TSTP Solution File: SEU375+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU375+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 0.21s 0.49s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU375+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 12:50:24 EDT 2022
% 0.13/0.34 % 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.
% 0.21/0.49 % SZS status Theorem
% 0.21/0.49 % SZS output start Proof
% 0.21/0.49 tff(related_type, type, (
% 0.21/0.49 related: ( $i * $i * $i ) > $o)).
% 0.21/0.49 tff(tptp_fun_G_20_type, type, (
% 0.21/0.49 tptp_fun_G_20: $i)).
% 0.21/0.49 tff(tptp_fun_F_19_type, type, (
% 0.21/0.49 tptp_fun_F_19: $i)).
% 0.21/0.49 tff(tptp_fun_B_15_type, type, (
% 0.21/0.49 tptp_fun_B_15: $i)).
% 0.21/0.49 tff(tptp_fun_E_18_type, type, (
% 0.21/0.49 tptp_fun_E_18: $i)).
% 0.21/0.49 tff(tptp_fun_D_17_type, type, (
% 0.21/0.49 tptp_fun_D_17: $i)).
% 0.21/0.49 tff(element_type, type, (
% 0.21/0.49 element: ( $i * $i ) > $o)).
% 0.21/0.49 tff(the_carrier_type, type, (
% 0.21/0.49 the_carrier: $i > $i)).
% 0.21/0.49 tff(tptp_fun_C_16_type, type, (
% 0.21/0.49 tptp_fun_C_16: $i)).
% 0.21/0.49 tff(subnetstr_type, type, (
% 0.21/0.49 subnetstr: ( $i * $i * $i ) > $o)).
% 0.21/0.49 tff(tptp_fun_A_14_type, type, (
% 0.21/0.49 tptp_fun_A_14: $i)).
% 0.21/0.49 tff(full_subnetstr_type, type, (
% 0.21/0.49 full_subnetstr: ( $i * $i * $i ) > $o)).
% 0.21/0.49 tff(empty_carrier_type, type, (
% 0.21/0.49 empty_carrier: $i > $o)).
% 0.21/0.49 tff(net_str_type, type, (
% 0.21/0.49 net_str: ( $i * $i ) > $o)).
% 0.21/0.49 tff(one_sorted_str_type, type, (
% 0.21/0.49 one_sorted_str: $i > $o)).
% 0.21/0.49 tff(in_type, type, (
% 0.21/0.49 in: ( $i * $i ) > $o)).
% 0.21/0.49 tff(full_subrelstr_type, type, (
% 0.21/0.49 full_subrelstr: ( $i * $i ) > $o)).
% 0.21/0.49 tff(subrelstr_type, type, (
% 0.21/0.49 subrelstr: ( $i * $i ) > $o)).
% 0.21/0.49 tff(rel_str_type, type, (
% 0.21/0.49 rel_str: $i > $o)).
% 0.21/0.49 tff(empty_type, type, (
% 0.21/0.49 empty: $i > $o)).
% 0.21/0.49 tff(1,plain,
% 0.21/0.49 ((one_sorted_str(A!14) & ((~empty_carrier(B!15)) & net_str(B!15, A!14) & (~empty_carrier(C!16)) & full_subnetstr(C!16, A!14, B!15) & subnetstr(C!16, A!14, B!15) & element(D!17, the_carrier(B!15)) & element(E!18, the_carrier(B!15)) & element(F!19, the_carrier(C!16)) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16))))))) <=> (one_sorted_str(A!14) & (~empty_carrier(B!15)) & net_str(B!15, A!14) & (~empty_carrier(C!16)) & full_subnetstr(C!16, A!14, B!15) & subnetstr(C!16, A!14, B!15) & element(D!17, the_carrier(B!15)) & element(E!18, the_carrier(B!15)) & element(F!19, the_carrier(C!16)) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(2,plain,
% 0.21/0.49 ((((~empty_carrier(B!15)) & net_str(B!15, A!14)) & ((~empty_carrier(C!16)) & full_subnetstr(C!16, A!14, B!15) & subnetstr(C!16, A!14, B!15) & element(D!17, the_carrier(B!15)) & element(E!18, the_carrier(B!15)) & element(F!19, the_carrier(C!16)) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16))))))) <=> ((~empty_carrier(B!15)) & net_str(B!15, A!14) & (~empty_carrier(C!16)) & full_subnetstr(C!16, A!14, B!15) & subnetstr(C!16, A!14, B!15) & element(D!17, the_carrier(B!15)) & element(E!18, the_carrier(B!15)) & element(F!19, the_carrier(C!16)) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(3,plain,
% 0.21/0.49 ((((~empty_carrier(C!16)) & full_subnetstr(C!16, A!14, B!15) & subnetstr(C!16, A!14, B!15)) & (element(D!17, the_carrier(B!15)) & element(E!18, the_carrier(B!15)) & element(F!19, the_carrier(C!16)) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16))))))) <=> ((~empty_carrier(C!16)) & full_subnetstr(C!16, A!14, B!15) & subnetstr(C!16, A!14, B!15) & element(D!17, the_carrier(B!15)) & element(E!18, the_carrier(B!15)) & element(F!19, the_carrier(C!16)) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(4,plain,
% 0.21/0.49 ((element(D!17, the_carrier(B!15)) & (element(E!18, the_carrier(B!15)) & element(F!19, the_carrier(C!16)) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16))))))) <=> (element(D!17, the_carrier(B!15)) & element(E!18, the_carrier(B!15)) & element(F!19, the_carrier(C!16)) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(5,plain,
% 0.21/0.49 ((element(E!18, the_carrier(B!15)) & (element(F!19, the_carrier(C!16)) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16))))))) <=> (element(E!18, the_carrier(B!15)) & element(F!19, the_carrier(C!16)) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(6,plain,
% 0.21/0.49 (((~(~element(F!19, the_carrier(C!16)))) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16)))))) <=> (element(F!19, the_carrier(C!16)) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(7,plain,
% 0.21/0.49 ((~(~element(E!18, the_carrier(B!15)))) <=> element(E!18, the_carrier(B!15))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(8,plain,
% 0.21/0.49 (((~(~element(E!18, the_carrier(B!15)))) & ((~(~element(F!19, the_carrier(C!16)))) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16))))))) <=> (element(E!18, the_carrier(B!15)) & (element(F!19, the_carrier(C!16)) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16)))))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[7, 6])).
% 0.21/0.49 tff(9,plain,
% 0.21/0.49 (((~(~element(E!18, the_carrier(B!15)))) & ((~(~element(F!19, the_carrier(C!16)))) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16))))))) <=> (element(E!18, the_carrier(B!15)) & element(F!19, the_carrier(C!16)) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[8, 5])).
% 0.21/0.49 tff(10,plain,
% 0.21/0.49 ((~(~element(D!17, the_carrier(B!15)))) <=> element(D!17, the_carrier(B!15))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(11,plain,
% 0.21/0.49 (((~(~element(D!17, the_carrier(B!15)))) & ((~(~element(E!18, the_carrier(B!15)))) & ((~(~element(F!19, the_carrier(C!16)))) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16)))))))) <=> (element(D!17, the_carrier(B!15)) & (element(E!18, the_carrier(B!15)) & element(F!19, the_carrier(C!16)) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16)))))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[10, 9])).
% 0.21/0.49 tff(12,plain,
% 0.21/0.49 (((~(~element(D!17, the_carrier(B!15)))) & ((~(~element(E!18, the_carrier(B!15)))) & ((~(~element(F!19, the_carrier(C!16)))) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16)))))))) <=> (element(D!17, the_carrier(B!15)) & element(E!18, the_carrier(B!15)) & element(F!19, the_carrier(C!16)) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[11, 4])).
% 0.21/0.49 tff(13,plain,
% 0.21/0.49 ((~(~((~empty_carrier(C!16)) & full_subnetstr(C!16, A!14, B!15) & subnetstr(C!16, A!14, B!15)))) <=> ((~empty_carrier(C!16)) & full_subnetstr(C!16, A!14, B!15) & subnetstr(C!16, A!14, B!15))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(14,plain,
% 0.21/0.49 (((~(~((~empty_carrier(C!16)) & full_subnetstr(C!16, A!14, B!15) & subnetstr(C!16, A!14, B!15)))) & ((~(~element(D!17, the_carrier(B!15)))) & ((~(~element(E!18, the_carrier(B!15)))) & ((~(~element(F!19, the_carrier(C!16)))) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16))))))))) <=> (((~empty_carrier(C!16)) & full_subnetstr(C!16, A!14, B!15) & subnetstr(C!16, A!14, B!15)) & (element(D!17, the_carrier(B!15)) & element(E!18, the_carrier(B!15)) & element(F!19, the_carrier(C!16)) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16)))))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[13, 12])).
