TSTP Solution File: SEU353+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU353+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU353+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 12:52:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 % SZS output start Proof
% 0.19/0.46 tff(quasi_total_type, type, (
% 0.19/0.46 quasi_total: ( $i * $i * $i ) > $o)).
% 0.19/0.46 tff(the_carrier_type, type, (
% 0.19/0.46 the_carrier: $i > $i)).
% 0.19/0.46 tff(tptp_fun_A_15_type, type, (
% 0.19/0.46 tptp_fun_A_15: $i)).
% 0.19/0.46 tff(identity_on_carrier_type, type, (
% 0.19/0.46 identity_on_carrier: $i > $i)).
% 0.19/0.46 tff(relation_of2_as_subset_type, type, (
% 0.19/0.46 relation_of2_as_subset: ( $i * $i * $i ) > $o)).
% 0.19/0.46 tff(function_type, type, (
% 0.19/0.46 function: $i > $o)).
% 0.19/0.46 tff(one_sorted_str_type, type, (
% 0.19/0.46 one_sorted_str: $i > $o)).
% 0.19/0.46 tff(tptp_fun_B_16_type, type, (
% 0.19/0.46 tptp_fun_B_16: $i)).
% 0.19/0.46 tff(apply_as_element_type, type, (
% 0.19/0.46 apply_as_element: ( $i * $i * $i * $i ) > $i)).
% 0.19/0.46 tff(element_type, type, (
% 0.19/0.46 element: ( $i * $i ) > $o)).
% 0.19/0.46 tff(empty_carrier_type, type, (
% 0.19/0.46 empty_carrier: $i > $o)).
% 0.19/0.46 tff(relation_of2_type, type, (
% 0.19/0.46 relation_of2: ( $i * $i * $i ) > $o)).
% 0.19/0.46 tff(identity_as_relation_of_type, type, (
% 0.19/0.46 identity_as_relation_of: $i > $i)).
% 0.19/0.46 tff(v1_partfun1_type, type, (
% 0.19/0.46 v1_partfun1: ( $i * $i * $i ) > $o)).
% 0.19/0.46 tff(apply_type, type, (
% 0.19/0.46 apply: ( $i * $i ) > $i)).
% 0.19/0.46 tff(identity_relation_type, type, (
% 0.19/0.46 identity_relation: $i > $i)).
% 0.19/0.46 tff(in_type, type, (
% 0.19/0.46 in: ( $i * $i ) > $o)).
% 0.19/0.46 tff(empty_type, type, (
% 0.19/0.46 empty: $i > $o)).
% 0.19/0.46 tff(1,plain,
% 0.19/0.46 ((((~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))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(2,plain,
% 0.19/0.46 ((~(~((~empty_carrier(A!15)) & one_sorted_str(A!15)))) <=> ((~empty_carrier(A!15)) & one_sorted_str(A!15))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(3,plain,
% 0.19/0.46 (((~(~((~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))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[2])).
% 0.19/0.46 tff(4,plain,
% 0.19/0.46 (((~(~((~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))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[3, 1])).
% 0.19/0.46 tff(5,plain,
% 0.19/0.46 ((~![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))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(6,plain,
% 0.19/0.46 ((~![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))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 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')).
% 0.19/0.46 tff(8,plain,
% 0.19/0.46 (~![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)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.19/0.46 tff(9,plain,
% 0.19/0.46 (~![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)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.19/0.46 tff(10,plain,
% 0.19/0.46 (~![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)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.46 tff(11,plain,
% 0.19/0.46 (~![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)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.19/0.46 tff(12,plain,
% 0.19/0.46 (~![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)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[11, 5])).
% 0.19/0.46 tff(13,plain,
% 0.19/0.46 (~![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)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.19/0.46 tff(14,plain,
% 0.19/0.46 (~![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)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[13, 5])).
% 0.19/0.46 tff(15,plain,
% 0.19/0.46 ((~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)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[14, 4])).
% 0.19/0.46 tff(16,plain,
% 0.19/0.46 (one_sorted_str(A!15)),
% 0.19/0.46 inference(and_elim,[status(thm)],[15])).
