%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU353+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:27:41 AM UTC 2025
% Result : Theorem 0.22s 0.45s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEU353+1 : TPTP v9.0.0. Released v3.3.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 06:50:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.22/0.45 % SZS status Theorem
% 0.22/0.45 % SZS output start Proof
% 0.22/0.45 tff(quasi_total_type, type, (
% 0.22/0.45 quasi_total: ( $i * $i * $i ) > $o)).
% 0.22/0.45 tff(the_carrier_type, type, (
% 0.22/0.45 the_carrier: $i > $i)).
% 0.22/0.45 tff(tptp_fun_A_15_type, type, (
% 0.22/0.45 tptp_fun_A_15: $i)).
% 0.22/0.45 tff(identity_on_carrier_type, type, (
% 0.22/0.45 identity_on_carrier: $i > $i)).
% 0.22/0.45 tff(relation_of2_as_subset_type, type, (
% 0.22/0.45 relation_of2_as_subset: ( $i * $i * $i ) > $o)).
% 0.22/0.45 tff(function_type, type, (
% 0.22/0.45 function: $i > $o)).
% 0.22/0.45 tff(one_sorted_str_type, type, (
% 0.22/0.45 one_sorted_str: $i > $o)).
% 0.22/0.45 tff(tptp_fun_B_16_type, type, (
% 0.22/0.45 tptp_fun_B_16: $i)).
% 0.22/0.45 tff(apply_as_element_type, type, (
% 0.22/0.45 apply_as_element: ( $i * $i * $i * $i ) > $i)).
% 0.22/0.45 tff(element_type, type, (
% 0.22/0.45 element: ( $i * $i ) > $o)).
% 0.22/0.45 tff(empty_carrier_type, type, (
% 0.22/0.45 empty_carrier: $i > $o)).
% 0.22/0.45 tff(relation_of2_type, type, (
% 0.22/0.45 relation_of2: ( $i * $i * $i ) > $o)).
% 0.22/0.45 tff(identity_as_relation_of_type, type, (
% 0.22/0.45 identity_as_relation_of: $i > $i)).
% 0.22/0.45 tff(v1_partfun1_type, type, (
% 0.22/0.45 v1_partfun1: ( $i * $i * $i ) > $o)).
% 0.22/0.45 tff(apply_type, type, (
% 0.22/0.45 apply: ( $i * $i ) > $i)).
% 0.22/0.45 tff(identity_relation_type, type, (
% 0.22/0.45 identity_relation: $i > $i)).
% 0.22/0.45 tff(in_type, type, (
% 0.22/0.45 in: ( $i * $i ) > $o)).
% 0.22/0.45 tff(empty_type, type, (
% 0.22/0.45 empty: $i > $o)).
% 0.22/0.45 tff(1,plain,
% 0.22/0.45 ((((~empty_carrier(A!15)) & one_sorted_str(A!15)) & (~((~element(B!16, the_carrier(A!15))) | (apply_as_element(the_carrier(A!15), the_carrier(A!15), identity_on_carrier(A!15), B!16) = B!16)))) <=> ((~empty_carrier(A!15)) & one_sorted_str(A!15) & (~((~element(B!16, the_carrier(A!15))) | (apply_as_element(the_carrier(A!15), the_carrier(A!15), identity_on_carrier(A!15), B!16) = B!16))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(2,plain,
% 0.22/0.45 ((~![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))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(3,plain,
% 0.22/0.45 ((~![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))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(4,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')).
% 0.22/0.45 tff(5,plain,
% 0.22/0.45 (~![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)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.22/0.45 tff(6,plain,
% 0.22/0.45 (~![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)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.22/0.45 tff(7,plain,
% 0.22/0.45 (~![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)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.22/0.45 tff(8,plain,
% 0.22/0.45 (~![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)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.22/0.45 tff(9,plain,
% 0.22/0.45 ((~empty_carrier(A!15)) & one_sorted_str(A!15) & (~((~element(B!16, the_carrier(A!15))) | (apply_as_element(the_carrier(A!15), the_carrier(A!15), identity_on_carrier(A!15), B!16) = B!16)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.22/0.45 tff(10,plain,
% 0.22/0.45 (one_sorted_str(A!15)),
% 0.22/0.45 inference(and_elim,[status(thm)],[9])).
