%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU023+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n016.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 13:14:40 EDT 2022
% Result : Theorem 2.04s 2.28s
% Output : Refutation 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of clauses : 16 ( 10 unt; 0 nHn; 15 RR)
% Number of literals : 35 ( 11 equ; 21 neg)
% Maximal clause size : 9 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
( ~ relation(A)
| ~ function(A)
| relation(function_inverse(A)) ),
file('SEU023+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ relation(A)
| ~ function(A)
| function(function_inverse(A)) ),
file('SEU023+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ relation(A)
| ~ function(A)
| ~ relation(B)
| ~ function(B)
| ~ in(C,relation_dom(A))
| apply(relation_composition(A,B),C) = apply(B,apply(A,C)) ),
file('SEU023+1.p',unknown),
[] ).
cnf(33,axiom,
( ~ relation(A)
| ~ function(A)
| ~ one_to_one(A)
| ~ relation(B)
| ~ function(B)
| B != function_inverse(A)
| ~ in(C,relation_dom(A))
| D != apply(A,C)
| C = apply(B,D) ),
file('SEU023+1.p',unknown),
[] ).
cnf(43,axiom,
( dollar_c10 != apply(function_inverse(dollar_c9),apply(dollar_c9,dollar_c10))
| dollar_c10 != apply(relation_composition(dollar_c9,function_inverse(dollar_c9)),dollar_c10) ),
file('SEU023+1.p',unknown),
[] ).
cnf(44,plain,
( apply(function_inverse(dollar_c9),apply(dollar_c9,dollar_c10)) != dollar_c10
| apply(relation_composition(dollar_c9,function_inverse(dollar_c9)),dollar_c10) != dollar_c10 ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[43])])]),
[iquote('copy,43,flip.1,flip.2')] ).
cnf(64,axiom,
A = A,
file('SEU023+1.p',unknown),
[] ).
cnf(87,axiom,
relation(dollar_c9),
file('SEU023+1.p',unknown),
[] ).
cnf(88,axiom,
function(dollar_c9),
file('SEU023+1.p',unknown),
[] ).
cnf(89,axiom,
one_to_one(dollar_c9),
file('SEU023+1.p',unknown),
[] ).
cnf(90,axiom,
in(dollar_c10,relation_dom(dollar_c9)),
file('SEU023+1.p',unknown),
[] ).
cnf(449,plain,
function(function_inverse(dollar_c9)),
inference(hyper,[status(thm)],[88,6,87]),
[iquote('hyper,88,6,87')] ).
cnf(450,plain,
relation(function_inverse(dollar_c9)),
inference(hyper,[status(thm)],[88,5,87]),
[iquote('hyper,88,5,87')] ).
cnf(880,plain,
apply(function_inverse(dollar_c9),apply(dollar_c9,dollar_c10)) = dollar_c10,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[450,33,87,88,89,449,64,90,64])]),
[iquote('hyper,450,33,87,88,89,449,64,90,64,flip.1')] ).
cnf(885,plain,
apply(relation_composition(dollar_c9,function_inverse(dollar_c9)),dollar_c10) = dollar_c10,
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[450,24,87,88,449,90]),880]),
[iquote('hyper,450,24,87,88,449,90,demod,880')] ).
cnf(926,plain,
$false,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[44]),880,885]),64,64]),
[iquote('back_demod,44,demod,880,885,unit_del,64,64')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU023+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.11/0.33 % Computer : n016.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Jul 27 07:54:07 EDT 2022
% 0.11/0.33 % CPUTime :
% 1.93/2.15 ----- Otter 3.3f, August 2004 -----
% 1.93/2.15 The process was started by sandbox on n016.cluster.edu,
% 1.93/2.15 Wed Jul 27 07:54:07 2022
% 1.93/2.15 The command was "./otter". The process ID is 22206.
% 1.93/2.15
% 1.93/2.15 set(prolog_style_variables).
% 1.93/2.15 set(auto).
% 1.93/2.15 dependent: set(auto1).
% 1.93/2.15 dependent: set(process_input).
% 1.93/2.15 dependent: clear(print_kept).
% 1.93/2.15 dependent: clear(print_new_demod).
