A,empty_set)|A=empty_set.
% 2.06/2.23
% 2.06/2.23 ------------> process sos:
% 2.06/2.23 ** KEPT (pick-wt=3): 15 [] A=A.
% 2.06/2.23 ** KEPT (pick-wt=14): 16 [] A=singleton(B)|in($f1(B,A),A)|$f1(B,A)=B.
% 2.06/2.23 ** KEPT (pick-wt=14): 17 [] A=powerset(B)|in($f2(B,A),A)|subset($f2(B,A),B).
% 2.06/2.23 ** KEPT (pick-wt=2): 18 [] empty(empty_set).
% 2.06/2.23 ** KEPT (pick-wt=2): 19 [] empty($c1).
% 2.06/2.23 ** KEPT (pick-wt=3): 20 [] subset(A,A).
% 2.06/2.23 ** KEPT (pick-wt=13): 21 [] in($f3(A,B),A)|in($f3(A,B),B)|A=B.
% 2.06/2.23 Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] A=A.
% 2.06/2.23 15 back subsumes 14.
% 2.06/2.23
% 2.06/2.23 ======= end of input processing =======
% 2.06/2.23
% 2.06/2.23 =========== start of search ===========
% 2.06/2.23
% 2.06/2.23 -------- PROOF --------
% 2.06/2.23
% 2.06/2.23 -----> EMPTY CLAUSE at 0.33 sec ----> 2174 [para_from,2090.1.1,4.3.1,demod,2091,unit_del,10,31,15] $F.
% 2.06/2.23
% 2.06/2.23 Length of proof is 5. Level of proof is 3.
% 2.06/2.23
% 2.06/2.23 ---------------- PROOF ----------------
% 2.06/2.23 % SZS status Theorem
% 2.06/2.23 % SZS output start Refutation
% See solution above
% 2.06/2.23 ------------ end of proof -------------
% 2.06/2.23
% 2.06/2.23
% 2.06/2.23 Search stopped by max_proofs option.
% 2.06/2.23
% 2.06/2.23
% 2.06/2.23 Search stopped by max_proofs option.
% 2.06/2.23
% 2.06/2.23 ============ end of search ============
% 2.06/2.23
% 2.06/2.23 -------------- statistics -------------
% 2.06/2.23 clauses given 57
% 2.06/2.23 clauses generated 3344
% 2.06/2.23 clauses kept 2171
% 2.06/2.23 clauses forward subsumed 1161
% 2.06/2.23 clauses back subsumed 11
% 2.06/2.23 Kbytes malloced 3906
% 2.06/2.23
% 2.06/2.23 ----------- times (seconds) -----------
% 2.06/2.23 user CPU time 0.33 (0 hr, 0 min, 0 sec)
% 2.06/2.23 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.06/2.23 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.06/2.23
% 2.06/2.23 That finishes the proof of the theorem.
% 2.06/2.23
% 2.06/2.23 Process 14689 finished Wed Jul 27 07:56:07 2022
% 2.06/2.23 Otter interrupted
% 2.06/2.23 PROOF FOUND
%------------------------------------------------------------------------------