% 0.19/0.46 tff(17,plain,
% 0.19/0.46 (^[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)))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(18,plain,
% 0.19/0.46 (![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))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.46 tff(19,plain,
% 0.19/0.46 (^[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)))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(20,plain,
% 0.19/0.46 (![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))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.46 tff(21,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(22,plain,
% 0.19/0.46 (^[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))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(23,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.46 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')).
% 0.19/0.46 tff(25,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.46 tff(26,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.19/0.46 tff(27,plain,(
% 0.19/0.46 ![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))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[26])).
% 0.19/0.46 tff(28,plain,
% 0.19/0.46 (![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))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.19/0.46 tff(29,plain,
% 0.19/0.46 (![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))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.19/0.46 tff(30,plain,
% 0.19/0.46 (((~![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))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(31,plain,
% 0.19/0.46 ((~![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))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(32,plain,
% 0.19/0.46 ((~![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)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.46 tff(33,plain,
% 0.19/0.46 (~((~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))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[32, 29, 16])).
% 0.19/0.46 tff(34,plain,
% 0.19/0.46 (((~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))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(35,plain,
% 0.19/0.46 (quasi_total(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.19/0.46 tff(36,plain,
% 0.19/0.46 (((~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))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(37,plain,
% 0.19/0.46 (function(identity_on_carrier(A!15))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[36, 33])).
% 0.19/0.46 tff(38,plain,
% 0.19/0.46 (^[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)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(39,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[38])).
% 0.19/0.46 tff(40,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(41,plain,
% 0.19/0.46 (^[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)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(42,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[41])).
% 0.19/0.46 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')).
% 0.19/0.46 tff(44,plain,
% 0.19/0.46 (![A: $i] : ((~one_sorted_str(A)) | (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.46 tff(45,plain,
% 0.19/0.46 (![A: $i] : ((~one_sorted_str(A)) | (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.19/0.46 tff(46,plain,(
% 0.19/0.46 ![A: $i] : ((~one_sorted_str(A)) | (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[45])).
% 0.19/0.46 tff(47,plain,
% 0.19/0.46 (![A: $i] : ((~one_sorted_str(A)) | (identity_on_carrier(A) = identity_as_relation_of(the_carrier(A))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.19/0.46 tff(48,plain,
% 0.19/0.46 (((~![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))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(49,plain,
% 0.19/0.46 ((~![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))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(50,plain,
% 0.19/0.46 ((~![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)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.46 tff(51,plain,
% 0.19/0.46 (identity_on_carrier(A!15) = identity_as_relation_of(the_carrier(A!15))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[50, 47, 16])).
% 0.19/0.46 tff(52,plain,
% 0.19/0.46 (identity_as_relation_of(the_carrier(A!15)) = identity_on_carrier(A!15)),
% 0.19/0.46 inference(symmetry,[status(thm)],[51])).
% 0.19/0.46 tff(53,plain,
% 0.19/0.46 (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))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[52])).
% 0.19/0.46 tff(54,plain,
% 0.19/0.46 (^[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)))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(55,plain,
% 0.19/0.46 (![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))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.47 tff(56,plain,
% 0.19/0.47 (![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))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 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')).
% 0.19/0.47 tff(58,plain,
% 0.19/0.47 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.19/0.47 tff(59,plain,(
% 0.19/0.47 ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.19/0.47 inference(skolemize,[status(sab)],[58])).
% 0.19/0.47 tff(60,plain,
% 0.19/0.47 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.19/0.47 tff(61,plain,
% 0.19/0.47 ((~![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)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(62,plain,
% 0.19/0.47 (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))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.19/0.47 tff(63,plain,
% 0.19/0.47 (^[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)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(64,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[63])).
% 0.19/0.47 tff(65,plain,
% 0.19/0.47 (^[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)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(66,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.47 tff(67,plain,
% 0.19/0.47 (![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))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 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')).
% 0.19/0.47 tff(69,plain,
% 0.19/0.47 (![A: $i] : (v1_partfun1(identity_as_relation_of(A), A, A) & relation_of2_as_subset(identity_as_relation_of(A), A, A))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.19/0.47 tff(70,plain,(
% 0.19/0.47 ![A: $i] : (v1_partfun1(identity_as_relation_of(A), A, A) & relation_of2_as_subset(identity_as_relation_of(A), A, A))),
% 0.19/0.47 inference(skolemize,[status(sab)],[69])).
