TSTP Solution File: SEU044+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU044+1 : TPTP v8.1.0. Released v3.2.0.
% 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 13:14:42 EDT 2022
% Result : Theorem 2.33s 2.54s
% Output : Refutation 2.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 11
% Syntax : Number of clauses : 17 ( 9 unt; 2 nHn; 12 RR)
% Number of literals : 43 ( 4 equ; 25 neg)
% Maximal clause size : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 19 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(16,axiom,
( ~ relation(A)
| relation(relation_rng_restriction(B,A)) ),
file('SEU044+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ relation(A)
| ~ function(A)
| function(relation_rng_restriction(B,A)) ),
file('SEU044+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ in(dollar_c10,relation_dom(relation_rng_restriction(dollar_c11,dollar_c9)))
| ~ in(dollar_c10,relation_dom(dollar_c9))
| ~ in(apply(dollar_c9,dollar_c10),dollar_c11) ),
file('SEU044+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ relation(A)
| ~ function(A)
| ~ relation(B)
| ~ function(B)
| A != relation_rng_restriction(C,B)
| ~ in(D,relation_dom(A))
| in(D,relation_dom(B)) ),
file('SEU044+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ relation(A)
| ~ function(A)
| ~ relation(B)
| ~ function(B)
| A != relation_rng_restriction(C,B)
| ~ in(D,relation_dom(A))
| in(apply(B,D),C) ),
file('SEU044+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ relation(A)
| ~ function(A)
| ~ relation(B)
| ~ function(B)
| A != relation_rng_restriction(C,B)
| in(D,relation_dom(A))
| ~ in(D,relation_dom(B))
| ~ in(apply(B,D),C) ),
file('SEU044+1.p',unknown),
[] ).
cnf(42,axiom,
A = A,
file('SEU044+1.p',unknown),
[] ).
cnf(65,axiom,
relation(dollar_c9),
file('SEU044+1.p',unknown),
[] ).
cnf(66,axiom,
function(dollar_c9),
file('SEU044+1.p',unknown),
[] ).
cnf(67,axiom,
( in(dollar_c10,relation_dom(relation_rng_restriction(dollar_c11,dollar_c9)))
| in(dollar_c10,relation_dom(dollar_c9)) ),
file('SEU044+1.p',unknown),
[] ).
cnf(68,axiom,
( in(dollar_c10,relation_dom(relation_rng_restriction(dollar_c11,dollar_c9)))
| in(apply(dollar_c9,dollar_c10),dollar_c11) ),
file('SEU044+1.p',unknown),
[] ).
cnf(227,plain,
relation(relation_rng_restriction(A,dollar_c9)),
inference(hyper,[status(thm)],[65,16]),
[iquote('hyper,65,16')] ).
cnf(242,plain,
function(relation_rng_restriction(A,dollar_c9)),
inference(hyper,[status(thm)],[66,17,65]),
[iquote('hyper,66,17,65')] ).
cnf(906,plain,
in(dollar_c10,relation_dom(relation_rng_restriction(dollar_c11,dollar_c9))),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[242,26,227,65,66,42,67,68])])]),
[iquote('hyper,242,26,227,65,66,42,67,68,factor_simp,factor_simp')] ).
cnf(907,plain,
in(apply(dollar_c9,dollar_c10),dollar_c11),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[242,25,227,65,66,42,68])]),
[iquote('hyper,242,25,227,65,66,42,68,factor_simp')] ).
cnf(908,plain,
in(dollar_c10,relation_dom(dollar_c9)),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[242,24,227,65,66,42,67])]),
[iquote('hyper,242,24,227,65,66,42,67,factor_simp')] ).
cnf(1179,plain,
$false,
inference(hyper,[status(thm)],[906,23,908,907]),
[iquote('hyper,906,23,908,907')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU044+1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n025.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 07:39:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.99/2.21 ----- Otter 3.3f, August 2004 -----
% 1.99/2.21 The process was started by sandbox on n025.cluster.edu,
% 1.99/2.21 Wed Jul 27 07:39:15 2022
% 1.99/2.21 The command was "./otter". The process ID is 18393.
