TSTP Solution File: SEU353+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU353+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 : Tue Sep 20 07:29:05 EDT 2022
% Result : Theorem 284.34s 181.70s
% Output : Proof 284.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU353+2 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n024.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 : Sat Sep 3 12:32:33 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 284.34/181.70 % SZS status Theorem
% 284.34/181.70 % SZS output start Proof
% 284.34/181.70 tff(quasi_total_type, type, (
% 284.34/181.70 quasi_total: ( $i * $i * $i ) > $o)).
% 284.34/181.70 tff(the_carrier_type, type, (
% 284.34/181.70 the_carrier: $i > $i)).
% 284.34/181.70 tff(tptp_fun_A_407_type, type, (
% 284.34/181.70 tptp_fun_A_407: $i)).
% 284.34/181.70 tff(identity_on_carrier_type, type, (
% 284.34/181.70 identity_on_carrier: $i > $i)).
% 284.34/181.70 tff(relation_of2_as_subset_type, type, (
% 284.34/181.70 relation_of2_as_subset: ( $i * $i * $i ) > $o)).
% 284.34/181.70 tff(function_type, type, (
% 284.34/181.70 function: $i > $o)).
% 284.34/181.70 tff(one_sorted_str_type, type, (
% 284.34/181.70 one_sorted_str: $i > $o)).
% 284.34/181.70 tff(tptp_fun_B_408_type, type, (
% 284.34/181.70 tptp_fun_B_408: $i)).
% 284.34/181.70 tff(apply_as_element_type, type, (
% 284.34/181.70 apply_as_element: ( $i * $i * $i * $i ) > $i)).
% 284.34/181.70 tff(element_type, type, (
% 284.34/181.70 element: ( $i * $i ) > $o)).
% 284.34/181.70 tff(empty_carrier_type, type, (
% 284.34/181.70 empty_carrier: $i > $o)).
% 284.34/181.70 tff(relation_of2_type, type, (
% 284.34/181.70 relation_of2: ( $i * $i * $i ) > $o)).
% 284.34/181.70 tff(identity_as_relation_of_type, type, (
% 284.34/181.70 identity_as_relation_of: $i > $i)).
% 284.34/181.70 tff(v1_partfun1_type, type, (
% 284.34/181.70 v1_partfun1: ( $i * $i * $i ) > $o)).
% 284.34/181.70 tff(apply_type, type, (
% 284.34/181.70 apply: ( $i * $i ) > $i)).
% 284.34/181.70 tff(identity_relation_type, type, (
% 284.34/181.70 identity_relation: $i > $i)).
% 284.34/181.70 tff(in_type, type, (
% 284.34/181.70 in: ( $i * $i ) > $o)).
% 284.34/181.70 tff(empty_type, type, (
% 284.34/181.70 empty: $i > $o)).
% 284.34/181.70 tff(1,plain,
% 284.34/181.70 ((((~empty_carrier(A!407)) & one_sorted_str(A!407)) & (~((~element(B!408, the_carrier(A!407))) | (apply_as_element(the_carrier(A!407), the_carrier(A!407), identity_on_carrier(A!407), B!408) = B!408)))) <=> ((~empty_carrier(A!407)) & one_sorted_str(A!407) & (~((~element(B!408, the_carrier(A!407))) | (apply_as_element(the_carrier(A!407), the_carrier(A!407), identity_on_carrier(A!407), B!408) = B!408))))),
% 284.34/181.70 inference(rewrite,[status(thm)],[])).
% 284.34/181.70 tff(2,plain,
% 284.34/181.70 ((~(~((~empty_carrier(A!407)) & one_sorted_str(A!407)))) <=> ((~empty_carrier(A!407)) & one_sorted_str(A!407))),
% 284.34/181.70 inference(rewrite,[status(thm)],[])).
% 284.34/181.70 tff(3,plain,
% 284.34/181.70 (((~(~((~empty_carrier(A!407)) & one_sorted_str(A!407)))) & (~((~element(B!408, the_carrier(A!407))) | (apply_as_element(the_carrier(A!407), the_carrier(A!407), identity_on_carrier(A!407), B!408) = B!408)))) <=> (((~empty_carrier(A!407)) & one_sorted_str(A!407)) & (~((~element(B!408, the_carrier(A!407))) | (apply_as_element(the_carrier(A!407), the_carrier(A!407), identity_on_carrier(A!407), B!408) = B!408))))),
% 284.34/181.70 inference(monotonicity,[status(thm)],[2])).
% 284.34/181.70 tff(4,plain,
% 284.34/181.70 (((~(~((~empty_carrier(A!407)) & one_sorted_str(A!407)))) & (~((~element(B!408, the_carrier(A!407))) | (apply_as_element(the_carrier(A!407), the_carrier(A!407), identity_on_carrier(A!407), B!408) = B!408)))) <=> ((~empty_carrier(A!407)) & one_sorted_str(A!407) & (~((~element(B!408, the_carrier(A!407))) | (apply_as_element(the_carrier(A!407), the_carrier(A!407), identity_on_carrier(A!407), B!408) = B!408))))),
% 284.34/181.70 inference(transitivity,[status(thm)],[3, 1])).
% 284.34/181.70 tff(5,plain,
% 284.34/181.70 ((~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (apply_as_element(the_carrier(A), the_carrier(A), identity_on_carrier(A), B) = B)))) <=> (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (apply_as_element(the_carrier(A), the_carrier(A), identity_on_carrier(A), B) = B))))),
% 284.34/181.70 inference(rewrite,[status(thm)],[])).
% 284.34/181.70 tff(6,plain,
% 284.34/181.70 ((~![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => (apply_as_element(the_carrier(A), the_carrier(A), identity_on_carrier(A), B) = B)))) <=> (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (apply_as_element(the_carrier(A), the_carrier(A), identity_on_carrier(A), B) = B))))),
% 284.34/181.70 inference(rewrite,[status(thm)],[])).
% 284.34/181.70 tff(7,axiom,(~![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => (apply_as_element(the_carrier(A), the_carrier(A), identity_on_carrier(A), B) = B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t91_tmap_1')).
% 284.34/181.70 tff(8,plain,
% 284.34/181.70 (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (apply_as_element(the_carrier(A), the_carrier(A), identity_on_carrier(A), B) = B)))),
% 284.34/181.70 inference(modus_ponens,[status(thm)],[7, 6])).
% 284.34/181.70 tff(9,plain,
% 284.34/181.70 (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (apply_as_element(the_carrier(A), the_carrier(A), identity_on_carrier(A), B) = B)))),
% 284.34/181.70 inference(modus_ponens,[status(thm)],[8, 5])).
% 284.34/181.70 tff(10,plain,
% 284.34/181.70 (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (apply_as_element(the_carrier(A), the_carrier(A), identity_on_carrier(A), B) = B)))),
% 284.34/181.70 inference(modus_ponens,[status(thm)],[9, 5])).
% 284.34/181.70 tff(11,plain,
% 284.34/181.70 (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (apply_as_element(the_carrier(A), the_carrier(A), identity_on_carrier(A), B) = B)))),
% 284.34/181.70 inference(modus_ponens,[status(thm)],[10, 5])).
% 284.34/181.70 tff(12,plain,
% 284.34/181.70 (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (apply_as_element(the_carrier(A), the_carrier(A), identity_on_carrier(A), B) = B)))),
% 284.34/181.70 inference(modus_ponens,[status(thm)],[11, 5])).
% 284.34/181.70 tff(13,plain,
% 284.34/181.70 (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (apply_as_element(the_carrier(A), the_carrier(A), identity_on_carrier(A), B) = B)))),
% 284.34/181.70 inference(modus_ponens,[status(thm)],[12, 5])).