% 0.22/0.45 tff(11,plain,
% 0.22/0.45 (^[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)))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(12,plain,
% 0.22/0.45 (![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))))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[11])).
% 0.22/0.45 tff(13,plain,
% 0.22/0.45 (^[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)))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(14,plain,
% 0.22/0.45 (![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))))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[13])).
% 0.22/0.45 tff(15,plain,
% 0.22/0.45 (![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))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(16,plain,
% 0.22/0.45 (^[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))))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(17,plain,
% 0.22/0.46 (![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))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[16])).
% 0.22/0.46 tff(18,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')).
% 0.22/0.46 tff(19,plain,
% 0.22/0.46 (![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))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.22/0.46 tff(20,plain,
% 0.22/0.46 (![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))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.22/0.46 tff(21,plain,(
% 0.22/0.46 ![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))))),
% 0.22/0.46 inference(skolemize,[status(sab)],[20])).
% 0.22/0.46 tff(22,plain,
% 0.22/0.46 (![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))))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.22/0.46 tff(23,plain,
% 0.22/0.46 (![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))))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.22/0.46 tff(24,plain,
% 0.22/0.46 (((~![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!15)) | (~((~function(identity_on_carrier(A!15))) | (~quasi_total(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (~relation_of2_as_subset(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))))))) <=> ((~![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!15)) | (~((~function(identity_on_carrier(A!15))) | (~quasi_total(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (~relation_of2_as_subset(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(25,plain,
% 0.22/0.46 ((~![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!15)) | (~((~function(identity_on_carrier(A!15))) | (~quasi_total(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (~relation_of2_as_subset(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(26,plain,
% 0.22/0.46 ((~![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!15)) | (~((~function(identity_on_carrier(A!15))) | (~quasi_total(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (~relation_of2_as_subset(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15)))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.22/0.46 tff(27,plain,
% 0.22/0.46 (~((~function(identity_on_carrier(A!15))) | (~quasi_total(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (~relation_of2_as_subset(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[26, 23, 10])).
% 0.22/0.46 tff(28,plain,
% 0.22/0.46 (((~function(identity_on_carrier(A!15))) | (~quasi_total(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (~relation_of2_as_subset(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15)))) | quasi_total(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(29,plain,
% 0.22/0.46 (quasi_total(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.22/0.46 tff(30,plain,
% 0.22/0.46 (((~function(identity_on_carrier(A!15))) | (~quasi_total(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (~relation_of2_as_subset(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15)))) | function(identity_on_carrier(A!15))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(31,plain,
% 0.22/0.46 (function(identity_on_carrier(A!15))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[30, 27])).
% 0.22/0.46 tff(32,plain,
% 0.22/0.46 (^[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)))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(33,plain,
% 0.22/0.46 (![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))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[32])).
% 0.22/0.46 tff(34,plain,
% 0.22/0.46 (![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))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(35,plain,
% 0.22/0.46 (^[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)))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(36,plain,
% 0.22/0.46 (![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))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[35])).
% 0.22/0.46 tff(37,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')).
% 0.22/0.46 tff(38,plain,
% 0.22/0.46 (![A: $i] : ((~one_sorted_str(A)) | (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.22/0.46 tff(39,plain,
% 0.22/0.46 (![A: $i] : ((~one_sorted_str(A)) | (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.22/0.46 tff(40,plain,(
% 0.22/0.46 ![A: $i] : ((~one_sorted_str(A)) | (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A))))),
% 0.22/0.46 inference(skolemize,[status(sab)],[39])).
% 0.22/0.46 tff(41,plain,
% 0.22/0.46 (![A: $i] : ((~one_sorted_str(A)) | (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.22/0.46 tff(42,plain,
% 0.22/0.46 (((~![A: $i] : ((~one_sorted_str(A)) | (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A))))) | ((~one_sorted_str(A!15)) | (identity_on_carrier(A!15) = identity_as_relation_of(the_carrier(A!15))))) <=> ((~![A: $i] : ((~one_sorted_str(A)) | (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A))))) | (~one_sorted_str(A!15)) | (identity_on_carrier(A!15) = identity_as_relation_of(the_carrier(A!15))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(43,plain,
% 0.22/0.46 ((~![A: $i] : ((~one_sorted_str(A)) | (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A))))) | ((~one_sorted_str(A!15)) | (identity_on_carrier(A!15) = identity_as_relation_of(the_carrier(A!15))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(44,plain,
% 0.22/0.46 ((~![A: $i] : ((~one_sorted_str(A)) | (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A))))) | (~one_sorted_str(A!15)) | (identity_on_carrier(A!15) = identity_as_relation_of(the_carrier(A!15)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.22/0.46 tff(45,plain,
% 0.22/0.46 (identity_on_carrier(A!15) = identity_as_relation_of(the_carrier(A!15))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[44, 41, 10])).
