TSTP Solution File: SEU177+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU177+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n025.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 13:15:04 EDT 2022
% Result : Theorem 1.97s 2.16s
% Output : Refutation 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of clauses : 9 ( 6 unt; 0 nHn; 8 RR)
% Number of literals : 16 ( 3 equ; 8 neg)
% Maximal clause size : 4 ( 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 : 9 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(11,axiom,
( ~ in(dollar_c6,relation_dom(dollar_c4))
| ~ in(dollar_c5,relation_rng(dollar_c4)) ),
file('SEU177+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ relation(A)
| B != relation_dom(A)
| in(C,B)
| ~ in(ordered_pair(C,D),A) ),
file('SEU177+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ relation(A)
| B != relation_rng(A)
| in(C,B)
| ~ in(ordered_pair(D,C),A) ),
file('SEU177+1.p',unknown),
[] ).
cnf(22,axiom,
A = A,
file('SEU177+1.p',unknown),
[] ).
cnf(32,axiom,
relation(dollar_c4),
file('SEU177+1.p',unknown),
[] ).
cnf(33,axiom,
in(ordered_pair(dollar_c6,dollar_c5),dollar_c4),
file('SEU177+1.p',unknown),
[] ).
cnf(92,plain,
in(dollar_c5,relation_rng(dollar_c4)),
inference(hyper,[status(thm)],[33,17,32,22]),
[iquote('hyper,33,17,32,22')] ).
cnf(93,plain,
in(dollar_c6,relation_dom(dollar_c4)),
inference(hyper,[status(thm)],[33,13,32,22]),
[iquote('hyper,33,13,32,22')] ).
cnf(132,plain,
$false,
inference(hyper,[status(thm)],[93,11,92]),
[iquote('hyper,93,11,92')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU177+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.11 % Command : otter-tptp-script %s
% 0.11/0.32 % Computer : n025.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Jul 27 07:47:45 EDT 2022
% 0.11/0.32 % CPUTime :
% 1.97/2.16 ----- Otter 3.3f, August 2004 -----
% 1.97/2.16 The process was started by sandbox2 on n025.cluster.edu,
% 1.97/2.16 Wed Jul 27 07:47:45 2022
% 1.97/2.16 The command was "./otter". The process ID is 8905.
% 1.97/2.16
% 1.97/2.16 set(prolog_style_variables).
% 1.97/2.16 set(auto).
% 1.97/2.16 dependent: set(auto1).
% 1.97/2.16 dependent: set(process_input).
% 1.97/2.16 dependent: clear(print_kept).
% 1.97/2.16 dependent: clear(print_new_demod).
% 1.97/2.16 dependent: clear(print_back_demod).
% 1.97/2.16 dependent: clear(print_back_sub).
% 1.97/2.16 dependent: set(control_memory).
% 1.97/2.16 dependent: assign(max_mem, 12000).
% 1.97/2.16 dependent: assign(pick_given_ratio, 4).
% 1.97/2.16 dependent: assign(stats_level, 1).
% 1.97/2.16 dependent: assign(max_seconds, 10800).
% 1.97/2.16 clear(print_given).
% 1.97/2.16
% 1.97/2.16 formula_list(usable).
% 1.97/2.16 all A (A=A).
% 1.97/2.16 $T.
% 1.97/2.16 empty(empty_set).
% 1.97/2.16 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.97/2.16 all A exists B element(B,A).
% 1.97/2.16 $T.
% 1.97/2.16 $T.
% 1.97/2.16 $T.
% 1.97/2.16 exists A (empty(A)&relation(A)).
% 1.97/2.16 exists A empty(A).
% 1.97/2.16 exists A (-empty(A)).
% 1.97/2.16 all A (-empty(singleton(A))).
% 1.97/2.16 all A B (-empty(unordered_pair(A,B))).
% 1.97/2.16 all A B (element(A,B)->empty(B)|in(A,B)).
% 1.97/2.16 all A (empty(A)->A=empty_set).