% 0.21/0.49 tff(15,plain,
% 0.21/0.49 (((~(~((~empty_carrier(C!16)) & full_subnetstr(C!16, A!14, B!15) & subnetstr(C!16, A!14, B!15)))) & ((~(~element(D!17, the_carrier(B!15)))) & ((~(~element(E!18, the_carrier(B!15)))) & ((~(~element(F!19, the_carrier(C!16)))) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16))))))))) <=> ((~empty_carrier(C!16)) & full_subnetstr(C!16, A!14, B!15) & subnetstr(C!16, A!14, B!15) & element(D!17, the_carrier(B!15)) & element(E!18, the_carrier(B!15)) & element(F!19, the_carrier(C!16)) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[14, 3])).
% 0.21/0.49 tff(16,plain,
% 0.21/0.49 ((~(~((~empty_carrier(B!15)) & net_str(B!15, A!14)))) <=> ((~empty_carrier(B!15)) & net_str(B!15, A!14))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(17,plain,
% 0.21/0.49 (((~(~((~empty_carrier(B!15)) & net_str(B!15, A!14)))) & ((~(~((~empty_carrier(C!16)) & full_subnetstr(C!16, A!14, B!15) & subnetstr(C!16, A!14, B!15)))) & ((~(~element(D!17, the_carrier(B!15)))) & ((~(~element(E!18, the_carrier(B!15)))) & ((~(~element(F!19, the_carrier(C!16)))) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16)))))))))) <=> (((~empty_carrier(B!15)) & net_str(B!15, A!14)) & ((~empty_carrier(C!16)) & full_subnetstr(C!16, A!14, B!15) & subnetstr(C!16, A!14, B!15) & element(D!17, the_carrier(B!15)) & element(E!18, the_carrier(B!15)) & element(F!19, the_carrier(C!16)) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16)))))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[16, 15])).
% 0.21/0.49 tff(18,plain,
% 0.21/0.49 (((~(~((~empty_carrier(B!15)) & net_str(B!15, A!14)))) & ((~(~((~empty_carrier(C!16)) & full_subnetstr(C!16, A!14, B!15) & subnetstr(C!16, A!14, B!15)))) & ((~(~element(D!17, the_carrier(B!15)))) & ((~(~element(E!18, the_carrier(B!15)))) & ((~(~element(F!19, the_carrier(C!16)))) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16)))))))))) <=> ((~empty_carrier(B!15)) & net_str(B!15, A!14) & (~empty_carrier(C!16)) & full_subnetstr(C!16, A!14, B!15) & subnetstr(C!16, A!14, B!15) & element(D!17, the_carrier(B!15)) & element(E!18, the_carrier(B!15)) & element(F!19, the_carrier(C!16)) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[17, 2])).
% 0.21/0.49 tff(19,plain,
% 0.21/0.49 ((~(~one_sorted_str(A!14))) <=> one_sorted_str(A!14)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(20,plain,
% 0.21/0.49 (((~(~one_sorted_str(A!14))) & ((~(~((~empty_carrier(B!15)) & net_str(B!15, A!14)))) & ((~(~((~empty_carrier(C!16)) & full_subnetstr(C!16, A!14, B!15) & subnetstr(C!16, A!14, B!15)))) & ((~(~element(D!17, the_carrier(B!15)))) & ((~(~element(E!18, the_carrier(B!15)))) & ((~(~element(F!19, the_carrier(C!16)))) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16))))))))))) <=> (one_sorted_str(A!14) & ((~empty_carrier(B!15)) & net_str(B!15, A!14) & (~empty_carrier(C!16)) & full_subnetstr(C!16, A!14, B!15) & subnetstr(C!16, A!14, B!15) & element(D!17, the_carrier(B!15)) & element(E!18, the_carrier(B!15)) & element(F!19, the_carrier(C!16)) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16)))))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[19, 18])).
% 0.21/0.49 tff(21,plain,
% 0.21/0.49 (((~(~one_sorted_str(A!14))) & ((~(~((~empty_carrier(B!15)) & net_str(B!15, A!14)))) & ((~(~((~empty_carrier(C!16)) & full_subnetstr(C!16, A!14, B!15) & subnetstr(C!16, A!14, B!15)))) & ((~(~element(D!17, the_carrier(B!15)))) & ((~(~element(E!18, the_carrier(B!15)))) & ((~(~element(F!19, the_carrier(C!16)))) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16))))))))))) <=> (one_sorted_str(A!14) & (~empty_carrier(B!15)) & net_str(B!15, A!14) & (~empty_carrier(C!16)) & full_subnetstr(C!16, A!14, B!15) & subnetstr(C!16, A!14, B!15) & element(D!17, the_carrier(B!15)) & element(E!18, the_carrier(B!15)) & element(F!19, the_carrier(C!16)) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[20, 1])).
% 0.21/0.49 tff(22,plain,
% 0.21/0.49 ((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : ((~((~empty_carrier(C)) & full_subnetstr(C, A, B) & subnetstr(C, A, B))) | ![D: $i] : ((~element(D, the_carrier(B))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : ((~element(F, the_carrier(C))) | ![G: $i] : (related(C, F, G) | (~((D = F) & (E = G) & related(B, D, E))) | (~element(G, the_carrier(C))))))))))) <=> (~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : ((~((~empty_carrier(C)) & full_subnetstr(C, A, B) & subnetstr(C, A, B))) | ![D: $i] : ((~element(D, the_carrier(B))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : ((~element(F, the_carrier(C))) | ![G: $i] : (related(C, F, G) | (~((D = F) & (E = G) & related(B, D, E))) | (~element(G, the_carrier(C)))))))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(23,plain,
% 0.21/0.49 ((~![A: $i] : (one_sorted_str(A) => ![B: $i] : (((~empty_carrier(B)) & net_str(B, A)) => ![C: $i] : ((((~empty_carrier(C)) & full_subnetstr(C, A, B)) & subnetstr(C, A, B)) => ![D: $i] : (element(D, the_carrier(B)) => ![E: $i] : (element(E, the_carrier(B)) => ![F: $i] : (element(F, the_carrier(C)) => ![G: $i] : (element(G, the_carrier(C)) => ((((D = F) & (E = G)) & related(B, D, E)) => related(C, F, G)))))))))) <=> (~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : ((~((~empty_carrier(C)) & full_subnetstr(C, A, B) & subnetstr(C, A, B))) | ![D: $i] : ((~element(D, the_carrier(B))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : ((~element(F, the_carrier(C))) | ![G: $i] : (related(C, F, G) | (~((D = F) & (E = G) & related(B, D, E))) | (~element(G, the_carrier(C)))))))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(24,axiom,(~![A: $i] : (one_sorted_str(A) => ![B: $i] : (((~empty_carrier(B)) & net_str(B, A)) => ![C: $i] : ((((~empty_carrier(C)) & full_subnetstr(C, A, B)) & subnetstr(C, A, B)) => ![D: $i] : (element(D, the_carrier(B)) => ![E: $i] : (element(E, the_carrier(B)) => ![F: $i] : (element(F, the_carrier(C)) => ![G: $i] : (element(G, the_carrier(C)) => ((((D = F) & (E = G)) & related(B, D, E)) => related(C, F, G)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t21_yellow_6')).
% 0.21/0.49 tff(25,plain,
% 0.21/0.49 (~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : ((~((~empty_carrier(C)) & full_subnetstr(C, A, B) & subnetstr(C, A, B))) | ![D: $i] : ((~element(D, the_carrier(B))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : ((~element(F, the_carrier(C))) | ![G: $i] : (related(C, F, G) | (~((D = F) & (E = G) & related(B, D, E))) | (~element(G, the_carrier(C))))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.21/0.49 tff(26,plain,
% 0.21/0.49 (~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : ((~((~empty_carrier(C)) & full_subnetstr(C, A, B) & subnetstr(C, A, B))) | ![D: $i] : ((~element(D, the_carrier(B))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : ((~element(F, the_carrier(C))) | ![G: $i] : (related(C, F, G) | (~((D = F) & (E = G) & related(B, D, E))) | (~element(G, the_carrier(C))))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[25, 22])).