% 0.22/0.46 tff(46,plain,
% 0.22/0.46 (identity_as_relation_of(the_carrier(A!15)) = identity_on_carrier(A!15)),
% 0.22/0.46 inference(symmetry,[status(thm)],[45])).
% 0.22/0.46 tff(47,plain,
% 0.22/0.46 (relation_of2(identity_as_relation_of(the_carrier(A!15)), the_carrier(A!15), the_carrier(A!15)) <=> relation_of2(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[46])).
% 0.22/0.46 tff(48,plain,
% 0.22/0.46 (^[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)))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(49,plain,
% 0.22/0.46 (![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))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[48])).
% 0.22/0.46 tff(50,plain,
% 0.22/0.46 (![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))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(51,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')).
% 0.22/0.46 tff(52,plain,
% 0.22/0.46 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.22/0.46 tff(53,plain,(
% 0.22/0.46 ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.22/0.46 inference(skolemize,[status(sab)],[52])).
% 0.22/0.46 tff(54,plain,
% 0.22/0.46 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.22/0.46 tff(55,plain,
% 0.22/0.46 ((~![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!15)), the_carrier(A!15), the_carrier(A!15)) <=> relation_of2(identity_as_relation_of(the_carrier(A!15)), the_carrier(A!15), the_carrier(A!15)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(56,plain,
% 0.22/0.46 (relation_of2_as_subset(identity_as_relation_of(the_carrier(A!15)), the_carrier(A!15), the_carrier(A!15)) <=> relation_of2(identity_as_relation_of(the_carrier(A!15)), the_carrier(A!15), the_carrier(A!15))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.22/0.46 tff(57,plain,
% 0.22/0.46 (^[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)))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(58,plain,
% 0.22/0.46 (![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))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[57])).
% 0.22/0.46 tff(59,plain,
% 0.22/0.46 (^[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)))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(60,plain,
% 0.22/0.46 (![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))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[59])).
% 0.22/0.46 tff(61,plain,
% 0.22/0.46 (![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))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(62,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')).
% 0.22/0.46 tff(63,plain,
% 0.22/0.46 (![A: $i] : (v1_partfun1(identity_as_relation_of(A), A, A) & relation_of2_as_subset(identity_as_relation_of(A), A, A))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.22/0.46 tff(64,plain,(
% 0.22/0.46 ![A: $i] : (v1_partfun1(identity_as_relation_of(A), A, A) & relation_of2_as_subset(identity_as_relation_of(A), A, A))),
% 0.22/0.46 inference(skolemize,[status(sab)],[63])).