% 1.99/2.21
% 1.99/2.21 set(prolog_style_variables).
% 1.99/2.21 set(auto).
% 1.99/2.21 dependent: set(auto1).
% 1.99/2.21 dependent: set(process_input).
% 1.99/2.21 dependent: clear(print_kept).
% 1.99/2.21 dependent: clear(print_new_demod).
% 1.99/2.21 dependent: clear(print_back_demod).
% 1.99/2.21 dependent: clear(print_back_sub).
% 1.99/2.21 dependent: set(control_memory).
% 1.99/2.21 dependent: assign(max_mem, 12000).
% 1.99/2.21 dependent: assign(pick_given_ratio, 4).
% 1.99/2.21 dependent: assign(stats_level, 1).
% 1.99/2.21 dependent: assign(max_seconds, 10800).
% 1.99/2.21 clear(print_given).
% 1.99/2.21
% 1.99/2.21 formula_list(usable).
% 1.99/2.21 all A (A=A).
% 1.99/2.21 all A B subset(A,A).
% 1.99/2.21 empty(empty_set).
% 1.99/2.21 relation(empty_set).
% 1.99/2.21 empty(empty_set).
% 1.99/2.21 relation(empty_set).
% 1.99/2.21 relation_empty_yielding(empty_set).
% 1.99/2.21 empty(empty_set).
% 1.99/2.21 all A exists B element(B,A).
% 1.99/2.21 all A (empty(A)->function(A)).
% 1.99/2.21 all A (relation(A)&empty(A)&function(A)->relation(A)&function(A)&one_to_one(A)).
% 1.99/2.21 all A (-empty(powerset(A))).
% 1.99/2.21 all A (-empty(A)&relation(A)-> -empty(relation_dom(A))).
% 1.99/2.21 all A (empty(A)->empty(relation_dom(A))&relation(relation_dom(A))).
% 1.99/2.21 all A (empty(A)->relation(A)).
% 1.99/2.21 all A B (element(A,B)->empty(B)|in(A,B)).
% 1.99/2.21 all A B (element(A,powerset(B))<->subset(A,B)).
% 1.99/2.21 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 1.99/2.21 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 1.99/2.21 all A (empty(A)->A=empty_set).
% 1.99/2.21 all A B (-(empty(A)&A!=B&empty(B))).
% 1.99/2.21 all A B (in(A,B)-> -in(B,A)).
% 1.99/2.21 all A B (relation(B)->relation(relation_rng_restriction(A,B))).
% 1.99/2.21 all A B (relation(B)&function(B)->relation(relation_rng_restriction(A,B))&function(relation_rng_restriction(A,B))).
% 1.99/2.21 exists A (relation(A)&function(A)).
% 1.99/2.21 exists A (relation(A)&empty(A)&function(A)).
% 1.99/2.21 exists A (relation(A)&function(A)&one_to_one(A)).
% 1.99/2.21 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 1.99/2.21 all A exists B (element(B,powerset(A))&empty(B)).
% 1.99/2.21 exists A (empty(A)&relation(A)).
% 1.99/2.21 exists A (-empty(A)&relation(A)).
% 1.99/2.21 exists A (relation(A)&relation_empty_yielding(A)).
% 1.99/2.21 exists A empty(A).
% 1.99/2.21 exists A (-empty(A)).
% 1.99/2.21 all A B (in(A,B)->element(A,B)).
% 1.99/2.21 all A B (-(in(A,B)&empty(B))).
% 1.99/2.21 -(all A B C (relation(C)&function(C)-> (in(B,relation_dom(relation_rng_restriction(A,C)))<->in(B,relation_dom(C))&in(apply(C,B),A)))).
% 1.99/2.21 all A B (relation(B)&function(B)-> (all C (relation(C)&function(C)-> (B=relation_rng_restriction(A,C)<-> (all D (in(D,relation_dom(B))<->in(D,relation_dom(C))&in(apply(C,D),A)))& (all D (in(D,relation_dom(B))->apply(B,D)=apply(C,D))))))).
