TSTP Solution File: SEU353+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU353+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n004.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 13:15:49 EDT 2022
% Result : Theorem 1.94s 2.19s
% Output : Refutation 1.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 17
% Syntax : Number of clauses : 32 ( 19 unt; 5 nHn; 22 RR)
% Number of literals : 53 ( 11 equ; 19 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-4 aty)
% Number of variables : 31 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ relation_of2(A,B,C)
| ~ function(A)
| ~ v1_partfun1(A,B,C)
| quasi_total(A,B,C) ),
file('SEU353+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ one_sorted_str(A)
| identity_on_carrier(A) = identity_as_relation_of(the_carrier(A)) ),
file('SEU353+1.p',unknown),
[] ).
cnf(14,plain,
( ~ one_sorted_str(A)
| identity_as_relation_of(the_carrier(A)) = identity_on_carrier(A) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13])]),
[iquote('copy,13,flip.2')] ).
cnf(20,axiom,
( empty_carrier(A)
| ~ one_sorted_str(A)
| ~ empty(the_carrier(A)) ),
file('SEU353+1.p',unknown),
[] ).
cnf(28,axiom,
( empty(A)
| ~ function(B)
| ~ quasi_total(B,A,C)
| ~ relation_of2(B,A,C)
| ~ element(D,A)
| apply_as_element(A,C,B,D) = apply(B,D) ),
file('SEU353+1.p',unknown),
[] ).
cnf(29,axiom,
( ~ relation_of2_as_subset(A,B,C)
| relation_of2(A,B,C) ),
file('SEU353+1.p',unknown),
[] ).
cnf(32,axiom,
( ~ element(A,B)
| empty(B)
| in(A,B) ),
file('SEU353+1.p',unknown),
[] ).
cnf(33,axiom,
( ~ in(A,B)
| apply(identity_relation(B),A) = A ),
file('SEU353+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ in(A,B)
| ~ empty(B) ),
file('SEU353+1.p',unknown),
[] ).
cnf(41,axiom,
~ empty_carrier(dollar_c7),
file('SEU353+1.p',unknown),
[] ).
cnf(42,axiom,
apply_as_element(the_carrier(dollar_c7),the_carrier(dollar_c7),identity_on_carrier(dollar_c7),dollar_c6) != dollar_c6,
file('SEU353+1.p',unknown),
[] ).
cnf(48,axiom,
v1_partfun1(identity_as_relation_of(A),A,A),
file('SEU353+1.p',unknown),
[] ).
cnf(49,axiom,
relation_of2_as_subset(identity_as_relation_of(A),A,A),
file('SEU353+1.p',unknown),
[] ).
cnf(53,axiom,
element(dollar_f2(A),A),
file('SEU353+1.p',unknown),
[] ).
cnf(56,axiom,
function(identity_relation(A)),
file('SEU353+1.p',unknown),
[] ).
cnf(91,axiom,
identity_as_relation_of(A) = identity_relation(A),
file('SEU353+1.p',unknown),
[] ).
cnf(93,plain,
identity_relation(A) = identity_as_relation_of(A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[91])]),
[iquote('copy,91,flip.1')] ).
cnf(95,axiom,
one_sorted_str(dollar_c7),
file('SEU353+1.p',unknown),
[] ).
cnf(96,axiom,
element(dollar_c6,the_carrier(dollar_c7)),
file('SEU353+1.p',unknown),
[] ).
cnf(101,plain,
function(identity_as_relation_of(A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[56]),93]),
[iquote('back_demod,56,demod,93')] ).
cnf(103,plain,
( ~ in(A,B)
| apply(identity_as_relation_of(B),A) = A ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[33]),93]),
[iquote('back_demod,33,demod,93')] ).
cnf(135,plain,
relation_of2(identity_as_relation_of(A),A,A),
inference(hyper,[status(thm)],[49,29]),
[iquote('hyper,49,29')] ).
cnf(143,plain,
identity_as_relation_of(the_carrier(dollar_c7)) = identity_on_carrier(dollar_c7),
inference(hyper,[status(thm)],[95,14]),
[iquote('hyper,95,14')] ).
cnf(154,plain,
( empty(A)
| in(dollar_f2(A),A) ),
inference(hyper,[status(thm)],[53,32]),
[iquote('hyper,53,32')] ).
cnf(181,plain,
( empty(the_carrier(dollar_c7))
| in(dollar_c6,the_carrier(dollar_c7)) ),
inference(hyper,[status(thm)],[96,32]),
[iquote('hyper,96,32')] ).
cnf(306,plain,
quasi_total(identity_as_relation_of(A),A,A),
inference(hyper,[status(thm)],[135,2,101,48]),
[iquote('hyper,135,2,101,48')] ).
cnf(503,plain,
( empty(the_carrier(dollar_c7))
| apply_as_element(the_carrier(dollar_c7),the_carrier(dollar_c7),identity_on_carrier(dollar_c7),dollar_c6) = apply(identity_on_carrier(dollar_c7),dollar_c6) ),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[306,28,101,135,96]),143,143]),
[iquote('hyper,306,28,101,135,96,demod,143,143')] ).