% 0.21/0.49 tff(27,plain,
% 0.21/0.49 (~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : ((~((~empty_carrier(C)) & full_subnetstr(C, A, B) & subnetstr(C, A, B))) | ![D: $i] : ((~element(D, the_carrier(B))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : ((~element(F, the_carrier(C))) | ![G: $i] : (related(C, F, G) | (~((D = F) & (E = G) & related(B, D, E))) | (~element(G, the_carrier(C))))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.21/0.49 tff(28,plain,
% 0.21/0.49 (~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : ((~((~empty_carrier(C)) & full_subnetstr(C, A, B) & subnetstr(C, A, B))) | ![D: $i] : ((~element(D, the_carrier(B))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : ((~element(F, the_carrier(C))) | ![G: $i] : (related(C, F, G) | (~((D = F) & (E = G) & related(B, D, E))) | (~element(G, the_carrier(C))))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[27, 22])).
% 0.21/0.49 tff(29,plain,
% 0.21/0.49 (~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : ((~((~empty_carrier(C)) & full_subnetstr(C, A, B) & subnetstr(C, A, B))) | ![D: $i] : ((~element(D, the_carrier(B))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : ((~element(F, the_carrier(C))) | ![G: $i] : (related(C, F, G) | (~((D = F) & (E = G) & related(B, D, E))) | (~element(G, the_carrier(C))))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[28, 22])).
% 0.21/0.49 tff(30,plain,
% 0.21/0.49 (~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : ((~((~empty_carrier(C)) & full_subnetstr(C, A, B) & subnetstr(C, A, B))) | ![D: $i] : ((~element(D, the_carrier(B))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : ((~element(F, the_carrier(C))) | ![G: $i] : (related(C, F, G) | (~((D = F) & (E = G) & related(B, D, E))) | (~element(G, the_carrier(C))))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.21/0.49 tff(31,plain,
% 0.21/0.49 (~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : ((~((~empty_carrier(C)) & full_subnetstr(C, A, B) & subnetstr(C, A, B))) | ![D: $i] : ((~element(D, the_carrier(B))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : ((~element(F, the_carrier(C))) | ![G: $i] : (related(C, F, G) | (~((D = F) & (E = G) & related(B, D, E))) | (~element(G, the_carrier(C))))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[30, 22])).
% 0.21/0.49 tff(32,plain,
% 0.21/0.49 (one_sorted_str(A!14) & (~empty_carrier(B!15)) & net_str(B!15, A!14) & (~empty_carrier(C!16)) & full_subnetstr(C!16, A!14, B!15) & subnetstr(C!16, A!14, B!15) & element(D!17, the_carrier(B!15)) & element(E!18, the_carrier(B!15)) & element(F!19, the_carrier(C!16)) & (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16)))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.21/0.49 tff(33,plain,
% 0.21/0.49 (~(related(C!16, F!19, G!20) | (~((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18))) | (~element(G!20, the_carrier(C!16))))),
% 0.21/0.49 inference(and_elim,[status(thm)],[32])).
% 0.21/0.49 tff(34,plain,
% 0.21/0.49 ((D!17 = F!19) & (E!18 = G!20) & related(B!15, D!17, E!18)),
% 0.21/0.49 inference(or_elim,[status(thm)],[33])).
% 0.21/0.49 tff(35,plain,
% 0.21/0.49 (E!18 = G!20),
% 0.21/0.49 inference(and_elim,[status(thm)],[34])).
% 0.21/0.49 tff(36,plain,
% 0.21/0.49 (G!20 = E!18),
% 0.21/0.49 inference(symmetry,[status(thm)],[35])).
% 0.21/0.49 tff(37,plain,
% 0.21/0.49 (D!17 = F!19),
% 0.21/0.49 inference(and_elim,[status(thm)],[34])).
% 0.21/0.49 tff(38,plain,
% 0.21/0.49 (F!19 = D!17),
% 0.21/0.49 inference(symmetry,[status(thm)],[37])).
% 0.21/0.49 tff(39,plain,
% 0.21/0.49 (related(B!15, F!19, G!20) <=> related(B!15, D!17, E!18)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[38, 36])).
% 0.21/0.49 tff(40,plain,
% 0.21/0.49 (related(B!15, D!17, E!18) <=> related(B!15, F!19, G!20)),
% 0.21/0.49 inference(symmetry,[status(thm)],[39])).
% 0.21/0.49 tff(41,plain,
% 0.21/0.49 (related(B!15, D!17, E!18)),
% 0.21/0.49 inference(and_elim,[status(thm)],[34])).
% 0.21/0.49 tff(42,plain,
% 0.21/0.50 (related(B!15, F!19, G!20)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.21/0.50 tff(43,plain,
% 0.21/0.50 (one_sorted_str(A!14)),
% 0.21/0.50 inference(and_elim,[status(thm)],[32])).
% 0.21/0.50 tff(44,plain,
% 0.21/0.50 (^[A: $i] : refl(((~one_sorted_str(A)) | ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (~((~full_subrelstr(C, B)) | (~subrelstr(C, B)))))))) <=> ((~one_sorted_str(A)) | ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (~((~full_subrelstr(C, B)) | (~subrelstr(C, B)))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(45,plain,
% 0.21/0.50 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (~((~full_subrelstr(C, B)) | (~subrelstr(C, B)))))))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (~((~full_subrelstr(C, B)) | (~subrelstr(C, B))))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[44])).
% 0.21/0.50 tff(46,plain,
% 0.21/0.50 (^[A: $i] : rewrite(((~one_sorted_str(A)) | ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (~((~full_subrelstr(C, B)) | (~subrelstr(C, B)))))))) <=> ((~one_sorted_str(A)) | ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (~((~full_subrelstr(C, B)) | (~subrelstr(C, B)))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(47,plain,
% 0.21/0.50 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (~((~full_subrelstr(C, B)) | (~subrelstr(C, B)))))))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (~((~full_subrelstr(C, B)) | (~subrelstr(C, B))))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[46])).
% 0.21/0.50 tff(48,plain,
% 0.21/0.50 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (~((~full_subrelstr(C, B)) | (~subrelstr(C, B)))))))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (~((~full_subrelstr(C, B)) | (~subrelstr(C, B))))))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[47, 45])).
% 0.21/0.50 tff(49,plain,
% 0.21/0.50 (^[A: $i] : rewrite(((~one_sorted_str(A)) | ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (full_subrelstr(C, B) & subrelstr(C, B)))))) <=> ((~one_sorted_str(A)) | ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (~((~full_subrelstr(C, B)) | (~subrelstr(C, B)))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(50,plain,
% 0.21/0.50 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (full_subrelstr(C, B) & subrelstr(C, B)))))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (~((~full_subrelstr(C, B)) | (~subrelstr(C, B))))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[49])).