% 1.99/2.21 end_of_list.
% 1.99/2.21
% 1.99/2.21 -------> usable clausifies to:
% 1.99/2.21
% 1.99/2.21 list(usable).
% 1.99/2.21 0 [] A=A.
% 1.99/2.21 0 [] subset(A,A).
% 1.99/2.21 0 [] empty(empty_set).
% 1.99/2.21 0 [] relation(empty_set).
% 1.99/2.21 0 [] empty(empty_set).
% 1.99/2.21 0 [] relation(empty_set).
% 1.99/2.21 0 [] relation_empty_yielding(empty_set).
% 1.99/2.21 0 [] empty(empty_set).
% 1.99/2.21 0 [] element($f1(A),A).
% 1.99/2.21 0 [] -empty(A)|function(A).
% 1.99/2.21 0 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 1.99/2.21 0 [] -empty(powerset(A)).
% 1.99/2.21 0 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 1.99/2.21 0 [] -empty(A)|empty(relation_dom(A)).
% 1.99/2.21 0 [] -empty(A)|relation(relation_dom(A)).
% 1.99/2.21 0 [] -empty(A)|relation(A).
% 1.99/2.21 0 [] -element(A,B)|empty(B)|in(A,B).
% 1.99/2.21 0 [] -element(A,powerset(B))|subset(A,B).
% 1.99/2.21 0 [] element(A,powerset(B))| -subset(A,B).
% 1.99/2.21 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.99/2.21 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.99/2.21 0 [] -empty(A)|A=empty_set.
% 1.99/2.21 0 [] -empty(A)|A=B| -empty(B).
% 1.99/2.21 0 [] -in(A,B)| -in(B,A).
% 1.99/2.21 0 [] -relation(B)|relation(relation_rng_restriction(A,B)).
% 1.99/2.21 0 [] -relation(B)| -function(B)|relation(relation_rng_restriction(A,B)).
% 1.99/2.21 0 [] -relation(B)| -function(B)|function(relation_rng_restriction(A,B)).
% 1.99/2.21 0 [] relation($c1).
% 1.99/2.21 0 [] function($c1).
% 1.99/2.21 0 [] relation($c2).
% 1.99/2.21 0 [] empty($c2).
% 1.99/2.21 0 [] function($c2).
% 1.99/2.21 0 [] relation($c3).
% 1.99/2.21 0 [] function($c3).
% 1.99/2.21 0 [] one_to_one($c3).
% 1.99/2.21 0 [] empty(A)|element($f2(A),powerset(A)).
% 1.99/2.21 0 [] empty(A)| -empty($f2(A)).
% 1.99/2.21 0 [] element($f3(A),powerset(A)).
% 1.99/2.21 0 [] empty($f3(A)).
% 1.99/2.21 0 [] empty($c4).
% 1.99/2.21 0 [] relation($c4).
% 1.99/2.21 0 [] -empty($c5).
% 1.99/2.21 0 [] relation($c5).
% 1.99/2.21 0 [] relation($c6).
% 1.99/2.21 0 [] relation_empty_yielding($c6).
% 1.99/2.21 0 [] empty($c7).
% 1.99/2.21 0 [] -empty($c8).
% 1.99/2.21 0 [] -in(A,B)|element(A,B).
% 1.99/2.21 0 [] -in(A,B)| -empty(B).
% 1.99/2.21 0 [] relation($c9).
% 1.99/2.21 0 [] function($c9).
% 1.99/2.21 0 [] in($c10,relation_dom(relation_rng_restriction($c11,$c9)))|in($c10,relation_dom($c9)).
% 1.99/2.21 0 [] in($c10,relation_dom(relation_rng_restriction($c11,$c9)))|in(apply($c9,$c10),$c11).
% 1.99/2.21 0 [] -in($c10,relation_dom(relation_rng_restriction($c11,$c9)))| -in($c10,relation_dom($c9))| -in(apply($c9,$c10),$c11).
% 1.99/2.21 0 [] -relation(B)| -function(B)| -relation(C)| -function(C)|B!=relation_rng_restriction(A,C)| -in(D,relation_dom(B))|in(D,relation_dom(C)).