cnf(803,plain,
in(dollar_f2(the_carrier(dollar_c7)),the_carrier(dollar_c7)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[154,20,95]),41]),
[iquote('hyper,154,20,95,unit_del,41')] ).
cnf(1014,plain,
in(dollar_c6,the_carrier(dollar_c7)),
inference(hyper,[status(thm)],[181,39,803]),
[iquote('hyper,181,39,803')] ).
cnf(1016,plain,
apply(identity_on_carrier(dollar_c7),dollar_c6) = dollar_c6,
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[1014,103]),143]),
[iquote('hyper,1014,103,demod,143')] ).
cnf(1017,plain,
empty(the_carrier(dollar_c7)),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[503]),1016]),42]),
[iquote('back_demod,503,demod,1016,unit_del,42')] ).
cnf(1030,plain,
$false,
inference(hyper,[status(thm)],[1017,39,1014]),
[iquote('hyper,1017,39,1014')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU353+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n004.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 08:00:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.94/2.13 ----- Otter 3.3f, August 2004 -----
% 1.94/2.13 The process was started by sandbox2 on n004.cluster.edu,
% 1.94/2.13 Wed Jul 27 08:00:06 2022
% 1.94/2.13 The command was "./otter". The process ID is 4060.
% 1.94/2.13
% 1.94/2.13 set(prolog_style_variables).
% 1.94/2.13 set(auto).
% 1.94/2.13 dependent: set(auto1).
% 1.94/2.13 dependent: set(process_input).
% 1.94/2.13 dependent: clear(print_kept).
% 1.94/2.13 dependent: clear(print_new_demod).
% 1.94/2.13 dependent: clear(print_back_demod).
% 1.94/2.13 dependent: clear(print_back_sub).
% 1.94/2.13 dependent: set(control_memory).
% 1.94/2.13 dependent: assign(max_mem, 12000).
% 1.94/2.13 dependent: assign(pick_given_ratio, 4).
% 1.94/2.13 dependent: assign(stats_level, 1).
% 1.94/2.13 dependent: assign(max_seconds, 10800).
% 1.94/2.13 clear(print_given).
% 1.94/2.13
% 1.94/2.13 formula_list(usable).
% 1.94/2.13 all A (A=A).
% 1.94/2.13 all A B (in(A,B)-> -in(B,A)).
% 1.94/2.13 all A B C (relation_of2(C,A,B)-> (function(C)&v1_partfun1(C,A,B)->function(C)&quasi_total(C,A,B))).
% 1.94/2.13 all A (relation(A)&symmetric(A)&transitive(A)->relation(A)&reflexive(A)).
% 1.94/2.13 all A B C (element(C,powerset(cartesian_product2(A,B)))->relation(C)).
% 1.94/2.13 all A B C (relation_of2(C,A,B)-> (function(C)&quasi_total(C,A,B)&bijective(C,A,B)->function(C)&one_to_one(C)&quasi_total(C,A,B)&onto(C,A,B))).
% 1.94/2.13 all A B C (relation_of2(C,A,B)-> (function(C)&one_to_one(C)&quasi_total(C,A,B)&onto(C,A,B)->function(C)&quasi_total(C,A,B)&bijective(C,A,B))).
% 1.94/2.13 all A B (relation_of2(B,A,A)-> (function(B)&v1_partfun1(B,A,A)&reflexive(B)&quasi_total(B,A,A)->function(B)&one_to_one(B)&quasi_total(B,A,A)&onto(B,A,A)&bijective(B,A,A))).
% 1.94/2.13 all A B (-empty(B)-> (all C (relation_of2(C,A,B)-> (function(C)&quasi_total(C,A,B)->function(C)&v1_partfun1(C,A,B)&quasi_total(C,A,B))))).
% 1.94/2.13 all A B (-empty(A)& -empty(B)-> (all C (relation_of2(C,A,B)-> (function(C)&quasi_total(C,A,B)->function(C)& -empty(C)&v1_partfun1(C,A,B)&quasi_total(C,A,B))))).
% 1.94/2.13 all A (one_sorted_str(A)->identity_on_carrier(A)=identity_as_relation_of(the_carrier(A))).
% 1.94/2.13 $T.
% 1.94/2.13 $T.
% 1.94/2.13 $T.
% 1.94/2.13 $T.
% 1.94/2.13 all A (v1_partfun1(identity_as_relation_of(A),A,A)&relation_of2_as_subset(identity_as_relation_of(A),A,A)).
% 1.94/2.13 all A relation(identity_relation(A)).
% 1.94/2.13 all A (one_sorted_str(A)->function(identity_on_carrier(A))&quasi_total(identity_on_carrier(A),the_carrier(A),the_carrier(A))&relation_of2_as_subset(identity_on_carrier(A),the_carrier(A),the_carrier(A))).