% 0.19/0.47 tff(71,plain,
% 0.19/0.47 (![A: $i] : (~((~v1_partfun1(identity_as_relation_of(A), A, A)) | (~relation_of2_as_subset(identity_as_relation_of(A), A, A))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.19/0.47 tff(72,plain,
% 0.19/0.47 (![A: $i] : (~((~v1_partfun1(identity_as_relation_of(A), A, A)) | (~relation_of2_as_subset(identity_as_relation_of(A), A, A))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.19/0.47 tff(73,plain,
% 0.19/0.47 ((~![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)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(74,plain,
% 0.19/0.47 (~((~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))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.19/0.47 tff(75,plain,
% 0.19/0.47 (((~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))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(76,plain,
% 0.19/0.47 (relation_of2_as_subset(identity_as_relation_of(the_carrier(A!15)), the_carrier(A!15), the_carrier(A!15))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.19/0.47 tff(77,plain,
% 0.19/0.47 ((~(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))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(78,plain,
% 0.19/0.47 (relation_of2(identity_as_relation_of(the_carrier(A!15)), the_carrier(A!15), the_carrier(A!15))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[77, 76, 62])).
% 0.19/0.47 tff(79,plain,
% 0.19/0.47 (relation_of2(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[78, 53])).
% 0.19/0.47 tff(80,plain,
% 0.19/0.47 (~empty_carrier(A!15)),
% 0.19/0.47 inference(and_elim,[status(thm)],[15])).
% 0.19/0.47 tff(81,plain,
% 0.19/0.47 (^[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))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(82,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[81])).
% 0.19/0.47 tff(83,plain,
% 0.19/0.47 (^[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)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(84,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.47 tff(85,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(86,plain,
% 0.19/0.47 (^[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)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(87,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[86])).
% 0.19/0.47 tff(88,axiom,(![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(the_carrier(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_struct_0')).
% 0.19/0.47 tff(89,plain,
% 0.19/0.47 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.19/0.47 tff(90,plain,
% 0.19/0.47 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.19/0.47 tff(91,plain,(
% 0.19/0.47 ![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[90])).
% 0.19/0.47 tff(92,plain,
% 0.19/0.47 (![A: $i] : ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.19/0.47 tff(93,plain,
% 0.19/0.47 (![A: $i] : ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[92, 82])).
% 0.19/0.47 tff(94,plain,
% 0.19/0.47 (((~![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))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(95,plain,
% 0.19/0.47 (((~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))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(96,plain,
% 0.19/0.47 (((~![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)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[95])).
% 0.19/0.47 tff(97,plain,
% 0.19/0.47 (((~![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))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[96, 94])).
% 0.19/0.47 tff(98,plain,
% 0.19/0.47 ((~![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)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(99,plain,
% 0.19/0.47 ((~![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)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.19/0.47 tff(100,plain,
% 0.19/0.47 (~empty(the_carrier(A!15))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[99, 93, 80, 16])).
% 0.19/0.47 tff(101,plain,
% 0.19/0.47 (~((~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))),
% 0.19/0.47 inference(and_elim,[status(thm)],[15])).
% 0.19/0.47 tff(102,plain,
% 0.19/0.47 (element(B!16, the_carrier(A!15))),
% 0.19/0.47 inference(or_elim,[status(thm)],[101])).
% 0.19/0.47 tff(103,plain,
% 0.19/0.47 (^[A: $i, B: $i] : refl((in(A, B) | empty(B) | (~element(A, B))) <=> (in(A, B) | empty(B) | (~element(A, B))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(104,plain,
% 0.19/0.47 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B))) <=> ![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[103])).
% 0.19/0.47 tff(105,plain,
% 0.19/0.47 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B))) <=> ![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(106,plain,
% 0.19/0.47 (^[A: $i, B: $i] : rewrite((element(A, B) => (empty(B) | in(A, B))) <=> (in(A, B) | empty(B) | (~element(A, B))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(107,plain,
% 0.19/0.47 (![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B))) <=> ![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[106])).
% 0.19/0.47 tff(108,axiom,(![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_subset')).