% 0.22/0.46 tff(65,plain,
% 0.22/0.46 (![A: $i] : (~((~v1_partfun1(identity_as_relation_of(A), A, A)) | (~relation_of2_as_subset(identity_as_relation_of(A), A, A))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.22/0.46 tff(66,plain,
% 0.22/0.46 (![A: $i] : (~((~v1_partfun1(identity_as_relation_of(A), A, A)) | (~relation_of2_as_subset(identity_as_relation_of(A), A, A))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.22/0.46 tff(67,plain,
% 0.22/0.46 ((~![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!15)), the_carrier(A!15), the_carrier(A!15))) | (~relation_of2_as_subset(identity_as_relation_of(the_carrier(A!15)), the_carrier(A!15), the_carrier(A!15)))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(68,plain,
% 0.22/0.46 (~((~v1_partfun1(identity_as_relation_of(the_carrier(A!15)), the_carrier(A!15), the_carrier(A!15))) | (~relation_of2_as_subset(identity_as_relation_of(the_carrier(A!15)), the_carrier(A!15), the_carrier(A!15))))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.22/0.46 tff(69,plain,
% 0.22/0.46 (((~v1_partfun1(identity_as_relation_of(the_carrier(A!15)), the_carrier(A!15), the_carrier(A!15))) | (~relation_of2_as_subset(identity_as_relation_of(the_carrier(A!15)), the_carrier(A!15), the_carrier(A!15)))) | relation_of2_as_subset(identity_as_relation_of(the_carrier(A!15)), the_carrier(A!15), the_carrier(A!15))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(70,plain,
% 0.22/0.46 (relation_of2_as_subset(identity_as_relation_of(the_carrier(A!15)), the_carrier(A!15), the_carrier(A!15))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.22/0.46 tff(71,plain,
% 0.22/0.46 ((~(relation_of2_as_subset(identity_as_relation_of(the_carrier(A!15)), the_carrier(A!15), the_carrier(A!15)) <=> relation_of2(identity_as_relation_of(the_carrier(A!15)), the_carrier(A!15), the_carrier(A!15)))) | (~relation_of2_as_subset(identity_as_relation_of(the_carrier(A!15)), the_carrier(A!15), the_carrier(A!15))) | relation_of2(identity_as_relation_of(the_carrier(A!15)), the_carrier(A!15), the_carrier(A!15))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(72,plain,
% 0.22/0.46 (relation_of2(identity_as_relation_of(the_carrier(A!15)), the_carrier(A!15), the_carrier(A!15))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[71, 70, 56])).
% 0.22/0.46 tff(73,plain,
% 0.22/0.46 (relation_of2(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[72, 47])).
% 0.22/0.46 tff(74,plain,
% 0.22/0.46 (~empty_carrier(A!15)),
% 0.22/0.46 inference(and_elim,[status(thm)],[9])).
% 0.22/0.46 tff(75,plain,
% 0.22/0.46 (^[A: $i] : refl(((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A))) <=> ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(76,plain,
% 0.22/0.46 (![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)))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[75])).
% 0.22/0.46 tff(77,plain,
% 0.22/0.46 (^[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(the_carrier(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)))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(78,plain,
% 0.22/0.46 (![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)))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[77])).
% 0.22/0.46 tff(79,plain,
% 0.22/0.46 (![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))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(80,plain,
% 0.22/0.46 (^[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)))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(81,plain,
% 0.22/0.46 (![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))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[80])).
% 0.22/0.46 tff(82,axiom,(![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(the_carrier(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_struct_0')).
% 0.22/0.46 tff(83,plain,
% 0.22/0.46 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.22/0.46 tff(84,plain,
% 0.22/0.46 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.22/0.46 tff(85,plain,(
% 0.22/0.46 ![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 0.22/0.46 inference(skolemize,[status(sab)],[84])).
% 0.22/0.46 tff(86,plain,
% 0.22/0.46 (![A: $i] : ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.22/0.46 tff(87,plain,
% 0.22/0.46 (![A: $i] : ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[86, 76])).
% 0.22/0.46 tff(88,plain,
% 0.22/0.46 (((~![A: $i] : ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A)))) | (empty_carrier(A!15) | (~one_sorted_str(A!15)) | (~empty(the_carrier(A!15))))) <=> ((~![A: $i] : ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A)))) | empty_carrier(A!15) | (~one_sorted_str(A!15)) | (~empty(the_carrier(A!15))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(89,plain,
% 0.22/0.46 (((~empty(the_carrier(A!15))) | empty_carrier(A!15) | (~one_sorted_str(A!15))) <=> (empty_carrier(A!15) | (~one_sorted_str(A!15)) | (~empty(the_carrier(A!15))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(90,plain,
% 0.22/0.46 (((~![A: $i] : ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A)))) | ((~empty(the_carrier(A!15))) | empty_carrier(A!15) | (~one_sorted_str(A!15)))) <=> ((~![A: $i] : ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A)))) | (empty_carrier(A!15) | (~one_sorted_str(A!15)) | (~empty(the_carrier(A!15)))))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[89])).
% 0.22/0.46 tff(91,plain,
% 0.22/0.46 (((~![A: $i] : ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A)))) | ((~empty(the_carrier(A!15))) | empty_carrier(A!15) | (~one_sorted_str(A!15)))) <=> ((~![A: $i] : ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A)))) | empty_carrier(A!15) | (~one_sorted_str(A!15)) | (~empty(the_carrier(A!15))))),
% 0.22/0.46 inference(transitivity,[status(thm)],[90, 88])).