% 1.99/2.21 0 [] -relation(B)| -function(B)| -relation(C)| -function(C)|B!=relation_rng_restriction(A,C)| -in(D,relation_dom(B))|in(apply(C,D),A).
% 1.99/2.21 0 [] -relation(B)| -function(B)| -relation(C)| -function(C)|B!=relation_rng_restriction(A,C)|in(D,relation_dom(B))| -in(D,relation_dom(C))| -in(apply(C,D),A).
% 1.99/2.21 0 [] -relation(B)| -function(B)| -relation(C)| -function(C)|B!=relation_rng_restriction(A,C)| -in(X1,relation_dom(B))|apply(B,X1)=apply(C,X1).
% 1.99/2.21 0 [] -relation(B)| -function(B)| -relation(C)| -function(C)|B=relation_rng_restriction(A,C)|in($f4(A,B,C),relation_dom(B))|in($f4(A,B,C),relation_dom(C))|in($f5(A,B,C),relation_dom(B)).
% 1.99/2.21 0 [] -relation(B)| -function(B)| -relation(C)| -function(C)|B=relation_rng_restriction(A,C)|in($f4(A,B,C),relation_dom(B))|in($f4(A,B,C),relation_dom(C))|apply(B,$f5(A,B,C))!=apply(C,$f5(A,B,C)).
% 1.99/2.21 0 [] -relation(B)| -function(B)| -relation(C)| -function(C)|B=relation_rng_restriction(A,C)|in($f4(A,B,C),relation_dom(B))|in(apply(C,$f4(A,B,C)),A)|in($f5(A,B,C),relation_dom(B)).
% 1.99/2.21 0 [] -relation(B)| -function(B)| -relation(C)| -function(C)|B=relation_rng_restriction(A,C)|in($f4(A,B,C),relation_dom(B))|in(apply(C,$f4(A,B,C)),A)|apply(B,$f5(A,B,C))!=apply(C,$f5(A,B,C)).
% 1.99/2.21 0 [] -relation(B)| -function(B)| -relation(C)| -function(C)|B=relation_rng_restriction(A,C)| -in($f4(A,B,C),relation_dom(B))| -in($f4(A,B,C),relation_dom(C))| -in(apply(C,$f4(A,B,C)),A)|in($f5(A,B,C),relation_dom(B)).
% 1.99/2.21 0 [] -relation(B)| -function(B)| -relation(C)| -function(C)|B=relation_rng_restriction(A,C)| -in($f4(A,B,C),relation_dom(B))| -in($f4(A,B,C),relation_dom(C))| -in(apply(C,$f4(A,B,C)),A)|apply(B,$f5(A,B,C))!=apply(C,$f5(A,B,C)).
% 1.99/2.21 end_of_list.
% 1.99/2.21
% 1.99/2.21 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=9.
% 1.99/2.21
% 1.99/2.21 This ia a non-Horn set with equality. The strategy will be
% 1.99/2.21 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.99/2.21 deletion, with positive clauses in sos and nonpositive
% 1.99/2.21 clauses in usable.
% 1.99/2.21
% 1.99/2.21 dependent: set(knuth_bendix).
% 1.99/2.21 dependent: set(anl_eq).
% 1.99/2.21 dependent: set(para_from).
% 1.99/2.21 dependent: set(para_into).
% 1.99/2.21 dependent: clear(para_from_right).
% 1.99/2.21 dependent: clear(para_into_right).
% 1.99/2.21 dependent: set(para_from_vars).
% 1.99/2.21 dependent: set(eq_units_both_ways).
% 1.99/2.21 dependent: set(dynamic_demod_all).
% 1.99/2.21 dependent: set(dynamic_demod).
% 1.99/2.21 dependent: set(order_eq).
% 1.99/2.21 dependent: set(back_demod).
% 1.99/2.21 dependent: set(lrpo).
% 1.99/2.21 dependent: set(hyper_res).
% 1.99/2.21 dependent: set(unit_deletion).
% 1.99/2.21 dependent: set(factor).