% 1.97/2.16 all A B (-(empty(A)&A!=B&empty(B))).
% 1.97/2.16 all A B (in(A,B)-> -in(B,A)).
% 1.97/2.16 $T.
% 1.97/2.16 $T.
% 1.97/2.16 $T.
% 1.97/2.16 all A B (-empty(ordered_pair(A,B))).
% 1.97/2.16 all A B (in(A,B)->element(A,B)).
% 1.97/2.16 all A B (-(in(A,B)&empty(B))).
% 1.97/2.16 all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 1.97/2.16 -(all A B C (relation(C)-> (in(ordered_pair(A,B),C)->in(A,relation_dom(C))&in(B,relation_rng(C))))).
% 1.97/2.16 all A (relation(A)-> (all B (B=relation_dom(A)<-> (all C (in(C,B)<-> (exists D in(ordered_pair(C,D),A))))))).
% 1.97/2.16 all A (relation(A)-> (all B (B=relation_rng(A)<-> (all C (in(C,B)<-> (exists D in(ordered_pair(D,C),A))))))).
% 1.97/2.16 end_of_list.
% 1.97/2.16
% 1.97/2.16 -------> usable clausifies to:
% 1.97/2.16
% 1.97/2.16 list(usable).
% 1.97/2.16 0 [] A=A.
% 1.97/2.16 0 [] $T.
% 1.97/2.16 0 [] empty(empty_set).
% 1.97/2.16 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.97/2.16 0 [] element($f1(A),A).
% 1.97/2.16 0 [] $T.
% 1.97/2.16 0 [] $T.
% 1.97/2.16 0 [] $T.
% 1.97/2.16 0 [] empty($c1).
% 1.97/2.16 0 [] relation($c1).
% 1.97/2.16 0 [] empty($c2).
% 1.97/2.16 0 [] -empty($c3).
% 1.97/2.16 0 [] -empty(singleton(A)).
% 1.97/2.16 0 [] -empty(unordered_pair(A,B)).
% 1.97/2.16 0 [] -element(A,B)|empty(B)|in(A,B).
% 1.97/2.16 0 [] -empty(A)|A=empty_set.
% 1.97/2.16 0 [] -empty(A)|A=B| -empty(B).
% 1.97/2.16 0 [] -in(A,B)| -in(B,A).
% 1.97/2.16 0 [] $T.
% 1.97/2.16 0 [] $T.
% 1.97/2.16 0 [] $T.
% 1.97/2.16 0 [] -empty(ordered_pair(A,B)).
% 1.97/2.16 0 [] -in(A,B)|element(A,B).
% 1.97/2.16 0 [] -in(A,B)| -empty(B).
% 1.97/2.16 0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 1.97/2.16 0 [] relation($c4).
% 1.97/2.16 0 [] in(ordered_pair($c6,$c5),$c4).
% 1.97/2.16 0 [] -in($c6,relation_dom($c4))| -in($c5,relation_rng($c4)).
% 1.97/2.16 0 [] -relation(A)|B!=relation_dom(A)| -in(C,B)|in(ordered_pair(C,$f2(A,B,C)),A).
% 1.97/2.16 0 [] -relation(A)|B!=relation_dom(A)|in(C,B)| -in(ordered_pair(C,D),A).
% 1.97/2.16 0 [] -relation(A)|B=relation_dom(A)|in($f4(A,B),B)|in(ordered_pair($f4(A,B),$f3(A,B)),A).
% 1.97/2.16 0 [] -relation(A)|B=relation_dom(A)| -in($f4(A,B),B)| -in(ordered_pair($f4(A,B),X1),A).
% 1.97/2.16 0 [] -relation(A)|B!=relation_rng(A)| -in(C,B)|in(ordered_pair($f5(A,B,C),C),A).
% 1.97/2.16 0 [] -relation(A)|B!=relation_rng(A)|in(C,B)| -in(ordered_pair(D,C),A).