% 0.22/0.46 tff(92,plain,
% 0.22/0.46 ((~![A: $i] : ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A)))) | ((~empty(the_carrier(A!15))) | empty_carrier(A!15) | (~one_sorted_str(A!15)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(93,plain,
% 0.22/0.46 ((~![A: $i] : ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A)))) | empty_carrier(A!15) | (~one_sorted_str(A!15)) | (~empty(the_carrier(A!15)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.22/0.46 tff(94,plain,
% 0.22/0.46 (~empty(the_carrier(A!15))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[93, 87, 74, 10])).
% 0.22/0.46 tff(95,plain,
% 0.22/0.46 (~((~element(B!16, the_carrier(A!15))) | (apply_as_element(the_carrier(A!15), the_carrier(A!15), identity_on_carrier(A!15), B!16) = B!16))),
% 0.22/0.46 inference(and_elim,[status(thm)],[9])).
% 0.22/0.46 tff(96,plain,
% 0.22/0.46 (element(B!16, the_carrier(A!15))),
% 0.22/0.46 inference(or_elim,[status(thm)],[95])).
% 0.22/0.46 tff(97,plain,
% 0.22/0.46 (^[A: $i, B: $i] : refl((in(A, B) | empty(B) | (~element(A, B))) <=> (in(A, B) | empty(B) | (~element(A, B))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(98,plain,
% 0.22/0.46 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B))) <=> ![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[97])).
% 0.22/0.46 tff(99,plain,
% 0.22/0.46 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B))) <=> ![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(100,plain,
% 0.22/0.46 (^[A: $i, B: $i] : rewrite((element(A, B) => (empty(B) | in(A, B))) <=> (in(A, B) | empty(B) | (~element(A, B))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(101,plain,
% 0.22/0.46 (![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B))) <=> ![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[100])).
% 0.22/0.46 tff(102,axiom,(![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_subset')).
% 0.22/0.46 tff(103,plain,
% 0.22/0.46 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.22/0.46 tff(104,plain,
% 0.22/0.46 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.22/0.46 tff(105,plain,(
% 0.22/0.46 ![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 0.22/0.46 inference(skolemize,[status(sab)],[104])).
% 0.22/0.46 tff(106,plain,
% 0.22/0.46 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.22/0.46 tff(107,plain,
% 0.22/0.46 (((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | ((~element(B!16, the_carrier(A!15))) | in(B!16, the_carrier(A!15)) | empty(the_carrier(A!15)))) <=> ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (~element(B!16, the_carrier(A!15))) | in(B!16, the_carrier(A!15)) | empty(the_carrier(A!15)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(108,plain,
% 0.22/0.46 ((in(B!16, the_carrier(A!15)) | empty(the_carrier(A!15)) | (~element(B!16, the_carrier(A!15)))) <=> ((~element(B!16, the_carrier(A!15))) | in(B!16, the_carrier(A!15)) | empty(the_carrier(A!15)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(109,plain,
% 0.22/0.46 (((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (in(B!16, the_carrier(A!15)) | empty(the_carrier(A!15)) | (~element(B!16, the_carrier(A!15))))) <=> ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | ((~element(B!16, the_carrier(A!15))) | in(B!16, the_carrier(A!15)) | empty(the_carrier(A!15))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[108])).
% 0.22/0.47 tff(110,plain,
% 0.22/0.47 (((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (in(B!16, the_carrier(A!15)) | empty(the_carrier(A!15)) | (~element(B!16, the_carrier(A!15))))) <=> ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (~element(B!16, the_carrier(A!15))) | in(B!16, the_carrier(A!15)) | empty(the_carrier(A!15)))),
% 0.22/0.47 inference(transitivity,[status(thm)],[109, 107])).
% 0.22/0.47 tff(111,plain,
% 0.22/0.47 ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (in(B!16, the_carrier(A!15)) | empty(the_carrier(A!15)) | (~element(B!16, the_carrier(A!15))))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(112,plain,
% 0.22/0.47 ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (~element(B!16, the_carrier(A!15))) | in(B!16, the_carrier(A!15)) | empty(the_carrier(A!15))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.22/0.47 tff(113,plain,
% 0.22/0.47 (in(B!16, the_carrier(A!15)) | empty(the_carrier(A!15))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[112, 106, 96])).