% 1.99/2.21
% 1.99/2.21 ------------> process usable:
% 1.99/2.21 ** KEPT (pick-wt=4): 1 [] -empty(A)|function(A).
% 1.99/2.21 ** KEPT (pick-wt=8): 2 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 1.99/2.21 ** KEPT (pick-wt=3): 3 [] -empty(powerset(A)).
% 1.99/2.21 ** KEPT (pick-wt=7): 4 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 1.99/2.21 ** KEPT (pick-wt=5): 5 [] -empty(A)|empty(relation_dom(A)).
% 1.99/2.21 ** KEPT (pick-wt=5): 6 [] -empty(A)|relation(relation_dom(A)).
% 1.99/2.21 ** KEPT (pick-wt=4): 7 [] -empty(A)|relation(A).
% 1.99/2.21 ** KEPT (pick-wt=8): 8 [] -element(A,B)|empty(B)|in(A,B).
% 1.99/2.21 ** KEPT (pick-wt=7): 9 [] -element(A,powerset(B))|subset(A,B).
% 1.99/2.21 ** KEPT (pick-wt=7): 10 [] element(A,powerset(B))| -subset(A,B).
% 1.99/2.21 ** KEPT (pick-wt=10): 11 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.99/2.21 ** KEPT (pick-wt=9): 12 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.99/2.21 ** KEPT (pick-wt=5): 13 [] -empty(A)|A=empty_set.
% 1.99/2.21 ** KEPT (pick-wt=7): 14 [] -empty(A)|A=B| -empty(B).
% 1.99/2.21 ** KEPT (pick-wt=6): 15 [] -in(A,B)| -in(B,A).
% 1.99/2.21 ** KEPT (pick-wt=6): 16 [] -relation(A)|relation(relation_rng_restriction(B,A)).
% 1.99/2.21 Following clause subsumed by 16 during input processing: 0 [] -relation(A)| -function(A)|relation(relation_rng_restriction(B,A)).
% 1.99/2.21 ** KEPT (pick-wt=8): 17 [] -relation(A)| -function(A)|function(relation_rng_restriction(B,A)).
% 1.99/2.21 ** KEPT (pick-wt=5): 18 [] empty(A)| -empty($f2(A)).
% 1.99/2.21 ** KEPT (pick-wt=2): 19 [] -empty($c5).
% 1.99/2.21 ** KEPT (pick-wt=2): 20 [] -empty($c8).
% 1.99/2.21 ** KEPT (pick-wt=6): 21 [] -in(A,B)|element(A,B).
% 1.99/2.21 ** KEPT (pick-wt=5): 22 [] -in(A,B)| -empty(B).
% 1.99/2.21 ** KEPT (pick-wt=15): 23 [] -in($c10,relation_dom(relation_rng_restriction($c11,$c9)))| -in($c10,relation_dom($c9))| -in(apply($c9,$c10),$c11).
% 1.99/2.21 ** KEPT (pick-wt=21): 24 [] -relation(A)| -function(A)| -relation(B)| -function(B)|A!=relation_rng_restriction(C,B)| -in(D,relation_dom(A))|in(D,relation_dom(B)).
% 1.99/2.21 ** KEPT (pick-wt=22): 25 [] -relation(A)| -function(A)| -relation(B)| -function(B)|A!=relation_rng_restriction(C,B)| -in(D,relation_dom(A))|in(apply(B,D),C).
% 1.99/2.21 ** KEPT (pick-wt=26): 26 [] -relation(A)| -function(A)| -relation(B)| -function(B)|A!=relation_rng_restriction(C,B)|in(D,relation_dom(A))| -in(D,relation_dom(B))| -in(apply(B,D),C).
% 1.99/2.21 ** KEPT (pick-wt=24): 27 [] -relation(A)| -function(A)| -relation(B)| -function(B)|A!=relation_rng_restriction(C,B)| -in(D,relation_dom(A))|apply(A,D)=apply(B,D).