% 1.94/2.13 all A B C D (-empty(A)&function(C)&quasi_total(C,A,B)&relation_of2(C,A,B)&element(D,A)->element(apply_as_element(A,B,C,D),B)).
% 1.94/2.13 $T.
% 1.94/2.13 $T.
% 1.94/2.13 $T.
% 1.94/2.13 all A B C (relation_of2_as_subset(C,A,B)->element(C,powerset(cartesian_product2(A,B)))).
% 1.94/2.13 $T.
% 1.94/2.13 exists A one_sorted_str(A).
% 1.94/2.13 all A B exists C relation_of2(C,A,B).
% 1.94/2.13 all A exists B element(B,A).
% 1.94/2.13 all A B exists C relation_of2_as_subset(C,A,B).
% 1.94/2.13 all A (-empty_carrier(A)&one_sorted_str(A)-> -empty(the_carrier(A))).
% 1.94/2.13 all A (-empty(powerset(A))).
% 1.94/2.13 empty(empty_set).
% 1.94/2.13 all A (relation(identity_relation(A))&function(identity_relation(A))&reflexive(identity_relation(A))&symmetric(identity_relation(A))&antisymmetric(identity_relation(A))&transitive(identity_relation(A))).
% 1.94/2.13 all A B (-empty(A)& -empty(B)-> -empty(cartesian_product2(A,B))).
% 1.94/2.13 all A B exists C (relation_of2(C,A,B)&relation(C)&function(C)&quasi_total(C,A,B)).
% 1.94/2.13 exists A (relation(A)&function(A)&one_to_one(A)&empty(A)).
% 1.94/2.13 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 1.94/2.13 exists A empty(A).
% 1.94/2.13 all A exists B (relation_of2(B,A,A)&relation(B)&function(B)&one_to_one(B)&quasi_total(B,A,A)&onto(B,A,A)&bijective(B,A,A)).
% 1.94/2.13 all A B exists C (relation_of2(C,A,B)&relation(C)&function(C)).
% 1.94/2.13 all A exists B (element(B,powerset(A))&empty(B)).
% 1.94/2.13 exists A (-empty(A)).
% 1.94/2.13 all A exists B (relation_of2(B,A,A)&relation(B)&reflexive(B)&symmetric(B)&antisymmetric(B)&transitive(B)&v1_partfun1(B,A,A)).
% 1.94/2.13 exists A (one_sorted_str(A)& -empty_carrier(A)).
% 1.94/2.13 all A (-empty_carrier(A)&one_sorted_str(A)-> (exists B (element(B,powerset(the_carrier(A)))& -empty(B)))).
% 1.94/2.13 all A (identity_as_relation_of(A)=identity_relation(A)).
% 1.94/2.13 all A B C D (-empty(A)&function(C)&quasi_total(C,A,B)&relation_of2(C,A,B)&element(D,A)->apply_as_element(A,B,C,D)=apply(C,D)).
% 1.94/2.13 all A B C (relation_of2_as_subset(C,A,B)<->relation_of2(C,A,B)).
% 1.94/2.13 all A B subset(A,A).
% 1.94/2.13 all A B (in(A,B)->element(A,B)).
% 1.94/2.13 all A B (element(A,B)->empty(B)|in(A,B)).
% 1.94/2.13 all A B (in(B,A)->apply(identity_relation(A),B)=B).
% 1.94/2.13 all A B (element(A,powerset(B))<->subset(A,B)).
% 1.94/2.13 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 1.94/2.13 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 1.94/2.13 all A (empty(A)->A=empty_set).
% 1.94/2.13 all A B (-(in(A,B)&empty(B))).
% 1.94/2.13 all A B (-(empty(A)&A!=B&empty(B))).
% 1.94/2.13 -(all A (-empty_carrier(A)&one_sorted_str(A)-> (all B (element(B,the_carrier(A))->apply_as_element(the_carrier(A),the_carrier(A),identity_on_carrier(A),B)=B)))).
% 1.94/2.13 end_of_list.
% 1.94/2.13
% 1.94/2.13 -------> usable clausifies to:
% 1.94/2.13
% 1.94/2.13 list(usable).
% 1.94/2.13 0 [] A=A.
% 1.94/2.13 0 [] -in(A,B)| -in(B,A).
% 1.94/2.13 0 [] -relation_of2(C,A,B)| -function(C)| -v1_partfun1(C,A,B)|quasi_total(C,A,B).
% 1.94/2.13 0 [] -relation(A)| -symmetric(A)| -transitive(A)|reflexive(A).
% 1.94/2.13 0 [] -element(C,powerset(cartesian_product2(A,B)))|relation(C).
% 1.94/2.13 0 [] -relation_of2(C,A,B)| -function(C)| -quasi_total(C,A,B)| -bijective(C,A,B)|one_to_one(C).
% 1.94/2.13 0 [] -relation_of2(C,A,B)| -function(C)| -quasi_total(C,A,B)| -bijective(C,A,B)|onto(C,A,B).