% 0.21/0.50 tff(51,plain,
% 0.21/0.50 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (full_subrelstr(C, B) & subrelstr(C, B)))))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (full_subrelstr(C, B) & subrelstr(C, B))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(52,plain,
% 0.21/0.50 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((subnetstr(C, A, B) => (full_subnetstr(C, A, B) <=> (full_subrelstr(C, B) & subrelstr(C, B)))) <=> ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (full_subrelstr(C, B) & subrelstr(C, B)))))), (![C: $i] : (subnetstr(C, A, B) => (full_subnetstr(C, A, B) <=> (full_subrelstr(C, B) & subrelstr(C, B)))) <=> ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (full_subrelstr(C, B) & subrelstr(C, B)))))), ((net_str(B, A) => ![C: $i] : (subnetstr(C, A, B) => (full_subnetstr(C, A, B) <=> (full_subrelstr(C, B) & subrelstr(C, B))))) <=> (net_str(B, A) => ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (full_subrelstr(C, B) & subrelstr(C, B))))))), rewrite((net_str(B, A) => ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (full_subrelstr(C, B) & subrelstr(C, B))))) <=> ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (full_subrelstr(C, B) & subrelstr(C, B)))))), ((net_str(B, A) => ![C: $i] : (subnetstr(C, A, B) => (full_subnetstr(C, A, B) <=> (full_subrelstr(C, B) & subrelstr(C, B))))) <=> ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (full_subrelstr(C, B) & subrelstr(C, B)))))))), (![B: $i] : (net_str(B, A) => ![C: $i] : (subnetstr(C, A, B) => (full_subnetstr(C, A, B) <=> (full_subrelstr(C, B) & subrelstr(C, B))))) <=> ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (full_subrelstr(C, B) & subrelstr(C, B))))))), ((one_sorted_str(A) => ![B: $i] : (net_str(B, A) => ![C: $i] : (subnetstr(C, A, B) => (full_subnetstr(C, A, B) <=> (full_subrelstr(C, B) & subrelstr(C, B)))))) <=> (one_sorted_str(A) => ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (full_subrelstr(C, B) & subrelstr(C, B)))))))), rewrite((one_sorted_str(A) => ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (full_subrelstr(C, B) & subrelstr(C, B)))))) <=> ((~one_sorted_str(A)) | ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (full_subrelstr(C, B) & subrelstr(C, B))))))), ((one_sorted_str(A) => ![B: $i] : (net_str(B, A) => ![C: $i] : (subnetstr(C, A, B) => (full_subnetstr(C, A, B) <=> (full_subrelstr(C, B) & subrelstr(C, B)))))) <=> ((~one_sorted_str(A)) | ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (full_subrelstr(C, B) & subrelstr(C, B))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(53,plain,
% 0.21/0.50 (![A: $i] : (one_sorted_str(A) => ![B: $i] : (net_str(B, A) => ![C: $i] : (subnetstr(C, A, B) => (full_subnetstr(C, A, B) <=> (full_subrelstr(C, B) & subrelstr(C, B)))))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (full_subrelstr(C, B) & subrelstr(C, B))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[52])).
% 0.21/0.50 tff(54,axiom,(![A: $i] : (one_sorted_str(A) => ![B: $i] : (net_str(B, A) => ![C: $i] : (subnetstr(C, A, B) => (full_subnetstr(C, A, B) <=> (full_subrelstr(C, B) & subrelstr(C, B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d9_yellow_6')).
% 0.21/0.50 tff(55,plain,
% 0.21/0.50 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (full_subrelstr(C, B) & subrelstr(C, B))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.21/0.50 tff(56,plain,
% 0.21/0.50 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (full_subrelstr(C, B) & subrelstr(C, B))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.21/0.50 tff(57,plain,(
% 0.21/0.50 ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (full_subrelstr(C, B) & subrelstr(C, B))))))),
% 0.21/0.50 inference(skolemize,[status(sab)],[56])).
% 0.21/0.50 tff(58,plain,
% 0.21/0.50 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (~((~full_subrelstr(C, B)) | (~subrelstr(C, B))))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.21/0.50 tff(59,plain,
% 0.21/0.50 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (~((~full_subrelstr(C, B)) | (~subrelstr(C, B))))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[58, 48])).
% 0.21/0.50 tff(60,plain,
% 0.21/0.50 (((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (~((~full_subrelstr(C, B)) | (~subrelstr(C, B))))))))) | ((~one_sorted_str(A!14)) | ![B: $i] : ((~net_str(B, A!14)) | ![C: $i] : ((~subnetstr(C, A!14, B)) | (full_subnetstr(C, A!14, B) <=> (~((~full_subrelstr(C, B)) | (~subrelstr(C, B))))))))) <=> ((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (~((~full_subrelstr(C, B)) | (~subrelstr(C, B))))))))) | (~one_sorted_str(A!14)) | ![B: $i] : ((~net_str(B, A!14)) | ![C: $i] : ((~subnetstr(C, A!14, B)) | (full_subnetstr(C, A!14, B) <=> (~((~full_subrelstr(C, B)) | (~subrelstr(C, B))))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(61,plain,
% 0.21/0.50 ((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (~((~full_subrelstr(C, B)) | (~subrelstr(C, B))))))))) | ((~one_sorted_str(A!14)) | ![B: $i] : ((~net_str(B, A!14)) | ![C: $i] : ((~subnetstr(C, A!14, B)) | (full_subnetstr(C, A!14, B) <=> (~((~full_subrelstr(C, B)) | (~subrelstr(C, B))))))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(62,plain,
% 0.21/0.50 ((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | (full_subnetstr(C, A, B) <=> (~((~full_subrelstr(C, B)) | (~subrelstr(C, B))))))))) | (~one_sorted_str(A!14)) | ![B: $i] : ((~net_str(B, A!14)) | ![C: $i] : ((~subnetstr(C, A!14, B)) | (full_subnetstr(C, A!14, B) <=> (~((~full_subrelstr(C, B)) | (~subrelstr(C, B)))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.21/0.50 tff(63,plain,
% 0.21/0.50 (![B: $i] : ((~net_str(B, A!14)) | ![C: $i] : ((~subnetstr(C, A!14, B)) | (full_subnetstr(C, A!14, B) <=> (~((~full_subrelstr(C, B)) | (~subrelstr(C, B)))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[62, 59, 43])).
% 0.21/0.50 tff(64,plain,
% 0.21/0.50 (net_str(B!15, A!14)),
% 0.21/0.50 inference(and_elim,[status(thm)],[32])).
% 0.21/0.50 tff(65,plain,
% 0.21/0.50 (((~![B: $i] : ((~net_str(B, A!14)) | ![C: $i] : ((~subnetstr(C, A!14, B)) | (full_subnetstr(C, A!14, B) <=> (~((~full_subrelstr(C, B)) | (~subrelstr(C, B)))))))) | ((~net_str(B!15, A!14)) | ![C: $i] : ((~subnetstr(C, A!14, B!15)) | (full_subnetstr(C, A!14, B!15) <=> (~((~full_subrelstr(C, B!15)) | (~subrelstr(C, B!15)))))))) <=> ((~![B: $i] : ((~net_str(B, A!14)) | ![C: $i] : ((~subnetstr(C, A!14, B)) | (full_subnetstr(C, A!14, B) <=> (~((~full_subrelstr(C, B)) | (~subrelstr(C, B)))))))) | (~net_str(B!15, A!14)) | ![C: $i] : ((~subnetstr(C, A!14, B!15)) | (full_subnetstr(C, A!14, B!15) <=> (~((~full_subrelstr(C, B!15)) | (~subrelstr(C, B!15)))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(66,plain,
% 0.21/0.50 ((~![B: $i] : ((~net_str(B, A!14)) | ![C: $i] : ((~subnetstr(C, A!14, B)) | (full_subnetstr(C, A!14, B) <=> (~((~full_subrelstr(C, B)) | (~subrelstr(C, B)))))))) | ((~net_str(B!15, A!14)) | ![C: $i] : ((~subnetstr(C, A!14, B!15)) | (full_subnetstr(C, A!14, B!15) <=> (~((~full_subrelstr(C, B!15)) | (~subrelstr(C, B!15)))))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(67,plain,
% 0.21/0.50 ((~![B: $i] : ((~net_str(B, A!14)) | ![C: $i] : ((~subnetstr(C, A!14, B)) | (full_subnetstr(C, A!14, B) <=> (~((~full_subrelstr(C, B)) | (~subrelstr(C, B)))))))) | (~net_str(B!15, A!14)) | ![C: $i] : ((~subnetstr(C, A!14, B!15)) | (full_subnetstr(C, A!14, B!15) <=> (~((~full_subrelstr(C, B!15)) | (~subrelstr(C, B!15))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.21/0.50 tff(68,plain,
% 0.21/0.50 (![C: $i] : ((~subnetstr(C, A!14, B!15)) | (full_subnetstr(C, A!14, B!15) <=> (~((~full_subrelstr(C, B!15)) | (~subrelstr(C, B!15))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[67, 64, 63])).
% 0.21/0.50 tff(69,plain,
% 0.21/0.50 (subnetstr(C!16, A!14, B!15)),
% 0.21/0.50 inference(and_elim,[status(thm)],[32])).