% 0.22/0.47 tff(114,plain,
% 0.22/0.47 (in(B!16, the_carrier(A!15))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[113, 94])).
% 0.22/0.47 tff(115,plain,
% 0.22/0.47 (^[A: $i, B: $i] : refl(((~in(B, A)) | (apply(identity_relation(A), B) = B)) <=> ((~in(B, A)) | (apply(identity_relation(A), B) = B)))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(116,plain,
% 0.22/0.47 (![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))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[115])).
% 0.22/0.47 tff(117,plain,
% 0.22/0.47 (![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))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(118,plain,
% 0.22/0.47 (^[A: $i, B: $i] : rewrite((in(B, A) => (apply(identity_relation(A), B) = B)) <=> ((~in(B, A)) | (apply(identity_relation(A), B) = B)))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(119,plain,
% 0.22/0.47 (![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))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[118])).
% 0.22/0.47 tff(120,axiom,(![A: $i, B: $i] : (in(B, A) => (apply(identity_relation(A), B) = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t35_funct_1')).
% 0.22/0.47 tff(121,plain,
% 0.22/0.47 (![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.22/0.47 tff(122,plain,
% 0.22/0.47 (![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.22/0.47 tff(123,plain,(
% 0.22/0.47 ![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 0.22/0.47 inference(skolemize,[status(sab)],[122])).
% 0.22/0.47 tff(124,plain,
% 0.22/0.47 (![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[123, 116])).
% 0.22/0.47 tff(125,plain,
% 0.22/0.47 (((~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))) | ((~in(B!16, the_carrier(A!15))) | (apply(identity_relation(the_carrier(A!15)), B!16) = B!16))) <=> ((~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))) | (~in(B!16, the_carrier(A!15))) | (apply(identity_relation(the_carrier(A!15)), B!16) = B!16))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(126,plain,
% 0.22/0.47 ((~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))) | ((~in(B!16, the_carrier(A!15))) | (apply(identity_relation(the_carrier(A!15)), B!16) = B!16))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(127,plain,
% 0.22/0.47 ((~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))) | (~in(B!16, the_carrier(A!15))) | (apply(identity_relation(the_carrier(A!15)), B!16) = B!16)),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.22/0.47 tff(128,plain,
% 0.22/0.47 (apply(identity_relation(the_carrier(A!15)), B!16) = B!16),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[127, 124, 114])).
% 0.22/0.47 tff(129,plain,
% 0.22/0.47 (^[A: $i] : refl((identity_as_relation_of(A) = identity_relation(A)) <=> (identity_as_relation_of(A) = identity_relation(A)))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(130,plain,
% 0.22/0.47 (![A: $i] : (identity_as_relation_of(A) = identity_relation(A)) <=> ![A: $i] : (identity_as_relation_of(A) = identity_relation(A))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[129])).
% 0.22/0.47 tff(131,plain,
% 0.22/0.47 (![A: $i] : (identity_as_relation_of(A) = identity_relation(A)) <=> ![A: $i] : (identity_as_relation_of(A) = identity_relation(A))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(132,axiom,(![A: $i] : (identity_as_relation_of(A) = identity_relation(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k6_partfun1')).
% 0.22/0.47 tff(133,plain,
% 0.22/0.47 (![A: $i] : (identity_as_relation_of(A) = identity_relation(A))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.22/0.47 tff(134,plain,(
% 0.22/0.47 ![A: $i] : (identity_as_relation_of(A) = identity_relation(A))),
% 0.22/0.47 inference(skolemize,[status(sab)],[133])).
% 0.22/0.47 tff(135,plain,
% 0.22/0.47 (![A: $i] : (identity_as_relation_of(A) = identity_relation(A))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.22/0.47 tff(136,plain,
% 0.22/0.47 ((~![A: $i] : (identity_as_relation_of(A) = identity_relation(A))) | (identity_as_relation_of(the_carrier(A!15)) = identity_relation(the_carrier(A!15)))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(137,plain,
% 0.22/0.47 (identity_as_relation_of(the_carrier(A!15)) = identity_relation(the_carrier(A!15))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.22/0.47 tff(138,plain,
% 0.22/0.47 (identity_on_carrier(A!15) = identity_relation(the_carrier(A!15))),
% 0.22/0.47 inference(transitivity,[status(thm)],[45, 137])).