% 1.94/2.13 0 [] -relation_of2(C,A,B)| -function(C)| -one_to_one(C)| -quasi_total(C,A,B)| -onto(C,A,B)|bijective(C,A,B).
% 1.94/2.13 0 [] -relation_of2(B,A,A)| -function(B)| -v1_partfun1(B,A,A)| -reflexive(B)| -quasi_total(B,A,A)|one_to_one(B).
% 1.94/2.13 0 [] -relation_of2(B,A,A)| -function(B)| -v1_partfun1(B,A,A)| -reflexive(B)| -quasi_total(B,A,A)|onto(B,A,A).
% 1.94/2.13 0 [] -relation_of2(B,A,A)| -function(B)| -v1_partfun1(B,A,A)| -reflexive(B)| -quasi_total(B,A,A)|bijective(B,A,A).
% 1.94/2.13 0 [] empty(B)| -relation_of2(C,A,B)| -function(C)| -quasi_total(C,A,B)|v1_partfun1(C,A,B).
% 1.94/2.13 0 [] empty(A)|empty(B)| -relation_of2(C,A,B)| -function(C)| -quasi_total(C,A,B)| -empty(C).
% 1.94/2.13 0 [] empty(A)|empty(B)| -relation_of2(C,A,B)| -function(C)| -quasi_total(C,A,B)|v1_partfun1(C,A,B).
% 1.94/2.13 0 [] -one_sorted_str(A)|identity_on_carrier(A)=identity_as_relation_of(the_carrier(A)).
% 1.94/2.13 0 [] $T.
% 1.94/2.13 0 [] $T.
% 1.94/2.13 0 [] $T.
% 1.94/2.13 0 [] $T.
% 1.94/2.13 0 [] v1_partfun1(identity_as_relation_of(A),A,A).
% 1.94/2.13 0 [] relation_of2_as_subset(identity_as_relation_of(A),A,A).
% 1.94/2.13 0 [] relation(identity_relation(A)).
% 1.94/2.13 0 [] -one_sorted_str(A)|function(identity_on_carrier(A)).
% 1.94/2.13 0 [] -one_sorted_str(A)|quasi_total(identity_on_carrier(A),the_carrier(A),the_carrier(A)).
% 1.94/2.13 0 [] -one_sorted_str(A)|relation_of2_as_subset(identity_on_carrier(A),the_carrier(A),the_carrier(A)).
% 1.94/2.13 0 [] empty(A)| -function(C)| -quasi_total(C,A,B)| -relation_of2(C,A,B)| -element(D,A)|element(apply_as_element(A,B,C,D),B).
% 1.94/2.13 0 [] $T.
% 1.94/2.13 0 [] $T.
% 1.94/2.13 0 [] $T.
% 1.94/2.13 0 [] -relation_of2_as_subset(C,A,B)|element(C,powerset(cartesian_product2(A,B))).
% 1.94/2.13 0 [] $T.
% 1.94/2.13 0 [] one_sorted_str($c1).
% 1.94/2.13 0 [] relation_of2($f1(A,B),A,B).
% 1.94/2.13 0 [] element($f2(A),A).
% 1.94/2.13 0 [] relation_of2_as_subset($f3(A,B),A,B).
% 1.94/2.13 0 [] empty_carrier(A)| -one_sorted_str(A)| -empty(the_carrier(A)).
% 1.94/2.13 0 [] -empty(powerset(A)).
% 1.94/2.13 0 [] empty(empty_set).
% 1.94/2.13 0 [] relation(identity_relation(A)).
% 1.94/2.13 0 [] function(identity_relation(A)).
% 1.94/2.13 0 [] reflexive(identity_relation(A)).
% 1.94/2.13 0 [] symmetric(identity_relation(A)).
% 1.94/2.13 0 [] antisymmetric(identity_relation(A)).
% 1.94/2.13 0 [] transitive(identity_relation(A)).
% 1.94/2.13 0 [] empty(A)|empty(B)| -empty(cartesian_product2(A,B)).
% 1.94/2.13 0 [] relation_of2($f4(A,B),A,B).
% 1.94/2.13 0 [] relation($f4(A,B)).
% 1.94/2.13 0 [] function($f4(A,B)).
% 1.94/2.13 0 [] quasi_total($f4(A,B),A,B).
% 1.94/2.13 0 [] relation($c2).
% 1.94/2.13 0 [] function($c2).
% 1.94/2.13 0 [] one_to_one($c2).
% 1.94/2.13 0 [] empty($c2).
% 1.94/2.13 0 [] empty(A)|element($f5(A),powerset(A)).
% 1.94/2.13 0 [] empty(A)| -empty($f5(A)).
% 1.94/2.13 0 [] empty($c3).
% 1.94/2.13 0 [] relation_of2($f6(A),A,A).
% 1.94/2.13 0 [] relation($f6(A)).
% 1.94/2.13 0 [] function($f6(A)).
% 1.94/2.13 0 [] one_to_one($f6(A)).