% 0.21/0.50 tff(70,plain,
% 0.21/0.50 (((~![C: $i] : ((~subnetstr(C, A!14, B!15)) | (full_subnetstr(C, A!14, B!15) <=> (~((~full_subrelstr(C, B!15)) | (~subrelstr(C, B!15))))))) | ((~subnetstr(C!16, A!14, B!15)) | (full_subnetstr(C!16, A!14, B!15) <=> (~((~full_subrelstr(C!16, B!15)) | (~subrelstr(C!16, B!15))))))) <=> ((~![C: $i] : ((~subnetstr(C, A!14, B!15)) | (full_subnetstr(C, A!14, B!15) <=> (~((~full_subrelstr(C, B!15)) | (~subrelstr(C, B!15))))))) | (~subnetstr(C!16, A!14, B!15)) | (full_subnetstr(C!16, A!14, B!15) <=> (~((~full_subrelstr(C!16, B!15)) | (~subrelstr(C!16, B!15))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(71,plain,
% 0.21/0.50 ((~![C: $i] : ((~subnetstr(C, A!14, B!15)) | (full_subnetstr(C, A!14, B!15) <=> (~((~full_subrelstr(C, B!15)) | (~subrelstr(C, B!15))))))) | ((~subnetstr(C!16, A!14, B!15)) | (full_subnetstr(C!16, A!14, B!15) <=> (~((~full_subrelstr(C!16, B!15)) | (~subrelstr(C!16, B!15))))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(72,plain,
% 0.21/0.50 ((~![C: $i] : ((~subnetstr(C, A!14, B!15)) | (full_subnetstr(C, A!14, B!15) <=> (~((~full_subrelstr(C, B!15)) | (~subrelstr(C, B!15))))))) | (~subnetstr(C!16, A!14, B!15)) | (full_subnetstr(C!16, A!14, B!15) <=> (~((~full_subrelstr(C!16, B!15)) | (~subrelstr(C!16, B!15)))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.21/0.50 tff(73,plain,
% 0.21/0.50 (full_subnetstr(C!16, A!14, B!15) <=> (~((~full_subrelstr(C!16, B!15)) | (~subrelstr(C!16, B!15))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[72, 69, 68])).
% 0.21/0.50 tff(74,plain,
% 0.21/0.50 (full_subnetstr(C!16, A!14, B!15)),
% 0.21/0.50 inference(and_elim,[status(thm)],[32])).
% 0.21/0.50 tff(75,plain,
% 0.21/0.50 ((~(full_subnetstr(C!16, A!14, B!15) <=> (~((~full_subrelstr(C!16, B!15)) | (~subrelstr(C!16, B!15)))))) | (~full_subnetstr(C!16, A!14, B!15)) | (~((~full_subrelstr(C!16, B!15)) | (~subrelstr(C!16, B!15))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(76,plain,
% 0.21/0.50 ((~(full_subnetstr(C!16, A!14, B!15) <=> (~((~full_subrelstr(C!16, B!15)) | (~subrelstr(C!16, B!15)))))) | (~((~full_subrelstr(C!16, B!15)) | (~subrelstr(C!16, B!15))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.21/0.50 tff(77,plain,
% 0.21/0.50 (~((~full_subrelstr(C!16, B!15)) | (~subrelstr(C!16, B!15)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[76, 73])).
% 0.21/0.50 tff(78,plain,
% 0.21/0.50 (((~full_subrelstr(C!16, B!15)) | (~subrelstr(C!16, B!15))) | full_subrelstr(C!16, B!15)),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(79,plain,
% 0.21/0.50 (full_subrelstr(C!16, B!15)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.21/0.50 tff(80,plain,
% 0.21/0.50 (((~full_subrelstr(C!16, B!15)) | (~subrelstr(C!16, B!15))) | subrelstr(C!16, B!15)),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(81,plain,
% 0.21/0.50 (subrelstr(C!16, B!15)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[80, 77])).
% 0.21/0.50 tff(82,plain,
% 0.21/0.50 (^[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)))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(83,plain,
% 0.21/0.50 (![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))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[82])).
% 0.21/0.50 tff(84,plain,
% 0.21/0.50 (^[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)))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(85,plain,
% 0.21/0.50 (![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))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[84])).
% 0.21/0.50 tff(86,plain,
% 0.21/0.50 (![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))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[85, 83])).
% 0.21/0.50 tff(87,plain,
% 0.21/0.50 (![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))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(88,plain,
% 0.21/0.50 (^[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))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(89,plain,
% 0.21/0.50 (![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))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[88])).
% 0.21/0.50 tff(90,axiom,(![A: $i] : (one_sorted_str(A) => ![B: $i] : (net_str(B, A) => rel_str(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_waybel_0')).
% 0.21/0.50 tff(91,plain,
% 0.21/0.50 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.21/0.50 tff(92,plain,
% 0.21/0.50 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.21/0.50 tff(93,plain,(
% 0.21/0.50 ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A))))),
% 0.21/0.50 inference(skolemize,[status(sab)],[92])).
% 0.21/0.50 tff(94,plain,
% 0.21/0.50 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.21/0.50 tff(95,plain,
% 0.21/0.50 (((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A))))) | ((~one_sorted_str(A!14)) | ![B: $i] : (rel_str(B) | (~net_str(B, A!14))))) <=> ((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A))))) | (~one_sorted_str(A!14)) | ![B: $i] : (rel_str(B) | (~net_str(B, A!14))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(96,plain,
% 0.21/0.50 ((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A))))) | ((~one_sorted_str(A!14)) | ![B: $i] : (rel_str(B) | (~net_str(B, A!14))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(97,plain,
% 0.21/0.50 ((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : (rel_str(B) | (~net_str(B, A))))) | (~one_sorted_str(A!14)) | ![B: $i] : (rel_str(B) | (~net_str(B, A!14)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.21/0.50 tff(98,plain,
% 0.21/0.50 (![B: $i] : (rel_str(B) | (~net_str(B, A!14)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[97, 94, 43])).
% 0.21/0.50 tff(99,plain,
% 0.21/0.50 (((~![B: $i] : (rel_str(B) | (~net_str(B, A!14)))) | (rel_str(B!15) | (~net_str(B!15, A!14)))) <=> ((~![B: $i] : (rel_str(B) | (~net_str(B, A!14)))) | rel_str(B!15) | (~net_str(B!15, A!14)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(100,plain,
% 0.21/0.50 ((~![B: $i] : (rel_str(B) | (~net_str(B, A!14)))) | (rel_str(B!15) | (~net_str(B!15, A!14)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(101,plain,
% 0.21/0.50 ((~![B: $i] : (rel_str(B) | (~net_str(B, A!14)))) | rel_str(B!15) | (~net_str(B!15, A!14))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.21/0.50 tff(102,plain,
% 0.21/0.50 (rel_str(B!15)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[101, 64, 98])).
% 0.21/0.50 tff(103,plain,
% 0.21/0.50 (^[A: $i] : refl(((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (~full_subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~related(A, C, D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B))))))))) <=> ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (~full_subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~related(A, C, D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B))))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(104,plain,
% 0.21/0.50 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (~full_subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~related(A, C, D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (~full_subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~related(A, C, D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B)))))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[103])).
% 0.21/0.50 tff(105,plain,
% 0.21/0.50 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (~full_subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~related(A, C, D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B))))))))) <=> ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (~full_subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~related(A, C, D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B))))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(106,plain,
% 0.21/0.50 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (~full_subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~related(A, C, D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (~full_subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~related(A, C, D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B)))))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[105])).
% 0.21/0.50 tff(107,plain,
% 0.21/0.50 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (~full_subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~related(A, C, D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (~full_subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~related(A, C, D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B)))))))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[106, 104])).
% 0.21/0.50 tff(108,plain,
% 0.21/0.50 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i] : ((~(full_subrelstr(B, A) & subrelstr(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))))))))) <=> ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (~full_subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~related(A, C, D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B))))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(109,plain,
% 0.21/0.50 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~(full_subrelstr(B, A) & subrelstr(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (~full_subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~related(A, C, D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B)))))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[108])).