% 0.22/0.47 tff(139,plain,
% 0.22/0.47 (apply(identity_on_carrier(A!15), B!16) = apply(identity_relation(the_carrier(A!15)), B!16)),
% 0.22/0.47 inference(monotonicity,[status(thm)],[138])).
% 0.22/0.47 tff(140,plain,
% 0.22/0.47 (apply(identity_on_carrier(A!15), B!16) = B!16),
% 0.22/0.47 inference(transitivity,[status(thm)],[139, 128])).
% 0.22/0.47 tff(141,plain,
% 0.22/0.47 ((apply_as_element(the_carrier(A!15), the_carrier(A!15), identity_on_carrier(A!15), B!16) = apply(identity_on_carrier(A!15), B!16)) <=> (apply_as_element(the_carrier(A!15), the_carrier(A!15), identity_on_carrier(A!15), B!16) = B!16)),
% 0.22/0.47 inference(monotonicity,[status(thm)],[140])).
% 0.22/0.47 tff(142,plain,
% 0.22/0.47 ((apply_as_element(the_carrier(A!15), the_carrier(A!15), identity_on_carrier(A!15), B!16) = B!16) <=> (apply_as_element(the_carrier(A!15), the_carrier(A!15), identity_on_carrier(A!15), B!16) = apply(identity_on_carrier(A!15), B!16))),
% 0.22/0.47 inference(symmetry,[status(thm)],[141])).
% 0.22/0.47 tff(143,plain,
% 0.22/0.47 ((~(apply_as_element(the_carrier(A!15), the_carrier(A!15), identity_on_carrier(A!15), B!16) = B!16)) <=> (~(apply_as_element(the_carrier(A!15), the_carrier(A!15), identity_on_carrier(A!15), B!16) = apply(identity_on_carrier(A!15), B!16)))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[142])).
% 0.22/0.47 tff(144,plain,
% 0.22/0.47 (~(apply_as_element(the_carrier(A!15), the_carrier(A!15), identity_on_carrier(A!15), B!16) = B!16)),
% 0.22/0.47 inference(or_elim,[status(thm)],[95])).
% 0.22/0.47 tff(145,plain,
% 0.22/0.47 (~(apply_as_element(the_carrier(A!15), the_carrier(A!15), identity_on_carrier(A!15), B!16) = apply(identity_on_carrier(A!15), B!16))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.22/0.47 tff(146,plain,
% 0.22/0.47 (^[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))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(147,plain,
% 0.22/0.47 (![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)))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[146])).
% 0.22/0.47 tff(148,plain,
% 0.22/0.47 (^[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)))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(149,plain,
% 0.22/0.47 (![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)))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[148])).
% 0.22/0.47 tff(150,plain,
% 0.22/0.47 (![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)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(151,plain,
% 0.22/0.47 (^[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)))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(152,plain,
% 0.22/0.47 (![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)))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[151])).
% 0.22/0.47 tff(153,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')).
% 0.22/0.47 tff(154,plain,
% 0.22/0.47 (![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)))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.22/0.47 tff(155,plain,
% 0.22/0.47 (![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)))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[154, 150])).
% 0.22/0.47 tff(156,plain,(
% 0.22/0.47 ![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)))),
% 0.22/0.47 inference(skolemize,[status(sab)],[155])).
% 0.22/0.47 tff(157,plain,
% 0.22/0.47 (![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)))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[156, 149])).
% 0.22/0.47 tff(158,plain,
% 0.22/0.47 (![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)))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[157, 147])).