% 1.93/2.15 dependent: clear(print_back_demod).
% 1.93/2.15 dependent: clear(print_back_sub).
% 1.93/2.15 dependent: set(control_memory).
% 1.93/2.15 dependent: assign(max_mem, 12000).
% 1.93/2.15 dependent: assign(pick_given_ratio, 4).
% 1.93/2.15 dependent: assign(stats_level, 1).
% 1.93/2.15 dependent: assign(max_seconds, 10800).
% 1.93/2.15 clear(print_given).
% 1.93/2.15
% 1.93/2.15 formula_list(usable).
% 1.93/2.15 all A (A=A).
% 1.93/2.15 all A B (in(A,B)-> -in(B,A)).
% 1.93/2.15 all A (empty(A)->function(A)).
% 1.93/2.15 all A (empty(A)->relation(A)).
% 1.93/2.15 all A (relation(A)&empty(A)&function(A)->relation(A)&function(A)&one_to_one(A)).
% 1.93/2.15 all A (relation(A)&function(A)->relation(function_inverse(A))&function(function_inverse(A))).
% 1.93/2.15 all A B (relation(A)&relation(B)->relation(relation_composition(A,B))).
% 1.93/2.15 all A exists B element(B,A).
% 1.93/2.15 all A B (empty(A)&relation(B)->empty(relation_composition(B,A))&relation(relation_composition(B,A))).
% 1.93/2.15 empty(empty_set).
% 1.93/2.15 relation(empty_set).
% 1.93/2.15 relation_empty_yielding(empty_set).
% 1.93/2.15 all A B (relation(A)&function(A)&relation(B)&function(B)->relation(relation_composition(A,B))&function(relation_composition(A,B))).
% 1.93/2.15 all A (-empty(powerset(A))).
% 1.93/2.15 empty(empty_set).
% 1.93/2.15 empty(empty_set).
% 1.93/2.15 relation(empty_set).
% 1.93/2.15 all A (-empty(A)&relation(A)-> -empty(relation_dom(A))).
% 1.93/2.15 all A (-empty(A)&relation(A)-> -empty(relation_rng(A))).
% 1.93/2.15 all A (empty(A)->empty(relation_dom(A))&relation(relation_dom(A))).
% 1.93/2.15 all A (empty(A)->empty(relation_rng(A))&relation(relation_rng(A))).
% 1.93/2.15 all A B (empty(A)&relation(B)->empty(relation_composition(A,B))&relation(relation_composition(A,B))).
% 1.93/2.15 exists A (relation(A)&function(A)).
% 1.93/2.15 exists A (empty(A)&relation(A)).
% 1.93/2.15 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 1.93/2.15 exists A empty(A).
% 1.93/2.15 exists A (relation(A)&empty(A)&function(A)).
% 1.93/2.15 exists A (-empty(A)&relation(A)).
% 1.93/2.15 all A exists B (element(B,powerset(A))&empty(B)).
% 1.93/2.15 exists A (-empty(A)).
% 1.93/2.15 exists A (relation(A)&function(A)&one_to_one(A)).
% 1.93/2.15 exists A (relation(A)&relation_empty_yielding(A)).
% 1.93/2.15 all A B subset(A,A).
% 1.93/2.15 all A B (in(A,B)->element(A,B)).
% 1.93/2.15 all A B (relation(B)&function(B)-> (all C (relation(C)&function(C)-> (in(A,relation_dom(B))->apply(relation_composition(B,C),A)=apply(C,apply(B,A)))))).
% 1.93/2.15 all A B (element(A,B)->empty(B)|in(A,B)).
% 1.93/2.15 all A B (element(A,powerset(B))<->subset(A,B)).
% 1.93/2.15 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 1.93/2.15 all A (relation(A)&function(A)-> (one_to_one(A)-> (all B (relation(B)&function(B)-> (B=function_inverse(A)<->relation_dom(B)=relation_rng(A)& (all C D ((in(C,relation_rng(A))&D=apply(B,C)->in(D,relation_dom(A))&C=apply(A,D))& (in(D,relation_dom(A))&C=apply(A,D)->in(C,relation_rng(A))&D=apply(B,C))))))))).