% 284.34/181.70 tff(14,plain,
% 284.34/181.70 (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (apply_as_element(the_carrier(A), the_carrier(A), identity_on_carrier(A), B) = B)))),
% 284.34/181.70 inference(modus_ponens,[status(thm)],[13, 5])).
% 284.34/181.70 tff(15,plain,
% 284.34/181.70 ((~empty_carrier(A!407)) & one_sorted_str(A!407) & (~((~element(B!408, the_carrier(A!407))) | (apply_as_element(the_carrier(A!407), the_carrier(A!407), identity_on_carrier(A!407), B!408) = B!408)))),
% 284.34/181.70 inference(modus_ponens,[status(thm)],[14, 4])).
% 284.34/181.70 tff(16,plain,
% 284.34/181.70 (one_sorted_str(A!407)),
% 284.34/181.70 inference(and_elim,[status(thm)],[15])).
% 284.34/181.70 tff(17,plain,
% 284.34/181.70 (^[A: $i] : refl(((~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)))))) <=> ((~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)))))))),
% 284.34/181.70 inference(bind,[status(th)],[])).
% 284.34/181.70 tff(18,plain,
% 284.34/181.70 (![A: $i] : ((~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)))))) <=> ![A: $i] : ((~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))))))),
% 284.34/181.70 inference(quant_intro,[status(thm)],[17])).
% 284.34/181.70 tff(19,plain,
% 284.34/181.70 (^[A: $i] : rewrite(((~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)))) <=> ((~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)))))))),
% 284.34/181.70 inference(bind,[status(th)],[])).
% 284.34/181.70 tff(20,plain,
% 284.34/181.70 (![A: $i] : ((~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)))) <=> ![A: $i] : ((~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))))))),
% 284.34/181.70 inference(quant_intro,[status(thm)],[19])).
% 284.34/181.70 tff(21,plain,
% 284.34/181.70 (![A: $i] : ((~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)))) <=> ![A: $i] : ((~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))))),
% 284.34/181.70 inference(rewrite,[status(thm)],[])).
% 284.34/181.70 tff(22,plain,
% 284.34/181.70 (^[A: $i] : trans(monotonicity(rewrite(((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))) <=> (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)))), ((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)))) <=> (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)))))), rewrite((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)))) <=> ((~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))))), ((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)))) <=> ((~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))))))),
% 284.34/181.70 inference(bind,[status(th)],[])).
% 284.34/181.70 tff(23,plain,
% 284.34/181.70 (![A: $i] : (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)))) <=> ![A: $i] : ((~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))))),
% 284.34/181.70 inference(quant_intro,[status(thm)],[22])).
% 284.34/181.70 tff(24,axiom,(![A: $i] : (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))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k7_grcat_1')).
% 284.34/181.70 tff(25,plain,
% 284.34/181.70 (![A: $i] : ((~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))))),
% 284.34/181.70 inference(modus_ponens,[status(thm)],[24, 23])).
% 284.34/181.70 tff(26,plain,
% 284.34/181.70 (![A: $i] : ((~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))))),
% 284.34/181.70 inference(modus_ponens,[status(thm)],[25, 21])).
% 284.34/181.70 tff(27,plain,(
% 284.34/181.70 ![A: $i] : ((~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))))),
% 284.34/181.70 inference(skolemize,[status(sab)],[26])).
% 284.34/181.70 tff(28,plain,
% 284.34/181.70 (![A: $i] : ((~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))))))),
% 284.34/181.70 inference(modus_ponens,[status(thm)],[27, 20])).
% 284.34/181.70 tff(29,plain,
% 284.34/181.70 (![A: $i] : ((~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))))))),
% 284.34/181.70 inference(modus_ponens,[status(thm)],[28, 18])).
% 284.34/181.70 tff(30,plain,
% 284.34/181.70 (((~![A: $i] : ((~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))))))) | ((~one_sorted_str(A!407)) | (~((~function(identity_on_carrier(A!407))) | (~quasi_total(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))) | (~relation_of2_as_subset(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))))))) <=> ((~![A: $i] : ((~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))))))) | (~one_sorted_str(A!407)) | (~((~function(identity_on_carrier(A!407))) | (~quasi_total(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))) | (~relation_of2_as_subset(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))))))),
% 284.34/181.70 inference(rewrite,[status(thm)],[])).
% 284.34/181.70 tff(31,plain,
% 284.34/181.70 ((~![A: $i] : ((~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))))))) | ((~one_sorted_str(A!407)) | (~((~function(identity_on_carrier(A!407))) | (~quasi_total(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))) | (~relation_of2_as_subset(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))))))),
% 284.34/181.70 inference(quant_inst,[status(thm)],[])).
% 284.34/181.70 tff(32,plain,
% 284.34/181.70 ((~![A: $i] : ((~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))))))) | (~one_sorted_str(A!407)) | (~((~function(identity_on_carrier(A!407))) | (~quasi_total(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))) | (~relation_of2_as_subset(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407)))))),
% 284.34/181.70 inference(modus_ponens,[status(thm)],[31, 30])).
% 284.34/181.70 tff(33,plain,
% 284.34/181.70 (~((~function(identity_on_carrier(A!407))) | (~quasi_total(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))) | (~relation_of2_as_subset(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))))),
% 284.34/181.70 inference(unit_resolution,[status(thm)],[32, 29, 16])).
% 284.34/181.70 tff(34,plain,
% 284.34/181.70 (((~function(identity_on_carrier(A!407))) | (~quasi_total(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))) | (~relation_of2_as_subset(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407)))) | quasi_total(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))),
% 284.34/181.70 inference(tautology,[status(thm)],[])).
% 284.34/181.70 tff(35,plain,
% 284.34/181.70 (quasi_total(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))),
% 284.34/181.70 inference(unit_resolution,[status(thm)],[34, 33])).
% 284.34/181.70 tff(36,plain,
% 284.34/181.70 (((~function(identity_on_carrier(A!407))) | (~quasi_total(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))) | (~relation_of2_as_subset(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407)))) | function(identity_on_carrier(A!407))),
% 284.34/181.70 inference(tautology,[status(thm)],[])).
% 284.34/181.70 tff(37,plain,
% 284.34/181.70 (function(identity_on_carrier(A!407))),
% 284.34/181.70 inference(unit_resolution,[status(thm)],[36, 33])).
% 284.34/181.70 tff(38,plain,
% 284.34/181.70 (^[A: $i] : refl(((~one_sorted_str(A)) | (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A)))) <=> ((~one_sorted_str(A)) | (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A)))))),
% 284.34/181.70 inference(bind,[status(th)],[])).
% 284.34/181.70 tff(39,plain,
% 284.34/181.70 (![A: $i] : ((~one_sorted_str(A)) | (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A)))) <=> ![A: $i] : ((~one_sorted_str(A)) | (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A))))),
% 284.34/181.70 inference(quant_intro,[status(thm)],[38])).
% 284.34/181.70 tff(40,plain,
% 284.34/181.70 (![A: $i] : ((~one_sorted_str(A)) | (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A)))) <=> ![A: $i] : ((~one_sorted_str(A)) | (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A))))),
% 284.34/181.70 inference(rewrite,[status(thm)],[])).
% 284.34/181.70 tff(41,plain,
% 284.34/181.70 (^[A: $i] : rewrite((one_sorted_str(A) => (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A)))) <=> ((~one_sorted_str(A)) | (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A)))))),
% 284.34/181.70 inference(bind,[status(th)],[])).
% 284.34/181.70 tff(42,plain,
% 284.34/181.70 (![A: $i] : (one_sorted_str(A) => (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A)))) <=> ![A: $i] : ((~one_sorted_str(A)) | (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A))))),
% 284.34/181.70 inference(quant_intro,[status(thm)],[41])).
% 284.34/181.70 tff(43,axiom,(![A: $i] : (one_sorted_str(A) => (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d11_grcat_1')).
