TSTP Solution File: SEU376+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU376+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 07:29:13 EDT 2022
% Result : Theorem 0.20s 0.51s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU376+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Sep 3 12:53:59 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.51 % SZS status Theorem
% 0.20/0.51 % SZS output start Proof
% 0.20/0.51 tff(in_type, type, (
% 0.20/0.51 in: ( $i * $i ) > $o)).
% 0.20/0.51 tff(tptp_fun_C_26_type, type, (
% 0.20/0.51 tptp_fun_C_26: $i)).
% 0.20/0.51 tff(apply_netmap_type, type, (
% 0.20/0.51 apply_netmap: ( $i * $i * $i ) > $i)).
% 0.20/0.51 tff(tptp_fun_D_4_type, type, (
% 0.20/0.51 tptp_fun_D_4: ( $i * $i * $i ) > $i)).
% 0.20/0.51 tff(tptp_fun_B_25_type, type, (
% 0.20/0.51 tptp_fun_B_25: $i)).
% 0.20/0.51 tff(tptp_fun_D_3_type, type, (
% 0.20/0.51 tptp_fun_D_3: ( $i * $i * $i ) > $i)).
% 0.20/0.51 tff(tptp_fun_A_24_type, type, (
% 0.20/0.51 tptp_fun_A_24: $i)).
% 0.20/0.51 tff(tptp_fun_D_0_type, type, (
% 0.20/0.51 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 0.20/0.51 tff(related_type, type, (
% 0.20/0.51 related: ( $i * $i * $i ) > $o)).
% 0.20/0.51 tff(element_type, type, (
% 0.20/0.51 element: ( $i * $i ) > $o)).
% 0.20/0.51 tff(the_carrier_type, type, (
% 0.20/0.51 the_carrier: $i > $i)).
% 0.20/0.51 tff(is_often_in_type, type, (
% 0.20/0.51 is_often_in: ( $i * $i * $i ) > $o)).
% 0.20/0.51 tff(tptp_fun_E_2_type, type, (
% 0.20/0.51 tptp_fun_E_2: ( $i * $i * $i * $i ) > $i)).
% 0.20/0.51 tff(net_str_type, type, (
% 0.20/0.51 net_str: ( $i * $i ) > $o)).
% 0.20/0.51 tff(empty_carrier_type, type, (
% 0.20/0.51 empty_carrier: $i > $o)).
% 0.20/0.51 tff(one_sorted_str_type, type, (
% 0.20/0.51 one_sorted_str: $i > $o)).
% 0.20/0.51 tff(is_eventually_in_type, type, (
% 0.20/0.51 is_eventually_in: ( $i * $i * $i ) > $o)).
% 0.20/0.51 tff(directed_relstr_type, type, (
% 0.20/0.51 directed_relstr: $i > $o)).
% 0.20/0.51 tff(transitive_relstr_type, type, (
% 0.20/0.51 transitive_relstr: $i > $o)).
% 0.20/0.51 tff(tptp_fun_C_6_type, type, (
% 0.20/0.51 tptp_fun_C_6: $i > $i)).
% 0.20/0.51 tff(tptp_fun_B_5_type, type, (
% 0.20/0.51 tptp_fun_B_5: $i > $i)).
% 0.20/0.51 tff(rel_str_type, type, (
% 0.20/0.51 rel_str: $i > $o)).
% 0.20/0.51 tff(tptp_fun_E_1_type, type, (
% 0.20/0.51 tptp_fun_E_1: ( $i * $i * $i * $i ) > $i)).
% 0.20/0.51 tff(1,plain,
% 0.20/0.51 ((((~empty_carrier(A!24)) & one_sorted_str(A!24)) & ((~empty_carrier(B!25)) & transitive_relstr(B!25) & directed_relstr(B!25) & net_str(B!25, A!24) & (~((~is_eventually_in(A!24, B!25, C!26)) | is_often_in(A!24, B!25, C!26))))) <=> ((~empty_carrier(A!24)) & one_sorted_str(A!24) & (~empty_carrier(B!25)) & transitive_relstr(B!25) & directed_relstr(B!25) & net_str(B!25, A!24) & (~((~is_eventually_in(A!24, B!25, C!26)) | is_often_in(A!24, B!25, C!26))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(2,plain,
% 0.20/0.51 ((((~empty_carrier(B!25)) & transitive_relstr(B!25) & directed_relstr(B!25) & net_str(B!25, A!24)) & (~((~is_eventually_in(A!24, B!25, C!26)) | is_often_in(A!24, B!25, C!26)))) <=> ((~empty_carrier(B!25)) & transitive_relstr(B!25) & directed_relstr(B!25) & net_str(B!25, A!24) & (~((~is_eventually_in(A!24, B!25, C!26)) | is_often_in(A!24, B!25, C!26))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(3,plain,
% 0.20/0.51 ((~(~((~empty_carrier(B!25)) & transitive_relstr(B!25) & directed_relstr(B!25) & net_str(B!25, A!24)))) <=> ((~empty_carrier(B!25)) & transitive_relstr(B!25) & directed_relstr(B!25) & net_str(B!25, A!24))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(4,plain,
% 0.20/0.51 (((~(~((~empty_carrier(B!25)) & transitive_relstr(B!25) & directed_relstr(B!25) & net_str(B!25, A!24)))) & (~((~is_eventually_in(A!24, B!25, C!26)) | is_often_in(A!24, B!25, C!26)))) <=> (((~empty_carrier(B!25)) & transitive_relstr(B!25) & directed_relstr(B!25) & net_str(B!25, A!24)) & (~((~is_eventually_in(A!24, B!25, C!26)) | is_often_in(A!24, B!25, C!26))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[3])).
% 0.20/0.51 tff(5,plain,
% 0.20/0.51 (((~(~((~empty_carrier(B!25)) & transitive_relstr(B!25) & directed_relstr(B!25) & net_str(B!25, A!24)))) & (~((~is_eventually_in(A!24, B!25, C!26)) | is_often_in(A!24, B!25, C!26)))) <=> ((~empty_carrier(B!25)) & transitive_relstr(B!25) & directed_relstr(B!25) & net_str(B!25, A!24) & (~((~is_eventually_in(A!24, B!25, C!26)) | is_often_in(A!24, B!25, C!26))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[4, 2])).
% 0.20/0.51 tff(6,plain,
% 0.20/0.51 ((~(~((~empty_carrier(A!24)) & one_sorted_str(A!24)))) <=> ((~empty_carrier(A!24)) & one_sorted_str(A!24))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(7,plain,
% 0.20/0.51 (((~(~((~empty_carrier(A!24)) & one_sorted_str(A!24)))) & ((~(~((~empty_carrier(B!25)) & transitive_relstr(B!25) & directed_relstr(B!25) & net_str(B!25, A!24)))) & (~((~is_eventually_in(A!24, B!25, C!26)) | is_often_in(A!24, B!25, C!26))))) <=> (((~empty_carrier(A!24)) & one_sorted_str(A!24)) & ((~empty_carrier(B!25)) & transitive_relstr(B!25) & directed_relstr(B!25) & net_str(B!25, A!24) & (~((~is_eventually_in(A!24, B!25, C!26)) | is_often_in(A!24, B!25, C!26)))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[6, 5])).
% 0.20/0.51 tff(8,plain,
% 0.20/0.51 (((~(~((~empty_carrier(A!24)) & one_sorted_str(A!24)))) & ((~(~((~empty_carrier(B!25)) & transitive_relstr(B!25) & directed_relstr(B!25) & net_str(B!25, A!24)))) & (~((~is_eventually_in(A!24, B!25, C!26)) | is_often_in(A!24, B!25, C!26))))) <=> ((~empty_carrier(A!24)) & one_sorted_str(A!24) & (~empty_carrier(B!25)) & transitive_relstr(B!25) & directed_relstr(B!25) & net_str(B!25, A!24) & (~((~is_eventually_in(A!24, B!25, C!26)) | is_often_in(A!24, B!25, C!26))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[7, 1])).
% 0.20/0.51 tff(9,plain,
% 0.20/0.51 ((~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))))) <=> (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(10,plain,
% 0.20/0.51 ((~![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (((((~empty_carrier(B)) & transitive_relstr(B)) & directed_relstr(B)) & net_str(B, A)) => ![C: $i] : (is_eventually_in(A, B, C) => is_often_in(A, B, C))))) <=> (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(11,axiom,(~![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (((((~empty_carrier(B)) & transitive_relstr(B)) & directed_relstr(B)) & net_str(B, A)) => ![C: $i] : (is_eventually_in(A, B, C) => is_often_in(A, B, C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t28_yellow_6')).
% 0.20/0.51 tff(12,plain,
% 0.20/0.51 (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.51 tff(13,plain,
% 0.20/0.51 (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[12, 9])).
% 0.20/0.51 tff(14,plain,
% 0.20/0.51 (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.20/0.51 tff(15,plain,
% 0.20/0.51 (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[14, 9])).
% 0.20/0.51 tff(16,plain,
% 0.20/0.51 (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[15, 9])).
% 0.20/0.51 tff(17,plain,
% 0.20/0.51 (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.20/0.51 tff(18,plain,
% 0.20/0.51 (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[17, 9])).
% 0.20/0.51 tff(19,plain,
% 0.20/0.51 ((~empty_carrier(A!24)) & one_sorted_str(A!24) & (~empty_carrier(B!25)) & transitive_relstr(B!25) & directed_relstr(B!25) & net_str(B!25, A!24) & (~((~is_eventually_in(A!24, B!25, C!26)) | is_often_in(A!24, B!25, C!26)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[18, 8])).
% 0.20/0.51 tff(20,plain,
% 0.20/0.51 (one_sorted_str(A!24)),
% 0.20/0.51 inference(and_elim,[status(thm)],[19])).
% 0.20/0.51 tff(21,plain,
% 0.20/0.51 (~empty_carrier(A!24)),
% 0.20/0.51 inference(and_elim,[status(thm)],[19])).
% 0.20/0.51 tff(22,plain,
% 0.20/0.51 (^[A: $i] : refl((empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))) | (~(is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C)))))))))))) <=> (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))) | (~(is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C)))))))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(23,plain,
% 0.20/0.51 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))) | (~(is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C)))))))))))) <=> ![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))) | (~(is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C))))))))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.51 tff(24,plain,
% 0.20/0.51 (^[A: $i] : rewrite((empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))) | (~(is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C)))))))))))) <=> (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))) | (~(is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C)))))))))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(25,plain,
% 0.20/0.52 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))) | (~(is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C)))))))))))) <=> ![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))) | (~(is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C))))))))))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.52 tff(26,plain,
% 0.20/0.52 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))) | (~(is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C)))))))))))) <=> ![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))) | (~(is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C))))))))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[25, 23])).
% 0.20/0.52 tff(27,plain,
% 0.20/0.52 (^[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))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(B)) & net_str(B, A)) <=> (~(empty_carrier(B) | (~net_str(B, A))))), ((~((~empty_carrier(B)) & net_str(B, A))) <=> (~(~(empty_carrier(B) | (~net_str(B, A))))))), rewrite((~(~(empty_carrier(B) | (~net_str(B, A))))) <=> (empty_carrier(B) | (~net_str(B, A)))), ((~((~empty_carrier(B)) & net_str(B, A))) <=> (empty_carrier(B) | (~net_str(B, A))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (element(tptp_fun_E_2(D, C, B, A), the_carrier(B)) & related(B, D, tptp_fun_E_2(D, C, B, A)) & in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C)))) <=> ((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))), trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(rewrite((element(E, the_carrier(B)) & related(B, tptp_fun_D_3(C, B, A), E) & in(apply_netmap(A, B, E), C)) <=> (~((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C))))), ((~(element(E, the_carrier(B)) & related(B, tptp_fun_D_3(C, B, A), E) & in(apply_netmap(A, B, E), C))) <=> (~(~((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C))))))), rewrite((~(~((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C))))) <=> ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C)))), ((~(element(E, the_carrier(B)) & related(B, tptp_fun_D_3(C, B, A), E) & in(apply_netmap(A, B, E), C))) <=> ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C)))))), (![E: $i] : (~(element(E, the_carrier(B)) & related(B, tptp_fun_D_3(C, B, A), E) & in(apply_netmap(A, B, E), C))) <=> ![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C))))), ((element(tptp_fun_D_3(C, B, A), the_carrier(B)) & ![E: $i] : (~(element(E, the_carrier(B)) & related(B, tptp_fun_D_3(C, B, A), E) & in(apply_netmap(A, B, E), C)))) <=> (element(tptp_fun_D_3(C, B, A), the_carrier(B)) & ![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C)))))), rewrite((element(tptp_fun_D_3(C, B, A), the_carrier(B)) & ![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C)))) <=> (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C))))))), ((element(tptp_fun_D_3(C, B, A), the_carrier(B)) & ![E: $i] : (~(element(E, the_carrier(B)) & related(B, tptp_fun_D_3(C, B, A), E) & in(apply_netmap(A, B, E), C)))) <=> (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C)))))))), ((is_often_in(A, B, C) | (element(tptp_fun_D_3(C, B, A), the_carrier(B)) & ![E: $i] : (~(element(E, the_carrier(B)) & related(B, tptp_fun_D_3(C, B, A), E) & in(apply_netmap(A, B, E), C))))) <=> (is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C))))))))), rewrite((is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C))))))) <=> (is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C)))))))), ((is_often_in(A, B, C) | (element(tptp_fun_D_3(C, B, A), the_carrier(B)) & ![E: $i] : (~(element(E, the_carrier(B)) & related(B, tptp_fun_D_3(C, B, A), E) & in(apply_netmap(A, B, E), C))))) <=> (is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C))))))))), ((((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (element(tptp_fun_E_2(D, C, B, A), the_carrier(B)) & related(B, D, tptp_fun_E_2(D, C, B, A)) & in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C)))) & (is_often_in(A, B, C) | (element(tptp_fun_D_3(C, B, A), the_carrier(B)) & ![E: $i] : (~(element(E, the_carrier(B)) & related(B, tptp_fun_D_3(C, B, A), E) & in(apply_netmap(A, B, E), C)))))) <=> (((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C)))))) & (is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C)))))))))), rewrite((((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C)))))) & (is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C)))))))) <=> (~((~((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))) | (~(is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C))))))))))), ((((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (element(tptp_fun_E_2(D, C, B, A), the_carrier(B)) & related(B, D, tptp_fun_E_2(D, C, B, A)) & in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C)))) & (is_often_in(A, B, C) | (element(tptp_fun_D_3(C, B, A), the_carrier(B)) & ![E: $i] : (~(element(E, the_carrier(B)) & related(B, tptp_fun_D_3(C, B, A), E) & in(apply_netmap(A, B, E), C)))))) <=> (~((~((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))) | (~(is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C))))))))))))), (![C: $i] : (((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (element(tptp_fun_E_2(D, C, B, A), the_carrier(B)) & related(B, D, tptp_fun_E_2(D, C, B, A)) & in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C)))) & (is_often_in(A, B, C) | (element(tptp_fun_D_3(C, B, A), the_carrier(B)) & ![E: $i] : (~(element(E, the_carrier(B)) & related(B, tptp_fun_D_3(C, B, A), E) & in(apply_netmap(A, B, E), C)))))) <=> ![C: $i] : (~((~((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))) | (~(is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C)))))))))))), (((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (element(tptp_fun_E_2(D, C, B, A), the_carrier(B)) & related(B, D, tptp_fun_E_2(D, C, B, A)) & in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C)))) & (is_often_in(A, B, C) | (element(tptp_fun_D_3(C, B, A), the_carrier(B)) & ![E: $i] : (~(element(E, the_carrier(B)) & related(B, tptp_fun_D_3(C, B, A), E) & in(apply_netmap(A, B, E), C))))))) <=> ((empty_carrier(B) | (~net_str(B, A))) | ![C: $i] : (~((~((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))) | (~(is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C))))))))))))), rewrite(((empty_carrier(B) | (~net_str(B, A))) | ![C: $i] : (~((~((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))) | (~(is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C))))))))))) <=> (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))) | (~(is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C)))))))))))), (((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (element(tptp_fun_E_2(D, C, B, A), the_carrier(B)) & related(B, D, tptp_fun_E_2(D, C, B, A)) & in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C)))) & (is_often_in(A, B, C) | (element(tptp_fun_D_3(C, B, A), the_carrier(B)) & ![E: $i] : (~(element(E, the_carrier(B)) & related(B, tptp_fun_D_3(C, B, A), E) & in(apply_netmap(A, B, E), C))))))) <=> (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))) | (~(is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C)))))))))))))), (![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (element(tptp_fun_E_2(D, C, B, A), the_carrier(B)) & related(B, D, tptp_fun_E_2(D, C, B, A)) & in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C)))) & (is_often_in(A, B, C) | (element(tptp_fun_D_3(C, B, A), the_carrier(B)) & ![E: $i] : (~(element(E, the_carrier(B)) & related(B, tptp_fun_D_3(C, B, A), E) & in(apply_netmap(A, B, E), C))))))) <=> ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))) | (~(is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C))))))))))))), (((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (element(tptp_fun_E_2(D, C, B, A), the_carrier(B)) & related(B, D, tptp_fun_E_2(D, C, B, A)) & in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C)))) & (is_often_in(A, B, C) | (element(tptp_fun_D_3(C, B, A), the_carrier(B)) & ![E: $i] : (~(element(E, the_carrier(B)) & related(B, tptp_fun_D_3(C, B, A), E) & in(apply_netmap(A, B, E), C)))))))) <=> ((empty_carrier(A) | (~one_sorted_str(A))) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))) | (~(is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C)))))))))))))), rewrite(((empty_carrier(A) | (~one_sorted_str(A))) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))) | (~(is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C)))))))))))) <=> (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))) | (~(is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C))))))))))))), (((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (element(tptp_fun_E_2(D, C, B, A), the_carrier(B)) & related(B, D, tptp_fun_E_2(D, C, B, A)) & in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C)))) & (is_often_in(A, B, C) | (element(tptp_fun_D_3(C, B, A), the_carrier(B)) & ![E: $i] : (~(element(E, the_carrier(B)) & related(B, tptp_fun_D_3(C, B, A), E) & in(apply_netmap(A, B, E), C)))))))) <=> (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))) | (~(is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C))))))))))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(28,plain,