% 1.94/2.13 0 [] quasi_total($f6(A),A,A).
% 1.94/2.13 0 [] onto($f6(A),A,A).
% 1.94/2.13 0 [] bijective($f6(A),A,A).
% 1.94/2.13 0 [] relation_of2($f7(A,B),A,B).
% 1.94/2.13 0 [] relation($f7(A,B)).
% 1.94/2.13 0 [] function($f7(A,B)).
% 1.94/2.13 0 [] element($f8(A),powerset(A)).
% 1.94/2.13 0 [] empty($f8(A)).
% 1.94/2.13 0 [] -empty($c4).
% 1.94/2.13 0 [] relation_of2($f9(A),A,A).
% 1.94/2.13 0 [] relation($f9(A)).
% 1.94/2.13 0 [] reflexive($f9(A)).
% 1.94/2.13 0 [] symmetric($f9(A)).
% 1.94/2.13 0 [] antisymmetric($f9(A)).
% 1.94/2.13 0 [] transitive($f9(A)).
% 1.94/2.13 0 [] v1_partfun1($f9(A),A,A).
% 1.94/2.13 0 [] one_sorted_str($c5).
% 1.94/2.13 0 [] -empty_carrier($c5).
% 1.94/2.13 0 [] empty_carrier(A)| -one_sorted_str(A)|element($f10(A),powerset(the_carrier(A))).
% 1.94/2.13 0 [] empty_carrier(A)| -one_sorted_str(A)| -empty($f10(A)).
% 1.94/2.13 0 [] identity_as_relation_of(A)=identity_relation(A).
% 1.94/2.13 0 [] empty(A)| -function(C)| -quasi_total(C,A,B)| -relation_of2(C,A,B)| -element(D,A)|apply_as_element(A,B,C,D)=apply(C,D).
% 1.94/2.13 0 [] -relation_of2_as_subset(C,A,B)|relation_of2(C,A,B).
% 1.94/2.13 0 [] relation_of2_as_subset(C,A,B)| -relation_of2(C,A,B).
% 1.94/2.13 0 [] subset(A,A).
% 1.94/2.13 0 [] -in(A,B)|element(A,B).
% 1.94/2.13 0 [] -element(A,B)|empty(B)|in(A,B).
% 1.94/2.13 0 [] -in(B,A)|apply(identity_relation(A),B)=B.
% 1.94/2.13 0 [] -element(A,powerset(B))|subset(A,B).
% 1.94/2.13 0 [] element(A,powerset(B))| -subset(A,B).
% 1.94/2.13 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.94/2.13 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.94/2.13 0 [] -empty(A)|A=empty_set.
% 1.94/2.13 0 [] -in(A,B)| -empty(B).
% 1.94/2.13 0 [] -empty(A)|A=B| -empty(B).
% 1.94/2.13 0 [] -empty_carrier($c7).
% 1.94/2.13 0 [] one_sorted_str($c7).
% 1.94/2.13 0 [] element($c6,the_carrier($c7)).
% 1.94/2.13 0 [] apply_as_element(the_carrier($c7),the_carrier($c7),identity_on_carrier($c7),$c6)!=$c6.
% 1.94/2.13 end_of_list.
% 1.94/2.13
% 1.94/2.13 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 1.94/2.13
% 1.94/2.13 This ia a non-Horn set with equality. The strategy will be
% 1.94/2.13 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.94/2.13 deletion, with positive clauses in sos and nonpositive
% 1.94/2.13 clauses in usable.
% 1.94/2.13
% 1.94/2.13 dependent: set(knuth_bendix).
% 1.94/2.13 dependent: set(anl_eq).
% 1.94/2.13 dependent: set(para_from).
% 1.94/2.13 dependent: set(para_into).
% 1.94/2.13 dependent: clear(para_from_right).
% 1.94/2.13 dependent: clear(para_into_right).
% 1.94/2.13 dependent: set(para_from_vars).
% 1.94/2.13 dependent: set(eq_units_both_ways).
% 1.94/2.13 dependent: set(dynamic_demod_all).
% 1.94/2.13 dependent: set(dynamic_demod).
% 1.94/2.13 dependent: set(order_eq).
% 1.94/2.13 dependent: set(back_demod).
% 1.94/2.13 dependent: set(lrpo).
% 1.94/2.13 dependent: set(hyper_res).
% 1.94/2.13 dependent: set(unit_deletion).
% 1.94/2.13 dependent: set(factor).
% 1.94/2.13
% 1.94/2.13 ------------> process usable:
% 1.94/2.13 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.94/2.13 ** KEPT (pick-wt=14): 2 [] -relation_of2(A,B,C)| -function(A)| -v1_partfun1(A,B,C)|quasi_total(A,B,C).
% 1.94/2.13 ** KEPT (pick-wt=8): 3 [] -relation(A)| -symmetric(A)| -transitive(A)|reflexive(A).
% 1.94/2.13 ** KEPT (pick-wt=8): 4 [] -element(A,powerset(cartesian_product2(B,C)))|relation(A).