% 284.34/181.70 tff(44,plain,
% 284.34/181.70 (![A: $i] : ((~one_sorted_str(A)) | (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A))))),
% 284.34/181.70 inference(modus_ponens,[status(thm)],[43, 42])).
% 284.34/181.70 tff(45,plain,
% 284.34/181.70 (![A: $i] : ((~one_sorted_str(A)) | (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A))))),
% 284.34/181.70 inference(modus_ponens,[status(thm)],[44, 40])).
% 284.34/181.70 tff(46,plain,(
% 284.34/181.70 ![A: $i] : ((~one_sorted_str(A)) | (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A))))),
% 284.34/181.70 inference(skolemize,[status(sab)],[45])).
% 284.34/181.70 tff(47,plain,
% 284.34/181.70 (![A: $i] : ((~one_sorted_str(A)) | (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A))))),
% 284.34/181.70 inference(modus_ponens,[status(thm)],[46, 39])).
% 284.34/181.70 tff(48,plain,
% 284.34/181.70 (((~![A: $i] : ((~one_sorted_str(A)) | (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A))))) | ((~one_sorted_str(A!407)) | (identity_on_carrier(A!407) = identity_as_relation_of(the_carrier(A!407))))) <=> ((~![A: $i] : ((~one_sorted_str(A)) | (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A))))) | (~one_sorted_str(A!407)) | (identity_on_carrier(A!407) = identity_as_relation_of(the_carrier(A!407))))),
% 284.34/181.70 inference(rewrite,[status(thm)],[])).
% 284.34/181.70 tff(49,plain,
% 284.34/181.70 ((~![A: $i] : ((~one_sorted_str(A)) | (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A))))) | ((~one_sorted_str(A!407)) | (identity_on_carrier(A!407) = identity_as_relation_of(the_carrier(A!407))))),
% 284.34/181.70 inference(quant_inst,[status(thm)],[])).
% 284.34/181.70 tff(50,plain,
% 284.34/181.70 ((~![A: $i] : ((~one_sorted_str(A)) | (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A))))) | (~one_sorted_str(A!407)) | (identity_on_carrier(A!407) = identity_as_relation_of(the_carrier(A!407)))),
% 284.34/181.70 inference(modus_ponens,[status(thm)],[49, 48])).
% 284.34/181.70 tff(51,plain,
% 284.34/181.70 (identity_on_carrier(A!407) = identity_as_relation_of(the_carrier(A!407))),
% 284.34/181.70 inference(unit_resolution,[status(thm)],[50, 47, 16])).
% 284.34/181.70 tff(52,plain,
% 284.34/181.70 (identity_as_relation_of(the_carrier(A!407)) = identity_on_carrier(A!407)),
% 284.34/181.70 inference(symmetry,[status(thm)],[51])).
% 284.34/181.70 tff(53,plain,
% 284.34/181.70 (relation_of2(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407)) <=> relation_of2(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))),
% 284.34/181.70 inference(monotonicity,[status(thm)],[52])).
% 284.34/181.70 tff(54,plain,
% 284.34/181.70 (^[A: $i, B: $i, C: $i] : refl((relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)))),
% 284.34/181.70 inference(bind,[status(th)],[])).
% 284.34/181.70 tff(55,plain,
% 284.34/181.70 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 284.34/181.71 inference(quant_intro,[status(thm)],[54])).
% 284.34/181.71 tff(56,plain,
% 284.34/181.71 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 284.34/181.71 inference(rewrite,[status(thm)],[])).
% 284.34/181.71 tff(57,axiom,(![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 284.34/181.71 tff(58,plain,
% 284.34/181.71 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 284.34/181.71 inference(modus_ponens,[status(thm)],[57, 56])).
% 284.34/181.71 tff(59,plain,(
% 284.34/181.71 ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 284.34/181.71 inference(skolemize,[status(sab)],[58])).
% 284.34/181.71 tff(60,plain,
% 284.34/181.71 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 284.34/181.71 inference(modus_ponens,[status(thm)],[59, 55])).
% 284.34/181.71 tff(61,plain,
% 284.34/181.71 ((~![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))) | (relation_of2_as_subset(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407)) <=> relation_of2(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407)))),
% 284.34/181.71 inference(quant_inst,[status(thm)],[])).
% 284.34/181.71 tff(62,plain,
% 284.34/181.71 (relation_of2_as_subset(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407)) <=> relation_of2(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407))),
% 284.34/181.71 inference(unit_resolution,[status(thm)],[61, 60])).
% 284.34/181.71 tff(63,plain,
% 284.34/181.71 (^[A: $i] : refl((~((~v1_partfun1(identity_as_relation_of(A), A, A)) | (~relation_of2_as_subset(identity_as_relation_of(A), A, A)))) <=> (~((~v1_partfun1(identity_as_relation_of(A), A, A)) | (~relation_of2_as_subset(identity_as_relation_of(A), A, A)))))),
% 284.34/181.71 inference(bind,[status(th)],[])).
% 284.34/181.71 tff(64,plain,
% 284.34/181.71 (![A: $i] : (~((~v1_partfun1(identity_as_relation_of(A), A, A)) | (~relation_of2_as_subset(identity_as_relation_of(A), A, A)))) <=> ![A: $i] : (~((~v1_partfun1(identity_as_relation_of(A), A, A)) | (~relation_of2_as_subset(identity_as_relation_of(A), A, A))))),
% 284.34/181.71 inference(quant_intro,[status(thm)],[63])).
% 284.34/181.71 tff(65,plain,
% 284.34/181.71 (^[A: $i] : rewrite((v1_partfun1(identity_as_relation_of(A), A, A) & relation_of2_as_subset(identity_as_relation_of(A), A, A)) <=> (~((~v1_partfun1(identity_as_relation_of(A), A, A)) | (~relation_of2_as_subset(identity_as_relation_of(A), A, A)))))),
% 284.34/181.71 inference(bind,[status(th)],[])).
% 284.34/181.71 tff(66,plain,
% 284.34/181.71 (![A: $i] : (v1_partfun1(identity_as_relation_of(A), A, A) & relation_of2_as_subset(identity_as_relation_of(A), A, A)) <=> ![A: $i] : (~((~v1_partfun1(identity_as_relation_of(A), A, A)) | (~relation_of2_as_subset(identity_as_relation_of(A), A, A))))),
% 284.34/181.71 inference(quant_intro,[status(thm)],[65])).
% 284.34/181.71 tff(67,plain,
% 284.34/181.71 (![A: $i] : (v1_partfun1(identity_as_relation_of(A), A, A) & relation_of2_as_subset(identity_as_relation_of(A), A, A)) <=> ![A: $i] : (v1_partfun1(identity_as_relation_of(A), A, A) & relation_of2_as_subset(identity_as_relation_of(A), A, A))),
% 284.34/181.71 inference(rewrite,[status(thm)],[])).
% 284.34/181.71 tff(68,axiom,(![A: $i] : (v1_partfun1(identity_as_relation_of(A), A, A) & relation_of2_as_subset(identity_as_relation_of(A), A, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k6_partfun1')).
% 284.34/181.71 tff(69,plain,
% 284.34/181.71 (![A: $i] : (v1_partfun1(identity_as_relation_of(A), A, A) & relation_of2_as_subset(identity_as_relation_of(A), A, A))),
% 284.34/181.71 inference(modus_ponens,[status(thm)],[68, 67])).
% 284.34/181.71 tff(70,plain,(
% 284.34/181.71 ![A: $i] : (v1_partfun1(identity_as_relation_of(A), A, A) & relation_of2_as_subset(identity_as_relation_of(A), A, A))),
% 284.34/181.71 inference(skolemize,[status(sab)],[69])).