% 0.20/0.52 (![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (element(tptp_fun_E_2(D, C, B, A), the_carrier(B)) & related(B, D, tptp_fun_E_2(D, C, B, A)) & in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C)))) & (is_often_in(A, B, C) | (element(tptp_fun_D_3(C, B, A), the_carrier(B)) & ![E: $i] : (~(element(E, the_carrier(B)) & related(B, tptp_fun_D_3(C, B, A), E) & in(apply_netmap(A, B, E), C)))))))) <=> ![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))) | (~(is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C))))))))))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.52 tff(29,plain,
% 0.20/0.52 (^[A: $i] : rewrite(((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (element(tptp_fun_E_2(D, C, B, A), the_carrier(B)) & related(B, D, tptp_fun_E_2(D, C, B, A)) & in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C)))) & (is_often_in(A, B, C) | ((~(~element(tptp_fun_D_3(C, B, A), the_carrier(B)))) & ![E: $i] : (~(element(E, the_carrier(B)) & related(B, tptp_fun_D_3(C, B, A), E) & in(apply_netmap(A, B, E), C)))))))) <=> ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (element(tptp_fun_E_2(D, C, B, A), the_carrier(B)) & related(B, D, tptp_fun_E_2(D, C, B, A)) & in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C)))) & (is_often_in(A, B, C) | (element(tptp_fun_D_3(C, B, A), the_carrier(B)) & ![E: $i] : (~(element(E, the_carrier(B)) & related(B, tptp_fun_D_3(C, B, A), E) & in(apply_netmap(A, B, E), C)))))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(30,plain,
% 0.20/0.52 (![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (element(tptp_fun_E_2(D, C, B, A), the_carrier(B)) & related(B, D, tptp_fun_E_2(D, C, B, A)) & in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C)))) & (is_often_in(A, B, C) | ((~(~element(tptp_fun_D_3(C, B, A), the_carrier(B)))) & ![E: $i] : (~(element(E, the_carrier(B)) & related(B, tptp_fun_D_3(C, B, A), E) & in(apply_netmap(A, B, E), C)))))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (element(tptp_fun_E_2(D, C, B, A), the_carrier(B)) & related(B, D, tptp_fun_E_2(D, C, B, A)) & in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C)))) & (is_often_in(A, B, C) | (element(tptp_fun_D_3(C, B, A), the_carrier(B)) & ![E: $i] : (~(element(E, the_carrier(B)) & related(B, tptp_fun_D_3(C, B, A), E) & in(apply_netmap(A, B, E), C))))))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.52 tff(31,plain,
% 0.20/0.52 (![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (is_often_in(A, B, C) <=> ![D: $i] : ((~element(D, the_carrier(B))) | ?[E: $i] : (element(E, the_carrier(B)) & related(B, D, E) & in(apply_netmap(A, B, E), C)))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (is_often_in(A, B, C) <=> ![D: $i] : ((~element(D, the_carrier(B))) | ?[E: $i] : (element(E, the_carrier(B)) & related(B, D, E) & in(apply_netmap(A, B, E), C))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(32,plain,
% 0.20/0.52 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((is_often_in(A, B, C) <=> ![D: $i] : (element(D, the_carrier(B)) => ?[E: $i] : ((element(E, the_carrier(B)) & related(B, D, E)) & in(apply_netmap(A, B, E), C)))) <=> (is_often_in(A, B, C) <=> ![D: $i] : ((~element(D, the_carrier(B))) | ?[E: $i] : (element(E, the_carrier(B)) & related(B, D, E) & in(apply_netmap(A, B, E), C)))))), (![C: $i] : (is_often_in(A, B, C) <=> ![D: $i] : (element(D, the_carrier(B)) => ?[E: $i] : ((element(E, the_carrier(B)) & related(B, D, E)) & in(apply_netmap(A, B, E), C)))) <=> ![C: $i] : (is_often_in(A, B, C) <=> ![D: $i] : ((~element(D, the_carrier(B))) | ?[E: $i] : (element(E, the_carrier(B)) & related(B, D, E) & in(apply_netmap(A, B, E), C)))))), ((((~empty_carrier(B)) & net_str(B, A)) => ![C: $i] : (is_often_in(A, B, C) <=> ![D: $i] : (element(D, the_carrier(B)) => ?[E: $i] : ((element(E, the_carrier(B)) & related(B, D, E)) & in(apply_netmap(A, B, E), C))))) <=> (((~empty_carrier(B)) & net_str(B, A)) => ![C: $i] : (is_often_in(A, B, C) <=> ![D: $i] : ((~element(D, the_carrier(B))) | ?[E: $i] : (element(E, the_carrier(B)) & related(B, D, E) & in(apply_netmap(A, B, E), C))))))), rewrite((((~empty_carrier(B)) & net_str(B, A)) => ![C: $i] : (is_often_in(A, B, C) <=> ![D: $i] : ((~element(D, the_carrier(B))) | ?[E: $i] : (element(E, the_carrier(B)) & related(B, D, E) & in(apply_netmap(A, B, E), C))))) <=> ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (is_often_in(A, B, C) <=> ![D: $i] : ((~element(D, the_carrier(B))) | ?[E: $i] : (element(E, the_carrier(B)) & related(B, D, E) & in(apply_netmap(A, B, E), C)))))), ((((~empty_carrier(B)) & net_str(B, A)) => ![C: $i] : (is_often_in(A, B, C) <=> ![D: $i] : (element(D, the_carrier(B)) => ?[E: $i] : ((element(E, the_carrier(B)) & related(B, D, E)) & in(apply_netmap(A, B, E), C))))) <=> ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (is_often_in(A, B, C) <=> ![D: $i] : ((~element(D, the_carrier(B))) | ?[E: $i] : (element(E, the_carrier(B)) & related(B, D, E) & in(apply_netmap(A, B, E), C)))))))), (![B: $i] : (((~empty_carrier(B)) & net_str(B, A)) => ![C: $i] : (is_often_in(A, B, C) <=> ![D: $i] : (element(D, the_carrier(B)) => ?[E: $i] : ((element(E, the_carrier(B)) & related(B, D, E)) & in(apply_netmap(A, B, E), C))))) <=> ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (is_often_in(A, B, C) <=> ![D: $i] : ((~element(D, the_carrier(B))) | ?[E: $i] : (element(E, the_carrier(B)) & related(B, D, E) & in(apply_netmap(A, B, E), C))))))), ((((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (((~empty_carrier(B)) & net_str(B, A)) => ![C: $i] : (is_often_in(A, B, C) <=> ![D: $i] : (element(D, the_carrier(B)) => ?[E: $i] : ((element(E, the_carrier(B)) & related(B, D, E)) & in(apply_netmap(A, B, E), C)))))) <=> (((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (is_often_in(A, B, C) <=> ![D: $i] : ((~element(D, the_carrier(B))) | ?[E: $i] : (element(E, the_carrier(B)) & related(B, D, E) & in(apply_netmap(A, B, E), C)))))))), rewrite((((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (is_often_in(A, B, C) <=> ![D: $i] : ((~element(D, the_carrier(B))) | ?[E: $i] : (element(E, the_carrier(B)) & related(B, D, E) & in(apply_netmap(A, B, E), C)))))) <=> ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (is_often_in(A, B, C) <=> ![D: $i] : ((~element(D, the_carrier(B))) | ?[E: $i] : (element(E, the_carrier(B)) & related(B, D, E) & in(apply_netmap(A, B, E), C))))))), ((((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (((~empty_carrier(B)) & net_str(B, A)) => ![C: $i] : (is_often_in(A, B, C) <=> ![D: $i] : (element(D, the_carrier(B)) => ?[E: $i] : ((element(E, the_carrier(B)) & related(B, D, E)) & in(apply_netmap(A, B, E), C)))))) <=> ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (is_often_in(A, B, C) <=> ![D: $i] : ((~element(D, the_carrier(B))) | ?[E: $i] : (element(E, the_carrier(B)) & related(B, D, E) & in(apply_netmap(A, B, E), C))))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(33,plain,
% 0.20/0.52 (![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (((~empty_carrier(B)) & net_str(B, A)) => ![C: $i] : (is_often_in(A, B, C) <=> ![D: $i] : (element(D, the_carrier(B)) => ?[E: $i] : ((element(E, the_carrier(B)) & related(B, D, E)) & in(apply_netmap(A, B, E), C)))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (is_often_in(A, B, C) <=> ![D: $i] : ((~element(D, the_carrier(B))) | ?[E: $i] : (element(E, the_carrier(B)) & related(B, D, E) & in(apply_netmap(A, B, E), C))))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.52 tff(34,axiom,(![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (((~empty_carrier(B)) & net_str(B, A)) => ![C: $i] : (is_often_in(A, B, C) <=> ![D: $i] : (element(D, the_carrier(B)) => ?[E: $i] : ((element(E, the_carrier(B)) & related(B, D, E)) & in(apply_netmap(A, B, E), C))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d12_waybel_0')).
% 0.20/0.52 tff(35,plain,
% 0.20/0.52 (![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (is_often_in(A, B, C) <=> ![D: $i] : ((~element(D, the_carrier(B))) | ?[E: $i] : (element(E, the_carrier(B)) & related(B, D, E) & in(apply_netmap(A, B, E), C))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.52 tff(36,plain,
% 0.20/0.52 (![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (is_often_in(A, B, C) <=> ![D: $i] : ((~element(D, the_carrier(B))) | ?[E: $i] : (element(E, the_carrier(B)) & related(B, D, E) & in(apply_netmap(A, B, E), C))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.20/0.52 tff(37,plain,(
% 0.20/0.52 ![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (element(tptp_fun_E_2(D, C, B, A), the_carrier(B)) & related(B, D, tptp_fun_E_2(D, C, B, A)) & in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C)))) & (is_often_in(A, B, C) | ((~(~element(tptp_fun_D_3(C, B, A), the_carrier(B)))) & ![E: $i] : (~(element(E, the_carrier(B)) & related(B, tptp_fun_D_3(C, B, A), E) & in(apply_netmap(A, B, E), C))))))))),
% 0.20/0.52 inference(skolemize,[status(sab)],[36])).
% 0.20/0.52 tff(38,plain,
% 0.20/0.52 (![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (element(tptp_fun_E_2(D, C, B, A), the_carrier(B)) & related(B, D, tptp_fun_E_2(D, C, B, A)) & in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C)))) & (is_often_in(A, B, C) | (element(tptp_fun_D_3(C, B, A), the_carrier(B)) & ![E: $i] : (~(element(E, the_carrier(B)) & related(B, tptp_fun_D_3(C, B, A), E) & in(apply_netmap(A, B, E), C))))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.20/0.52 tff(39,plain,
% 0.20/0.52 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))) | (~(is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C))))))))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[38, 28])).
% 0.20/0.52 tff(40,plain,
% 0.20/0.52 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))) | (~(is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C))))))))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[39, 26])).
% 0.20/0.52 tff(41,plain,
% 0.20/0.52 (((~![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))) | (~(is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C))))))))))))) | (empty_carrier(A!24) | (~one_sorted_str(A!24)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A!24)) | ![C: $i] : (~((~((~is_often_in(A!24, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A!24), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A!24))) | (~in(apply_netmap(A!24, B, tptp_fun_E_2(D, C, B, A!24)), C))))))) | (~(is_often_in(A!24, B, C) | (~((~element(tptp_fun_D_3(C, B, A!24), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A!24), E)) | (~in(apply_netmap(A!24, B, E), C))))))))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))) | (~(is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C))))))))))))) | empty_carrier(A!24) | (~one_sorted_str(A!24)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A!24)) | ![C: $i] : (~((~((~is_often_in(A!24, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A!24), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A!24))) | (~in(apply_netmap(A!24, B, tptp_fun_E_2(D, C, B, A!24)), C))))))) | (~(is_often_in(A!24, B, C) | (~((~element(tptp_fun_D_3(C, B, A!24), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A!24), E)) | (~in(apply_netmap(A!24, B, E), C))))))))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(42,plain,
% 0.20/0.52 ((~![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))) | (~(is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C))))))))))))) | (empty_carrier(A!24) | (~one_sorted_str(A!24)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A!24)) | ![C: $i] : (~((~((~is_often_in(A!24, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A!24), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A!24))) | (~in(apply_netmap(A!24, B, tptp_fun_E_2(D, C, B, A!24)), C))))))) | (~(is_often_in(A!24, B, C) | (~((~element(tptp_fun_D_3(C, B, A!24), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A!24), E)) | (~in(apply_netmap(A!24, B, E), C))))))))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(43,plain,
% 0.20/0.52 ((~![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_often_in(A, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A))) | (~in(apply_netmap(A, B, tptp_fun_E_2(D, C, B, A)), C))))))) | (~(is_often_in(A, B, C) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A), E)) | (~in(apply_netmap(A, B, E), C))))))))))))) | empty_carrier(A!24) | (~one_sorted_str(A!24)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A!24)) | ![C: $i] : (~((~((~is_often_in(A!24, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A!24), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A!24))) | (~in(apply_netmap(A!24, B, tptp_fun_E_2(D, C, B, A!24)), C))))))) | (~(is_often_in(A!24, B, C) | (~((~element(tptp_fun_D_3(C, B, A!24), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A!24), E)) | (~in(apply_netmap(A!24, B, E), C)))))))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.52 tff(44,plain,
% 0.20/0.52 (![B: $i] : (empty_carrier(B) | (~net_str(B, A!24)) | ![C: $i] : (~((~((~is_often_in(A!24, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A!24), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A!24))) | (~in(apply_netmap(A!24, B, tptp_fun_E_2(D, C, B, A!24)), C))))))) | (~(is_often_in(A!24, B, C) | (~((~element(tptp_fun_D_3(C, B, A!24), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A!24), E)) | (~in(apply_netmap(A!24, B, E), C)))))))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[43, 40, 21, 20])).