% 1.93/2.15 -(all A B (relation(B)&function(B)-> (one_to_one(B)&in(A,relation_dom(B))->A=apply(function_inverse(B),apply(B,A))&A=apply(relation_composition(B,function_inverse(B)),A)))).
% 1.93/2.15 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 1.93/2.15 all A (empty(A)->A=empty_set).
% 1.93/2.15 all A B (-(in(A,B)&empty(B))).
% 1.93/2.15 all A B (-(empty(A)&A!=B&empty(B))).
% 1.93/2.15 end_of_list.
% 1.93/2.15
% 1.93/2.15 -------> usable clausifies to:
% 1.93/2.15
% 1.93/2.15 list(usable).
% 1.93/2.15 0 [] A=A.
% 1.93/2.15 0 [] -in(A,B)| -in(B,A).
% 1.93/2.15 0 [] -empty(A)|function(A).
% 1.93/2.15 0 [] -empty(A)|relation(A).
% 1.93/2.15 0 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 1.93/2.15 0 [] -relation(A)| -function(A)|relation(function_inverse(A)).
% 1.93/2.15 0 [] -relation(A)| -function(A)|function(function_inverse(A)).
% 1.93/2.15 0 [] -relation(A)| -relation(B)|relation(relation_composition(A,B)).
% 1.93/2.15 0 [] element($f1(A),A).
% 1.93/2.15 0 [] -empty(A)| -relation(B)|empty(relation_composition(B,A)).
% 1.93/2.15 0 [] -empty(A)| -relation(B)|relation(relation_composition(B,A)).
% 1.93/2.15 0 [] empty(empty_set).
% 1.93/2.15 0 [] relation(empty_set).
% 1.93/2.15 0 [] relation_empty_yielding(empty_set).
% 1.93/2.15 0 [] -relation(A)| -function(A)| -relation(B)| -function(B)|relation(relation_composition(A,B)).
% 1.93/2.15 0 [] -relation(A)| -function(A)| -relation(B)| -function(B)|function(relation_composition(A,B)).
% 1.93/2.15 0 [] -empty(powerset(A)).
% 1.93/2.15 0 [] empty(empty_set).
% 1.93/2.15 0 [] empty(empty_set).
% 1.93/2.16 0 [] relation(empty_set).
% 1.93/2.16 0 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 1.93/2.16 0 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 1.93/2.16 0 [] -empty(A)|empty(relation_dom(A)).
% 1.93/2.16 0 [] -empty(A)|relation(relation_dom(A)).
% 1.93/2.16 0 [] -empty(A)|empty(relation_rng(A)).
% 1.93/2.16 0 [] -empty(A)|relation(relation_rng(A)).
% 1.93/2.16 0 [] -empty(A)| -relation(B)|empty(relation_composition(A,B)).
% 1.93/2.16 0 [] -empty(A)| -relation(B)|relation(relation_composition(A,B)).
% 1.93/2.16 0 [] relation($c1).
% 1.93/2.16 0 [] function($c1).
% 1.93/2.16 0 [] empty($c2).
% 1.93/2.16 0 [] relation($c2).
% 1.93/2.16 0 [] empty(A)|element($f2(A),powerset(A)).
% 1.93/2.16 0 [] empty(A)| -empty($f2(A)).
% 1.93/2.16 0 [] empty($c3).
% 1.93/2.16 0 [] relation($c4).
% 1.93/2.16 0 [] empty($c4).
% 1.93/2.16 0 [] function($c4).
% 1.93/2.16 0 [] -empty($c5).
% 1.93/2.16 0 [] relation($c5).
% 1.93/2.16 0 [] element($f3(A),powerset(A)).
% 1.93/2.16 0 [] empty($f3(A)).
% 1.93/2.16 0 [] -empty($c6).
% 1.93/2.16 0 [] relation($c7).
% 1.93/2.16 0 [] function($c7).
% 1.93/2.16 0 [] one_to_one($c7).
% 1.93/2.16 0 [] relation($c8).
% 1.93/2.16 0 [] relation_empty_yielding($c8).
% 1.93/2.16 0 [] subset(A,A).