% 0.21/0.50 tff(110,plain,
% 0.21/0.50 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~(full_subrelstr(B, A) & subrelstr(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~(full_subrelstr(B, A) & subrelstr(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B))))))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(111,plain,
% 0.21/0.50 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(quant_intro(proof_bind(^[F: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((E = C) & (F = D)) & related(A, C, D)) <=> ((E = C) & (F = D) & related(A, C, D))), (((((E = C) & (F = D)) & related(A, C, D)) & in(E, the_carrier(B))) <=> (((E = C) & (F = D) & related(A, C, D)) & in(E, the_carrier(B))))), rewrite((((E = C) & (F = D) & related(A, C, D)) & in(E, the_carrier(B))) <=> ((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)))), (((((E = C) & (F = D)) & related(A, C, D)) & in(E, the_carrier(B))) <=> ((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B))))), ((((((E = C) & (F = D)) & related(A, C, D)) & in(E, the_carrier(B))) & in(F, the_carrier(B))) <=> (((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B))) & in(F, the_carrier(B))))), rewrite((((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B))) & in(F, the_carrier(B))) <=> ((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))), ((((((E = C) & (F = D)) & related(A, C, D)) & in(E, the_carrier(B))) & in(F, the_carrier(B))) <=> ((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B))))), (((((((E = C) & (F = D)) & related(A, C, D)) & in(E, the_carrier(B))) & in(F, the_carrier(B))) => related(B, E, F)) <=> (((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B))) => related(B, E, F)))), rewrite((((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B))) => related(B, E, F)) <=> ((~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))) | related(B, E, F))), (((((((E = C) & (F = D)) & related(A, C, D)) & in(E, the_carrier(B))) & in(F, the_carrier(B))) => related(B, E, F)) <=> ((~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))) | related(B, E, F)))), ((element(F, the_carrier(B)) => ((((((E = C) & (F = D)) & related(A, C, D)) & in(E, the_carrier(B))) & in(F, the_carrier(B))) => related(B, E, F))) <=> (element(F, the_carrier(B)) => ((~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))) | related(B, E, F))))), rewrite((element(F, the_carrier(B)) => ((~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))) | related(B, E, F))) <=> (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))))), ((element(F, the_carrier(B)) => ((((((E = C) & (F = D)) & related(A, C, D)) & in(E, the_carrier(B))) & in(F, the_carrier(B))) => related(B, E, F))) <=> (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))))))), (![F: $i] : (element(F, the_carrier(B)) => ((((((E = C) & (F = D)) & related(A, C, D)) & in(E, the_carrier(B))) & in(F, the_carrier(B))) => related(B, E, F))) <=> ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B))))))), ((element(E, the_carrier(B)) => ![F: $i] : (element(F, the_carrier(B)) => ((((((E = C) & (F = D)) & related(A, C, D)) & in(E, the_carrier(B))) & in(F, the_carrier(B))) => related(B, E, F)))) <=> (element(E, the_carrier(B)) => ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))))))), rewrite((element(E, the_carrier(B)) => ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))))) <=> ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B))))))), ((element(E, the_carrier(B)) => ![F: $i] : (element(F, the_carrier(B)) => ((((((E = C) & (F = D)) & related(A, C, D)) & in(E, the_carrier(B))) & in(F, the_carrier(B))) => related(B, E, F)))) <=> ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B))))))))), (![E: $i] : (element(E, the_carrier(B)) => ![F: $i] : (element(F, the_carrier(B)) => ((((((E = C) & (F = D)) & related(A, C, D)) & in(E, the_carrier(B))) & in(F, the_carrier(B))) => related(B, E, F)))) <=> ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))))))), ((element(D, the_carrier(A)) => ![E: $i] : (element(E, the_carrier(B)) => ![F: $i] : (element(F, the_carrier(B)) => ((((((E = C) & (F = D)) & related(A, C, D)) & in(E, the_carrier(B))) & in(F, the_carrier(B))) => related(B, E, F))))) <=> (element(D, the_carrier(A)) => ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B))))))))), rewrite((element(D, the_carrier(A)) => ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B))))))) <=> ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))))))), ((element(D, the_carrier(A)) => ![E: $i] : (element(E, the_carrier(B)) => ![F: $i] : (element(F, the_carrier(B)) => ((((((E = C) & (F = D)) & related(A, C, D)) & in(E, the_carrier(B))) & in(F, the_carrier(B))) => related(B, E, F))))) <=> ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))))))))), (![D: $i] : (element(D, the_carrier(A)) => ![E: $i] : (element(E, the_carrier(B)) => ![F: $i] : (element(F, the_carrier(B)) => ((((((E = C) & (F = D)) & related(A, C, D)) & in(E, the_carrier(B))) & in(F, the_carrier(B))) => related(B, E, F))))) <=> ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B))))))))), ((element(C, the_carrier(A)) => ![D: $i] : (element(D, the_carrier(A)) => ![E: $i] : (element(E, the_carrier(B)) => ![F: $i] : (element(F, the_carrier(B)) => ((((((E = C) & (F = D)) & related(A, C, D)) & in(E, the_carrier(B))) & in(F, the_carrier(B))) => related(B, E, F)))))) <=> (element(C, the_carrier(A)) => ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))))))))), rewrite((element(C, the_carrier(A)) => ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))))))) <=> ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B))))))))), ((element(C, the_carrier(A)) => ![D: $i] : (element(D, the_carrier(A)) => ![E: $i] : (element(E, the_carrier(B)) => ![F: $i] : (element(F, the_carrier(B)) => ((((((E = C) & (F = D)) & related(A, C, D)) & in(E, the_carrier(B))) & in(F, the_carrier(B))) => related(B, E, F)))))) <=> ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B))))))))))), (![C: $i] : (element(C, the_carrier(A)) => ![D: $i] : (element(D, the_carrier(A)) => ![E: $i] : (element(E, the_carrier(B)) => ![F: $i] : (element(F, the_carrier(B)) => ((((((E = C) & (F = D)) & related(A, C, D)) & in(E, the_carrier(B))) & in(F, the_carrier(B))) => related(B, E, F)))))) <=> ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))))))))), (((full_subrelstr(B, A) & subrelstr(B, A)) => ![C: $i] : (element(C, the_carrier(A)) => ![D: $i] : (element(D, the_carrier(A)) => ![E: $i] : (element(E, the_carrier(B)) => ![F: $i] : (element(F, the_carrier(B)) => ((((((E = C) & (F = D)) & related(A, C, D)) & in(E, the_carrier(B))) & in(F, the_carrier(B))) => related(B, E, F))))))) <=> ((full_subrelstr(B, A) & subrelstr(B, A)) => ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B))))))))))), rewrite(((full_subrelstr(B, A) & subrelstr(B, A)) => ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B))))))))) <=> ((~(full_subrelstr(B, A) & subrelstr(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))))))))), (((full_subrelstr(B, A) & subrelstr(B, A)) => ![C: $i] : (element(C, the_carrier(A)) => ![D: $i] : (element(D, the_carrier(A)) => ![E: $i] : (element(E, the_carrier(B)) => ![F: $i] : (element(F, the_carrier(B)) => ((((((E = C) & (F = D)) & related(A, C, D)) & in(E, the_carrier(B))) & in(F, the_carrier(B))) => related(B, E, F))))))) <=> ((~(full_subrelstr(B, A) & subrelstr(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))))))))))), (![B: $i] : ((full_subrelstr(B, A) & subrelstr(B, A)) => ![C: $i] : (element(C, the_carrier(A)) => ![D: $i] : (element(D, the_carrier(A)) => ![E: $i] : (element(E, the_carrier(B)) => ![F: $i] : (element(F, the_carrier(B)) => ((((((E = C) & (F = D)) & related(A, C, D)) & in(E, the_carrier(B))) & in(F, the_carrier(B))) => related(B, E, F))))))) <=> ![B: $i] : ((~(full_subrelstr(B, A) & subrelstr(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B))))))))))), ((rel_str(A) => ![B: $i] : ((full_subrelstr(B, A) & subrelstr(B, A)) => ![C: $i] : (element(C, the_carrier(A)) => ![D: $i] : (element(D, the_carrier(A)) => ![E: $i] : (element(E, the_carrier(B)) => ![F: $i] : (element(F, the_carrier(B)) => ((((((E = C) & (F = D)) & related(A, C, D)) & in(E, the_carrier(B))) & in(F, the_carrier(B))) => related(B, E, F)))))))) <=> (rel_str(A) => ![B: $i] : ((~(full_subrelstr(B, A) & subrelstr(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))))))))))), rewrite((rel_str(A) => ![B: $i] : ((~(full_subrelstr(B, A) & subrelstr(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))))))))) <=> ((~rel_str(A)) | ![B: $i] : ((~(full_subrelstr(B, A) & subrelstr(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B))))))))))), ((rel_str(A) => ![B: $i] : ((full_subrelstr(B, A) & subrelstr(B, A)) => ![C: $i] : (element(C, the_carrier(A)) => ![D: $i] : (element(D, the_carrier(A)) => ![E: $i] : (element(E, the_carrier(B)) => ![F: $i] : (element(F, the_carrier(B)) => ((((((E = C) & (F = D)) & related(A, C, D)) & in(E, the_carrier(B))) & in(F, the_carrier(B))) => related(B, E, F)))))))) <=> ((~rel_str(A)) | ![B: $i] : ((~(full_subrelstr(B, A) & subrelstr(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B))))))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(112,plain,
% 0.21/0.51 (![A: $i] : (rel_str(A) => ![B: $i] : ((full_subrelstr(B, A) & subrelstr(B, A)) => ![C: $i] : (element(C, the_carrier(A)) => ![D: $i] : (element(D, the_carrier(A)) => ![E: $i] : (element(E, the_carrier(B)) => ![F: $i] : (element(F, the_carrier(B)) => ((((((E = C) & (F = D)) & related(A, C, D)) & in(E, the_carrier(B))) & in(F, the_carrier(B))) => related(B, E, F)))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~(full_subrelstr(B, A) & subrelstr(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B))))))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[111])).