% 0.20/0.52 tff(45,plain,
% 0.20/0.52 (net_str(B!25, A!24)),
% 0.20/0.52 inference(and_elim,[status(thm)],[19])).
% 0.20/0.52 tff(46,plain,
% 0.20/0.52 (~empty_carrier(B!25)),
% 0.20/0.52 inference(and_elim,[status(thm)],[19])).
% 0.20/0.52 tff(47,plain,
% 0.20/0.52 (((~![B: $i] : (empty_carrier(B) | (~net_str(B, A!24)) | ![C: $i] : (~((~((~is_often_in(A!24, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A!24), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A!24))) | (~in(apply_netmap(A!24, B, tptp_fun_E_2(D, C, B, A!24)), C))))))) | (~(is_often_in(A!24, B, C) | (~((~element(tptp_fun_D_3(C, B, A!24), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A!24), E)) | (~in(apply_netmap(A!24, B, E), C)))))))))))) | (empty_carrier(B!25) | (~net_str(B!25, A!24)) | ![C: $i] : (~((~((~is_often_in(A!24, B!25, C)) | ![D: $i] : ((~element(D, the_carrier(B!25))) | (~((~element(tptp_fun_E_2(D, C, B!25, A!24), the_carrier(B!25))) | (~related(B!25, D, tptp_fun_E_2(D, C, B!25, A!24))) | (~in(apply_netmap(A!24, B!25, tptp_fun_E_2(D, C, B!25, A!24)), C))))))) | (~(is_often_in(A!24, B!25, C) | (~((~element(tptp_fun_D_3(C, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C, B!25, A!24), E)) | (~in(apply_netmap(A!24, B!25, E), C)))))))))))) <=> ((~![B: $i] : (empty_carrier(B) | (~net_str(B, A!24)) | ![C: $i] : (~((~((~is_often_in(A!24, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A!24), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A!24))) | (~in(apply_netmap(A!24, B, tptp_fun_E_2(D, C, B, A!24)), C))))))) | (~(is_often_in(A!24, B, C) | (~((~element(tptp_fun_D_3(C, B, A!24), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A!24), E)) | (~in(apply_netmap(A!24, B, E), C)))))))))))) | empty_carrier(B!25) | (~net_str(B!25, A!24)) | ![C: $i] : (~((~((~is_often_in(A!24, B!25, C)) | ![D: $i] : ((~element(D, the_carrier(B!25))) | (~((~element(tptp_fun_E_2(D, C, B!25, A!24), the_carrier(B!25))) | (~related(B!25, D, tptp_fun_E_2(D, C, B!25, A!24))) | (~in(apply_netmap(A!24, B!25, tptp_fun_E_2(D, C, B!25, A!24)), C))))))) | (~(is_often_in(A!24, B!25, C) | (~((~element(tptp_fun_D_3(C, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C, B!25, A!24), E)) | (~in(apply_netmap(A!24, B!25, E), C)))))))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(48,plain,
% 0.20/0.53 ((~![B: $i] : (empty_carrier(B) | (~net_str(B, A!24)) | ![C: $i] : (~((~((~is_often_in(A!24, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A!24), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A!24))) | (~in(apply_netmap(A!24, B, tptp_fun_E_2(D, C, B, A!24)), C))))))) | (~(is_often_in(A!24, B, C) | (~((~element(tptp_fun_D_3(C, B, A!24), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A!24), E)) | (~in(apply_netmap(A!24, B, E), C)))))))))))) | (empty_carrier(B!25) | (~net_str(B!25, A!24)) | ![C: $i] : (~((~((~is_often_in(A!24, B!25, C)) | ![D: $i] : ((~element(D, the_carrier(B!25))) | (~((~element(tptp_fun_E_2(D, C, B!25, A!24), the_carrier(B!25))) | (~related(B!25, D, tptp_fun_E_2(D, C, B!25, A!24))) | (~in(apply_netmap(A!24, B!25, tptp_fun_E_2(D, C, B!25, A!24)), C))))))) | (~(is_often_in(A!24, B!25, C) | (~((~element(tptp_fun_D_3(C, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C, B!25, A!24), E)) | (~in(apply_netmap(A!24, B!25, E), C)))))))))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(49,plain,
% 0.20/0.53 ((~![B: $i] : (empty_carrier(B) | (~net_str(B, A!24)) | ![C: $i] : (~((~((~is_often_in(A!24, B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~((~element(tptp_fun_E_2(D, C, B, A!24), the_carrier(B))) | (~related(B, D, tptp_fun_E_2(D, C, B, A!24))) | (~in(apply_netmap(A!24, B, tptp_fun_E_2(D, C, B, A!24)), C))))))) | (~(is_often_in(A!24, B, C) | (~((~element(tptp_fun_D_3(C, B, A!24), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | (~related(B, tptp_fun_D_3(C, B, A!24), E)) | (~in(apply_netmap(A!24, B, E), C)))))))))))) | empty_carrier(B!25) | (~net_str(B!25, A!24)) | ![C: $i] : (~((~((~is_often_in(A!24, B!25, C)) | ![D: $i] : ((~element(D, the_carrier(B!25))) | (~((~element(tptp_fun_E_2(D, C, B!25, A!24), the_carrier(B!25))) | (~related(B!25, D, tptp_fun_E_2(D, C, B!25, A!24))) | (~in(apply_netmap(A!24, B!25, tptp_fun_E_2(D, C, B!25, A!24)), C))))))) | (~(is_often_in(A!24, B!25, C) | (~((~element(tptp_fun_D_3(C, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C, B!25, A!24), E)) | (~in(apply_netmap(A!24, B!25, E), C))))))))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.53 tff(50,plain,
% 0.20/0.53 (![C: $i] : (~((~((~is_often_in(A!24, B!25, C)) | ![D: $i] : ((~element(D, the_carrier(B!25))) | (~((~element(tptp_fun_E_2(D, C, B!25, A!24), the_carrier(B!25))) | (~related(B!25, D, tptp_fun_E_2(D, C, B!25, A!24))) | (~in(apply_netmap(A!24, B!25, tptp_fun_E_2(D, C, B!25, A!24)), C))))))) | (~(is_often_in(A!24, B!25, C) | (~((~element(tptp_fun_D_3(C, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C, B!25, A!24), E)) | (~in(apply_netmap(A!24, B!25, E), C))))))))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[49, 46, 45, 44])).
% 0.20/0.53 tff(51,plain,
% 0.20/0.53 ((~![C: $i] : (~((~((~is_often_in(A!24, B!25, C)) | ![D: $i] : ((~element(D, the_carrier(B!25))) | (~((~element(tptp_fun_E_2(D, C, B!25, A!24), the_carrier(B!25))) | (~related(B!25, D, tptp_fun_E_2(D, C, B!25, A!24))) | (~in(apply_netmap(A!24, B!25, tptp_fun_E_2(D, C, B!25, A!24)), C))))))) | (~(is_often_in(A!24, B!25, C) | (~((~element(tptp_fun_D_3(C, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C, B!25, A!24), E)) | (~in(apply_netmap(A!24, B!25, E), C))))))))))) | (~((~((~is_often_in(A!24, B!25, C!26)) | ![D: $i] : ((~element(D, the_carrier(B!25))) | (~((~element(tptp_fun_E_2(D, C!26, B!25, A!24), the_carrier(B!25))) | (~related(B!25, D, tptp_fun_E_2(D, C!26, B!25, A!24))) | (~in(apply_netmap(A!24, B!25, tptp_fun_E_2(D, C!26, B!25, A!24)), C!26))))))) | (~(is_often_in(A!24, B!25, C!26) | (~((~element(tptp_fun_D_3(C!26, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), E)) | (~in(apply_netmap(A!24, B!25, E), C!26))))))))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(52,plain,
% 0.20/0.53 (~((~((~is_often_in(A!24, B!25, C!26)) | ![D: $i] : ((~element(D, the_carrier(B!25))) | (~((~element(tptp_fun_E_2(D, C!26, B!25, A!24), the_carrier(B!25))) | (~related(B!25, D, tptp_fun_E_2(D, C!26, B!25, A!24))) | (~in(apply_netmap(A!24, B!25, tptp_fun_E_2(D, C!26, B!25, A!24)), C!26))))))) | (~(is_often_in(A!24, B!25, C!26) | (~((~element(tptp_fun_D_3(C!26, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), E)) | (~in(apply_netmap(A!24, B!25, E), C!26)))))))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.53 tff(53,plain,
% 0.20/0.53 (((~((~is_often_in(A!24, B!25, C!26)) | ![D: $i] : ((~element(D, the_carrier(B!25))) | (~((~element(tptp_fun_E_2(D, C!26, B!25, A!24), the_carrier(B!25))) | (~related(B!25, D, tptp_fun_E_2(D, C!26, B!25, A!24))) | (~in(apply_netmap(A!24, B!25, tptp_fun_E_2(D, C!26, B!25, A!24)), C!26))))))) | (~(is_often_in(A!24, B!25, C!26) | (~((~element(tptp_fun_D_3(C!26, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), E)) | (~in(apply_netmap(A!24, B!25, E), C!26))))))))) | (is_often_in(A!24, B!25, C!26) | (~((~element(tptp_fun_D_3(C!26, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), E)) | (~in(apply_netmap(A!24, B!25, E), C!26)))))))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(54,plain,
% 0.20/0.53 (is_often_in(A!24, B!25, C!26) | (~((~element(tptp_fun_D_3(C!26, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), E)) | (~in(apply_netmap(A!24, B!25, E), C!26))))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.20/0.53 tff(55,plain,
% 0.20/0.53 (~((~is_eventually_in(A!24, B!25, C!26)) | is_often_in(A!24, B!25, C!26))),
% 0.20/0.53 inference(and_elim,[status(thm)],[19])).
% 0.20/0.53 tff(56,plain,
% 0.20/0.53 (~is_often_in(A!24, B!25, C!26)),
% 0.20/0.53 inference(or_elim,[status(thm)],[55])).
% 0.20/0.53 tff(57,plain,
% 0.20/0.53 ((~(is_often_in(A!24, B!25, C!26) | (~((~element(tptp_fun_D_3(C!26, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), E)) | (~in(apply_netmap(A!24, B!25, E), C!26)))))))) | is_often_in(A!24, B!25, C!26) | (~((~element(tptp_fun_D_3(C!26, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), E)) | (~in(apply_netmap(A!24, B!25, E), C!26))))))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(58,plain,
% 0.20/0.53 ((~(is_often_in(A!24, B!25, C!26) | (~((~element(tptp_fun_D_3(C!26, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), E)) | (~in(apply_netmap(A!24, B!25, E), C!26)))))))) | (~((~element(tptp_fun_D_3(C!26, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), E)) | (~in(apply_netmap(A!24, B!25, E), C!26))))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.20/0.53 tff(59,plain,
% 0.20/0.53 (~((~element(tptp_fun_D_3(C!26, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), E)) | (~in(apply_netmap(A!24, B!25, E), C!26)))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[58, 54])).
% 0.20/0.53 tff(60,plain,
% 0.20/0.53 (((~element(tptp_fun_D_3(C!26, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), E)) | (~in(apply_netmap(A!24, B!25, E), C!26))))) | element(tptp_fun_D_3(C!26, B!25, A!24), the_carrier(B!25))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(61,plain,
% 0.20/0.53 (element(tptp_fun_D_3(C!26, B!25, A!24), the_carrier(B!25))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.20/0.53 tff(62,plain,
% 0.20/0.53 (^[A: $i] : refl(((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A)))) <=> ((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A)))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(63,plain,
% 0.20/0.53 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A)))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[62])).
% 0.20/0.53 tff(64,plain,
% 0.20/0.53 (^[A: $i] : rewrite(((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A)))) <=> ((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A)))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(65,plain,
% 0.20/0.53 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A)))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.53 tff(66,plain,
% 0.20/0.53 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A)))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[65, 63])).
% 0.20/0.53 tff(67,plain,
% 0.20/0.53 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A)))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(68,plain,
% 0.20/0.53 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((net_str(B, A) => rel_str(B)) <=> (rel_str(B) | (~net_str(B, A))))), (![B: $i] : (net_str(B, A) => rel_str(B)) <=> ![B: $i] : (rel_str(B) | (~net_str(B, A))))), ((one_sorted_str(A) => ![B: $i] : (net_str(B, A) => rel_str(B))) <=> (one_sorted_str(A) => ![B: $i] : (rel_str(B) | (~net_str(B, A)))))), rewrite((one_sorted_str(A) => ![B: $i] : (rel_str(B) | (~net_str(B, A)))) <=> ((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A))))), ((one_sorted_str(A) => ![B: $i] : (net_str(B, A) => rel_str(B))) <=> ((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(69,plain,
% 0.20/0.53 (![A: $i] : (one_sorted_str(A) => ![B: $i] : (net_str(B, A) => rel_str(B))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.53 tff(70,axiom,(![A: $i] : (one_sorted_str(A) => ![B: $i] : (net_str(B, A) => rel_str(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l1_waybel_0')).
% 0.20/0.53 tff(71,plain,
% 0.20/0.53 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.53 tff(72,plain,
% 0.20/0.53 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.20/0.53 tff(73,plain,(
% 0.20/0.53 ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A))))),
% 0.20/0.53 inference(skolemize,[status(sab)],[72])).
% 0.20/0.53 tff(74,plain,
% 0.20/0.53 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.20/0.53 tff(75,plain,
% 0.20/0.53 (((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A))))) | ((~one_sorted_str(A!24)) | ![B: $i] : (rel_str(B) | (~net_str(B, A!24))))) <=> ((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A))))) | (~one_sorted_str(A!24)) | ![B: $i] : (rel_str(B) | (~net_str(B, A!24))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(76,plain,
% 0.20/0.53 ((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A))))) | ((~one_sorted_str(A!24)) | ![B: $i] : (rel_str(B) | (~net_str(B, A!24))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(77,plain,
% 0.20/0.53 ((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A))))) | (~one_sorted_str(A!24)) | ![B: $i] : (rel_str(B) | (~net_str(B, A!24)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.53 tff(78,plain,
% 0.20/0.53 (![B: $i] : (rel_str(B) | (~net_str(B, A!24)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[77, 74, 20])).