% 1.99/2.21 ** KEPT (pick-wt=34): 28 [] -relation(A)| -function(A)| -relation(B)| -function(B)|A=relation_rng_restriction(C,B)|in($f4(C,A,B),relation_dom(A))|in($f4(C,A,B),relation_dom(B))|in($f5(C,A,B),relation_dom(A)).
% 1.99/2.21 ** KEPT (pick-wt=40): 29 [] -relation(A)| -function(A)| -relation(B)| -function(B)|A=relation_rng_restriction(C,B)|in($f4(C,A,B),relation_dom(A))|in($f4(C,A,B),relation_dom(B))|apply(A,$f5(C,A,B))!=apply(B,$f5(C,A,B)).
% 1.99/2.21 ** KEPT (pick-wt=35): 30 [] -relation(A)| -function(A)| -relation(B)| -function(B)|A=relation_rng_restriction(C,B)|in($f4(C,A,B),relation_dom(A))|in(apply(B,$f4(C,A,B)),C)|in($f5(C,A,B),relation_dom(A)).
% 1.99/2.21 ** KEPT (pick-wt=41): 31 [] -relation(A)| -function(A)| -relation(B)| -function(B)|A=relation_rng_restriction(C,B)|in($f4(C,A,B),relation_dom(A))|in(apply(B,$f4(C,A,B)),C)|apply(A,$f5(C,A,B))!=apply(B,$f5(C,A,B)).
% 1.99/2.21 ** KEPT (pick-wt=42): 32 [] -relation(A)| -function(A)| -relation(B)| -function(B)|A=relation_rng_restriction(C,B)| -in($f4(C,A,B),relation_dom(A))| -in($f4(C,A,B),relation_dom(B))| -in(apply(B,$f4(C,A,B)),C)|in($f5(C,A,B),relation_dom(A)).
% 1.99/2.21 ** KEPT (pick-wt=48): 33 [] -relation(A)| -function(A)| -relation(B)| -function(B)|A=relation_rng_restriction(C,B)| -in($f4(C,A,B),relation_dom(A))| -in($f4(C,A,B),relation_dom(B))| -in(apply(B,$f4(C,A,B)),C)|apply(A,$f5(C,A,B))!=apply(B,$f5(C,A,B)).
% 1.99/2.21
% 1.99/2.21 ------------> process sos:
% 1.99/2.21 ** KEPT (pick-wt=3): 42 [] A=A.
% 1.99/2.21 ** KEPT (pick-wt=3): 43 [] subset(A,A).
% 1.99/2.21 ** KEPT (pick-wt=2): 44 [] empty(empty_set).
% 1.99/2.21 ** KEPT (pick-wt=2): 45 [] relation(empty_set).
% 1.99/2.21 Following clause subsumed by 44 during input processing: 0 [] empty(empty_set).
% 1.99/2.21 Following clause subsumed by 45 during input processing: 0 [] relation(empty_set).
% 1.99/2.21 ** KEPT (pick-wt=2): 46 [] relation_empty_yielding(empty_set).
% 1.99/2.21 Following clause subsumed by 44 during input processing: 0 [] empty(empty_set).
% 1.99/2.21 ** KEPT (pick-wt=4): 47 [] element($f1(A),A).
% 1.99/2.21 ** KEPT (pick-wt=2): 48 [] relation($c1).
% 1.99/2.21 ** KEPT (pick-wt=2): 49 [] function($c1).
% 1.99/2.21 ** KEPT (pick-wt=2): 50 [] relation($c2).
% 1.99/2.21 ** KEPT (pick-wt=2): 51 [] empty($c2).
% 1.99/2.21 ** KEPT (pick-wt=2): 52 [] function($c2).
% 1.99/2.21 ** KEPT (pick-wt=2): 53 [] relation($c3).
% 1.99/2.21 ** KEPT (pick-wt=2): 54 [] function($c3).
% 1.99/2.21 ** KEPT (pick-wt=2): 55 [] one_to_one($c3).
% 1.99/2.21 ** KEPT (pick-wt=7): 56 [] empty(A)|element($f2(A),powerset(A)).
% 1.99/2.21 ** KEPT (pick-wt=5): 57 [] element($f3(A),powerset(A)).