% 1.93/2.16 0 [] -in(A,B)|element(A,B).
% 1.93/2.16 0 [] -relation(B)| -function(B)| -relation(C)| -function(C)| -in(A,relation_dom(B))|apply(relation_composition(B,C),A)=apply(C,apply(B,A)).
% 1.93/2.16 0 [] -element(A,B)|empty(B)|in(A,B).
% 1.93/2.16 0 [] -element(A,powerset(B))|subset(A,B).
% 1.93/2.16 0 [] element(A,powerset(B))| -subset(A,B).
% 1.93/2.16 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.93/2.16 0 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B!=function_inverse(A)|relation_dom(B)=relation_rng(A).
% 1.93/2.16 0 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B!=function_inverse(A)| -in(C,relation_rng(A))|D!=apply(B,C)|in(D,relation_dom(A)).
% 1.93/2.16 0 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B!=function_inverse(A)| -in(C,relation_rng(A))|D!=apply(B,C)|C=apply(A,D).
% 1.93/2.16 0 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B!=function_inverse(A)| -in(D,relation_dom(A))|C!=apply(A,D)|in(C,relation_rng(A)).
% 1.93/2.16 0 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B!=function_inverse(A)| -in(D,relation_dom(A))|C!=apply(A,D)|D=apply(B,C).
% 1.93/2.16 0 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B=function_inverse(A)|relation_dom(B)!=relation_rng(A)|in($f5(A,B),relation_rng(A))|in($f4(A,B),relation_dom(A)).
% 1.93/2.16 0 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B=function_inverse(A)|relation_dom(B)!=relation_rng(A)|in($f5(A,B),relation_rng(A))|$f5(A,B)=apply(A,$f4(A,B)).
% 1.93/2.16 0 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B=function_inverse(A)|relation_dom(B)!=relation_rng(A)|$f4(A,B)=apply(B,$f5(A,B))|in($f4(A,B),relation_dom(A)).
% 1.93/2.16 0 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B=function_inverse(A)|relation_dom(B)!=relation_rng(A)|$f4(A,B)=apply(B,$f5(A,B))|$f5(A,B)=apply(A,$f4(A,B)).
% 1.93/2.16 0 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B=function_inverse(A)|relation_dom(B)!=relation_rng(A)| -in($f4(A,B),relation_dom(A))|$f5(A,B)!=apply(A,$f4(A,B))| -in($f5(A,B),relation_rng(A))|$f4(A,B)!=apply(B,$f5(A,B)).
% 1.93/2.16 0 [] relation($c9).
% 1.93/2.16 0 [] function($c9).
% 1.93/2.16 0 [] one_to_one($c9).
% 1.93/2.16 0 [] in($c10,relation_dom($c9)).
% 1.93/2.16 0 [] $c10!=apply(function_inverse($c9),apply($c9,$c10))|$c10!=apply(relation_composition($c9,function_inverse($c9)),$c10).
% 1.93/2.16 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.93/2.16 0 [] -empty(A)|A=empty_set.
% 1.93/2.16 0 [] -in(A,B)| -empty(B).
% 1.93/2.16 0 [] -empty(A)|A=B| -empty(B).
% 1.93/2.16 end_of_list.
% 1.93/2.16
% 1.93/2.16 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=11.
% 1.93/2.16
% 1.93/2.16 This ia a non-Horn set with equality. The strategy will be
% 1.93/2.16 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.93/2.16 deletion, with positive clauses in sos and nonpositive
% 1.93/2.16 clauses in usable.
% 1.93/2.16
% 1.93/2.16 dependent: set(knuth_bendix).
% 1.93/2.16 dependent: set(anl_eq).
% 1.93/2.16 dependent: set(para_from).
% 1.93/2.16 dependent: set(para_into).
% 1.93/2.16 dependent: clear(para_from_right).
% 1.93/2.16 dependent: clear(para_into_right).
% 1.93/2.16 dependent: set(para_from_vars).
% 1.93/2.16 dependent: set(eq_units_both_ways).
% 1.93/2.16 dependent: set(dynamic_demod_all).
% 1.93/2.16 dependent: set(dynamic_demod).