% 0.21/0.51 tff(113,axiom,(![A: $i] : (rel_str(A) => ![B: $i] : ((full_subrelstr(B, A) & subrelstr(B, A)) => ![C: $i] : (element(C, the_carrier(A)) => ![D: $i] : (element(D, the_carrier(A)) => ![E: $i] : (element(E, the_carrier(B)) => ![F: $i] : (element(F, the_carrier(B)) => ((((((E = C) & (F = D)) & related(A, C, D)) & in(E, the_carrier(B))) & in(F, the_carrier(B))) => related(B, E, F))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t61_yellow_0')).
% 0.21/0.51 tff(114,plain,
% 0.21/0.51 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~(full_subrelstr(B, A) & subrelstr(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B))))))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.21/0.51 tff(115,plain,
% 0.21/0.51 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~(full_subrelstr(B, A) & subrelstr(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B))))))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.21/0.51 tff(116,plain,(
% 0.21/0.51 ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~(full_subrelstr(B, A) & subrelstr(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B))))))))))),
% 0.21/0.51 inference(skolemize,[status(sab)],[115])).
% 0.21/0.51 tff(117,plain,
% 0.21/0.51 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (~full_subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~related(A, C, D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B)))))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.21/0.51 tff(118,plain,
% 0.21/0.51 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (~full_subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~related(A, C, D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B)))))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[117, 107])).
% 0.21/0.51 tff(119,plain,
% 0.21/0.51 (((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (~full_subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~related(A, C, D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B)))))))))) | ((~rel_str(B!15)) | ![B: $i] : ((~subrelstr(B, B!15)) | (~full_subrelstr(B, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B))) | (~related(B!15, C, D))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (~full_subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~related(A, C, D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B)))))))))) | (~rel_str(B!15)) | ![B: $i] : ((~subrelstr(B, B!15)) | (~full_subrelstr(B, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B))) | (~related(B!15, C, D))))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(120,plain,
% 0.21/0.51 (((~rel_str(B!15)) | ![B: $i] : ((~subrelstr(B, B!15)) | (~full_subrelstr(B, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~related(B!15, C, D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B))))))))) <=> ((~rel_str(B!15)) | ![B: $i] : ((~subrelstr(B, B!15)) | (~full_subrelstr(B, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B))) | (~related(B!15, C, D))))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(121,plain,
% 0.21/0.51 (((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (~full_subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~related(A, C, D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B)))))))))) | ((~rel_str(B!15)) | ![B: $i] : ((~subrelstr(B, B!15)) | (~full_subrelstr(B, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~related(B!15, C, D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B)))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (~full_subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~related(A, C, D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B)))))))))) | ((~rel_str(B!15)) | ![B: $i] : ((~subrelstr(B, B!15)) | (~full_subrelstr(B, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B))) | (~related(B!15, C, D)))))))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[120])).
% 0.21/0.51 tff(122,plain,
% 0.21/0.51 (((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (~full_subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~related(A, C, D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B)))))))))) | ((~rel_str(B!15)) | ![B: $i] : ((~subrelstr(B, B!15)) | (~full_subrelstr(B, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~related(B!15, C, D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B)))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (~full_subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~related(A, C, D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B)))))))))) | (~rel_str(B!15)) | ![B: $i] : ((~subrelstr(B, B!15)) | (~full_subrelstr(B, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B))) | (~related(B!15, C, D))))))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[121, 119])).
% 0.21/0.51 tff(123,plain,
% 0.21/0.51 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (~full_subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~related(A, C, D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B)))))))))) | ((~rel_str(B!15)) | ![B: $i] : ((~subrelstr(B, B!15)) | (~full_subrelstr(B, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~related(B!15, C, D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B)))))))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(124,plain,
% 0.21/0.51 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (~full_subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~related(A, C, D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B)))))))))) | (~rel_str(B!15)) | ![B: $i] : ((~subrelstr(B, B!15)) | (~full_subrelstr(B, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B))) | (~related(B!15, C, D)))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.21/0.51 tff(125,plain,
% 0.21/0.51 ((~rel_str(B!15)) | ![B: $i] : ((~subrelstr(B, B!15)) | (~full_subrelstr(B, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B))) | (~related(B!15, C, D)))))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[124, 118])).
% 0.21/0.51 tff(126,plain,
% 0.21/0.51 (![B: $i] : ((~subrelstr(B, B!15)) | (~full_subrelstr(B, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B))) | (~related(B!15, C, D)))))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[125, 102])).
% 0.21/0.51 tff(127,plain,
% 0.21/0.51 (((~![B: $i] : ((~subrelstr(B, B!15)) | (~full_subrelstr(B, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B))) | (~related(B!15, C, D)))))))) | ((~full_subrelstr(C!16, B!15)) | (~subrelstr(C!16, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(E = C)) | (~(F = D)) | (~related(B!15, C, D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))))))))) <=> ((~![B: $i] : ((~subrelstr(B, B!15)) | (~full_subrelstr(B, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B))) | (~related(B!15, C, D)))))))) | (~full_subrelstr(C!16, B!15)) | (~subrelstr(C!16, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(E = C)) | (~(F = D)) | (~related(B!15, C, D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(128,plain,
% 0.21/0.51 (((~subrelstr(C!16, B!15)) | (~full_subrelstr(C!16, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(E = C)) | (~(F = D)) | (~related(B!15, C, D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16)))))))) <=> ((~full_subrelstr(C!16, B!15)) | (~subrelstr(C!16, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(E = C)) | (~(F = D)) | (~related(B!15, C, D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(129,plain,
% 0.21/0.51 (^[C: $i] : rewrite(((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : (related(C!16, E, F) | (~element(F, the_carrier(C!16))) | (~(E = C)) | (~(F = D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~related(B!15, C, D)))))) <=> ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(E = C)) | (~(F = D)) | (~related(B!15, C, D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(130,plain,
% 0.21/0.51 (![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : (related(C!16, E, F) | (~element(F, the_carrier(C!16))) | (~(E = C)) | (~(F = D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~related(B!15, C, D)))))) <=> ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(E = C)) | (~(F = D)) | (~related(B!15, C, D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16)))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[129])).
% 0.21/0.51 tff(131,plain,
% 0.21/0.51 (((~subrelstr(C!16, B!15)) | (~full_subrelstr(C!16, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : (related(C!16, E, F) | (~element(F, the_carrier(C!16))) | (~(E = C)) | (~(F = D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~related(B!15, C, D))))))) <=> ((~subrelstr(C!16, B!15)) | (~full_subrelstr(C!16, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(E = C)) | (~(F = D)) | (~related(B!15, C, D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))))))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[130])).
% 0.21/0.51 tff(132,plain,
% 0.21/0.51 (((~subrelstr(C!16, B!15)) | (~full_subrelstr(C!16, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : (related(C!16, E, F) | (~element(F, the_carrier(C!16))) | (~(E = C)) | (~(F = D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~related(B!15, C, D))))))) <=> ((~full_subrelstr(C!16, B!15)) | (~subrelstr(C!16, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(E = C)) | (~(F = D)) | (~related(B!15, C, D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))))))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[131, 128])).