% 0.19/0.47 tff(109,plain,
% 0.19/0.47 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.19/0.47 tff(110,plain,
% 0.19/0.47 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.19/0.47 tff(111,plain,(
% 0.19/0.47 ![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[110])).
% 0.19/0.47 tff(112,plain,
% 0.19/0.47 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.19/0.47 tff(113,plain,
% 0.19/0.47 (((~![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)))) <=> ((~![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)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(114,plain,
% 0.19/0.47 ((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)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(115,plain,
% 0.19/0.47 (((~![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))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[114])).
% 0.19/0.47 tff(116,plain,
% 0.19/0.47 (((~![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)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[115, 113])).
% 0.19/0.47 tff(117,plain,
% 0.19/0.47 ((~![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))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(118,plain,
% 0.19/0.47 ((~![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))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.19/0.47 tff(119,plain,
% 0.19/0.47 (in(B!16, the_carrier(A!15)) | empty(the_carrier(A!15))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[118, 112, 102])).
% 0.19/0.47 tff(120,plain,
% 0.19/0.47 (in(B!16, the_carrier(A!15))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[119, 100])).
% 0.19/0.47 tff(121,plain,
% 0.19/0.47 (^[A: $i, B: $i] : refl(((~in(B, A)) | (apply(identity_relation(A), B) = B)) <=> ((~in(B, A)) | (apply(identity_relation(A), B) = B)))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(122,plain,
% 0.19/0.47 (![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))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[121])).
% 0.19/0.47 tff(123,plain,
% 0.19/0.47 (![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))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(124,plain,
% 0.19/0.47 (^[A: $i, B: $i] : rewrite((in(B, A) => (apply(identity_relation(A), B) = B)) <=> ((~in(B, A)) | (apply(identity_relation(A), B) = B)))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(125,plain,
% 0.19/0.47 (![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))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[124])).
% 0.19/0.47 tff(126,axiom,(![A: $i, B: $i] : (in(B, A) => (apply(identity_relation(A), B) = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t35_funct_1')).
% 0.19/0.47 tff(127,plain,
% 0.19/0.47 (![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.19/0.47 tff(128,plain,
% 0.19/0.47 (![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.19/0.47 tff(129,plain,(
% 0.19/0.47 ![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 0.19/0.47 inference(skolemize,[status(sab)],[128])).
% 0.19/0.47 tff(130,plain,
% 0.19/0.47 (![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[129, 122])).
% 0.19/0.47 tff(131,plain,
% 0.19/0.47 (((~![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))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(132,plain,
% 0.19/0.47 ((~![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))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(133,plain,
% 0.19/0.47 ((~![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)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.19/0.47 tff(134,plain,
% 0.19/0.47 (apply(identity_relation(the_carrier(A!15)), B!16) = B!16),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[133, 130, 120])).
% 0.19/0.47 tff(135,plain,
% 0.19/0.47 (^[A: $i] : refl((identity_as_relation_of(A) = identity_relation(A)) <=> (identity_as_relation_of(A) = identity_relation(A)))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(136,plain,
% 0.19/0.47 (![A: $i] : (identity_as_relation_of(A) = identity_relation(A)) <=> ![A: $i] : (identity_as_relation_of(A) = identity_relation(A))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[135])).
% 0.19/0.47 tff(137,plain,
% 0.19/0.47 (![A: $i] : (identity_as_relation_of(A) = identity_relation(A)) <=> ![A: $i] : (identity_as_relation_of(A) = identity_relation(A))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(138,axiom,(![A: $i] : (identity_as_relation_of(A) = identity_relation(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k6_partfun1')).
% 0.19/0.47 tff(139,plain,
% 0.19/0.47 (![A: $i] : (identity_as_relation_of(A) = identity_relation(A))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.19/0.47 tff(140,plain,(
% 0.19/0.47 ![A: $i] : (identity_as_relation_of(A) = identity_relation(A))),
% 0.19/0.47 inference(skolemize,[status(sab)],[139])).