% 1.93/2.16 dependent: set(order_eq).
% 1.93/2.16 dependent: set(back_demod).
% 1.93/2.16 dependent: set(lrpo).
% 1.93/2.16 dependent: set(hyper_res).
% 1.93/2.16 dependent: set(unit_deletion).
% 1.93/2.16 dependent: set(factor).
% 1.93/2.16
% 1.93/2.16 ------------> process usable:
% 1.93/2.16 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.93/2.16 ** KEPT (pick-wt=4): 2 [] -empty(A)|function(A).
% 1.93/2.16 ** KEPT (pick-wt=4): 3 [] -empty(A)|relation(A).
% 1.93/2.16 ** KEPT (pick-wt=8): 4 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 1.93/2.16 ** KEPT (pick-wt=7): 5 [] -relation(A)| -function(A)|relation(function_inverse(A)).
% 1.93/2.16 ** KEPT (pick-wt=7): 6 [] -relation(A)| -function(A)|function(function_inverse(A)).
% 1.93/2.16 ** KEPT (pick-wt=8): 7 [] -relation(A)| -relation(B)|relation(relation_composition(A,B)).
% 1.93/2.16 ** KEPT (pick-wt=8): 8 [] -empty(A)| -relation(B)|empty(relation_composition(B,A)).
% 1.93/2.16 ** KEPT (pick-wt=8): 9 [] -empty(A)| -relation(B)|relation(relation_composition(B,A)).
% 1.93/2.16 Following clause subsumed by 7 during input processing: 0 [] -relation(A)| -function(A)| -relation(B)| -function(B)|relation(relation_composition(A,B)).
% 1.93/2.16 ** KEPT (pick-wt=12): 10 [] -relation(A)| -function(A)| -relation(B)| -function(B)|function(relation_composition(A,B)).
% 1.93/2.16 ** KEPT (pick-wt=3): 11 [] -empty(powerset(A)).
% 1.93/2.16 ** KEPT (pick-wt=7): 12 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 1.93/2.16 ** KEPT (pick-wt=7): 13 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 1.93/2.16 ** KEPT (pick-wt=5): 14 [] -empty(A)|empty(relation_dom(A)).
% 1.93/2.16 ** KEPT (pick-wt=5): 15 [] -empty(A)|relation(relation_dom(A)).
% 1.93/2.16 ** KEPT (pick-wt=5): 16 [] -empty(A)|empty(relation_rng(A)).
% 1.93/2.16 ** KEPT (pick-wt=5): 17 [] -empty(A)|relation(relation_rng(A)).
% 1.93/2.16 ** KEPT (pick-wt=8): 18 [] -empty(A)| -relation(B)|empty(relation_composition(A,B)).
% 1.93/2.16 ** KEPT (pick-wt=8): 19 [] -empty(A)| -relation(B)|relation(relation_composition(A,B)).
% 1.93/2.16 ** KEPT (pick-wt=5): 20 [] empty(A)| -empty($f2(A)).
% 1.93/2.16 ** KEPT (pick-wt=2): 21 [] -empty($c5).
% 1.93/2.16 ** KEPT (pick-wt=2): 22 [] -empty($c6).
% 1.93/2.16 ** KEPT (pick-wt=6): 23 [] -in(A,B)|element(A,B).
% 1.93/2.16 ** KEPT (pick-wt=23): 24 [] -relation(A)| -function(A)| -relation(B)| -function(B)| -in(C,relation_dom(A))|apply(relation_composition(A,B),C)=apply(B,apply(A,C)).
% 1.93/2.16 ** KEPT (pick-wt=8): 25 [] -element(A,B)|empty(B)|in(A,B).
% 1.93/2.16 ** KEPT (pick-wt=7): 26 [] -element(A,powerset(B))|subset(A,B).
% 1.93/2.16 ** KEPT (pick-wt=7): 27 [] element(A,powerset(B))| -subset(A,B).
% 1.93/2.16 ** KEPT (pick-wt=10): 28 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.93/2.16 ** KEPT (pick-wt=19): 29 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B!=function_inverse(A)|relation_dom(B)=relation_rng(A).