% 1.97/2.16 0 [] -relation(A)|B=relation_rng(A)|in($f7(A,B),B)|in(ordered_pair($f6(A,B),$f7(A,B)),A).
% 1.97/2.16 0 [] -relation(A)|B=relation_rng(A)| -in($f7(A,B),B)| -in(ordered_pair(X2,$f7(A,B)),A).
% 1.97/2.16 end_of_list.
% 1.97/2.16
% 1.97/2.16 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.97/2.16
% 1.97/2.16 This ia a non-Horn set with equality. The strategy will be
% 1.97/2.16 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.97/2.16 deletion, with positive clauses in sos and nonpositive
% 1.97/2.16 clauses in usable.
% 1.97/2.16
% 1.97/2.16 dependent: set(knuth_bendix).
% 1.97/2.16 dependent: set(anl_eq).
% 1.97/2.16 dependent: set(para_from).
% 1.97/2.16 dependent: set(para_into).
% 1.97/2.16 dependent: clear(para_from_right).
% 1.97/2.16 dependent: clear(para_into_right).
% 1.97/2.16 dependent: set(para_from_vars).
% 1.97/2.16 dependent: set(eq_units_both_ways).
% 1.97/2.16 dependent: set(dynamic_demod_all).
% 1.97/2.16 dependent: set(dynamic_demod).
% 1.97/2.16 dependent: set(order_eq).
% 1.97/2.16 dependent: set(back_demod).
% 1.97/2.16 dependent: set(lrpo).
% 1.97/2.16 dependent: set(hyper_res).
% 1.97/2.16 dependent: set(unit_deletion).
% 1.97/2.16 dependent: set(factor).
% 1.97/2.16
% 1.97/2.16 ------------> process usable:
% 1.97/2.16 ** KEPT (pick-wt=2): 1 [] -empty($c3).
% 1.97/2.16 ** KEPT (pick-wt=3): 2 [] -empty(singleton(A)).
% 1.97/2.16 ** KEPT (pick-wt=4): 3 [] -empty(unordered_pair(A,B)).
% 1.97/2.16 ** KEPT (pick-wt=8): 4 [] -element(A,B)|empty(B)|in(A,B).
% 1.97/2.16 ** KEPT (pick-wt=5): 5 [] -empty(A)|A=empty_set.
% 1.97/2.16 ** KEPT (pick-wt=7): 6 [] -empty(A)|A=B| -empty(B).
% 1.97/2.16 ** KEPT (pick-wt=6): 7 [] -in(A,B)| -in(B,A).
% 1.97/2.16 ** KEPT (pick-wt=4): 8 [] -empty(ordered_pair(A,B)).
% 1.97/2.16 ** KEPT (pick-wt=6): 9 [] -in(A,B)|element(A,B).
% 1.97/2.16 ** KEPT (pick-wt=5): 10 [] -in(A,B)| -empty(B).
% 1.97/2.16 ** KEPT (pick-wt=8): 11 [] -in($c6,relation_dom($c4))| -in($c5,relation_rng($c4)).
% 1.97/2.16 ** KEPT (pick-wt=17): 12 [] -relation(A)|B!=relation_dom(A)| -in(C,B)|in(ordered_pair(C,$f2(A,B,C)),A).
% 1.97/2.16 ** KEPT (pick-wt=14): 13 [] -relation(A)|B!=relation_dom(A)|in(C,B)| -in(ordered_pair(C,D),A).
% 1.97/2.16 ** KEPT (pick-wt=20): 14 [] -relation(A)|B=relation_dom(A)|in($f4(A,B),B)|in(ordered_pair($f4(A,B),$f3(A,B)),A).
% 1.97/2.16 ** KEPT (pick-wt=18): 15 [] -relation(A)|B=relation_dom(A)| -in($f4(A,B),B)| -in(ordered_pair($f4(A,B),C),A).
% 1.97/2.16 ** KEPT (pick-wt=17): 16 [] -relation(A)|B!=relation_rng(A)| -in(C,B)|in(ordered_pair($f5(A,B,C),C),A).