% 284.34/181.71 tff(71,plain,
% 284.34/181.71 (![A: $i] : (~((~v1_partfun1(identity_as_relation_of(A), A, A)) | (~relation_of2_as_subset(identity_as_relation_of(A), A, A))))),
% 284.34/181.71 inference(modus_ponens,[status(thm)],[70, 66])).
% 284.34/181.71 tff(72,plain,
% 284.34/181.71 (![A: $i] : (~((~v1_partfun1(identity_as_relation_of(A), A, A)) | (~relation_of2_as_subset(identity_as_relation_of(A), A, A))))),
% 284.34/181.71 inference(modus_ponens,[status(thm)],[71, 64])).
% 284.34/181.71 tff(73,plain,
% 284.34/181.71 (((~![A: $i] : (~((~v1_partfun1(identity_as_relation_of(A), A, A)) | (~relation_of2_as_subset(identity_as_relation_of(A), A, A))))) | (~((~relation_of2_as_subset(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407))) | (~v1_partfun1(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407)))))) <=> ((~![A: $i] : (~((~v1_partfun1(identity_as_relation_of(A), A, A)) | (~relation_of2_as_subset(identity_as_relation_of(A), A, A))))) | (~((~relation_of2_as_subset(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407))) | (~v1_partfun1(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407))))))),
% 284.34/181.71 inference(rewrite,[status(thm)],[])).
% 284.34/181.71 tff(74,plain,
% 284.34/181.71 ((~((~v1_partfun1(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407))) | (~relation_of2_as_subset(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407))))) <=> (~((~relation_of2_as_subset(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407))) | (~v1_partfun1(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407)))))),
% 284.34/181.71 inference(rewrite,[status(thm)],[])).
% 284.34/181.71 tff(75,plain,
% 284.34/181.71 (((~![A: $i] : (~((~v1_partfun1(identity_as_relation_of(A), A, A)) | (~relation_of2_as_subset(identity_as_relation_of(A), A, A))))) | (~((~v1_partfun1(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407))) | (~relation_of2_as_subset(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407)))))) <=> ((~![A: $i] : (~((~v1_partfun1(identity_as_relation_of(A), A, A)) | (~relation_of2_as_subset(identity_as_relation_of(A), A, A))))) | (~((~relation_of2_as_subset(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407))) | (~v1_partfun1(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407))))))),
% 284.34/181.71 inference(monotonicity,[status(thm)],[74])).
% 284.34/181.71 tff(76,plain,
% 284.34/181.71 (((~![A: $i] : (~((~v1_partfun1(identity_as_relation_of(A), A, A)) | (~relation_of2_as_subset(identity_as_relation_of(A), A, A))))) | (~((~v1_partfun1(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407))) | (~relation_of2_as_subset(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407)))))) <=> ((~![A: $i] : (~((~v1_partfun1(identity_as_relation_of(A), A, A)) | (~relation_of2_as_subset(identity_as_relation_of(A), A, A))))) | (~((~relation_of2_as_subset(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407))) | (~v1_partfun1(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407))))))),
% 284.34/181.71 inference(transitivity,[status(thm)],[75, 73])).
% 284.34/181.71 tff(77,plain,
% 284.34/181.71 ((~![A: $i] : (~((~v1_partfun1(identity_as_relation_of(A), A, A)) | (~relation_of2_as_subset(identity_as_relation_of(A), A, A))))) | (~((~v1_partfun1(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407))) | (~relation_of2_as_subset(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407)))))),
% 284.34/181.71 inference(quant_inst,[status(thm)],[])).
% 284.34/181.71 tff(78,plain,
% 284.34/181.71 ((~![A: $i] : (~((~v1_partfun1(identity_as_relation_of(A), A, A)) | (~relation_of2_as_subset(identity_as_relation_of(A), A, A))))) | (~((~relation_of2_as_subset(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407))) | (~v1_partfun1(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407)))))),
% 284.34/181.71 inference(modus_ponens,[status(thm)],[77, 76])).
% 284.34/181.71 tff(79,plain,
% 284.34/181.71 (~((~relation_of2_as_subset(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407))) | (~v1_partfun1(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407))))),
% 284.34/181.71 inference(unit_resolution,[status(thm)],[78, 72])).
% 284.34/181.71 tff(80,plain,
% 284.34/181.71 (((~relation_of2_as_subset(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407))) | (~v1_partfun1(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407)))) | relation_of2_as_subset(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407))),
% 284.34/181.71 inference(tautology,[status(thm)],[])).
% 284.34/181.71 tff(81,plain,
% 284.34/181.71 (relation_of2_as_subset(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407))),
% 284.34/181.71 inference(unit_resolution,[status(thm)],[80, 79])).
% 284.34/181.71 tff(82,plain,
% 284.34/181.71 ((~(relation_of2_as_subset(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407)) <=> relation_of2(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407)))) | (~relation_of2_as_subset(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407))) | relation_of2(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407))),
% 284.34/181.71 inference(tautology,[status(thm)],[])).
% 284.34/181.71 tff(83,plain,
% 284.34/181.71 (relation_of2(identity_as_relation_of(the_carrier(A!407)), the_carrier(A!407), the_carrier(A!407))),
% 284.34/181.71 inference(unit_resolution,[status(thm)],[82, 81, 62])).
% 284.34/181.71 tff(84,plain,
% 284.34/181.71 (relation_of2(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))),
% 284.34/181.71 inference(modus_ponens,[status(thm)],[83, 53])).
% 284.34/181.71 tff(85,plain,
% 284.34/181.71 (~empty_carrier(A!407)),
% 284.34/181.71 inference(and_elim,[status(thm)],[15])).
% 284.34/181.71 tff(86,plain,
% 284.34/181.71 (^[A: $i] : refl((empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A))) <=> (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A))))),
% 284.34/181.71 inference(bind,[status(th)],[])).
% 284.34/181.71 tff(87,plain,
% 284.34/181.71 (![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A))) <=> ![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 284.34/181.71 inference(quant_intro,[status(thm)],[86])).
% 284.34/181.71 tff(88,plain,
% 284.34/181.71 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & one_sorted_str(A)) <=> (~(empty_carrier(A) | (~one_sorted_str(A))))), ((~((~empty_carrier(A)) & one_sorted_str(A))) <=> (~(~(empty_carrier(A) | (~one_sorted_str(A))))))), rewrite((~(~(empty_carrier(A) | (~one_sorted_str(A))))) <=> (empty_carrier(A) | (~one_sorted_str(A)))), ((~((~empty_carrier(A)) & one_sorted_str(A))) <=> (empty_carrier(A) | (~one_sorted_str(A))))), (((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> ((~empty(the_carrier(A))) | (empty_carrier(A) | (~one_sorted_str(A)))))), rewrite(((~empty(the_carrier(A))) | (empty_carrier(A) | (~one_sorted_str(A)))) <=> (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))), (((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))))),
% 284.34/181.71 inference(bind,[status(th)],[])).
% 284.34/181.71 tff(89,plain,
% 284.34/181.71 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> ![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 284.34/181.71 inference(quant_intro,[status(thm)],[88])).
% 284.34/181.71 tff(90,plain,
% 284.34/181.71 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> ![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 284.34/181.71 inference(rewrite,[status(thm)],[])).
% 284.34/181.71 tff(91,plain,
% 284.34/181.71 (^[A: $i] : rewrite((((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(the_carrier(A)))) <=> ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))))),
% 284.34/181.71 inference(bind,[status(th)],[])).
% 284.34/181.71 tff(92,plain,
% 284.34/181.71 (![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(the_carrier(A)))) <=> ![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 284.34/181.71 inference(quant_intro,[status(thm)],[91])).
% 284.34/181.71 tff(93,axiom,(![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(the_carrier(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_struct_0')).
% 284.34/181.71 tff(94,plain,
% 284.34/181.71 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 284.34/181.71 inference(modus_ponens,[status(thm)],[93, 92])).