% 1.93/2.16 ** KEPT (pick-wt=27): 30 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B!=function_inverse(A)| -in(C,relation_rng(A))|D!=apply(B,C)|in(D,relation_dom(A)).
% 1.93/2.16 ** KEPT (pick-wt=28): 31 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B!=function_inverse(A)| -in(C,relation_rng(A))|D!=apply(B,C)|C=apply(A,D).
% 1.93/2.16 ** KEPT (pick-wt=27): 32 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B!=function_inverse(A)| -in(C,relation_dom(A))|D!=apply(A,C)|in(D,relation_rng(A)).
% 1.93/2.16 ** KEPT (pick-wt=28): 33 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B!=function_inverse(A)| -in(C,relation_dom(A))|D!=apply(A,C)|C=apply(B,D).
% 1.93/2.16 ** KEPT (pick-wt=31): 34 [] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B=function_inverse(A)|relation_dom(B)!=relation_rng(A)|in($f5(A,B),relation_rng(A))|in($f4(A,B),relation_dom(A)).
% 1.93/2.16 ** KEPT (pick-wt=34): 36 [copy,35,flip.9] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B=function_inverse(A)|relation_dom(B)!=relation_rng(A)|in($f5(A,B),relation_rng(A))|apply(A,$f4(A,B))=$f5(A,B).
% 1.93/2.16 ** KEPT (pick-wt=34): 38 [copy,37,flip.8] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B=function_inverse(A)|relation_dom(B)!=relation_rng(A)|apply(B,$f5(A,B))=$f4(A,B)|in($f4(A,B),relation_dom(A)).
% 1.93/2.16 ** KEPT (pick-wt=37): 40 [copy,39,flip.8,flip.9] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B=function_inverse(A)|relation_dom(B)!=relation_rng(A)|apply(B,$f5(A,B))=$f4(A,B)|apply(A,$f4(A,B))=$f5(A,B).
% 1.93/2.16 ** KEPT (pick-wt=49): 42 [copy,41,flip.9,flip.11] -relation(A)| -function(A)| -one_to_one(A)| -relation(B)| -function(B)|B=function_inverse(A)|relation_dom(B)!=relation_rng(A)| -in($f4(A,B),relation_dom(A))|apply(A,$f4(A,B))!=$f5(A,B)| -in($f5(A,B),relation_rng(A))|apply(B,$f5(A,B))!=$f4(A,B).
% 2.04/2.28 ** KEPT (pick-wt=16): 44 [copy,43,flip.1,flip.2] apply(function_inverse($c9),apply($c9,$c10))!=$c10|apply(relation_composition($c9,function_inverse($c9)),$c10)!=$c10.
% 2.04/2.28 ** KEPT (pick-wt=9): 45 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.04/2.28 ** KEPT (pick-wt=5): 46 [] -empty(A)|A=empty_set.
% 2.04/2.28 ** KEPT (pick-wt=5): 47 [] -in(A,B)| -empty(B).
% 2.04/2.28 ** KEPT (pick-wt=7): 48 [] -empty(A)|A=B| -empty(B).
% 2.04/2.28
% 2.04/2.28 ------------> process sos:
% 2.04/2.28 ** KEPT (pick-wt=3): 64 [] A=A.
% 2.04/2.28 ** KEPT (pick-wt=4): 65 [] element($f1(A),A).
% 2.04/2.28 ** KEPT (pick-wt=2): 66 [] empty(empty_set).
% 2.04/2.28 ** KEPT (pick-wt=2): 67 [] relation(empty_set).
% 2.04/2.28 ** KEPT (pick-wt=2): 68 [] relation_empty_yielding(empty_set).
% 2.04/2.28 Following clause subsumed by 66 during input processing: 0 [] empty(empty_set).
% 2.04/2.28 Following clause subsumed by 66 during input processing: 0 [] empty(empty_set).
% 2.04/2.28 Following clause subsumed by 67 during input processing: 0 [] relation(empty_set).
% 2.04/2.28 ** KEPT (pick-wt=2): 69 [] relation($c1).
% 2.04/2.28 ** KEPT (pick-wt=2): 70 [] function($c1).