% 0.20/0.53 tff(79,plain,
% 0.20/0.53 (((~![B: $i] : (rel_str(B) | (~net_str(B, A!24)))) | (rel_str(B!25) | (~net_str(B!25, A!24)))) <=> ((~![B: $i] : (rel_str(B) | (~net_str(B, A!24)))) | rel_str(B!25) | (~net_str(B!25, A!24)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(80,plain,
% 0.20/0.53 ((~![B: $i] : (rel_str(B) | (~net_str(B, A!24)))) | (rel_str(B!25) | (~net_str(B!25, A!24)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(81,plain,
% 0.20/0.53 ((~![B: $i] : (rel_str(B) | (~net_str(B, A!24)))) | rel_str(B!25) | (~net_str(B!25, A!24))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.20/0.53 tff(82,plain,
% 0.20/0.53 (rel_str(B!25)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[81, 45, 78])).
% 0.20/0.53 tff(83,plain,
% 0.20/0.53 (^[A: $i] : refl((empty_carrier(A) | (~rel_str(A)) | (~((~((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~element(tptp_fun_D_4(C, B, A), the_carrier(A))) | (~related(A, B, tptp_fun_D_4(C, B, A))) | (~related(A, C, tptp_fun_D_4(C, B, A))))))))) | (~(directed_relstr(A) | (~((~element(tptp_fun_B_5(A), the_carrier(A))) | (~element(tptp_fun_C_6(A), the_carrier(A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~related(A, tptp_fun_B_5(A), D)) | (~related(A, tptp_fun_C_6(A), D))))))))))) <=> (empty_carrier(A) | (~rel_str(A)) | (~((~((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~element(tptp_fun_D_4(C, B, A), the_carrier(A))) | (~related(A, B, tptp_fun_D_4(C, B, A))) | (~related(A, C, tptp_fun_D_4(C, B, A))))))))) | (~(directed_relstr(A) | (~((~element(tptp_fun_B_5(A), the_carrier(A))) | (~element(tptp_fun_C_6(A), the_carrier(A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~related(A, tptp_fun_B_5(A), D)) | (~related(A, tptp_fun_C_6(A), D))))))))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(84,plain,
% 0.20/0.53 (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~((~((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~element(tptp_fun_D_4(C, B, A), the_carrier(A))) | (~related(A, B, tptp_fun_D_4(C, B, A))) | (~related(A, C, tptp_fun_D_4(C, B, A))))))))) | (~(directed_relstr(A) | (~((~element(tptp_fun_B_5(A), the_carrier(A))) | (~element(tptp_fun_C_6(A), the_carrier(A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~related(A, tptp_fun_B_5(A), D)) | (~related(A, tptp_fun_C_6(A), D))))))))))) <=> ![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~((~((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~element(tptp_fun_D_4(C, B, A), the_carrier(A))) | (~related(A, B, tptp_fun_D_4(C, B, A))) | (~related(A, C, tptp_fun_D_4(C, B, A))))))))) | (~(directed_relstr(A) | (~((~element(tptp_fun_B_5(A), the_carrier(A))) | (~element(tptp_fun_C_6(A), the_carrier(A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~related(A, tptp_fun_B_5(A), D)) | (~related(A, tptp_fun_C_6(A), D)))))))))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[83])).
% 0.20/0.53 tff(85,plain,
% 0.20/0.53 (^[A: $i] : rewrite((empty_carrier(A) | (~rel_str(A)) | (~((~((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~element(tptp_fun_D_4(C, B, A), the_carrier(A))) | (~related(A, B, tptp_fun_D_4(C, B, A))) | (~related(A, C, tptp_fun_D_4(C, B, A))))))))) | (~(directed_relstr(A) | (~((~element(tptp_fun_B_5(A), the_carrier(A))) | (~element(tptp_fun_C_6(A), the_carrier(A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~related(A, tptp_fun_B_5(A), D)) | (~related(A, tptp_fun_C_6(A), D))))))))))) <=> (empty_carrier(A) | (~rel_str(A)) | (~((~((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~element(tptp_fun_D_4(C, B, A), the_carrier(A))) | (~related(A, B, tptp_fun_D_4(C, B, A))) | (~related(A, C, tptp_fun_D_4(C, B, A))))))))) | (~(directed_relstr(A) | (~((~element(tptp_fun_B_5(A), the_carrier(A))) | (~element(tptp_fun_C_6(A), the_carrier(A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~related(A, tptp_fun_B_5(A), D)) | (~related(A, tptp_fun_C_6(A), D))))))))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(86,plain,
% 0.20/0.53 (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~((~((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~element(tptp_fun_D_4(C, B, A), the_carrier(A))) | (~related(A, B, tptp_fun_D_4(C, B, A))) | (~related(A, C, tptp_fun_D_4(C, B, A))))))))) | (~(directed_relstr(A) | (~((~element(tptp_fun_B_5(A), the_carrier(A))) | (~element(tptp_fun_C_6(A), the_carrier(A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~related(A, tptp_fun_B_5(A), D)) | (~related(A, tptp_fun_C_6(A), D))))))))))) <=> ![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~((~((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~element(tptp_fun_D_4(C, B, A), the_carrier(A))) | (~related(A, B, tptp_fun_D_4(C, B, A))) | (~related(A, C, tptp_fun_D_4(C, B, A))))))))) | (~(directed_relstr(A) | (~((~element(tptp_fun_B_5(A), the_carrier(A))) | (~element(tptp_fun_C_6(A), the_carrier(A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~related(A, tptp_fun_B_5(A), D)) | (~related(A, tptp_fun_C_6(A), D)))))))))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[85])).
% 0.20/0.53 tff(87,plain,
% 0.20/0.53 (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~((~((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~element(tptp_fun_D_4(C, B, A), the_carrier(A))) | (~related(A, B, tptp_fun_D_4(C, B, A))) | (~related(A, C, tptp_fun_D_4(C, B, A))))))))) | (~(directed_relstr(A) | (~((~element(tptp_fun_B_5(A), the_carrier(A))) | (~element(tptp_fun_C_6(A), the_carrier(A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~related(A, tptp_fun_B_5(A), D)) | (~related(A, tptp_fun_C_6(A), D))))))))))) <=> ![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~((~((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~element(tptp_fun_D_4(C, B, A), the_carrier(A))) | (~related(A, B, tptp_fun_D_4(C, B, A))) | (~related(A, C, tptp_fun_D_4(C, B, A))))))))) | (~(directed_relstr(A) | (~((~element(tptp_fun_B_5(A), the_carrier(A))) | (~element(tptp_fun_C_6(A), the_carrier(A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~related(A, tptp_fun_B_5(A), D)) | (~related(A, tptp_fun_C_6(A), D)))))))))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[86, 84])).
% 0.20/0.53 tff(88,plain,
% 0.20/0.53 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & rel_str(A)) <=> (~(empty_carrier(A) | (~rel_str(A))))), ((~((~empty_carrier(A)) & rel_str(A))) <=> (~(~(empty_carrier(A) | (~rel_str(A))))))), rewrite((~(~(empty_carrier(A) | (~rel_str(A))))) <=> (empty_carrier(A) | (~rel_str(A)))), ((~((~empty_carrier(A)) & rel_str(A))) <=> (empty_carrier(A) | (~rel_str(A))))), trans(monotonicity(rewrite(((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (element(tptp_fun_D_4(C, B, A), the_carrier(A)) & related(A, B, tptp_fun_D_4(C, B, A)) & related(A, C, tptp_fun_D_4(C, B, A)))))) <=> ((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~element(tptp_fun_D_4(C, B, A), the_carrier(A))) | (~related(A, B, tptp_fun_D_4(C, B, A))) | (~related(A, C, tptp_fun_D_4(C, B, A))))))))), rewrite((directed_relstr(A) | (element(tptp_fun_B_5(A), the_carrier(A)) & element(tptp_fun_C_6(A), the_carrier(A)) & ![D: $i] : (~(element(D, the_carrier(A)) & related(A, tptp_fun_B_5(A), D) & related(A, tptp_fun_C_6(A), D))))) <=> (directed_relstr(A) | (~((~element(tptp_fun_B_5(A), the_carrier(A))) | (~element(tptp_fun_C_6(A), the_carrier(A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~related(A, tptp_fun_B_5(A), D)) | (~related(A, tptp_fun_C_6(A), D)))))))), ((((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (element(tptp_fun_D_4(C, B, A), the_carrier(A)) & related(A, B, tptp_fun_D_4(C, B, A)) & related(A, C, tptp_fun_D_4(C, B, A)))))) & (directed_relstr(A) | (element(tptp_fun_B_5(A), the_carrier(A)) & element(tptp_fun_C_6(A), the_carrier(A)) & ![D: $i] : (~(element(D, the_carrier(A)) & related(A, tptp_fun_B_5(A), D) & related(A, tptp_fun_C_6(A), D)))))) <=> (((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~element(tptp_fun_D_4(C, B, A), the_carrier(A))) | (~related(A, B, tptp_fun_D_4(C, B, A))) | (~related(A, C, tptp_fun_D_4(C, B, A)))))))) & (directed_relstr(A) | (~((~element(tptp_fun_B_5(A), the_carrier(A))) | (~element(tptp_fun_C_6(A), the_carrier(A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~related(A, tptp_fun_B_5(A), D)) | (~related(A, tptp_fun_C_6(A), D)))))))))), rewrite((((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~element(tptp_fun_D_4(C, B, A), the_carrier(A))) | (~related(A, B, tptp_fun_D_4(C, B, A))) | (~related(A, C, tptp_fun_D_4(C, B, A)))))))) & (directed_relstr(A) | (~((~element(tptp_fun_B_5(A), the_carrier(A))) | (~element(tptp_fun_C_6(A), the_carrier(A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~related(A, tptp_fun_B_5(A), D)) | (~related(A, tptp_fun_C_6(A), D)))))))) <=> (~((~((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~element(tptp_fun_D_4(C, B, A), the_carrier(A))) | (~related(A, B, tptp_fun_D_4(C, B, A))) | (~related(A, C, tptp_fun_D_4(C, B, A))))))))) | (~(directed_relstr(A) | (~((~element(tptp_fun_B_5(A), the_carrier(A))) | (~element(tptp_fun_C_6(A), the_carrier(A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~related(A, tptp_fun_B_5(A), D)) | (~related(A, tptp_fun_C_6(A), D))))))))))), ((((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (element(tptp_fun_D_4(C, B, A), the_carrier(A)) & related(A, B, tptp_fun_D_4(C, B, A)) & related(A, C, tptp_fun_D_4(C, B, A)))))) & (directed_relstr(A) | (element(tptp_fun_B_5(A), the_carrier(A)) & element(tptp_fun_C_6(A), the_carrier(A)) & ![D: $i] : (~(element(D, the_carrier(A)) & related(A, tptp_fun_B_5(A), D) & related(A, tptp_fun_C_6(A), D)))))) <=> (~((~((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~element(tptp_fun_D_4(C, B, A), the_carrier(A))) | (~related(A, B, tptp_fun_D_4(C, B, A))) | (~related(A, C, tptp_fun_D_4(C, B, A))))))))) | (~(directed_relstr(A) | (~((~element(tptp_fun_B_5(A), the_carrier(A))) | (~element(tptp_fun_C_6(A), the_carrier(A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~related(A, tptp_fun_B_5(A), D)) | (~related(A, tptp_fun_C_6(A), D)))))))))))), (((~((~empty_carrier(A)) & rel_str(A))) | (((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (element(tptp_fun_D_4(C, B, A), the_carrier(A)) & related(A, B, tptp_fun_D_4(C, B, A)) & related(A, C, tptp_fun_D_4(C, B, A)))))) & (directed_relstr(A) | (element(tptp_fun_B_5(A), the_carrier(A)) & element(tptp_fun_C_6(A), the_carrier(A)) & ![D: $i] : (~(element(D, the_carrier(A)) & related(A, tptp_fun_B_5(A), D) & related(A, tptp_fun_C_6(A), D))))))) <=> ((empty_carrier(A) | (~rel_str(A))) | (~((~((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~element(tptp_fun_D_4(C, B, A), the_carrier(A))) | (~related(A, B, tptp_fun_D_4(C, B, A))) | (~related(A, C, tptp_fun_D_4(C, B, A))))))))) | (~(directed_relstr(A) | (~((~element(tptp_fun_B_5(A), the_carrier(A))) | (~element(tptp_fun_C_6(A), the_carrier(A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~related(A, tptp_fun_B_5(A), D)) | (~related(A, tptp_fun_C_6(A), D))))))))))))), rewrite(((empty_carrier(A) | (~rel_str(A))) | (~((~((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~element(tptp_fun_D_4(C, B, A), the_carrier(A))) | (~related(A, B, tptp_fun_D_4(C, B, A))) | (~related(A, C, tptp_fun_D_4(C, B, A))))))))) | (~(directed_relstr(A) | (~((~element(tptp_fun_B_5(A), the_carrier(A))) | (~element(tptp_fun_C_6(A), the_carrier(A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~related(A, tptp_fun_B_5(A), D)) | (~related(A, tptp_fun_C_6(A), D))))))))))) <=> (empty_carrier(A) | (~rel_str(A)) | (~((~((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~element(tptp_fun_D_4(C, B, A), the_carrier(A))) | (~related(A, B, tptp_fun_D_4(C, B, A))) | (~related(A, C, tptp_fun_D_4(C, B, A))))))))) | (~(directed_relstr(A) | (~((~element(tptp_fun_B_5(A), the_carrier(A))) | (~element(tptp_fun_C_6(A), the_carrier(A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~related(A, tptp_fun_B_5(A), D)) | (~related(A, tptp_fun_C_6(A), D)))))))))))), (((~((~empty_carrier(A)) & rel_str(A))) | (((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (element(tptp_fun_D_4(C, B, A), the_carrier(A)) & related(A, B, tptp_fun_D_4(C, B, A)) & related(A, C, tptp_fun_D_4(C, B, A)))))) & (directed_relstr(A) | (element(tptp_fun_B_5(A), the_carrier(A)) & element(tptp_fun_C_6(A), the_carrier(A)) & ![D: $i] : (~(element(D, the_carrier(A)) & related(A, tptp_fun_B_5(A), D) & related(A, tptp_fun_C_6(A), D))))))) <=> (empty_carrier(A) | (~rel_str(A)) | (~((~((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~element(tptp_fun_D_4(C, B, A), the_carrier(A))) | (~related(A, B, tptp_fun_D_4(C, B, A))) | (~related(A, C, tptp_fun_D_4(C, B, A))))))))) | (~(directed_relstr(A) | (~((~element(tptp_fun_B_5(A), the_carrier(A))) | (~element(tptp_fun_C_6(A), the_carrier(A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~related(A, tptp_fun_B_5(A), D)) | (~related(A, tptp_fun_C_6(A), D)))))))))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(89,plain,
% 0.20/0.54 (![A: $i] : ((~((~empty_carrier(A)) & rel_str(A))) | (((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (element(tptp_fun_D_4(C, B, A), the_carrier(A)) & related(A, B, tptp_fun_D_4(C, B, A)) & related(A, C, tptp_fun_D_4(C, B, A)))))) & (directed_relstr(A) | (element(tptp_fun_B_5(A), the_carrier(A)) & element(tptp_fun_C_6(A), the_carrier(A)) & ![D: $i] : (~(element(D, the_carrier(A)) & related(A, tptp_fun_B_5(A), D) & related(A, tptp_fun_C_6(A), D))))))) <=> ![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~((~((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~element(tptp_fun_D_4(C, B, A), the_carrier(A))) | (~related(A, B, tptp_fun_D_4(C, B, A))) | (~related(A, C, tptp_fun_D_4(C, B, A))))))))) | (~(directed_relstr(A) | (~((~element(tptp_fun_B_5(A), the_carrier(A))) | (~element(tptp_fun_C_6(A), the_carrier(A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~related(A, tptp_fun_B_5(A), D)) | (~related(A, tptp_fun_C_6(A), D)))))))))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[88])).