% 1.94/2.13 ** KEPT (pick-wt=16): 5 [] -relation_of2(A,B,C)| -function(A)| -quasi_total(A,B,C)| -bijective(A,B,C)|one_to_one(A).
% 1.94/2.13 ** KEPT (pick-wt=18): 6 [] -relation_of2(A,B,C)| -function(A)| -quasi_total(A,B,C)| -bijective(A,B,C)|onto(A,B,C).
% 1.94/2.13 ** KEPT (pick-wt=20): 7 [] -relation_of2(A,B,C)| -function(A)| -one_to_one(A)| -quasi_total(A,B,C)| -onto(A,B,C)|bijective(A,B,C).
% 1.94/2.13 ** KEPT (pick-wt=18): 8 [] -relation_of2(A,B,B)| -function(A)| -v1_partfun1(A,B,B)| -reflexive(A)| -quasi_total(A,B,B)|one_to_one(A).
% 1.94/2.13 ** KEPT (pick-wt=20): 9 [] -relation_of2(A,B,B)| -function(A)| -v1_partfun1(A,B,B)| -reflexive(A)| -quasi_total(A,B,B)|onto(A,B,B).
% 1.94/2.13 ** KEPT (pick-wt=20): 10 [] -relation_of2(A,B,B)| -function(A)| -v1_partfun1(A,B,B)| -reflexive(A)| -quasi_total(A,B,B)|bijective(A,B,B).
% 1.94/2.13 ** KEPT (pick-wt=16): 11 [] empty(A)| -relation_of2(B,C,A)| -function(B)| -quasi_total(B,C,A)|v1_partfun1(B,C,A).
% 1.94/2.13 ** KEPT (pick-wt=16): 12 [] empty(A)|empty(B)| -relation_of2(C,A,B)| -function(C)| -quasi_total(C,A,B)| -empty(C).
% 1.94/2.13 Following clause subsumed by 11 during input processing: 0 [] empty(A)|empty(B)| -relation_of2(C,A,B)| -function(C)| -quasi_total(C,A,B)|v1_partfun1(C,A,B).
% 1.94/2.13 ** KEPT (pick-wt=8): 14 [copy,13,flip.2] -one_sorted_str(A)|identity_as_relation_of(the_carrier(A))=identity_on_carrier(A).
% 1.94/2.13 ** KEPT (pick-wt=5): 15 [] -one_sorted_str(A)|function(identity_on_carrier(A)).
% 1.94/2.13 ** KEPT (pick-wt=9): 16 [] -one_sorted_str(A)|quasi_total(identity_on_carrier(A),the_carrier(A),the_carrier(A)).
% 1.94/2.13 ** KEPT (pick-wt=9): 17 [] -one_sorted_str(A)|relation_of2_as_subset(identity_on_carrier(A),the_carrier(A),the_carrier(A)).
% 1.94/2.13 ** KEPT (pick-wt=22): 18 [] empty(A)| -function(B)| -quasi_total(B,A,C)| -relation_of2(B,A,C)| -element(D,A)|element(apply_as_element(A,C,B,D),C).
% 1.94/2.13 ** KEPT (pick-wt=10): 19 [] -relation_of2_as_subset(A,B,C)|element(A,powerset(cartesian_product2(B,C))).
% 1.94/2.13 ** KEPT (pick-wt=7): 20 [] empty_carrier(A)| -one_sorted_str(A)| -empty(the_carrier(A)).
% 1.94/2.13 ** KEPT (pick-wt=3): 21 [] -empty(powerset(A)).
% 1.94/2.13 ** KEPT (pick-wt=8): 22 [] empty(A)|empty(B)| -empty(cartesian_product2(A,B)).
% 1.94/2.13 ** KEPT (pick-wt=5): 23 [] empty(A)| -empty($f5(A)).
% 1.94/2.13 ** KEPT (pick-wt=2): 24 [] -empty($c4).
% 1.94/2.13 ** KEPT (pick-wt=2): 25 [] -empty_carrier($c5).
% 1.94/2.13 ** KEPT (pick-wt=10): 26 [] empty_carrier(A)| -one_sorted_str(A)|element($f10(A),powerset(the_carrier(A))).
% 1.94/2.13 ** KEPT (pick-wt=7): 27 [] empty_carrier(A)| -one_sorted_str(A)| -empty($f10(A)).
% 1.94/2.13 ** KEPT (pick-wt=24): 28 [] empty(A)| -function(B)| -quasi_total(B,A,C)| -relation_of2(B,A,C)| -element(D,A)|apply_as_element(A,C,B,D)=apply(B,D).
% 1.94/2.13 ** KEPT (pick-wt=8): 29 [] -relation_of2_as_subset(A,B,C)|relation_of2(A,B,C).
% 1.94/2.13 ** KEPT (pick-wt=8): 30 [] relation_of2_as_subset(A,B,C)| -relation_of2(A,B,C).