% 284.34/181.71 tff(95,plain,
% 284.34/181.71 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 284.34/181.71 inference(modus_ponens,[status(thm)],[94, 90])).
% 284.34/181.71 tff(96,plain,(
% 284.34/181.71 ![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 284.34/181.71 inference(skolemize,[status(sab)],[95])).
% 284.34/181.71 tff(97,plain,
% 284.34/181.71 (![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 284.34/181.71 inference(modus_ponens,[status(thm)],[96, 89])).
% 284.34/181.71 tff(98,plain,
% 284.34/181.71 (![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 284.34/181.71 inference(modus_ponens,[status(thm)],[97, 87])).
% 284.34/181.71 tff(99,plain,
% 284.34/181.71 (((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!407) | (~one_sorted_str(A!407)) | (~empty(the_carrier(A!407))))) <=> ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | empty_carrier(A!407) | (~one_sorted_str(A!407)) | (~empty(the_carrier(A!407))))),
% 284.34/181.71 inference(rewrite,[status(thm)],[])).
% 284.34/181.71 tff(100,plain,
% 284.34/181.71 ((empty_carrier(A!407) | (~empty(the_carrier(A!407))) | (~one_sorted_str(A!407))) <=> (empty_carrier(A!407) | (~one_sorted_str(A!407)) | (~empty(the_carrier(A!407))))),
% 284.34/181.71 inference(rewrite,[status(thm)],[])).
% 284.34/181.71 tff(101,plain,
% 284.34/181.71 (((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!407) | (~empty(the_carrier(A!407))) | (~one_sorted_str(A!407)))) <=> ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!407) | (~one_sorted_str(A!407)) | (~empty(the_carrier(A!407)))))),
% 284.34/181.71 inference(monotonicity,[status(thm)],[100])).
% 284.34/181.71 tff(102,plain,
% 284.34/181.71 (((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!407) | (~empty(the_carrier(A!407))) | (~one_sorted_str(A!407)))) <=> ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | empty_carrier(A!407) | (~one_sorted_str(A!407)) | (~empty(the_carrier(A!407))))),
% 284.34/181.71 inference(transitivity,[status(thm)],[101, 99])).
% 284.34/181.71 tff(103,plain,
% 284.34/181.71 ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!407) | (~empty(the_carrier(A!407))) | (~one_sorted_str(A!407)))),
% 284.34/181.71 inference(quant_inst,[status(thm)],[])).
% 284.34/181.71 tff(104,plain,
% 284.34/181.71 ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | empty_carrier(A!407) | (~one_sorted_str(A!407)) | (~empty(the_carrier(A!407)))),
% 284.34/181.71 inference(modus_ponens,[status(thm)],[103, 102])).
% 284.34/181.71 tff(105,plain,
% 284.34/181.71 (~empty(the_carrier(A!407))),
% 284.34/181.71 inference(unit_resolution,[status(thm)],[104, 98, 85, 16])).
% 284.34/181.71 tff(106,plain,
% 284.34/181.71 (~((~element(B!408, the_carrier(A!407))) | (apply_as_element(the_carrier(A!407), the_carrier(A!407), identity_on_carrier(A!407), B!408) = B!408))),
% 284.34/181.71 inference(and_elim,[status(thm)],[15])).
% 284.34/181.71 tff(107,plain,
% 284.34/181.71 (element(B!408, the_carrier(A!407))),
% 284.34/181.71 inference(or_elim,[status(thm)],[106])).
% 284.34/181.71 tff(108,plain,
% 284.34/181.71 (^[A: $i, B: $i] : refl((in(A, B) | empty(B) | (~element(A, B))) <=> (in(A, B) | empty(B) | (~element(A, B))))),
% 284.34/181.71 inference(bind,[status(th)],[])).
% 284.34/181.71 tff(109,plain,
% 284.34/181.71 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B))) <=> ![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 284.34/181.71 inference(quant_intro,[status(thm)],[108])).
% 284.34/181.71 tff(110,plain,
% 284.34/181.71 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B))) <=> ![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 284.34/181.71 inference(rewrite,[status(thm)],[])).
% 284.34/181.71 tff(111,plain,
% 284.34/181.71 (^[A: $i, B: $i] : rewrite((element(A, B) => (empty(B) | in(A, B))) <=> (in(A, B) | empty(B) | (~element(A, B))))),
% 284.34/181.71 inference(bind,[status(th)],[])).
% 284.34/181.71 tff(112,plain,
% 284.34/181.71 (![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B))) <=> ![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 284.34/181.71 inference(quant_intro,[status(thm)],[111])).
% 284.34/181.71 tff(113,axiom,(![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_subset')).
% 284.34/181.71 tff(114,plain,
% 284.34/181.71 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 284.34/181.71 inference(modus_ponens,[status(thm)],[113, 112])).
% 284.34/181.71 tff(115,plain,
% 284.34/181.71 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 284.34/181.71 inference(modus_ponens,[status(thm)],[114, 110])).
% 284.34/181.71 tff(116,plain,(
% 284.34/181.71 ![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 284.34/181.71 inference(skolemize,[status(sab)],[115])).
% 284.34/181.71 tff(117,plain,
% 284.34/181.71 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 284.34/181.71 inference(modus_ponens,[status(thm)],[116, 109])).
% 284.34/181.71 tff(118,plain,
% 284.34/181.71 (((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | ((~element(B!408, the_carrier(A!407))) | empty(the_carrier(A!407)) | in(B!408, the_carrier(A!407)))) <=> ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (~element(B!408, the_carrier(A!407))) | empty(the_carrier(A!407)) | in(B!408, the_carrier(A!407)))),
% 284.34/181.71 inference(rewrite,[status(thm)],[])).
% 284.34/181.71 tff(119,plain,
% 284.34/181.71 ((in(B!408, the_carrier(A!407)) | empty(the_carrier(A!407)) | (~element(B!408, the_carrier(A!407)))) <=> ((~element(B!408, the_carrier(A!407))) | empty(the_carrier(A!407)) | in(B!408, the_carrier(A!407)))),
% 284.34/181.71 inference(rewrite,[status(thm)],[])).
% 284.34/181.71 tff(120,plain,
% 284.34/181.71 (((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (in(B!408, the_carrier(A!407)) | empty(the_carrier(A!407)) | (~element(B!408, the_carrier(A!407))))) <=> ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | ((~element(B!408, the_carrier(A!407))) | empty(the_carrier(A!407)) | in(B!408, the_carrier(A!407))))),
% 284.34/181.71 inference(monotonicity,[status(thm)],[119])).
% 284.34/181.71 tff(121,plain,
% 284.34/181.71 (((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (in(B!408, the_carrier(A!407)) | empty(the_carrier(A!407)) | (~element(B!408, the_carrier(A!407))))) <=> ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (~element(B!408, the_carrier(A!407))) | empty(the_carrier(A!407)) | in(B!408, the_carrier(A!407)))),
% 284.34/181.71 inference(transitivity,[status(thm)],[120, 118])).
% 284.34/181.71 tff(122,plain,
% 284.34/181.71 ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (in(B!408, the_carrier(A!407)) | empty(the_carrier(A!407)) | (~element(B!408, the_carrier(A!407))))),
% 284.34/181.71 inference(quant_inst,[status(thm)],[])).
% 284.34/181.71 tff(123,plain,
% 284.34/181.71 ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (~element(B!408, the_carrier(A!407))) | empty(the_carrier(A!407)) | in(B!408, the_carrier(A!407))),
% 284.34/181.71 inference(modus_ponens,[status(thm)],[122, 121])).
% 284.34/181.71 tff(124,plain,
% 284.34/181.71 (in(B!408, the_carrier(A!407))),
% 284.34/181.71 inference(unit_resolution,[status(thm)],[123, 117, 107, 105])).