% 2.04/2.28 ** KEPT (pick-wt=2): 71 [] empty($c2).
% 2.04/2.28 ** KEPT (pick-wt=2): 72 [] relation($c2).
% 2.04/2.28 ** KEPT (pick-wt=7): 73 [] empty(A)|element($f2(A),powerset(A)).
% 2.04/2.28 ** KEPT (pick-wt=2): 74 [] empty($c3).
% 2.04/2.28 ** KEPT (pick-wt=2): 75 [] relation($c4).
% 2.04/2.28 ** KEPT (pick-wt=2): 76 [] empty($c4).
% 2.04/2.28 ** KEPT (pick-wt=2): 77 [] function($c4).
% 2.04/2.28 ** KEPT (pick-wt=2): 78 [] relation($c5).
% 2.04/2.28 ** KEPT (pick-wt=5): 79 [] element($f3(A),powerset(A)).
% 2.04/2.28 ** KEPT (pick-wt=3): 80 [] empty($f3(A)).
% 2.04/2.28 ** KEPT (pick-wt=2): 81 [] relation($c7).
% 2.04/2.28 ** KEPT (pick-wt=2): 82 [] function($c7).
% 2.04/2.28 ** KEPT (pick-wt=2): 83 [] one_to_one($c7).
% 2.04/2.28 ** KEPT (pick-wt=2): 84 [] relation($c8).
% 2.04/2.28 ** KEPT (pick-wt=2): 85 [] relation_empty_yielding($c8).
% 2.04/2.28 ** KEPT (pick-wt=3): 86 [] subset(A,A).
% 2.04/2.28 ** KEPT (pick-wt=2): 87 [] relation($c9).
% 2.04/2.28 ** KEPT (pick-wt=2): 88 [] function($c9).
% 2.04/2.28 ** KEPT (pick-wt=2): 89 [] one_to_one($c9).
% 2.04/2.28 ** KEPT (pick-wt=4): 90 [] in($c10,relation_dom($c9)).
% 2.04/2.28 Following clause subsumed by 64 during input processing: 0 [copy,64,flip.1] A=A.
% 2.04/2.28 64 back subsumes 63.
% 2.04/2.28
% 2.04/2.28 ======= end of input processing =======
% 2.04/2.28
% 2.04/2.28 =========== start of search ===========
% 2.04/2.28
% 2.04/2.28 -------- PROOF --------
% 2.04/2.28
% 2.04/2.28 -----> EMPTY CLAUSE at 0.13 sec ----> 926 [back_demod,44,demod,880,885,unit_del,64,64] $F.
% 2.04/2.28
% 2.04/2.28 Length of proof is 5. Level of proof is 3.
% 2.04/2.28
% 2.04/2.28 ---------------- PROOF ----------------
% 2.04/2.28 % SZS status Theorem
% 2.04/2.28 % SZS output start Refutation
% See solution above
% 2.04/2.28 ------------ end of proof -------------
% 2.04/2.28
% 2.04/2.28
% 2.04/2.28 Search stopped by max_proofs option.
% 2.04/2.28
% 2.04/2.28
% 2.04/2.28 Search stopped by max_proofs option.
% 2.04/2.28
% 2.04/2.28 ============ end of search ============
% 2.04/2.28
% 2.04/2.28 -------------- statistics -------------
% 2.04/2.28 clauses given 45
% 2.04/2.28 clauses generated 1463
% 2.04/2.28 clauses kept 904
% 2.04/2.28 clauses forward subsumed 828
% 2.04/2.28 clauses back subsumed 6
% 2.04/2.28 Kbytes malloced 3906
% 2.04/2.28
% 2.04/2.28 ----------- times (seconds) -----------
% 2.04/2.28 user CPU time 0.13 (0 hr, 0 min, 0 sec)
% 2.04/2.28 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.04/2.28 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.04/2.28
% 2.04/2.28 That finishes the proof of the theorem.
% 2.04/2.28
% 2.04/2.28 Process 22206 finished Wed Jul 27 07:54:09 2022
% 2.04/2.28 Otter interrupted
% 2.04/2.28 PROOF FOUND
%------------------------------------------------------------------------------