% 0.19/0.47 tff(141,plain,
% 0.19/0.47 (![A: $i] : (identity_as_relation_of(A) = identity_relation(A))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.19/0.47 tff(142,plain,
% 0.19/0.47 ((~![A: $i] : (identity_as_relation_of(A) = identity_relation(A))) | (identity_as_relation_of(the_carrier(A!15)) = identity_relation(the_carrier(A!15)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(143,plain,
% 0.19/0.47 (identity_as_relation_of(the_carrier(A!15)) = identity_relation(the_carrier(A!15))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.19/0.47 tff(144,plain,
% 0.19/0.47 (identity_on_carrier(A!15) = identity_relation(the_carrier(A!15))),
% 0.19/0.47 inference(transitivity,[status(thm)],[51, 143])).
% 0.19/0.47 tff(145,plain,
% 0.19/0.47 (apply(identity_on_carrier(A!15), B!16) = apply(identity_relation(the_carrier(A!15)), B!16)),
% 0.19/0.47 inference(monotonicity,[status(thm)],[144])).
% 0.19/0.47 tff(146,plain,
% 0.19/0.47 (apply(identity_on_carrier(A!15), B!16) = B!16),
% 0.19/0.47 inference(transitivity,[status(thm)],[145, 134])).
% 0.19/0.47 tff(147,plain,
% 0.19/0.47 ((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)),
% 0.19/0.47 inference(monotonicity,[status(thm)],[146])).
% 0.19/0.47 tff(148,plain,
% 0.19/0.47 ((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))),
% 0.19/0.47 inference(symmetry,[status(thm)],[147])).
% 0.19/0.47 tff(149,plain,
% 0.19/0.47 ((~(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)))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[148])).
% 0.19/0.47 tff(150,plain,
% 0.19/0.47 (~(apply_as_element(the_carrier(A!15), the_carrier(A!15), identity_on_carrier(A!15), B!16) = B!16)),
% 0.19/0.47 inference(or_elim,[status(thm)],[101])).
% 0.19/0.47 tff(151,plain,
% 0.19/0.47 (~(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))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.19/0.47 tff(152,plain,
% 0.19/0.47 (^[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))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(153,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[152])).
% 0.19/0.47 tff(154,plain,
% 0.19/0.47 (^[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)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(155,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[154])).
% 0.19/0.48 tff(156,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(157,plain,
% 0.19/0.48 (^[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)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(158,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[157])).
% 0.19/0.48 tff(159,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')).
% 0.19/0.48 tff(160,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.19/0.48 tff(161,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[160, 156])).
% 0.19/0.48 tff(162,plain,(
% 0.19/0.48 ![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)))),
% 0.19/0.48 inference(skolemize,[status(sab)],[161])).
% 0.19/0.48 tff(163,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[162, 155])).
% 0.19/0.48 tff(164,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[163, 153])).
% 0.19/0.48 tff(165,plain,
% 0.19/0.48 (((~![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)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(166,plain,
% 0.19/0.48 ((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)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(167,plain,
% 0.19/0.48 (((~![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))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[166])).
% 0.19/0.48 tff(168,plain,
% 0.19/0.48 (((~![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)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[167, 165])).
% 0.19/0.48 tff(169,plain,
% 0.19/0.48 ((~![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))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(170,plain,
% 0.19/0.48 ((~![A: $i, B: $i, C: $i, D: $i] : (empty(A) | (apply_as_element(A, B, C, D) = apply(C, D)) | (~function(C)) | (~quasi_total(C, A, B)) | (~relation_of2(C, A, B)) | (~element(D, A)))) | (~element(B!16, the_carrier(A!15))) | empty(the_carrier(A!15)) | (~function(identity_on_carrier(A!15))) | (~quasi_total(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (~relation_of2(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (apply_as_element(the_carrier(A!15), the_carrier(A!15), identity_on_carrier(A!15), B!16) = apply(identity_on_carrier(A!15), B!16))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.19/0.48 tff(171,plain,
% 0.19/0.48 ((~function(identity_on_carrier(A!15))) | (~quasi_total(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (~relation_of2(identity_on_carrier(A!15), the_carrier(A!15), the_carrier(A!15))) | (apply_as_element(the_carrier(A!15), the_carrier(A!15), identity_on_carrier(A!15), B!16) = apply(identity_on_carrier(A!15), B!16))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[170, 164, 102, 100])).
% 0.19/0.48 tff(172,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[171, 151, 79, 37, 35])).
% 0.19/0.48 % SZS output end Proof
%------------------------------------------------------------------------------