% 284.34/181.71 tff(125,plain,
% 284.34/181.71 (^[A: $i, B: $i] : refl(((~in(B, A)) | (apply(identity_relation(A), B) = B)) <=> ((~in(B, A)) | (apply(identity_relation(A), B) = B)))),
% 284.34/181.71 inference(bind,[status(th)],[])).
% 284.34/181.71 tff(126,plain,
% 284.34/181.71 (![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B)) <=> ![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 284.34/181.71 inference(quant_intro,[status(thm)],[125])).
% 284.34/181.71 tff(127,plain,
% 284.34/181.71 (![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B)) <=> ![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 284.34/181.71 inference(rewrite,[status(thm)],[])).
% 284.34/181.71 tff(128,plain,
% 284.34/181.71 (^[A: $i, B: $i] : rewrite((in(B, A) => (apply(identity_relation(A), B) = B)) <=> ((~in(B, A)) | (apply(identity_relation(A), B) = B)))),
% 284.34/181.71 inference(bind,[status(th)],[])).
% 284.34/181.71 tff(129,plain,
% 284.34/181.71 (![A: $i, B: $i] : (in(B, A) => (apply(identity_relation(A), B) = B)) <=> ![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 284.34/181.71 inference(quant_intro,[status(thm)],[128])).
% 284.34/181.71 tff(130,axiom,(![A: $i, B: $i] : (in(B, A) => (apply(identity_relation(A), B) = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t35_funct_1')).
% 284.34/181.71 tff(131,plain,
% 284.34/181.71 (![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 284.34/181.71 inference(modus_ponens,[status(thm)],[130, 129])).
% 284.34/181.71 tff(132,plain,
% 284.34/181.71 (![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 284.34/181.72 inference(modus_ponens,[status(thm)],[131, 127])).
% 284.34/181.72 tff(133,plain,(
% 284.34/181.72 ![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 284.34/181.72 inference(skolemize,[status(sab)],[132])).
% 284.34/181.72 tff(134,plain,
% 284.34/181.72 (![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 284.34/181.72 inference(modus_ponens,[status(thm)],[133, 126])).
% 284.34/181.72 tff(135,plain,
% 284.34/181.72 (((~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))) | ((~in(B!408, the_carrier(A!407))) | (apply(identity_relation(the_carrier(A!407)), B!408) = B!408))) <=> ((~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))) | (~in(B!408, the_carrier(A!407))) | (apply(identity_relation(the_carrier(A!407)), B!408) = B!408))),
% 284.34/181.72 inference(rewrite,[status(thm)],[])).
% 284.34/181.72 tff(136,plain,
% 284.34/181.72 ((~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))) | ((~in(B!408, the_carrier(A!407))) | (apply(identity_relation(the_carrier(A!407)), B!408) = B!408))),
% 284.34/181.72 inference(quant_inst,[status(thm)],[])).
% 284.34/181.72 tff(137,plain,
% 284.34/181.72 ((~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))) | (~in(B!408, the_carrier(A!407))) | (apply(identity_relation(the_carrier(A!407)), B!408) = B!408)),
% 284.34/181.72 inference(modus_ponens,[status(thm)],[136, 135])).
% 284.34/181.72 tff(138,plain,
% 284.34/181.72 (apply(identity_relation(the_carrier(A!407)), B!408) = B!408),
% 284.34/181.72 inference(unit_resolution,[status(thm)],[137, 134, 124])).
% 284.34/181.72 tff(139,plain,
% 284.34/181.72 (^[A: $i] : refl((identity_as_relation_of(A) = identity_relation(A)) <=> (identity_as_relation_of(A) = identity_relation(A)))),
% 284.34/181.72 inference(bind,[status(th)],[])).
% 284.34/181.72 tff(140,plain,
% 284.34/181.72 (![A: $i] : (identity_as_relation_of(A) = identity_relation(A)) <=> ![A: $i] : (identity_as_relation_of(A) = identity_relation(A))),
% 284.34/181.72 inference(quant_intro,[status(thm)],[139])).
% 284.34/181.72 tff(141,plain,
% 284.34/181.72 (![A: $i] : (identity_as_relation_of(A) = identity_relation(A)) <=> ![A: $i] : (identity_as_relation_of(A) = identity_relation(A))),
% 284.34/181.72 inference(rewrite,[status(thm)],[])).
% 284.34/181.72 tff(142,axiom,(![A: $i] : (identity_as_relation_of(A) = identity_relation(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k6_partfun1')).
% 284.34/181.72 tff(143,plain,
% 284.34/181.72 (![A: $i] : (identity_as_relation_of(A) = identity_relation(A))),
% 284.34/181.72 inference(modus_ponens,[status(thm)],[142, 141])).
% 284.34/181.72 tff(144,plain,(
% 284.34/181.72 ![A: $i] : (identity_as_relation_of(A) = identity_relation(A))),
% 284.34/181.72 inference(skolemize,[status(sab)],[143])).
% 284.34/181.72 tff(145,plain,
% 284.34/181.72 (![A: $i] : (identity_as_relation_of(A) = identity_relation(A))),
% 284.34/181.72 inference(modus_ponens,[status(thm)],[144, 140])).
% 284.34/181.72 tff(146,plain,
% 284.34/181.72 ((~![A: $i] : (identity_as_relation_of(A) = identity_relation(A))) | (identity_as_relation_of(the_carrier(A!407)) = identity_relation(the_carrier(A!407)))),
% 284.34/181.72 inference(quant_inst,[status(thm)],[])).
% 284.34/181.72 tff(147,plain,
% 284.34/181.72 (identity_as_relation_of(the_carrier(A!407)) = identity_relation(the_carrier(A!407))),
% 284.34/181.72 inference(unit_resolution,[status(thm)],[146, 145])).
% 284.34/181.72 tff(148,plain,
% 284.34/181.72 (identity_on_carrier(A!407) = identity_relation(the_carrier(A!407))),
% 284.34/181.72 inference(transitivity,[status(thm)],[51, 147])).
% 284.34/181.72 tff(149,plain,
% 284.34/181.72 (apply(identity_on_carrier(A!407), B!408) = apply(identity_relation(the_carrier(A!407)), B!408)),
% 284.34/181.72 inference(monotonicity,[status(thm)],[148])).
% 284.34/181.72 tff(150,plain,
% 284.34/181.72 (apply(identity_on_carrier(A!407), B!408) = B!408),
% 284.34/181.72 inference(transitivity,[status(thm)],[149, 138])).
% 284.34/181.72 tff(151,plain,
% 284.34/181.72 ((apply_as_element(the_carrier(A!407), the_carrier(A!407), identity_on_carrier(A!407), B!408) = apply(identity_on_carrier(A!407), B!408)) <=> (apply_as_element(the_carrier(A!407), the_carrier(A!407), identity_on_carrier(A!407), B!408) = B!408)),
% 284.34/181.72 inference(monotonicity,[status(thm)],[150])).
% 284.34/181.72 tff(152,plain,
% 284.34/181.72 ((apply_as_element(the_carrier(A!407), the_carrier(A!407), identity_on_carrier(A!407), B!408) = B!408) <=> (apply_as_element(the_carrier(A!407), the_carrier(A!407), identity_on_carrier(A!407), B!408) = apply(identity_on_carrier(A!407), B!408))),
% 284.34/181.72 inference(symmetry,[status(thm)],[151])).
% 284.34/181.72 tff(153,plain,
% 284.34/181.72 ((~(apply_as_element(the_carrier(A!407), the_carrier(A!407), identity_on_carrier(A!407), B!408) = B!408)) <=> (~(apply_as_element(the_carrier(A!407), the_carrier(A!407), identity_on_carrier(A!407), B!408) = apply(identity_on_carrier(A!407), B!408)))),
% 284.34/181.72 inference(monotonicity,[status(thm)],[152])).