% 1.94/2.13 ** KEPT (pick-wt=6): 31 [] -in(A,B)|element(A,B).
% 1.94/2.13 ** KEPT (pick-wt=8): 32 [] -element(A,B)|empty(B)|in(A,B).
% 1.94/2.13 ** KEPT (pick-wt=9): 33 [] -in(A,B)|apply(identity_relation(B),A)=A.
% 1.94/2.13 ** KEPT (pick-wt=7): 34 [] -element(A,powerset(B))|subset(A,B).
% 1.94/2.13 ** KEPT (pick-wt=7): 35 [] element(A,powerset(B))| -subset(A,B).
% 1.94/2.13 ** KEPT (pick-wt=10): 36 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.94/2.13 ** KEPT (pick-wt=9): 37 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.94/2.13 ** KEPT (pick-wt=5): 38 [] -empty(A)|A=empty_set.
% 1.94/2.13 ** KEPT (pick-wt=5): 39 [] -in(A,B)| -empty(B).
% 1.94/2.13 ** KEPT (pick-wt=7): 40 [] -empty(A)|A=B| -empty(B).
% 1.94/2.13 ** KEPT (pick-wt=2): 41 [] -empty_carrier($c7).
% 1.94/2.13 ** KEPT (pick-wt=10): 42 [] apply_as_element(the_carrier($c7),the_carrier($c7),identity_on_carrier($c7),$c6)!=$c6.
% 1.94/2.13
% 1.94/2.13 ------------> process sos:
% 1.94/2.13 ** KEPT (pick-wt=3): 47 [] A=A.
% 1.94/2.13 ** KEPT (pick-wt=5): 48 [] v1_partfun1(identity_as_relation_of(A),A,A).
% 1.94/2.13 ** KEPT (pick-wt=5): 49 [] relation_of2_as_subset(identity_as_relation_of(A),A,A).
% 1.94/2.13 ** KEPT (pick-wt=3): 50 [] relation(identity_relation(A)).
% 1.94/2.13 ** KEPT (pick-wt=2): 51 [] one_sorted_str($c1).
% 1.94/2.13 ** KEPT (pick-wt=6): 52 [] relation_of2($f1(A,B),A,B).
% 1.94/2.13 ** KEPT (pick-wt=4): 53 [] element($f2(A),A).
% 1.94/2.13 ** KEPT (pick-wt=6): 54 [] relation_of2_as_subset($f3(A,B),A,B).
% 1.94/2.13 ** KEPT (pick-wt=2): 55 [] empty(empty_set).
% 1.94/2.13 Following clause subsumed by 50 during input processing: 0 [] relation(identity_relation(A)).
% 1.94/2.13 ** KEPT (pick-wt=3): 56 [] function(identity_relation(A)).
% 1.94/2.13 ** KEPT (pick-wt=3): 57 [] reflexive(identity_relation(A)).
% 1.94/2.13 ** KEPT (pick-wt=3): 58 [] symmetric(identity_relation(A)).
% 1.94/2.13 ** KEPT (pick-wt=3): 59 [] antisymmetric(identity_relation(A)).
% 1.94/2.13 ** KEPT (pick-wt=3): 60 [] transitive(identity_relation(A)).
% 1.94/2.13 ** KEPT (pick-wt=6): 61 [] relation_of2($f4(A,B),A,B).
% 1.94/2.13 ** KEPT (pick-wt=4): 62 [] relation($f4(A,B)).
% 1.94/2.13 ** KEPT (pick-wt=4): 63 [] function($f4(A,B)).
% 1.94/2.13 ** KEPT (pick-wt=6): 64 [] quasi_total($f4(A,B),A,B).
% 1.94/2.13 ** KEPT (pick-wt=2): 65 [] relation($c2).
% 1.94/2.13 ** KEPT (pick-wt=2): 66 [] function($c2).
% 1.94/2.13 ** KEPT (pick-wt=2): 67 [] one_to_one($c2).
% 1.94/2.13 ** KEPT (pick-wt=2): 68 [] empty($c2).
% 1.94/2.13 ** KEPT (pick-wt=7): 69 [] empty(A)|element($f5(A),powerset(A)).
% 1.94/2.13 ** KEPT (pick-wt=2): 70 [] empty($c3).
% 1.94/2.13 ** KEPT (pick-wt=5): 71 [] relation_of2($f6(A),A,A).
% 1.94/2.13 ** KEPT (pick-wt=3): 72 [] relation($f6(A)).
% 1.94/2.13 ** KEPT (pick-wt=3): 73 [] function($f6(A)).
% 1.94/2.13 ** KEPT (pick-wt=3): 74 [] one_to_one($f6(A)).
% 1.94/2.13 ** KEPT (pick-wt=5): 75 [] quasi_total($f6(A),A,A).
% 1.94/2.13 ** KEPT (pick-wt=5): 76 [] onto($f6(A),A,A).
% 1.94/2.13 ** KEPT (pick-wt=5): 77 [] bijective($f6(A),A,A).