% 0.20/0.54 tff(90,plain,
% 0.20/0.54 (^[A: $i] : rewrite(((~((~empty_carrier(A)) & rel_str(A))) | (((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (element(tptp_fun_D_4(C, B, A), the_carrier(A)) & related(A, B, tptp_fun_D_4(C, B, A)) & related(A, C, tptp_fun_D_4(C, B, A)))))) & (directed_relstr(A) | ((~(~element(tptp_fun_B_5(A), the_carrier(A)))) & ((~(~element(tptp_fun_C_6(A), the_carrier(A)))) & ![D: $i] : (~(element(D, the_carrier(A)) & related(A, tptp_fun_B_5(A), D) & related(A, tptp_fun_C_6(A), D)))))))) <=> ((~((~empty_carrier(A)) & rel_str(A))) | (((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (element(tptp_fun_D_4(C, B, A), the_carrier(A)) & related(A, B, tptp_fun_D_4(C, B, A)) & related(A, C, tptp_fun_D_4(C, B, A)))))) & (directed_relstr(A) | (element(tptp_fun_B_5(A), the_carrier(A)) & element(tptp_fun_C_6(A), the_carrier(A)) & ![D: $i] : (~(element(D, the_carrier(A)) & related(A, tptp_fun_B_5(A), D) & related(A, tptp_fun_C_6(A), D))))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(91,plain,
% 0.20/0.54 (![A: $i] : ((~((~empty_carrier(A)) & rel_str(A))) | (((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (element(tptp_fun_D_4(C, B, A), the_carrier(A)) & related(A, B, tptp_fun_D_4(C, B, A)) & related(A, C, tptp_fun_D_4(C, B, A)))))) & (directed_relstr(A) | ((~(~element(tptp_fun_B_5(A), the_carrier(A)))) & ((~(~element(tptp_fun_C_6(A), the_carrier(A)))) & ![D: $i] : (~(element(D, the_carrier(A)) & related(A, tptp_fun_B_5(A), D) & related(A, tptp_fun_C_6(A), D)))))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & rel_str(A))) | (((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (element(tptp_fun_D_4(C, B, A), the_carrier(A)) & related(A, B, tptp_fun_D_4(C, B, A)) & related(A, C, tptp_fun_D_4(C, B, A)))))) & (directed_relstr(A) | (element(tptp_fun_B_5(A), the_carrier(A)) & element(tptp_fun_C_6(A), the_carrier(A)) & ![D: $i] : (~(element(D, the_carrier(A)) & related(A, tptp_fun_B_5(A), D) & related(A, tptp_fun_C_6(A), D)))))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[90])).
% 0.20/0.54 tff(92,plain,
% 0.20/0.54 (![A: $i] : ((~((~empty_carrier(A)) & rel_str(A))) | (directed_relstr(A) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ?[D: $i] : (element(D, the_carrier(A)) & related(A, B, D) & related(A, C, D)))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & rel_str(A))) | (directed_relstr(A) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ?[D: $i] : (element(D, the_carrier(A)) & related(A, B, D) & related(A, C, D))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(93,plain,
% 0.20/0.54 (^[A: $i] : trans(monotonicity(rewrite((directed_relstr(A) <=> ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => ?[D: $i] : ((element(D, the_carrier(A)) & related(A, B, D)) & related(A, C, D))))) <=> (directed_relstr(A) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ?[D: $i] : (element(D, the_carrier(A)) & related(A, B, D) & related(A, C, D)))))), ((((~empty_carrier(A)) & rel_str(A)) => (directed_relstr(A) <=> ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => ?[D: $i] : ((element(D, the_carrier(A)) & related(A, B, D)) & related(A, C, D)))))) <=> (((~empty_carrier(A)) & rel_str(A)) => (directed_relstr(A) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ?[D: $i] : (element(D, the_carrier(A)) & related(A, B, D) & related(A, C, D)))))))), rewrite((((~empty_carrier(A)) & rel_str(A)) => (directed_relstr(A) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ?[D: $i] : (element(D, the_carrier(A)) & related(A, B, D) & related(A, C, D)))))) <=> ((~((~empty_carrier(A)) & rel_str(A))) | (directed_relstr(A) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ?[D: $i] : (element(D, the_carrier(A)) & related(A, B, D) & related(A, C, D))))))), ((((~empty_carrier(A)) & rel_str(A)) => (directed_relstr(A) <=> ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => ?[D: $i] : ((element(D, the_carrier(A)) & related(A, B, D)) & related(A, C, D)))))) <=> ((~((~empty_carrier(A)) & rel_str(A))) | (directed_relstr(A) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ?[D: $i] : (element(D, the_carrier(A)) & related(A, B, D) & related(A, C, D))))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(94,plain,
% 0.20/0.54 (![A: $i] : (((~empty_carrier(A)) & rel_str(A)) => (directed_relstr(A) <=> ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => ?[D: $i] : ((element(D, the_carrier(A)) & related(A, B, D)) & related(A, C, D)))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & rel_str(A))) | (directed_relstr(A) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ?[D: $i] : (element(D, the_carrier(A)) & related(A, B, D) & related(A, C, D))))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[93])).
% 0.20/0.54 tff(95,axiom,(![A: $i] : (((~empty_carrier(A)) & rel_str(A)) => (directed_relstr(A) <=> ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => ?[D: $i] : ((element(D, the_carrier(A)) & related(A, B, D)) & related(A, C, D))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d5_yellow_6')).
% 0.20/0.54 tff(96,plain,
% 0.20/0.54 (![A: $i] : ((~((~empty_carrier(A)) & rel_str(A))) | (directed_relstr(A) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ?[D: $i] : (element(D, the_carrier(A)) & related(A, B, D) & related(A, C, D))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.54 tff(97,plain,
% 0.20/0.54 (![A: $i] : ((~((~empty_carrier(A)) & rel_str(A))) | (directed_relstr(A) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ?[D: $i] : (element(D, the_carrier(A)) & related(A, B, D) & related(A, C, D))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.20/0.54 tff(98,plain,(
% 0.20/0.54 ![A: $i] : ((~((~empty_carrier(A)) & rel_str(A))) | (((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (element(tptp_fun_D_4(C, B, A), the_carrier(A)) & related(A, B, tptp_fun_D_4(C, B, A)) & related(A, C, tptp_fun_D_4(C, B, A)))))) & (directed_relstr(A) | ((~(~element(tptp_fun_B_5(A), the_carrier(A)))) & ((~(~element(tptp_fun_C_6(A), the_carrier(A)))) & ![D: $i] : (~(element(D, the_carrier(A)) & related(A, tptp_fun_B_5(A), D) & related(A, tptp_fun_C_6(A), D))))))))),
% 0.20/0.54 inference(skolemize,[status(sab)],[97])).
% 0.20/0.54 tff(99,plain,
% 0.20/0.54 (![A: $i] : ((~((~empty_carrier(A)) & rel_str(A))) | (((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (element(tptp_fun_D_4(C, B, A), the_carrier(A)) & related(A, B, tptp_fun_D_4(C, B, A)) & related(A, C, tptp_fun_D_4(C, B, A)))))) & (directed_relstr(A) | (element(tptp_fun_B_5(A), the_carrier(A)) & element(tptp_fun_C_6(A), the_carrier(A)) & ![D: $i] : (~(element(D, the_carrier(A)) & related(A, tptp_fun_B_5(A), D) & related(A, tptp_fun_C_6(A), D)))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.20/0.54 tff(100,plain,
% 0.20/0.54 (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~((~((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~element(tptp_fun_D_4(C, B, A), the_carrier(A))) | (~related(A, B, tptp_fun_D_4(C, B, A))) | (~related(A, C, tptp_fun_D_4(C, B, A))))))))) | (~(directed_relstr(A) | (~((~element(tptp_fun_B_5(A), the_carrier(A))) | (~element(tptp_fun_C_6(A), the_carrier(A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~related(A, tptp_fun_B_5(A), D)) | (~related(A, tptp_fun_C_6(A), D)))))))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[99, 89])).
% 0.20/0.54 tff(101,plain,
% 0.20/0.54 (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~((~((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~element(tptp_fun_D_4(C, B, A), the_carrier(A))) | (~related(A, B, tptp_fun_D_4(C, B, A))) | (~related(A, C, tptp_fun_D_4(C, B, A))))))))) | (~(directed_relstr(A) | (~((~element(tptp_fun_B_5(A), the_carrier(A))) | (~element(tptp_fun_C_6(A), the_carrier(A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~related(A, tptp_fun_B_5(A), D)) | (~related(A, tptp_fun_C_6(A), D)))))))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[100, 87])).
% 0.20/0.54 tff(102,plain,
% 0.20/0.54 (((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~((~((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~element(tptp_fun_D_4(C, B, A), the_carrier(A))) | (~related(A, B, tptp_fun_D_4(C, B, A))) | (~related(A, C, tptp_fun_D_4(C, B, A))))))))) | (~(directed_relstr(A) | (~((~element(tptp_fun_B_5(A), the_carrier(A))) | (~element(tptp_fun_C_6(A), the_carrier(A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~related(A, tptp_fun_B_5(A), D)) | (~related(A, tptp_fun_C_6(A), D)))))))))))) | (empty_carrier(B!25) | (~rel_str(B!25)) | (~((~((~directed_relstr(B!25)) | ![B: $i] : ((~element(B, the_carrier(B!25))) | ![C: $i] : ((~element(C, the_carrier(B!25))) | (~((~element(tptp_fun_D_4(C, B, B!25), the_carrier(B!25))) | (~related(B!25, B, tptp_fun_D_4(C, B, B!25))) | (~related(B!25, C, tptp_fun_D_4(C, B, B!25))))))))) | (~(directed_relstr(B!25) | (~((~element(tptp_fun_B_5(B!25), the_carrier(B!25))) | (~element(tptp_fun_C_6(B!25), the_carrier(B!25))) | (~![D: $i] : ((~element(D, the_carrier(B!25))) | (~related(B!25, tptp_fun_B_5(B!25), D)) | (~related(B!25, tptp_fun_C_6(B!25), D)))))))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~((~((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~element(tptp_fun_D_4(C, B, A), the_carrier(A))) | (~related(A, B, tptp_fun_D_4(C, B, A))) | (~related(A, C, tptp_fun_D_4(C, B, A))))))))) | (~(directed_relstr(A) | (~((~element(tptp_fun_B_5(A), the_carrier(A))) | (~element(tptp_fun_C_6(A), the_carrier(A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~related(A, tptp_fun_B_5(A), D)) | (~related(A, tptp_fun_C_6(A), D)))))))))))) | empty_carrier(B!25) | (~rel_str(B!25)) | (~((~((~directed_relstr(B!25)) | ![B: $i] : ((~element(B, the_carrier(B!25))) | ![C: $i] : ((~element(C, the_carrier(B!25))) | (~((~element(tptp_fun_D_4(C, B, B!25), the_carrier(B!25))) | (~related(B!25, B, tptp_fun_D_4(C, B, B!25))) | (~related(B!25, C, tptp_fun_D_4(C, B, B!25))))))))) | (~(directed_relstr(B!25) | (~((~element(tptp_fun_B_5(B!25), the_carrier(B!25))) | (~element(tptp_fun_C_6(B!25), the_carrier(B!25))) | (~![D: $i] : ((~element(D, the_carrier(B!25))) | (~related(B!25, tptp_fun_B_5(B!25), D)) | (~related(B!25, tptp_fun_C_6(B!25), D)))))))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(103,plain,
% 0.20/0.54 ((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~((~((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~element(tptp_fun_D_4(C, B, A), the_carrier(A))) | (~related(A, B, tptp_fun_D_4(C, B, A))) | (~related(A, C, tptp_fun_D_4(C, B, A))))))))) | (~(directed_relstr(A) | (~((~element(tptp_fun_B_5(A), the_carrier(A))) | (~element(tptp_fun_C_6(A), the_carrier(A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~related(A, tptp_fun_B_5(A), D)) | (~related(A, tptp_fun_C_6(A), D)))))))))))) | (empty_carrier(B!25) | (~rel_str(B!25)) | (~((~((~directed_relstr(B!25)) | ![B: $i] : ((~element(B, the_carrier(B!25))) | ![C: $i] : ((~element(C, the_carrier(B!25))) | (~((~element(tptp_fun_D_4(C, B, B!25), the_carrier(B!25))) | (~related(B!25, B, tptp_fun_D_4(C, B, B!25))) | (~related(B!25, C, tptp_fun_D_4(C, B, B!25))))))))) | (~(directed_relstr(B!25) | (~((~element(tptp_fun_B_5(B!25), the_carrier(B!25))) | (~element(tptp_fun_C_6(B!25), the_carrier(B!25))) | (~![D: $i] : ((~element(D, the_carrier(B!25))) | (~related(B!25, tptp_fun_B_5(B!25), D)) | (~related(B!25, tptp_fun_C_6(B!25), D)))))))))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(104,plain,
% 0.20/0.55 ((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~((~((~directed_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~element(tptp_fun_D_4(C, B, A), the_carrier(A))) | (~related(A, B, tptp_fun_D_4(C, B, A))) | (~related(A, C, tptp_fun_D_4(C, B, A))))))))) | (~(directed_relstr(A) | (~((~element(tptp_fun_B_5(A), the_carrier(A))) | (~element(tptp_fun_C_6(A), the_carrier(A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~related(A, tptp_fun_B_5(A), D)) | (~related(A, tptp_fun_C_6(A), D)))))))))))) | empty_carrier(B!25) | (~rel_str(B!25)) | (~((~((~directed_relstr(B!25)) | ![B: $i] : ((~element(B, the_carrier(B!25))) | ![C: $i] : ((~element(C, the_carrier(B!25))) | (~((~element(tptp_fun_D_4(C, B, B!25), the_carrier(B!25))) | (~related(B!25, B, tptp_fun_D_4(C, B, B!25))) | (~related(B!25, C, tptp_fun_D_4(C, B, B!25))))))))) | (~(directed_relstr(B!25) | (~((~element(tptp_fun_B_5(B!25), the_carrier(B!25))) | (~element(tptp_fun_C_6(B!25), the_carrier(B!25))) | (~![D: $i] : ((~element(D, the_carrier(B!25))) | (~related(B!25, tptp_fun_B_5(B!25), D)) | (~related(B!25, tptp_fun_C_6(B!25), D))))))))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.55 tff(105,plain,
% 0.20/0.55 ((~rel_str(B!25)) | (~((~((~directed_relstr(B!25)) | ![B: $i] : ((~element(B, the_carrier(B!25))) | ![C: $i] : ((~element(C, the_carrier(B!25))) | (~((~element(tptp_fun_D_4(C, B, B!25), the_carrier(B!25))) | (~related(B!25, B, tptp_fun_D_4(C, B, B!25))) | (~related(B!25, C, tptp_fun_D_4(C, B, B!25))))))))) | (~(directed_relstr(B!25) | (~((~element(tptp_fun_B_5(B!25), the_carrier(B!25))) | (~element(tptp_fun_C_6(B!25), the_carrier(B!25))) | (~![D: $i] : ((~element(D, the_carrier(B!25))) | (~related(B!25, tptp_fun_B_5(B!25), D)) | (~related(B!25, tptp_fun_C_6(B!25), D))))))))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[104, 101, 46])).