% 284.34/181.72 tff(154,plain,
% 284.34/181.72 (~(apply_as_element(the_carrier(A!407), the_carrier(A!407), identity_on_carrier(A!407), B!408) = B!408)),
% 284.34/181.72 inference(or_elim,[status(thm)],[106])).
% 284.34/181.72 tff(155,plain,
% 284.34/181.72 (~(apply_as_element(the_carrier(A!407), the_carrier(A!407), identity_on_carrier(A!407), B!408) = apply(identity_on_carrier(A!407), B!408))),
% 284.34/181.72 inference(modus_ponens,[status(thm)],[154, 153])).
% 284.34/181.72 tff(156,plain,
% 284.34/181.72 (^[A: $i, B: $i, C: $i, D: $i] : refl((empty(A) | (apply_as_element(A, B, C, D) = apply(C, D)) | (~function(C)) | (~quasi_total(C, A, B)) | (~relation_of2(C, A, B)) | (~element(D, A))) <=> (empty(A) | (apply_as_element(A, B, C, D) = apply(C, D)) | (~function(C)) | (~quasi_total(C, A, B)) | (~relation_of2(C, A, B)) | (~element(D, A))))),
% 284.34/181.72 inference(bind,[status(th)],[])).
% 284.34/181.72 tff(157,plain,
% 284.34/181.72 (![A: $i, B: $i, C: $i, D: $i] : (empty(A) | (apply_as_element(A, B, C, D) = apply(C, D)) | (~function(C)) | (~quasi_total(C, A, B)) | (~relation_of2(C, A, B)) | (~element(D, A))) <=> ![A: $i, B: $i, C: $i, D: $i] : (empty(A) | (apply_as_element(A, B, C, D) = apply(C, D)) | (~function(C)) | (~quasi_total(C, A, B)) | (~relation_of2(C, A, B)) | (~element(D, A)))),
% 284.34/181.72 inference(quant_intro,[status(thm)],[156])).
% 284.34/181.72 tff(158,plain,
% 284.34/181.72 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty(A)) & function(C) & quasi_total(C, A, B) & relation_of2(C, A, B) & element(D, A)) <=> (~(empty(A) | (~function(C)) | (~quasi_total(C, A, B)) | (~relation_of2(C, A, B)) | (~element(D, A))))), ((~((~empty(A)) & function(C) & quasi_total(C, A, B) & relation_of2(C, A, B) & element(D, A))) <=> (~(~(empty(A) | (~function(C)) | (~quasi_total(C, A, B)) | (~relation_of2(C, A, B)) | (~element(D, A))))))), rewrite((~(~(empty(A) | (~function(C)) | (~quasi_total(C, A, B)) | (~relation_of2(C, A, B)) | (~element(D, A))))) <=> (empty(A) | (~function(C)) | (~quasi_total(C, A, B)) | (~relation_of2(C, A, B)) | (~element(D, A)))), ((~((~empty(A)) & function(C) & quasi_total(C, A, B) & relation_of2(C, A, B) & element(D, A))) <=> (empty(A) | (~function(C)) | (~quasi_total(C, A, B)) | (~relation_of2(C, A, B)) | (~element(D, A))))), (((~((~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))) <=> ((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))))), rewrite(((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))) <=> (empty(A) | (apply_as_element(A, B, C, D) = apply(C, D)) | (~function(C)) | (~quasi_total(C, A, B)) | (~relation_of2(C, A, B)) | (~element(D, A)))), (((~((~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))) <=> (empty(A) | (apply_as_element(A, B, C, D) = apply(C, D)) | (~function(C)) | (~quasi_total(C, A, B)) | (~relation_of2(C, A, B)) | (~element(D, A)))))),
% 284.34/181.72 inference(bind,[status(th)],[])).
% 284.34/181.72 tff(159,plain,
% 284.34/181.72 (![A: $i, B: $i, C: $i, D: $i] : ((~((~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))) <=> ![A: $i, B: $i, C: $i, D: $i] : (empty(A) | (apply_as_element(A, B, C, D) = apply(C, D)) | (~function(C)) | (~quasi_total(C, A, B)) | (~relation_of2(C, A, B)) | (~element(D, A)))),
% 284.34/181.72 inference(quant_intro,[status(thm)],[158])).
% 284.34/181.72 tff(160,plain,
% 284.34/181.72 (![A: $i, B: $i, C: $i, D: $i] : ((~((~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))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~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)))),
% 284.34/181.72 inference(rewrite,[status(thm)],[])).
% 284.34/181.72 tff(161,plain,
% 284.34/181.72 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~empty(A)) & function(C)) & quasi_total(C, A, B)) <=> ((~empty(A)) & function(C) & quasi_total(C, A, B))), (((((~empty(A)) & function(C)) & quasi_total(C, A, B)) & relation_of2(C, A, B)) <=> (((~empty(A)) & function(C) & quasi_total(C, A, B)) & relation_of2(C, A, B)))), rewrite((((~empty(A)) & function(C) & quasi_total(C, A, B)) & relation_of2(C, A, B)) <=> ((~empty(A)) & function(C) & quasi_total(C, A, B) & relation_of2(C, A, B))), (((((~empty(A)) & function(C)) & quasi_total(C, A, B)) & relation_of2(C, A, B)) <=> ((~empty(A)) & function(C) & quasi_total(C, A, B) & relation_of2(C, A, B)))), ((((((~empty(A)) & function(C)) & quasi_total(C, A, B)) & relation_of2(C, A, B)) & element(D, A)) <=> (((~empty(A)) & function(C) & quasi_total(C, A, B) & relation_of2(C, A, B)) & element(D, A)))), rewrite((((~empty(A)) & function(C) & quasi_total(C, A, B) & relation_of2(C, A, B)) & element(D, A)) <=> ((~empty(A)) & function(C) & quasi_total(C, A, B) & relation_of2(C, A, B) & element(D, A))), ((((((~empty(A)) & function(C)) & quasi_total(C, A, B)) & relation_of2(C, A, B)) & element(D, A)) <=> ((~empty(A)) & function(C) & quasi_total(C, A, B) & relation_of2(C, A, B) & element(D, A)))), (((((((~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))) <=> (((~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))))), rewrite((((~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))) <=> ((~((~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)))), (((((((~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))) <=> ((~((~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)))))),
% 284.34/181.72 inference(bind,[status(th)],[])).
% 284.34/181.72 tff(162,plain,
% 284.34/181.72 (![A: $i, B: $i, C: $i, D: $i] : ((((((~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))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~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)))),
% 284.34/181.72 inference(quant_intro,[status(thm)],[161])).
% 284.34/181.72 tff(163,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((((((~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)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k8_funct_2')).
% 284.34/181.72 tff(164,plain,
% 284.34/181.72 (![A: $i, B: $i, C: $i, D: $i] : ((~((~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)))),
% 284.34/181.72 inference(modus_ponens,[status(thm)],[163, 162])).
% 284.34/181.72 tff(165,plain,
% 284.34/181.72 (![A: $i, B: $i, C: $i, D: $i] : ((~((~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)))),
% 284.34/181.72 inference(modus_ponens,[status(thm)],[164, 160])).
% 284.34/181.72 tff(166,plain,(
% 284.34/181.72 ![A: $i, B: $i, C: $i, D: $i] : ((~((~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)))),
% 284.34/181.72 inference(skolemize,[status(sab)],[165])).
% 284.34/181.72 tff(167,plain,
% 284.34/181.72 (![A: $i, B: $i, C: $i, D: $i] : (empty(A) | (apply_as_element(A, B, C, D) = apply(C, D)) | (~function(C)) | (~quasi_total(C, A, B)) | (~relation_of2(C, A, B)) | (~element(D, A)))),
% 284.34/181.72 inference(modus_ponens,[status(thm)],[166, 159])).