% 1.94/2.13 ** KEPT (pick-wt=6): 78 [] relation_of2($f7(A,B),A,B).
% 1.94/2.13 ** KEPT (pick-wt=4): 79 [] relation($f7(A,B)).
% 1.94/2.13 ** KEPT (pick-wt=4): 80 [] function($f7(A,B)).
% 1.94/2.13 ** KEPT (pick-wt=5): 81 [] element($f8(A),powerset(A)).
% 1.94/2.13 ** KEPT (pick-wt=3): 82 [] empty($f8(A)).
% 1.94/2.13 ** KEPT (pick-wt=5): 83 [] relation_of2($f9(A),A,A).
% 1.94/2.13 ** KEPT (pick-wt=3): 84 [] relation($f9(A)).
% 1.94/2.13 ** KEPT (pick-wt=3): 85 [] reflexive($f9(A)).
% 1.94/2.13 ** KEPT (pick-wt=3): 86 [] symmetric($f9(A)).
% 1.94/2.13 ** KEPT (pick-wt=3): 87 [] antisymmetric($f9(A)).
% 1.94/2.13 ** KEPT (pick-wt=3): 88 [] transitive($f9(A)).
% 1.94/2.13 ** KEPT (pick-wt=5): 89 [] v1_partfun1($f9(A),A,A).
% 1.94/2.13 ** KEPT (pick-wt=2): 90 [] one_sorted_str($c5).
% 1.94/2.13 ** KEPT (pick-wt=5): 92 [copy,91,flip.1] identity_relation(A)=identity_as_relation_of(A).
% 1.94/2.13 ---> New Demodulator: 93 [new_demod,92] identity_relation(A)=identity_as_relation_of(A).
% 1.94/2.13 ** KEPT (pick-wt=3): 94 [] subset(A,A).
% 1.94/2.13 ** KEPT (pick-wt=2): 95 [] one_sorted_str($c7).
% 1.94/2.13 ** KEPT (pick-wt=4): 96 [] element($c6,the_carrier($c7)).
% 1.94/2.13 Following clause subsumed by 47 during input processing: 0 [copy,47,flip.1] A=A.
% 1.94/2.13 47 back subsumes 46.
% 1.94/2.13 >>>> Starting back demodulation with 93.
% 1.94/2.13 >> back demodulating 60 with 93.
% 1.94/2.19 >> back demodulating 59 with 93.
% 1.94/2.19 >> back demodulating 58 with 93.
% 1.94/2.19 >> back demodulating 57 with 93.
% 1.94/2.19 >> back demodulating 56 with 93.
% 1.94/2.19 >> back demodulating 50 with 93.
% 1.94/2.19 >> back demodulating 33 with 93.
% 1.94/2.19
% 1.94/2.19 ======= end of input processing =======
% 1.94/2.19
% 1.94/2.19 =========== start of search ===========
% 1.94/2.19
% 1.94/2.19
% 1.94/2.19 Resetting weight limit to 7.
% 1.94/2.19
% 1.94/2.19
% 1.94/2.19 Resetting weight limit to 7.
% 1.94/2.19
% 1.94/2.19 sos_size=695
% 1.94/2.19
% 1.94/2.19 -------- PROOF --------
% 1.94/2.19
% 1.94/2.19 -----> EMPTY CLAUSE at 0.06 sec ----> 1030 [hyper,1017,39,1014] $F.
% 1.94/2.19
% 1.94/2.19 Length of proof is 14. Level of proof is 5.
% 1.94/2.19
% 1.94/2.19 ---------------- PROOF ----------------
% 1.94/2.19 % SZS status Theorem
% 1.94/2.19 % SZS output start Refutation
% See solution above
% 1.94/2.19 ------------ end of proof -------------
% 1.94/2.19
% 1.94/2.19
% 1.94/2.19 Search stopped by max_proofs option.
% 1.94/2.19
% 1.94/2.19
% 1.94/2.19 Search stopped by max_proofs option.
% 1.94/2.19
% 1.94/2.19 ============ end of search ============
% 1.94/2.19
% 1.94/2.19 -------------- statistics -------------
% 1.94/2.19 clauses given 220
% 1.94/2.19 clauses generated 2188
% 1.94/2.19 clauses kept 986
% 1.94/2.19 clauses forward subsumed 1101
% 1.94/2.19 clauses back subsumed 12
% 1.94/2.19 Kbytes malloced 4882
% 1.94/2.19
% 1.94/2.19 ----------- times (seconds) -----------
% 1.94/2.19 user CPU time 0.06 (0 hr, 0 min, 0 sec)
% 1.94/2.19 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.94/2.19 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.94/2.19
% 1.94/2.19 That finishes the proof of the theorem.
% 1.94/2.19
% 1.94/2.19 Process 4060 finished Wed Jul 27 08:00:08 2022
% 1.94/2.19 Otter interrupted
% 1.94/2.19 PROOF FOUND
%------------------------------------------------------------------------------