% 0.20/0.55 tff(106,plain,
% 0.20/0.55 (~((~((~directed_relstr(B!25)) | ![B: $i] : ((~element(B, the_carrier(B!25))) | ![C: $i] : ((~element(C, the_carrier(B!25))) | (~((~element(tptp_fun_D_4(C, B, B!25), the_carrier(B!25))) | (~related(B!25, B, tptp_fun_D_4(C, B, B!25))) | (~related(B!25, C, tptp_fun_D_4(C, B, B!25))))))))) | (~(directed_relstr(B!25) | (~((~element(tptp_fun_B_5(B!25), the_carrier(B!25))) | (~element(tptp_fun_C_6(B!25), the_carrier(B!25))) | (~![D: $i] : ((~element(D, the_carrier(B!25))) | (~related(B!25, tptp_fun_B_5(B!25), D)) | (~related(B!25, tptp_fun_C_6(B!25), D)))))))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[105, 82])).
% 0.20/0.55 tff(107,plain,
% 0.20/0.55 (((~((~directed_relstr(B!25)) | ![B: $i] : ((~element(B, the_carrier(B!25))) | ![C: $i] : ((~element(C, the_carrier(B!25))) | (~((~element(tptp_fun_D_4(C, B, B!25), the_carrier(B!25))) | (~related(B!25, B, tptp_fun_D_4(C, B, B!25))) | (~related(B!25, C, tptp_fun_D_4(C, B, B!25))))))))) | (~(directed_relstr(B!25) | (~((~element(tptp_fun_B_5(B!25), the_carrier(B!25))) | (~element(tptp_fun_C_6(B!25), the_carrier(B!25))) | (~![D: $i] : ((~element(D, the_carrier(B!25))) | (~related(B!25, tptp_fun_B_5(B!25), D)) | (~related(B!25, tptp_fun_C_6(B!25), D))))))))) | ((~directed_relstr(B!25)) | ![B: $i] : ((~element(B, the_carrier(B!25))) | ![C: $i] : ((~element(C, the_carrier(B!25))) | (~((~element(tptp_fun_D_4(C, B, B!25), the_carrier(B!25))) | (~related(B!25, B, tptp_fun_D_4(C, B, B!25))) | (~related(B!25, C, tptp_fun_D_4(C, B, B!25))))))))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(108,plain,
% 0.20/0.55 ((~directed_relstr(B!25)) | ![B: $i] : ((~element(B, the_carrier(B!25))) | ![C: $i] : ((~element(C, the_carrier(B!25))) | (~((~element(tptp_fun_D_4(C, B, B!25), the_carrier(B!25))) | (~related(B!25, B, tptp_fun_D_4(C, B, B!25))) | (~related(B!25, C, tptp_fun_D_4(C, B, B!25)))))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.20/0.55 tff(109,plain,
% 0.20/0.55 (directed_relstr(B!25)),
% 0.20/0.55 inference(and_elim,[status(thm)],[19])).
% 0.20/0.55 tff(110,plain,
% 0.20/0.55 ((~((~directed_relstr(B!25)) | ![B: $i] : ((~element(B, the_carrier(B!25))) | ![C: $i] : ((~element(C, the_carrier(B!25))) | (~((~element(tptp_fun_D_4(C, B, B!25), the_carrier(B!25))) | (~related(B!25, B, tptp_fun_D_4(C, B, B!25))) | (~related(B!25, C, tptp_fun_D_4(C, B, B!25))))))))) | (~directed_relstr(B!25)) | ![B: $i] : ((~element(B, the_carrier(B!25))) | ![C: $i] : ((~element(C, the_carrier(B!25))) | (~((~element(tptp_fun_D_4(C, B, B!25), the_carrier(B!25))) | (~related(B!25, B, tptp_fun_D_4(C, B, B!25))) | (~related(B!25, C, tptp_fun_D_4(C, B, B!25)))))))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(111,plain,
% 0.20/0.55 ((~((~directed_relstr(B!25)) | ![B: $i] : ((~element(B, the_carrier(B!25))) | ![C: $i] : ((~element(C, the_carrier(B!25))) | (~((~element(tptp_fun_D_4(C, B, B!25), the_carrier(B!25))) | (~related(B!25, B, tptp_fun_D_4(C, B, B!25))) | (~related(B!25, C, tptp_fun_D_4(C, B, B!25))))))))) | ![B: $i] : ((~element(B, the_carrier(B!25))) | ![C: $i] : ((~element(C, the_carrier(B!25))) | (~((~element(tptp_fun_D_4(C, B, B!25), the_carrier(B!25))) | (~related(B!25, B, tptp_fun_D_4(C, B, B!25))) | (~related(B!25, C, tptp_fun_D_4(C, B, B!25)))))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.20/0.55 tff(112,plain,
% 0.20/0.55 (![B: $i] : ((~element(B, the_carrier(B!25))) | ![C: $i] : ((~element(C, the_carrier(B!25))) | (~((~element(tptp_fun_D_4(C, B, B!25), the_carrier(B!25))) | (~related(B!25, B, tptp_fun_D_4(C, B, B!25))) | (~related(B!25, C, tptp_fun_D_4(C, B, B!25)))))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[111, 108])).
% 0.20/0.55 tff(113,plain,
% 0.20/0.55 (((~![B: $i] : ((~element(B, the_carrier(B!25))) | ![C: $i] : ((~element(C, the_carrier(B!25))) | (~((~element(tptp_fun_D_4(C, B, B!25), the_carrier(B!25))) | (~related(B!25, B, tptp_fun_D_4(C, B, B!25))) | (~related(B!25, C, tptp_fun_D_4(C, B, B!25)))))))) | ((~element(tptp_fun_D_3(C!26, B!25, A!24), the_carrier(B!25))) | ![C: $i] : ((~element(C, the_carrier(B!25))) | (~((~element(tptp_fun_D_4(C, tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), tptp_fun_D_4(C, tptp_fun_D_3(C!26, B!25, A!24), B!25))) | (~related(B!25, C, tptp_fun_D_4(C, tptp_fun_D_3(C!26, B!25, A!24), B!25)))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(B!25))) | ![C: $i] : ((~element(C, the_carrier(B!25))) | (~((~element(tptp_fun_D_4(C, B, B!25), the_carrier(B!25))) | (~related(B!25, B, tptp_fun_D_4(C, B, B!25))) | (~related(B!25, C, tptp_fun_D_4(C, B, B!25)))))))) | (~element(tptp_fun_D_3(C!26, B!25, A!24), the_carrier(B!25))) | ![C: $i] : ((~element(C, the_carrier(B!25))) | (~((~element(tptp_fun_D_4(C, tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), tptp_fun_D_4(C, tptp_fun_D_3(C!26, B!25, A!24), B!25))) | (~related(B!25, C, tptp_fun_D_4(C, tptp_fun_D_3(C!26, B!25, A!24), B!25)))))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(114,plain,
% 0.20/0.55 ((~![B: $i] : ((~element(B, the_carrier(B!25))) | ![C: $i] : ((~element(C, the_carrier(B!25))) | (~((~element(tptp_fun_D_4(C, B, B!25), the_carrier(B!25))) | (~related(B!25, B, tptp_fun_D_4(C, B, B!25))) | (~related(B!25, C, tptp_fun_D_4(C, B, B!25)))))))) | ((~element(tptp_fun_D_3(C!26, B!25, A!24), the_carrier(B!25))) | ![C: $i] : ((~element(C, the_carrier(B!25))) | (~((~element(tptp_fun_D_4(C, tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), tptp_fun_D_4(C, tptp_fun_D_3(C!26, B!25, A!24), B!25))) | (~related(B!25, C, tptp_fun_D_4(C, tptp_fun_D_3(C!26, B!25, A!24), B!25)))))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(115,plain,
% 0.20/0.55 ((~![B: $i] : ((~element(B, the_carrier(B!25))) | ![C: $i] : ((~element(C, the_carrier(B!25))) | (~((~element(tptp_fun_D_4(C, B, B!25), the_carrier(B!25))) | (~related(B!25, B, tptp_fun_D_4(C, B, B!25))) | (~related(B!25, C, tptp_fun_D_4(C, B, B!25)))))))) | (~element(tptp_fun_D_3(C!26, B!25, A!24), the_carrier(B!25))) | ![C: $i] : ((~element(C, the_carrier(B!25))) | (~((~element(tptp_fun_D_4(C, tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), tptp_fun_D_4(C, tptp_fun_D_3(C!26, B!25, A!24), B!25))) | (~related(B!25, C, tptp_fun_D_4(C, tptp_fun_D_3(C!26, B!25, A!24), B!25))))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.20/0.55 tff(116,plain,
% 0.20/0.55 (![C: $i] : ((~element(C, the_carrier(B!25))) | (~((~element(tptp_fun_D_4(C, tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), tptp_fun_D_4(C, tptp_fun_D_3(C!26, B!25, A!24), B!25))) | (~related(B!25, C, tptp_fun_D_4(C, tptp_fun_D_3(C!26, B!25, A!24), B!25))))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[115, 112, 61])).
% 0.20/0.55 tff(117,plain,
% 0.20/0.55 (^[A: $i] : refl((empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))) | (~(is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B)))))))))))) <=> (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))) | (~(is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B)))))))))))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(118,plain,
% 0.20/0.55 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))) | (~(is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B)))))))))))) <=> ![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))) | (~(is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B))))))))))))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[117])).
% 0.20/0.55 tff(119,plain,
% 0.20/0.55 (^[A: $i] : rewrite((empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))) | (~(is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B)))))))))))) <=> (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))) | (~(is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B)))))))))))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(120,plain,
% 0.20/0.55 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))) | (~(is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B)))))))))))) <=> ![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))) | (~(is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B))))))))))))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[119])).
% 0.20/0.55 tff(121,plain,
% 0.20/0.55 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))) | (~(is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B)))))))))))) <=> ![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))) | (~(is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B))))))))))))),
% 0.20/0.55 inference(transitivity,[status(thm)],[120, 118])).
% 0.20/0.55 tff(122,plain,
% 0.20/0.55 (^[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))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(B)) & net_str(B, A)) <=> (~(empty_carrier(B) | (~net_str(B, A))))), ((~((~empty_carrier(B)) & net_str(B, A))) <=> (~(~(empty_carrier(B) | (~net_str(B, A))))))), rewrite((~(~(empty_carrier(B) | (~net_str(B, A))))) <=> (empty_carrier(B) | (~net_str(B, A)))), ((~((~empty_carrier(B)) & net_str(B, A))) <=> (empty_carrier(B) | (~net_str(B, A))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((~is_eventually_in(A, B, C)) | (element(tptp_fun_D_0(C, B, A), the_carrier(B)) & ![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E))))) <=> ((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))), rewrite((is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B))))))) <=> (is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B)))))))), ((((~is_eventually_in(A, B, C)) | (element(tptp_fun_D_0(C, B, A), the_carrier(B)) & ![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E))))) & (is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B)))))))) <=> (((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E))))))) & (is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B)))))))))), rewrite((((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E))))))) & (is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B)))))))) <=> (~((~((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))) | (~(is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B))))))))))), ((((~is_eventually_in(A, B, C)) | (element(tptp_fun_D_0(C, B, A), the_carrier(B)) & ![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E))))) & (is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B)))))))) <=> (~((~((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))) | (~(is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B))))))))))))), (![C: $i] : (((~is_eventually_in(A, B, C)) | (element(tptp_fun_D_0(C, B, A), the_carrier(B)) & ![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E))))) & (is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B)))))))) <=> ![C: $i] : (~((~((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))) | (~(is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B)))))))))))), (((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (((~is_eventually_in(A, B, C)) | (element(tptp_fun_D_0(C, B, A), the_carrier(B)) & ![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E))))) & (is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B))))))))) <=> ((empty_carrier(B) | (~net_str(B, A))) | ![C: $i] : (~((~((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))) | (~(is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B))))))))))))), rewrite(((empty_carrier(B) | (~net_str(B, A))) | ![C: $i] : (~((~((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))) | (~(is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B))))))))))) <=> (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))) | (~(is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B)))))))))))), (((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (((~is_eventually_in(A, B, C)) | (element(tptp_fun_D_0(C, B, A), the_carrier(B)) & ![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E))))) & (is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B))))))))) <=> (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))) | (~(is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B)))))))))))))), (![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (((~is_eventually_in(A, B, C)) | (element(tptp_fun_D_0(C, B, A), the_carrier(B)) & ![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E))))) & (is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B))))))))) <=> ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))) | (~(is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B))))))))))))), (((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (((~is_eventually_in(A, B, C)) | (element(tptp_fun_D_0(C, B, A), the_carrier(B)) & ![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E))))) & (is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B)))))))))) <=> ((empty_carrier(A) | (~one_sorted_str(A))) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))) | (~(is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B)))))))))))))), rewrite(((empty_carrier(A) | (~one_sorted_str(A))) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))) | (~(is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B)))))))))))) <=> (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))) | (~(is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B))))))))))))), (((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (((~is_eventually_in(A, B, C)) | (element(tptp_fun_D_0(C, B, A), the_carrier(B)) & ![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E))))) & (is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B)))))))))) <=> (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))) | (~(is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B))))))))))))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(123,plain,
% 0.20/0.56 (![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (((~is_eventually_in(A, B, C)) | (element(tptp_fun_D_0(C, B, A), the_carrier(B)) & ![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E))))) & (is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B)))))))))) <=> ![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))) | (~(is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B))))))))))))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[122])).
% 0.20/0.56 tff(124,plain,
% 0.20/0.56 (^[A: $i] : rewrite(((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (((~is_eventually_in(A, B, C)) | (element(tptp_fun_D_0(C, B, A), the_carrier(B)) & ![E: $i] : (in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)) | (~element(E, the_carrier(B)))))) & (is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B)))))))))) <=> ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (((~is_eventually_in(A, B, C)) | (element(tptp_fun_D_0(C, B, A), the_carrier(B)) & ![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E))))) & (is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B)))))))))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(125,plain,
% 0.20/0.56 (![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (((~is_eventually_in(A, B, C)) | (element(tptp_fun_D_0(C, B, A), the_carrier(B)) & ![E: $i] : (in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)) | (~element(E, the_carrier(B)))))) & (is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B)))))))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (((~is_eventually_in(A, B, C)) | (element(tptp_fun_D_0(C, B, A), the_carrier(B)) & ![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E))))) & (is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B))))))))))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[124])).