% 0.22/0.47 tff(159,plain,
% 0.22/0.47 (((~![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!16, the_carrier(A!15))) | empty(the_carrier(A!15)) | (~function(identity_on_carrier(A!15))) | (~quasi_total(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (~relation_of2(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (apply_as_element(the_carrier(A!15), the_carrier(A!15), identity_on_carrier(A!15), B!16) = apply(identity_on_carrier(A!15), B!16)))) <=> ((~![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!16, the_carrier(A!15))) | empty(the_carrier(A!15)) | (~function(identity_on_carrier(A!15))) | (~quasi_total(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (~relation_of2(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (apply_as_element(the_carrier(A!15), the_carrier(A!15), identity_on_carrier(A!15), B!16) = apply(identity_on_carrier(A!15), B!16)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(160,plain,
% 0.22/0.47 ((empty(the_carrier(A!15)) | (apply_as_element(the_carrier(A!15), the_carrier(A!15), identity_on_carrier(A!15), B!16) = apply(identity_on_carrier(A!15), B!16)) | (~function(identity_on_carrier(A!15))) | (~quasi_total(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (~relation_of2(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (~element(B!16, the_carrier(A!15)))) <=> ((~element(B!16, the_carrier(A!15))) | empty(the_carrier(A!15)) | (~function(identity_on_carrier(A!15))) | (~quasi_total(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (~relation_of2(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (apply_as_element(the_carrier(A!15), the_carrier(A!15), identity_on_carrier(A!15), B!16) = apply(identity_on_carrier(A!15), B!16)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(161,plain,
% 0.22/0.47 (((~![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!15)) | (apply_as_element(the_carrier(A!15), the_carrier(A!15), identity_on_carrier(A!15), B!16) = apply(identity_on_carrier(A!15), B!16)) | (~function(identity_on_carrier(A!15))) | (~quasi_total(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (~relation_of2(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (~element(B!16, the_carrier(A!15))))) <=> ((~![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!16, the_carrier(A!15))) | empty(the_carrier(A!15)) | (~function(identity_on_carrier(A!15))) | (~quasi_total(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (~relation_of2(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (apply_as_element(the_carrier(A!15), the_carrier(A!15), identity_on_carrier(A!15), B!16) = apply(identity_on_carrier(A!15), B!16))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[160])).
% 0.22/0.47 tff(162,plain,
% 0.22/0.47 (((~![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!15)) | (apply_as_element(the_carrier(A!15), the_carrier(A!15), identity_on_carrier(A!15), B!16) = apply(identity_on_carrier(A!15), B!16)) | (~function(identity_on_carrier(A!15))) | (~quasi_total(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (~relation_of2(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (~element(B!16, the_carrier(A!15))))) <=> ((~![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!16, the_carrier(A!15))) | empty(the_carrier(A!15)) | (~function(identity_on_carrier(A!15))) | (~quasi_total(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (~relation_of2(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (apply_as_element(the_carrier(A!15), the_carrier(A!15), identity_on_carrier(A!15), B!16) = apply(identity_on_carrier(A!15), B!16)))),
% 0.22/0.47 inference(transitivity,[status(thm)],[161, 159])).
% 0.22/0.47 tff(163,plain,
% 0.22/0.47 ((~![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!15)) | (apply_as_element(the_carrier(A!15), the_carrier(A!15), identity_on_carrier(A!15), B!16) = apply(identity_on_carrier(A!15), B!16)) | (~function(identity_on_carrier(A!15))) | (~quasi_total(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (~relation_of2(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (~element(B!16, the_carrier(A!15))))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(164,plain,
% 0.22/0.47 ((~![A: $i, B: $i, C: $i, D: $i] : (empty(A) | (apply_as_element(A, B, C, D) = apply(C, D)) | (~function(C)) | (~quasi_total(C, A, B)) | (~relation_of2(C, A, B)) | (~element(D, A)))) | (~element(B!16, the_carrier(A!15))) | empty(the_carrier(A!15)) | (~function(identity_on_carrier(A!15))) | (~quasi_total(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (~relation_of2(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (apply_as_element(the_carrier(A!15), the_carrier(A!15), identity_on_carrier(A!15), B!16) = apply(identity_on_carrier(A!15), B!16))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.22/0.47 tff(165,plain,
% 0.22/0.47 ((~function(identity_on_carrier(A!15))) | (~quasi_total(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (~relation_of2(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (apply_as_element(the_carrier(A!15), the_carrier(A!15), identity_on_carrier(A!15), B!16) = apply(identity_on_carrier(A!15), B!16))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[164, 158, 96, 94])).
% 0.22/0.48 tff(166,plain,
% 0.22/0.48 ($false),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[165, 145, 73, 31, 29])).
% 0.22/0.48 % SZS output end Proof
% 0.22/0.48 % E exiting
%------------------------------------------------------------------------------