% 284.34/181.72 tff(168,plain,
% 284.34/181.72 (![A: $i, B: $i, C: $i, D: $i] : (empty(A) | (apply_as_element(A, B, C, D) = apply(C, D)) | (~function(C)) | (~quasi_total(C, A, B)) | (~relation_of2(C, A, B)) | (~element(D, A)))),
% 284.34/181.72 inference(modus_ponens,[status(thm)],[167, 157])).
% 284.34/181.72 tff(169,plain,
% 284.34/181.72 (((~![A: $i, B: $i, C: $i, D: $i] : (empty(A) | (apply_as_element(A, B, C, D) = apply(C, D)) | (~function(C)) | (~quasi_total(C, A, B)) | (~relation_of2(C, A, B)) | (~element(D, A)))) | ((~element(B!408, the_carrier(A!407))) | empty(the_carrier(A!407)) | (~function(identity_on_carrier(A!407))) | (~quasi_total(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))) | (~relation_of2(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))) | (apply_as_element(the_carrier(A!407), the_carrier(A!407), identity_on_carrier(A!407), B!408) = apply(identity_on_carrier(A!407), B!408)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (empty(A) | (apply_as_element(A, B, C, D) = apply(C, D)) | (~function(C)) | (~quasi_total(C, A, B)) | (~relation_of2(C, A, B)) | (~element(D, A)))) | (~element(B!408, the_carrier(A!407))) | empty(the_carrier(A!407)) | (~function(identity_on_carrier(A!407))) | (~quasi_total(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))) | (~relation_of2(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))) | (apply_as_element(the_carrier(A!407), the_carrier(A!407), identity_on_carrier(A!407), B!408) = apply(identity_on_carrier(A!407), B!408)))),
% 284.34/181.72 inference(rewrite,[status(thm)],[])).
% 284.34/181.72 tff(170,plain,
% 284.34/181.72 ((empty(the_carrier(A!407)) | (apply_as_element(the_carrier(A!407), the_carrier(A!407), identity_on_carrier(A!407), B!408) = apply(identity_on_carrier(A!407), B!408)) | (~function(identity_on_carrier(A!407))) | (~quasi_total(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))) | (~relation_of2(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))) | (~element(B!408, the_carrier(A!407)))) <=> ((~element(B!408, the_carrier(A!407))) | empty(the_carrier(A!407)) | (~function(identity_on_carrier(A!407))) | (~quasi_total(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))) | (~relation_of2(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))) | (apply_as_element(the_carrier(A!407), the_carrier(A!407), identity_on_carrier(A!407), B!408) = apply(identity_on_carrier(A!407), B!408)))),
% 284.34/181.72 inference(rewrite,[status(thm)],[])).
% 284.34/181.72 tff(171,plain,
% 284.34/181.72 (((~![A: $i, B: $i, C: $i, D: $i] : (empty(A) | (apply_as_element(A, B, C, D) = apply(C, D)) | (~function(C)) | (~quasi_total(C, A, B)) | (~relation_of2(C, A, B)) | (~element(D, A)))) | (empty(the_carrier(A!407)) | (apply_as_element(the_carrier(A!407), the_carrier(A!407), identity_on_carrier(A!407), B!408) = apply(identity_on_carrier(A!407), B!408)) | (~function(identity_on_carrier(A!407))) | (~quasi_total(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))) | (~relation_of2(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))) | (~element(B!408, the_carrier(A!407))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (empty(A) | (apply_as_element(A, B, C, D) = apply(C, D)) | (~function(C)) | (~quasi_total(C, A, B)) | (~relation_of2(C, A, B)) | (~element(D, A)))) | ((~element(B!408, the_carrier(A!407))) | empty(the_carrier(A!407)) | (~function(identity_on_carrier(A!407))) | (~quasi_total(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))) | (~relation_of2(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))) | (apply_as_element(the_carrier(A!407), the_carrier(A!407), identity_on_carrier(A!407), B!408) = apply(identity_on_carrier(A!407), B!408))))),
% 284.34/181.72 inference(monotonicity,[status(thm)],[170])).
% 284.34/181.72 tff(172,plain,
% 284.34/181.72 (((~![A: $i, B: $i, C: $i, D: $i] : (empty(A) | (apply_as_element(A, B, C, D) = apply(C, D)) | (~function(C)) | (~quasi_total(C, A, B)) | (~relation_of2(C, A, B)) | (~element(D, A)))) | (empty(the_carrier(A!407)) | (apply_as_element(the_carrier(A!407), the_carrier(A!407), identity_on_carrier(A!407), B!408) = apply(identity_on_carrier(A!407), B!408)) | (~function(identity_on_carrier(A!407))) | (~quasi_total(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))) | (~relation_of2(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))) | (~element(B!408, the_carrier(A!407))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (empty(A) | (apply_as_element(A, B, C, D) = apply(C, D)) | (~function(C)) | (~quasi_total(C, A, B)) | (~relation_of2(C, A, B)) | (~element(D, A)))) | (~element(B!408, the_carrier(A!407))) | empty(the_carrier(A!407)) | (~function(identity_on_carrier(A!407))) | (~quasi_total(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))) | (~relation_of2(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))) | (apply_as_element(the_carrier(A!407), the_carrier(A!407), identity_on_carrier(A!407), B!408) = apply(identity_on_carrier(A!407), B!408)))),
% 284.63/181.99 inference(transitivity,[status(thm)],[171, 169])).
% 284.63/181.99 tff(173,plain,
% 284.63/181.99 ((~![A: $i, B: $i, C: $i, D: $i] : (empty(A) | (apply_as_element(A, B, C, D) = apply(C, D)) | (~function(C)) | (~quasi_total(C, A, B)) | (~relation_of2(C, A, B)) | (~element(D, A)))) | (empty(the_carrier(A!407)) | (apply_as_element(the_carrier(A!407), the_carrier(A!407), identity_on_carrier(A!407), B!408) = apply(identity_on_carrier(A!407), B!408)) | (~function(identity_on_carrier(A!407))) | (~quasi_total(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))) | (~relation_of2(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))) | (~element(B!408, the_carrier(A!407))))),
% 284.63/181.99 inference(quant_inst,[status(thm)],[])).
% 284.63/181.99 tff(174,plain,
% 284.63/181.99 ((~![A: $i, B: $i, C: $i, D: $i] : (empty(A) | (apply_as_element(A, B, C, D) = apply(C, D)) | (~function(C)) | (~quasi_total(C, A, B)) | (~relation_of2(C, A, B)) | (~element(D, A)))) | (~element(B!408, the_carrier(A!407))) | empty(the_carrier(A!407)) | (~function(identity_on_carrier(A!407))) | (~quasi_total(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))) | (~relation_of2(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))) | (apply_as_element(the_carrier(A!407), the_carrier(A!407), identity_on_carrier(A!407), B!408) = apply(identity_on_carrier(A!407), B!408))),
% 284.63/181.99 inference(modus_ponens,[status(thm)],[173, 172])).
% 284.63/181.99 tff(175,plain,
% 284.63/181.99 ((~function(identity_on_carrier(A!407))) | (~quasi_total(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))) | (~relation_of2(identity_on_carrier(A!407), the_carrier(A!407), the_carrier(A!407))) | (apply_as_element(the_carrier(A!407), the_carrier(A!407), identity_on_carrier(A!407), B!408) = apply(identity_on_carrier(A!407), B!408))),
% 284.63/181.99 inference(unit_resolution,[status(thm)],[174, 168, 107, 105])).
% 284.63/181.99 tff(176,plain,
% 284.63/181.99 ($false),
% 284.63/181.99 inference(unit_resolution,[status(thm)],[175, 155, 84, 37, 35])).
% 284.63/181.99 % SZS output end Proof
%------------------------------------------------------------------------------