% 0.20/0.56 tff(126,plain,
% 0.20/0.56 (![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (is_eventually_in(A, B, C) <=> ?[D: $i] : (element(D, the_carrier(B)) & ![E: $i] : (in(apply_netmap(A, B, E), C) | (~related(B, D, E)) | (~element(E, the_carrier(B)))))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (is_eventually_in(A, B, C) <=> ?[D: $i] : (element(D, the_carrier(B)) & ![E: $i] : (in(apply_netmap(A, B, E), C) | (~related(B, D, E)) | (~element(E, the_carrier(B))))))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(127,plain,
% 0.20/0.56 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((is_eventually_in(A, B, C) <=> ?[D: $i] : (element(D, the_carrier(B)) & ![E: $i] : (element(E, the_carrier(B)) => (related(B, D, E) => in(apply_netmap(A, B, E), C))))) <=> (is_eventually_in(A, B, C) <=> ?[D: $i] : (element(D, the_carrier(B)) & ![E: $i] : (in(apply_netmap(A, B, E), C) | (~related(B, D, E)) | (~element(E, the_carrier(B)))))))), (![C: $i] : (is_eventually_in(A, B, C) <=> ?[D: $i] : (element(D, the_carrier(B)) & ![E: $i] : (element(E, the_carrier(B)) => (related(B, D, E) => in(apply_netmap(A, B, E), C))))) <=> ![C: $i] : (is_eventually_in(A, B, C) <=> ?[D: $i] : (element(D, the_carrier(B)) & ![E: $i] : (in(apply_netmap(A, B, E), C) | (~related(B, D, E)) | (~element(E, the_carrier(B)))))))), ((((~empty_carrier(B)) & net_str(B, A)) => ![C: $i] : (is_eventually_in(A, B, C) <=> ?[D: $i] : (element(D, the_carrier(B)) & ![E: $i] : (element(E, the_carrier(B)) => (related(B, D, E) => in(apply_netmap(A, B, E), C)))))) <=> (((~empty_carrier(B)) & net_str(B, A)) => ![C: $i] : (is_eventually_in(A, B, C) <=> ?[D: $i] : (element(D, the_carrier(B)) & ![E: $i] : (in(apply_netmap(A, B, E), C) | (~related(B, D, E)) | (~element(E, the_carrier(B))))))))), rewrite((((~empty_carrier(B)) & net_str(B, A)) => ![C: $i] : (is_eventually_in(A, B, C) <=> ?[D: $i] : (element(D, the_carrier(B)) & ![E: $i] : (in(apply_netmap(A, B, E), C) | (~related(B, D, E)) | (~element(E, the_carrier(B))))))) <=> ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (is_eventually_in(A, B, C) <=> ?[D: $i] : (element(D, the_carrier(B)) & ![E: $i] : (in(apply_netmap(A, B, E), C) | (~related(B, D, E)) | (~element(E, the_carrier(B)))))))), ((((~empty_carrier(B)) & net_str(B, A)) => ![C: $i] : (is_eventually_in(A, B, C) <=> ?[D: $i] : (element(D, the_carrier(B)) & ![E: $i] : (element(E, the_carrier(B)) => (related(B, D, E) => in(apply_netmap(A, B, E), C)))))) <=> ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (is_eventually_in(A, B, C) <=> ?[D: $i] : (element(D, the_carrier(B)) & ![E: $i] : (in(apply_netmap(A, B, E), C) | (~related(B, D, E)) | (~element(E, the_carrier(B)))))))))), (![B: $i] : (((~empty_carrier(B)) & net_str(B, A)) => ![C: $i] : (is_eventually_in(A, B, C) <=> ?[D: $i] : (element(D, the_carrier(B)) & ![E: $i] : (element(E, the_carrier(B)) => (related(B, D, E) => in(apply_netmap(A, B, E), C)))))) <=> ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (is_eventually_in(A, B, C) <=> ?[D: $i] : (element(D, the_carrier(B)) & ![E: $i] : (in(apply_netmap(A, B, E), C) | (~related(B, D, E)) | (~element(E, the_carrier(B))))))))), ((((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (((~empty_carrier(B)) & net_str(B, A)) => ![C: $i] : (is_eventually_in(A, B, C) <=> ?[D: $i] : (element(D, the_carrier(B)) & ![E: $i] : (element(E, the_carrier(B)) => (related(B, D, E) => in(apply_netmap(A, B, E), C))))))) <=> (((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (is_eventually_in(A, B, C) <=> ?[D: $i] : (element(D, the_carrier(B)) & ![E: $i] : (in(apply_netmap(A, B, E), C) | (~related(B, D, E)) | (~element(E, the_carrier(B)))))))))), rewrite((((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (is_eventually_in(A, B, C) <=> ?[D: $i] : (element(D, the_carrier(B)) & ![E: $i] : (in(apply_netmap(A, B, E), C) | (~related(B, D, E)) | (~element(E, the_carrier(B)))))))) <=> ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (is_eventually_in(A, B, C) <=> ?[D: $i] : (element(D, the_carrier(B)) & ![E: $i] : (in(apply_netmap(A, B, E), C) | (~related(B, D, E)) | (~element(E, the_carrier(B))))))))), ((((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (((~empty_carrier(B)) & net_str(B, A)) => ![C: $i] : (is_eventually_in(A, B, C) <=> ?[D: $i] : (element(D, the_carrier(B)) & ![E: $i] : (element(E, the_carrier(B)) => (related(B, D, E) => in(apply_netmap(A, B, E), C))))))) <=> ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (is_eventually_in(A, B, C) <=> ?[D: $i] : (element(D, the_carrier(B)) & ![E: $i] : (in(apply_netmap(A, B, E), C) | (~related(B, D, E)) | (~element(E, the_carrier(B))))))))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(128,plain,
% 0.20/0.56 (![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (((~empty_carrier(B)) & net_str(B, A)) => ![C: $i] : (is_eventually_in(A, B, C) <=> ?[D: $i] : (element(D, the_carrier(B)) & ![E: $i] : (element(E, the_carrier(B)) => (related(B, D, E) => in(apply_netmap(A, B, E), C))))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (is_eventually_in(A, B, C) <=> ?[D: $i] : (element(D, the_carrier(B)) & ![E: $i] : (in(apply_netmap(A, B, E), C) | (~related(B, D, E)) | (~element(E, the_carrier(B))))))))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[127])).
% 0.20/0.56 tff(129,axiom,(![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (((~empty_carrier(B)) & net_str(B, A)) => ![C: $i] : (is_eventually_in(A, B, C) <=> ?[D: $i] : (element(D, the_carrier(B)) & ![E: $i] : (element(E, the_carrier(B)) => (related(B, D, E) => in(apply_netmap(A, B, E), C)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d11_waybel_0')).
% 0.20/0.56 tff(130,plain,
% 0.20/0.56 (![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (is_eventually_in(A, B, C) <=> ?[D: $i] : (element(D, the_carrier(B)) & ![E: $i] : (in(apply_netmap(A, B, E), C) | (~related(B, D, E)) | (~element(E, the_carrier(B))))))))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.20/0.56 tff(131,plain,
% 0.20/0.56 (![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (is_eventually_in(A, B, C) <=> ?[D: $i] : (element(D, the_carrier(B)) & ![E: $i] : (in(apply_netmap(A, B, E), C) | (~related(B, D, E)) | (~element(E, the_carrier(B))))))))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.20/0.56 tff(132,plain,(
% 0.20/0.56 ![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (((~is_eventually_in(A, B, C)) | (element(tptp_fun_D_0(C, B, A), the_carrier(B)) & ![E: $i] : (in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)) | (~element(E, the_carrier(B)))))) & (is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B))))))))))),
% 0.20/0.56 inference(skolemize,[status(sab)],[131])).
% 0.20/0.56 tff(133,plain,
% 0.20/0.56 (![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : (((~is_eventually_in(A, B, C)) | (element(tptp_fun_D_0(C, B, A), the_carrier(B)) & ![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E))))) & (is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B))))))))))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[132, 125])).
% 0.20/0.56 tff(134,plain,
% 0.20/0.56 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))) | (~(is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B))))))))))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[133, 123])).
% 0.20/0.57 tff(135,plain,
% 0.20/0.57 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))) | (~(is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B))))))))))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[134, 121])).
% 0.20/0.57 tff(136,plain,
% 0.20/0.57 (((~![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))) | (~(is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B))))))))))))) | (empty_carrier(A!24) | (~one_sorted_str(A!24)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A!24)) | ![C: $i] : (~((~((~is_eventually_in(A!24, B, C)) | (~((~element(tptp_fun_D_0(C, B, A!24), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A!24, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A!24), E)))))))) | (~(is_eventually_in(A!24, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A!24, B, tptp_fun_E_1(D, C, B, A!24)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A!24))) | (~element(tptp_fun_E_1(D, C, B, A!24), the_carrier(B))))))))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))) | (~(is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B))))))))))))) | empty_carrier(A!24) | (~one_sorted_str(A!24)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A!24)) | ![C: $i] : (~((~((~is_eventually_in(A!24, B, C)) | (~((~element(tptp_fun_D_0(C, B, A!24), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A!24, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A!24), E)))))))) | (~(is_eventually_in(A!24, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A!24, B, tptp_fun_E_1(D, C, B, A!24)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A!24))) | (~element(tptp_fun_E_1(D, C, B, A!24), the_carrier(B))))))))))))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(137,plain,
% 0.20/0.57 ((~![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))) | (~(is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B))))))))))))) | (empty_carrier(A!24) | (~one_sorted_str(A!24)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A!24)) | ![C: $i] : (~((~((~is_eventually_in(A!24, B, C)) | (~((~element(tptp_fun_D_0(C, B, A!24), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A!24, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A!24), E)))))))) | (~(is_eventually_in(A!24, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A!24, B, tptp_fun_E_1(D, C, B, A!24)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A!24))) | (~element(tptp_fun_E_1(D, C, B, A!24), the_carrier(B))))))))))))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(138,plain,
% 0.20/0.57 ((~![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : (~((~((~is_eventually_in(A, B, C)) | (~((~element(tptp_fun_D_0(C, B, A), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A), E)))))))) | (~(is_eventually_in(A, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A, B, tptp_fun_E_1(D, C, B, A)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A))) | (~element(tptp_fun_E_1(D, C, B, A), the_carrier(B))))))))))))) | empty_carrier(A!24) | (~one_sorted_str(A!24)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A!24)) | ![C: $i] : (~((~((~is_eventually_in(A!24, B, C)) | (~((~element(tptp_fun_D_0(C, B, A!24), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A!24, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A!24), E)))))))) | (~(is_eventually_in(A!24, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A!24, B, tptp_fun_E_1(D, C, B, A!24)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A!24))) | (~element(tptp_fun_E_1(D, C, B, A!24), the_carrier(B)))))))))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.20/0.57 tff(139,plain,
% 0.20/0.57 (![B: $i] : (empty_carrier(B) | (~net_str(B, A!24)) | ![C: $i] : (~((~((~is_eventually_in(A!24, B, C)) | (~((~element(tptp_fun_D_0(C, B, A!24), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A!24, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A!24), E)))))))) | (~(is_eventually_in(A!24, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A!24, B, tptp_fun_E_1(D, C, B, A!24)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A!24))) | (~element(tptp_fun_E_1(D, C, B, A!24), the_carrier(B)))))))))))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[138, 135, 21, 20])).
% 0.20/0.57 tff(140,plain,
% 0.20/0.57 (((~![B: $i] : (empty_carrier(B) | (~net_str(B, A!24)) | ![C: $i] : (~((~((~is_eventually_in(A!24, B, C)) | (~((~element(tptp_fun_D_0(C, B, A!24), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A!24, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A!24), E)))))))) | (~(is_eventually_in(A!24, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A!24, B, tptp_fun_E_1(D, C, B, A!24)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A!24))) | (~element(tptp_fun_E_1(D, C, B, A!24), the_carrier(B)))))))))))) | (empty_carrier(B!25) | (~net_str(B!25, A!24)) | ![C: $i] : (~((~((~is_eventually_in(A!24, B!25, C)) | (~((~element(tptp_fun_D_0(C, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | in(apply_netmap(A!24, B!25, E), C) | (~related(B!25, tptp_fun_D_0(C, B!25, A!24), E)))))))) | (~(is_eventually_in(A!24, B!25, C) | ![D: $i] : ((~element(D, the_carrier(B!25))) | (~(in(apply_netmap(A!24, B!25, tptp_fun_E_1(D, C, B!25, A!24)), C) | (~related(B!25, D, tptp_fun_E_1(D, C, B!25, A!24))) | (~element(tptp_fun_E_1(D, C, B!25, A!24), the_carrier(B!25)))))))))))) <=> ((~![B: $i] : (empty_carrier(B) | (~net_str(B, A!24)) | ![C: $i] : (~((~((~is_eventually_in(A!24, B, C)) | (~((~element(tptp_fun_D_0(C, B, A!24), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A!24, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A!24), E)))))))) | (~(is_eventually_in(A!24, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A!24, B, tptp_fun_E_1(D, C, B, A!24)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A!24))) | (~element(tptp_fun_E_1(D, C, B, A!24), the_carrier(B)))))))))))) | empty_carrier(B!25) | (~net_str(B!25, A!24)) | ![C: $i] : (~((~((~is_eventually_in(A!24, B!25, C)) | (~((~element(tptp_fun_D_0(C, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | in(apply_netmap(A!24, B!25, E), C) | (~related(B!25, tptp_fun_D_0(C, B!25, A!24), E)))))))) | (~(is_eventually_in(A!24, B!25, C) | ![D: $i] : ((~element(D, the_carrier(B!25))) | (~(in(apply_netmap(A!24, B!25, tptp_fun_E_1(D, C, B!25, A!24)), C) | (~related(B!25, D, tptp_fun_E_1(D, C, B!25, A!24))) | (~element(tptp_fun_E_1(D, C, B!25, A!24), the_carrier(B!25)))))))))))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(141,plain,
% 0.20/0.57 ((~![B: $i] : (empty_carrier(B) | (~net_str(B, A!24)) | ![C: $i] : (~((~((~is_eventually_in(A!24, B, C)) | (~((~element(tptp_fun_D_0(C, B, A!24), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A!24, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A!24), E)))))))) | (~(is_eventually_in(A!24, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A!24, B, tptp_fun_E_1(D, C, B, A!24)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A!24))) | (~element(tptp_fun_E_1(D, C, B, A!24), the_carrier(B)))))))))))) | (empty_carrier(B!25) | (~net_str(B!25, A!24)) | ![C: $i] : (~((~((~is_eventually_in(A!24, B!25, C)) | (~((~element(tptp_fun_D_0(C, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | in(apply_netmap(A!24, B!25, E), C) | (~related(B!25, tptp_fun_D_0(C, B!25, A!24), E)))))))) | (~(is_eventually_in(A!24, B!25, C) | ![D: $i] : ((~element(D, the_carrier(B!25))) | (~(in(apply_netmap(A!24, B!25, tptp_fun_E_1(D, C, B!25, A!24)), C) | (~related(B!25, D, tptp_fun_E_1(D, C, B!25, A!24))) | (~element(tptp_fun_E_1(D, C, B!25, A!24), the_carrier(B!25)))))))))))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(142,plain,
% 0.20/0.57 ((~![B: $i] : (empty_carrier(B) | (~net_str(B, A!24)) | ![C: $i] : (~((~((~is_eventually_in(A!24, B, C)) | (~((~element(tptp_fun_D_0(C, B, A!24), the_carrier(B))) | (~![E: $i] : ((~element(E, the_carrier(B))) | in(apply_netmap(A!24, B, E), C) | (~related(B, tptp_fun_D_0(C, B, A!24), E)))))))) | (~(is_eventually_in(A!24, B, C) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(in(apply_netmap(A!24, B, tptp_fun_E_1(D, C, B, A!24)), C) | (~related(B, D, tptp_fun_E_1(D, C, B, A!24))) | (~element(tptp_fun_E_1(D, C, B, A!24), the_carrier(B)))))))))))) | empty_carrier(B!25) | (~net_str(B!25, A!24)) | ![C: $i] : (~((~((~is_eventually_in(A!24, B!25, C)) | (~((~element(tptp_fun_D_0(C, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | in(apply_netmap(A!24, B!25, E), C) | (~related(B!25, tptp_fun_D_0(C, B!25, A!24), E)))))))) | (~(is_eventually_in(A!24, B!25, C) | ![D: $i] : ((~element(D, the_carrier(B!25))) | (~(in(apply_netmap(A!24, B!25, tptp_fun_E_1(D, C, B!25, A!24)), C) | (~related(B!25, D, tptp_fun_E_1(D, C, B!25, A!24))) | (~element(tptp_fun_E_1(D, C, B!25, A!24), the_carrier(B!25))))))))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.20/0.57 tff(143,plain,
% 0.20/0.57 (![C: $i] : (~((~((~is_eventually_in(A!24, B!25, C)) | (~((~element(tptp_fun_D_0(C, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | in(apply_netmap(A!24, B!25, E), C) | (~related(B!25, tptp_fun_D_0(C, B!25, A!24), E)))))))) | (~(is_eventually_in(A!24, B!25, C) | ![D: $i] : ((~element(D, the_carrier(B!25))) | (~(in(apply_netmap(A!24, B!25, tptp_fun_E_1(D, C, B!25, A!24)), C) | (~related(B!25, D, tptp_fun_E_1(D, C, B!25, A!24))) | (~element(tptp_fun_E_1(D, C, B!25, A!24), the_carrier(B!25))))))))))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[142, 46, 45, 139])).