% 1.97/2.16 ** KEPT (pick-wt=14): 17 [] -relation(A)|B!=relation_rng(A)|in(C,B)| -in(ordered_pair(D,C),A).
% 1.97/2.16 ** KEPT (pick-wt=20): 18 [] -relation(A)|B=relation_rng(A)|in($f7(A,B),B)|in(ordered_pair($f6(A,B),$f7(A,B)),A).
% 1.97/2.16 ** KEPT (pick-wt=18): 19 [] -relation(A)|B=relation_rng(A)| -in($f7(A,B),B)| -in(ordered_pair(C,$f7(A,B)),A).
% 1.97/2.16
% 1.97/2.16 ------------> process sos:
% 1.97/2.16 ** KEPT (pick-wt=3): 22 [] A=A.
% 1.97/2.16 ** KEPT (pick-wt=2): 23 [] empty(empty_set).
% 1.97/2.16 ** KEPT (pick-wt=7): 24 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.97/2.16 ** KEPT (pick-wt=4): 25 [] element($f1(A),A).
% 1.97/2.16 ** KEPT (pick-wt=2): 26 [] empty($c1).
% 1.97/2.16 ** KEPT (pick-wt=2): 27 [] relation($c1).
% 1.97/2.16 ** KEPT (pick-wt=2): 28 [] empty($c2).
% 1.97/2.16 ** KEPT (pick-wt=10): 30 [copy,29,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.97/2.16 ---> New Demodulator: 31 [new_demod,30] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.97/2.16 ** KEPT (pick-wt=2): 32 [] relation($c4).
% 1.97/2.16 ** KEPT (pick-wt=5): 33 [] in(ordered_pair($c6,$c5),$c4).
% 1.97/2.16 Following clause subsumed by 22 during input processing: 0 [copy,22,flip.1] A=A.
% 1.97/2.16 22 back subsumes 20.
% 1.97/2.16 Following clause subsumed by 24 during input processing: 0 [copy,24,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.97/2.16 >>>> Starting back demodulation with 31.
% 1.97/2.16
% 1.97/2.16 ======= end of input processing =======
% 1.97/2.16
% 1.97/2.16 =========== start of search ===========
% 1.97/2.16
% 1.97/2.16 -------- PROOF --------
% 1.97/2.16
% 1.97/2.16 -----> EMPTY CLAUSE at 0.01 sec ----> 132 [hyper,93,11,92] $F.
% 1.97/2.16
% 1.97/2.16 Length of proof is 2. Level of proof is 1.
% 1.97/2.16
% 1.97/2.16 ---------------- PROOF ----------------
% 1.97/2.16 % SZS status Theorem
% 1.97/2.16 % SZS output start Refutation
% See solution above
% 1.97/2.16 ------------ end of proof -------------
% 1.97/2.16
% 1.97/2.16
% 1.97/2.16 Search stopped by max_proofs option.
% 1.97/2.16
% 1.97/2.16
% 1.97/2.16 Search stopped by max_proofs option.
% 1.97/2.16
% 1.97/2.16 ============ end of search ============
% 1.97/2.16
% 1.97/2.16 -------------- statistics -------------
% 1.97/2.16 clauses given 15
% 1.97/2.16 clauses generated 140
% 1.97/2.16 clauses kept 124
% 1.97/2.16 clauses forward subsumed 51
% 1.97/2.16 clauses back subsumed 1
% 1.97/2.16 Kbytes malloced 1953
% 1.97/2.16
% 1.97/2.16 ----------- times (seconds) -----------
% 1.97/2.16 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.97/2.16 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.97/2.16 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.97/2.16
% 1.97/2.16 That finishes the proof of the theorem.
% 1.97/2.16
% 1.97/2.16 Process 8905 finished Wed Jul 27 07:47:47 2022
% 1.97/2.16 Otter interrupted
% 1.97/2.16 PROOF FOUND
%------------------------------------------------------------------------------