% 1.99/2.21 ** KEPT (pick-wt=3): 58 [] empty($f3(A)).
% 1.99/2.21 ** KEPT (pick-wt=2): 59 [] empty($c4).
% 1.99/2.21 ** KEPT (pick-wt=2): 60 [] relation($c4).
% 1.99/2.21 ** KEPT (pick-wt=2): 61 [] relation($c5).
% 1.99/2.21 ** KEPT (pick-wt=2): 62 [] relation($c6).
% 1.99/2.21 ** KEPT (pick-wt=2): 63 [] relation_empty_yielding($c6).
% 1.99/2.21 ** KEPT (pick-wt=2): 64 [] empty($c7).
% 1.99/2.21 ** KEPT (pick-wt=2): 65 [] relation($c9).
% 1.99/2.21 ** KEPT (pick-wt=2): 66 [] function($c9).
% 1.99/2.21 ** KEPT (pick-wt=10): 67 [] in($c10,relation_dom(relation_rng_restriction($c11,$c9)))|in($c10,relation_dom($c9)).
% 1.99/2.21 ** KEPT (pick-wt=11): 68 [] in($c10,relation_dom(relation_rng_restriction($c11,$c9)))|in(apply($c9,$c10),$c11).
% 1.99/2.21 Following clause subsumed by 42 during input processing: 0 [copy,42,flip.1] A=A.
% 1.99/2.21 42 back subsumes 37.
% 2.33/2.54 42 back subsumes 34.
% 2.33/2.54
% 2.33/2.54 ======= end of input processing =======
% 2.33/2.54
% 2.33/2.54 =========== start of search ===========
% 2.33/2.54
% 2.33/2.54
% 2.33/2.54 Resetting weight limit to 8.
% 2.33/2.54
% 2.33/2.54
% 2.33/2.54 Resetting weight limit to 8.
% 2.33/2.54
% 2.33/2.54 sos_size=688
% 2.33/2.54
% 2.33/2.54
% 2.33/2.54 Resetting weight limit to 6.
% 2.33/2.54
% 2.33/2.54
% 2.33/2.54 Resetting weight limit to 6.
% 2.33/2.54
% 2.33/2.54 sos_size=729
% 2.33/2.54
% 2.33/2.54 -------- PROOF --------
% 2.33/2.54
% 2.33/2.54 -----> EMPTY CLAUSE at 0.33 sec ----> 1179 [hyper,906,23,908,907] $F.
% 2.33/2.54
% 2.33/2.54 Length of proof is 5. Level of proof is 2.
% 2.33/2.54
% 2.33/2.54 ---------------- PROOF ----------------
% 2.33/2.54 % SZS status Theorem
% 2.33/2.54 % SZS output start Refutation
% See solution above
% 2.33/2.54 ------------ end of proof -------------
% 2.33/2.54
% 2.33/2.54
% 2.33/2.54 Search stopped by max_proofs option.
% 2.33/2.54
% 2.33/2.54
% 2.33/2.54 Search stopped by max_proofs option.
% 2.33/2.54
% 2.33/2.54 ============ end of search ============
% 2.33/2.54
% 2.33/2.54 -------------- statistics -------------
% 2.33/2.54 clauses given 99
% 2.33/2.54 clauses generated 4221
% 2.33/2.54 clauses kept 1173
% 2.33/2.54 clauses forward subsumed 1297
% 2.33/2.54 clauses back subsumed 231
% 2.33/2.54 Kbytes malloced 4882
% 2.33/2.54
% 2.33/2.54 ----------- times (seconds) -----------
% 2.33/2.54 user CPU time 0.33 (0 hr, 0 min, 0 sec)
% 2.33/2.54 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.33/2.54 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.33/2.54
% 2.33/2.54 That finishes the proof of the theorem.
% 2.33/2.54
% 2.33/2.54 Process 18393 finished Wed Jul 27 07:39:17 2022
% 2.33/2.54 Otter interrupted
% 2.33/2.54 PROOF FOUND
%------------------------------------------------------------------------------