% 0.20/0.57 tff(144,plain,
% 0.20/0.57 ((~![C: $i] : (~((~((~is_eventually_in(A!24, B!25, C)) | (~((~element(tptp_fun_D_0(C, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | in(apply_netmap(A!24, B!25, E), C) | (~related(B!25, tptp_fun_D_0(C, B!25, A!24), E)))))))) | (~(is_eventually_in(A!24, B!25, C) | ![D: $i] : ((~element(D, the_carrier(B!25))) | (~(in(apply_netmap(A!24, B!25, tptp_fun_E_1(D, C, B!25, A!24)), C) | (~related(B!25, D, tptp_fun_E_1(D, C, B!25, A!24))) | (~element(tptp_fun_E_1(D, C, B!25, A!24), the_carrier(B!25))))))))))) | (~((~((~is_eventually_in(A!24, B!25, C!26)) | (~((~element(tptp_fun_D_0(C!26, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | in(apply_netmap(A!24, B!25, E), C!26) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), E)))))))) | (~(is_eventually_in(A!24, B!25, C!26) | ![D: $i] : ((~element(D, the_carrier(B!25))) | (~(in(apply_netmap(A!24, B!25, tptp_fun_E_1(D, C!26, B!25, A!24)), C!26) | (~related(B!25, D, tptp_fun_E_1(D, C!26, B!25, A!24))) | (~element(tptp_fun_E_1(D, C!26, B!25, A!24), the_carrier(B!25))))))))))),
% 0.20/0.58 inference(quant_inst,[status(thm)],[])).
% 0.20/0.58 tff(145,plain,
% 0.20/0.58 (~((~((~is_eventually_in(A!24, B!25, C!26)) | (~((~element(tptp_fun_D_0(C!26, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | in(apply_netmap(A!24, B!25, E), C!26) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), E)))))))) | (~(is_eventually_in(A!24, B!25, C!26) | ![D: $i] : ((~element(D, the_carrier(B!25))) | (~(in(apply_netmap(A!24, B!25, tptp_fun_E_1(D, C!26, B!25, A!24)), C!26) | (~related(B!25, D, tptp_fun_E_1(D, C!26, B!25, A!24))) | (~element(tptp_fun_E_1(D, C!26, B!25, A!24), the_carrier(B!25)))))))))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[144, 143])).
% 0.20/0.58 tff(146,plain,
% 0.20/0.58 (((~((~is_eventually_in(A!24, B!25, C!26)) | (~((~element(tptp_fun_D_0(C!26, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | in(apply_netmap(A!24, B!25, E), C!26) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), E)))))))) | (~(is_eventually_in(A!24, B!25, C!26) | ![D: $i] : ((~element(D, the_carrier(B!25))) | (~(in(apply_netmap(A!24, B!25, tptp_fun_E_1(D, C!26, B!25, A!24)), C!26) | (~related(B!25, D, tptp_fun_E_1(D, C!26, B!25, A!24))) | (~element(tptp_fun_E_1(D, C!26, B!25, A!24), the_carrier(B!25))))))))) | ((~is_eventually_in(A!24, B!25, C!26)) | (~((~element(tptp_fun_D_0(C!26, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | in(apply_netmap(A!24, B!25, E), C!26) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), E)))))))),
% 0.20/0.58 inference(tautology,[status(thm)],[])).
% 0.20/0.58 tff(147,plain,
% 0.20/0.58 ((~is_eventually_in(A!24, B!25, C!26)) | (~((~element(tptp_fun_D_0(C!26, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | in(apply_netmap(A!24, B!25, E), C!26) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), E))))))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.20/0.58 tff(148,plain,
% 0.20/0.58 (is_eventually_in(A!24, B!25, C!26)),
% 0.20/0.58 inference(or_elim,[status(thm)],[55])).
% 0.20/0.58 tff(149,plain,
% 0.20/0.58 ((~((~is_eventually_in(A!24, B!25, C!26)) | (~((~element(tptp_fun_D_0(C!26, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | in(apply_netmap(A!24, B!25, E), C!26) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), E)))))))) | (~is_eventually_in(A!24, B!25, C!26)) | (~((~element(tptp_fun_D_0(C!26, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | in(apply_netmap(A!24, B!25, E), C!26) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), E))))))),
% 0.20/0.58 inference(tautology,[status(thm)],[])).
% 0.20/0.58 tff(150,plain,
% 0.20/0.58 ((~((~is_eventually_in(A!24, B!25, C!26)) | (~((~element(tptp_fun_D_0(C!26, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | in(apply_netmap(A!24, B!25, E), C!26) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), E)))))))) | (~((~element(tptp_fun_D_0(C!26, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | in(apply_netmap(A!24, B!25, E), C!26) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), E))))))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.20/0.58 tff(151,plain,
% 0.20/0.58 (~((~element(tptp_fun_D_0(C!26, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | in(apply_netmap(A!24, B!25, E), C!26) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), E)))))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[150, 147])).
% 0.20/0.58 tff(152,plain,
% 0.20/0.58 (((~element(tptp_fun_D_0(C!26, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | in(apply_netmap(A!24, B!25, E), C!26) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), E))))) | element(tptp_fun_D_0(C!26, B!25, A!24), the_carrier(B!25))),
% 0.20/0.58 inference(tautology,[status(thm)],[])).
% 0.20/0.58 tff(153,plain,
% 0.20/0.58 (element(tptp_fun_D_0(C!26, B!25, A!24), the_carrier(B!25))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.20/0.58 tff(154,plain,
% 0.20/0.58 (((~![C: $i] : ((~element(C, the_carrier(B!25))) | (~((~element(tptp_fun_D_4(C, tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), tptp_fun_D_4(C, tptp_fun_D_3(C!26, B!25, A!24), B!25))) | (~related(B!25, C, tptp_fun_D_4(C, tptp_fun_D_3(C!26, B!25, A!24), B!25))))))) | ((~element(tptp_fun_D_0(C!26, B!25, A!24), the_carrier(B!25))) | (~((~element(tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25))) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(B!25))) | (~((~element(tptp_fun_D_4(C, tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), tptp_fun_D_4(C, tptp_fun_D_3(C!26, B!25, A!24), B!25))) | (~related(B!25, C, tptp_fun_D_4(C, tptp_fun_D_3(C!26, B!25, A!24), B!25))))))) | (~element(tptp_fun_D_0(C!26, B!25, A!24), the_carrier(B!25))) | (~((~element(tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25))) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25))))))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(155,plain,
% 0.20/0.58 ((~![C: $i] : ((~element(C, the_carrier(B!25))) | (~((~element(tptp_fun_D_4(C, tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), tptp_fun_D_4(C, tptp_fun_D_3(C!26, B!25, A!24), B!25))) | (~related(B!25, C, tptp_fun_D_4(C, tptp_fun_D_3(C!26, B!25, A!24), B!25))))))) | ((~element(tptp_fun_D_0(C!26, B!25, A!24), the_carrier(B!25))) | (~((~element(tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25))) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25))))))),
% 0.20/0.58 inference(quant_inst,[status(thm)],[])).
% 0.20/0.58 tff(156,plain,
% 0.20/0.58 ((~![C: $i] : ((~element(C, the_carrier(B!25))) | (~((~element(tptp_fun_D_4(C, tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), tptp_fun_D_4(C, tptp_fun_D_3(C!26, B!25, A!24), B!25))) | (~related(B!25, C, tptp_fun_D_4(C, tptp_fun_D_3(C!26, B!25, A!24), B!25))))))) | (~element(tptp_fun_D_0(C!26, B!25, A!24), the_carrier(B!25))) | (~((~element(tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25))) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25)))))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.20/0.58 tff(157,plain,
% 0.20/0.58 (~((~element(tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25))) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25))))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[156, 153, 116])).
% 0.20/0.59 tff(158,plain,
% 0.20/0.59 (((~element(tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25))) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25)))) | related(B!25, tptp_fun_D_3(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25))),
% 0.20/0.59 inference(tautology,[status(thm)],[])).
% 0.20/0.59 tff(159,plain,
% 0.20/0.59 (related(B!25, tptp_fun_D_3(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.20/0.59 tff(160,plain,
% 0.20/0.59 (((~element(tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25))) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25)))) | element(tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))),
% 0.20/0.59 inference(tautology,[status(thm)],[])).
% 0.20/0.59 tff(161,plain,
% 0.20/0.59 (element(tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[160, 157])).
% 0.20/0.59 tff(162,plain,
% 0.20/0.59 (((~element(tptp_fun_D_3(C!26, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), E)) | (~in(apply_netmap(A!24, B!25, E), C!26))))) | ![E: $i] : ((~element(E, the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), E)) | (~in(apply_netmap(A!24, B!25, E), C!26)))),
% 0.20/0.59 inference(tautology,[status(thm)],[])).
% 0.20/0.59 tff(163,plain,
% 0.20/0.59 (![E: $i] : ((~element(E, the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), E)) | (~in(apply_netmap(A!24, B!25, E), C!26)))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[162, 59])).
% 0.20/0.59 tff(164,plain,
% 0.20/0.59 (((~![E: $i] : ((~element(E, the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), E)) | (~in(apply_netmap(A!24, B!25, E), C!26)))) | ((~element(tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25))) | (~in(apply_netmap(A!24, B!25, tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25)), C!26)))) <=> ((~![E: $i] : ((~element(E, the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), E)) | (~in(apply_netmap(A!24, B!25, E), C!26)))) | (~element(tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25))) | (~in(apply_netmap(A!24, B!25, tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25)), C!26)))),
% 0.20/0.59 inference(rewrite,[status(thm)],[])).
% 0.20/0.59 tff(165,plain,
% 0.20/0.59 ((~![E: $i] : ((~element(E, the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), E)) | (~in(apply_netmap(A!24, B!25, E), C!26)))) | ((~element(tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25))) | (~in(apply_netmap(A!24, B!25, tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25)), C!26)))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(166,plain,
% 0.20/0.59 ((~![E: $i] : ((~element(E, the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), E)) | (~in(apply_netmap(A!24, B!25, E), C!26)))) | (~element(tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25))) | (~in(apply_netmap(A!24, B!25, tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25)), C!26))),
% 0.20/0.60 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.20/0.60 tff(167,plain,
% 0.20/0.60 (~in(apply_netmap(A!24, B!25, tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25)), C!26)),
% 0.20/0.60 inference(unit_resolution,[status(thm)],[166, 163, 161, 159])).
% 0.20/0.60 tff(168,plain,
% 0.20/0.60 (((~element(tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | (~related(B!25, tptp_fun_D_3(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25))) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25)))) | related(B!25, tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25))),
% 0.20/0.60 inference(tautology,[status(thm)],[])).
% 0.20/0.60 tff(169,plain,
% 0.20/0.60 (related(B!25, tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25))),
% 0.20/0.60 inference(unit_resolution,[status(thm)],[168, 157])).
% 0.20/0.60 tff(170,plain,
% 0.20/0.60 (((~element(tptp_fun_D_0(C!26, B!25, A!24), the_carrier(B!25))) | (~![E: $i] : ((~element(E, the_carrier(B!25))) | in(apply_netmap(A!24, B!25, E), C!26) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), E))))) | ![E: $i] : ((~element(E, the_carrier(B!25))) | in(apply_netmap(A!24, B!25, E), C!26) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), E)))),
% 0.20/0.60 inference(tautology,[status(thm)],[])).
% 0.20/0.60 tff(171,plain,
% 0.20/0.60 (![E: $i] : ((~element(E, the_carrier(B!25))) | in(apply_netmap(A!24, B!25, E), C!26) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), E)))),
% 0.20/0.60 inference(unit_resolution,[status(thm)],[170, 151])).
% 0.20/0.60 tff(172,plain,
% 0.20/0.60 (((~![E: $i] : ((~element(E, the_carrier(B!25))) | in(apply_netmap(A!24, B!25, E), C!26) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), E)))) | ((~element(tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25))) | in(apply_netmap(A!24, B!25, tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25)), C!26))) <=> ((~![E: $i] : ((~element(E, the_carrier(B!25))) | in(apply_netmap(A!24, B!25, E), C!26) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), E)))) | (~element(tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25))) | in(apply_netmap(A!24, B!25, tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25)), C!26))),
% 0.20/0.60 inference(rewrite,[status(thm)],[])).
% 0.20/0.60 tff(173,plain,
% 0.20/0.60 (((~element(tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | in(apply_netmap(A!24, B!25, tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25)), C!26) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25)))) <=> ((~element(tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25))) | in(apply_netmap(A!24, B!25, tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25)), C!26))),
% 0.20/0.60 inference(rewrite,[status(thm)],[])).
% 0.20/0.60 tff(174,plain,
% 0.20/0.60 (((~![E: $i] : ((~element(E, the_carrier(B!25))) | in(apply_netmap(A!24, B!25, E), C!26) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), E)))) | ((~element(tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | in(apply_netmap(A!24, B!25, tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25)), C!26) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25))))) <=> ((~![E: $i] : ((~element(E, the_carrier(B!25))) | in(apply_netmap(A!24, B!25, E), C!26) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), E)))) | ((~element(tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25))) | in(apply_netmap(A!24, B!25, tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25)), C!26)))),
% 0.20/0.61 inference(monotonicity,[status(thm)],[173])).
% 0.20/0.61 tff(175,plain,
% 0.20/0.61 (((~![E: $i] : ((~element(E, the_carrier(B!25))) | in(apply_netmap(A!24, B!25, E), C!26) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), E)))) | ((~element(tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | in(apply_netmap(A!24, B!25, tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25)), C!26) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25))))) <=> ((~![E: $i] : ((~element(E, the_carrier(B!25))) | in(apply_netmap(A!24, B!25, E), C!26) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), E)))) | (~element(tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25))) | in(apply_netmap(A!24, B!25, tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25)), C!26))),
% 0.20/0.61 inference(transitivity,[status(thm)],[174, 172])).
% 0.20/0.61 tff(176,plain,
% 0.20/0.61 ((~![E: $i] : ((~element(E, the_carrier(B!25))) | in(apply_netmap(A!24, B!25, E), C!26) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), E)))) | ((~element(tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | in(apply_netmap(A!24, B!25, tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25)), C!26) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25))))),
% 0.20/0.61 inference(quant_inst,[status(thm)],[])).
% 0.20/0.61 tff(177,plain,
% 0.20/0.61 ((~![E: $i] : ((~element(E, the_carrier(B!25))) | in(apply_netmap(A!24, B!25, E), C!26) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), E)))) | (~element(tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25), the_carrier(B!25))) | (~related(B!25, tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25))) | in(apply_netmap(A!24, B!25, tptp_fun_D_4(tptp_fun_D_0(C!26, B!25, A!24), tptp_fun_D_3(C!26, B!25, A!24), B!25)), C!26)),
% 0.20/0.61 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.20/0.61 tff(178,plain,
% 0.20/0.61 ($false),
% 0.20/0.61 inference(unit_resolution,[status(thm)],[177, 171, 161, 169, 167])).
% 0.20/0.61 % SZS output end Proof
%------------------------------------------------------------------------------