% 0.21/0.51 tff(133,plain,
% 0.21/0.51 (((~![B: $i] : ((~subrelstr(B, B!15)) | (~full_subrelstr(B, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B))) | (~related(B!15, C, D)))))))) | ((~subrelstr(C!16, B!15)) | (~full_subrelstr(C!16, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : (related(C!16, E, F) | (~element(F, the_carrier(C!16))) | (~(E = C)) | (~(F = D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~related(B!15, C, D)))))))) <=> ((~![B: $i] : ((~subrelstr(B, B!15)) | (~full_subrelstr(B, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B))) | (~related(B!15, C, D)))))))) | ((~full_subrelstr(C!16, B!15)) | (~subrelstr(C!16, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(E = C)) | (~(F = D)) | (~related(B!15, C, D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16)))))))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[132])).
% 0.21/0.51 tff(134,plain,
% 0.21/0.51 (((~![B: $i] : ((~subrelstr(B, B!15)) | (~full_subrelstr(B, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B))) | (~related(B!15, C, D)))))))) | ((~subrelstr(C!16, B!15)) | (~full_subrelstr(C!16, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : (related(C!16, E, F) | (~element(F, the_carrier(C!16))) | (~(E = C)) | (~(F = D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~related(B!15, C, D)))))))) <=> ((~![B: $i] : ((~subrelstr(B, B!15)) | (~full_subrelstr(B, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B))) | (~related(B!15, C, D)))))))) | (~full_subrelstr(C!16, B!15)) | (~subrelstr(C!16, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(E = C)) | (~(F = D)) | (~related(B!15, C, D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))))))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[133, 127])).
% 0.21/0.51 tff(135,plain,
% 0.21/0.51 ((~![B: $i] : ((~subrelstr(B, B!15)) | (~full_subrelstr(B, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B))) | (~related(B!15, C, D)))))))) | ((~subrelstr(C!16, B!15)) | (~full_subrelstr(C!16, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : (related(C!16, E, F) | (~element(F, the_carrier(C!16))) | (~(E = C)) | (~(F = D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~related(B!15, C, D)))))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(136,plain,
% 0.21/0.52 ((~![B: $i] : ((~subrelstr(B, B!15)) | (~full_subrelstr(B, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(B, E, F) | (~element(F, the_carrier(B))) | (~(E = C)) | (~(F = D)) | (~in(E, the_carrier(B))) | (~in(F, the_carrier(B))) | (~related(B!15, C, D)))))))) | (~full_subrelstr(C!16, B!15)) | (~subrelstr(C!16, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(E = C)) | (~(F = D)) | (~related(B!15, C, D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16)))))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.21/0.52 tff(137,plain,
% 0.21/0.52 ((~full_subrelstr(C!16, B!15)) | (~subrelstr(C!16, B!15)) | ![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(E = C)) | (~(F = D)) | (~related(B!15, C, D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16)))))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[136, 126])).
% 0.21/0.52 tff(138,plain,
% 0.21/0.52 (![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(E = C)) | (~(F = D)) | (~related(B!15, C, D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16)))))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[137, 81, 79])).
% 0.21/0.52 tff(139,plain,
% 0.21/0.52 (element(F!19, the_carrier(B!15)) <=> element(D!17, the_carrier(B!15))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[38])).
% 0.21/0.52 tff(140,plain,
% 0.21/0.52 (element(D!17, the_carrier(B!15)) <=> element(F!19, the_carrier(B!15))),
% 0.21/0.52 inference(symmetry,[status(thm)],[139])).
% 0.21/0.52 tff(141,plain,
% 0.21/0.52 (element(D!17, the_carrier(B!15))),
% 0.21/0.52 inference(and_elim,[status(thm)],[32])).
% 0.21/0.52 tff(142,plain,
% 0.21/0.52 (element(F!19, the_carrier(B!15))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.21/0.52 tff(143,plain,
% 0.21/0.52 (((~![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(E = C)) | (~(F = D)) | (~related(B!15, C, D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16)))))))) | ((~element(F!19, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(F = D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~related(B!15, F!19, D))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(E = C)) | (~(F = D)) | (~related(B!15, C, D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16)))))))) | (~element(F!19, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(F = D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~related(B!15, F!19, D))))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(144,plain,
% 0.21/0.52 (((~element(F!19, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(E = F!19)) | (~(F = D)) | (~related(B!15, F!19, D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))))))) <=> ((~element(F!19, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(F = D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~related(B!15, F!19, D))))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(145,plain,
% 0.21/0.52 (((~![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(E = C)) | (~(F = D)) | (~related(B!15, C, D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16)))))))) | ((~element(F!19, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(E = F!19)) | (~(F = D)) | (~related(B!15, F!19, D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16)))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(E = C)) | (~(F = D)) | (~related(B!15, C, D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16)))))))) | ((~element(F!19, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(F = D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~related(B!15, F!19, D)))))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[144])).
% 0.21/0.52 tff(146,plain,
% 0.21/0.52 (((~![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(E = C)) | (~(F = D)) | (~related(B!15, C, D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16)))))))) | ((~element(F!19, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(E = F!19)) | (~(F = D)) | (~related(B!15, F!19, D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16)))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(E = C)) | (~(F = D)) | (~related(B!15, C, D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16)))))))) | (~element(F!19, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(F = D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~related(B!15, F!19, D))))))),
% 0.21/0.52 inference(transitivity,[status(thm)],[145, 143])).
% 0.21/0.52 tff(147,plain,
% 0.21/0.52 ((~![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(E = C)) | (~(F = D)) | (~related(B!15, C, D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16)))))))) | ((~element(F!19, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(E = F!19)) | (~(F = D)) | (~related(B!15, F!19, D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16)))))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(148,plain,
% 0.21/0.52 ((~![C: $i] : ((~element(C, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(E = C)) | (~(F = D)) | (~related(B!15, C, D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16)))))))) | (~element(F!19, the_carrier(B!15))) | ![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(F = D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~related(B!15, F!19, D)))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.21/0.52 tff(149,plain,
% 0.21/0.52 (![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(F = D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~related(B!15, F!19, D)))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[148, 142, 138])).
% 0.21/0.52 tff(150,plain,
% 0.21/0.52 (element(G!20, the_carrier(B!15)) <=> element(E!18, the_carrier(B!15))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[36])).
% 0.21/0.52 tff(151,plain,
% 0.21/0.52 (element(E!18, the_carrier(B!15)) <=> element(G!20, the_carrier(B!15))),
% 0.21/0.52 inference(symmetry,[status(thm)],[150])).
% 0.21/0.52 tff(152,plain,
% 0.21/0.52 (element(E!18, the_carrier(B!15))),
% 0.21/0.52 inference(and_elim,[status(thm)],[32])).
% 0.21/0.52 tff(153,plain,
% 0.21/0.52 (element(G!20, the_carrier(B!15))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.21/0.52 tff(154,plain,
% 0.21/0.52 (((~![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(F = D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~related(B!15, F!19, D)))))) | ((~element(G!20, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~(F = G!20)) | (~related(B!15, F!19, G!20)))))) <=> ((~![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(F = D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~related(B!15, F!19, D)))))) | (~element(G!20, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~(F = G!20)) | (~related(B!15, F!19, G!20)))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(155,plain,
% 0.21/0.52 (((~element(G!20, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(F = G!20)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~related(B!15, F!19, G!20))))) <=> ((~element(G!20, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~(F = G!20)) | (~related(B!15, F!19, G!20)))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(156,plain,
% 0.21/0.52 (((~![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(F = D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~related(B!15, F!19, D)))))) | ((~element(G!20, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(F = G!20)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~related(B!15, F!19, G!20)))))) <=> ((~![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(F = D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~related(B!15, F!19, D)))))) | ((~element(G!20, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~(F = G!20)) | (~related(B!15, F!19, G!20))))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[155])).
% 0.21/0.52 tff(157,plain,
% 0.21/0.52 (((~![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(F = D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~related(B!15, F!19, D)))))) | ((~element(G!20, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(F = G!20)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~related(B!15, F!19, G!20)))))) <=> ((~![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(F = D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~related(B!15, F!19, D)))))) | (~element(G!20, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~(F = G!20)) | (~related(B!15, F!19, G!20)))))),
% 0.21/0.52 inference(transitivity,[status(thm)],[156, 154])).
% 0.21/0.52 tff(158,plain,
% 0.21/0.52 ((~![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(F = D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~related(B!15, F!19, D)))))) | ((~element(G!20, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(F = G!20)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~related(B!15, F!19, G!20)))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(159,plain,
% 0.21/0.52 ((~![D: $i] : ((~element(D, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~(F = D)) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~related(B!15, F!19, D)))))) | (~element(G!20, the_carrier(B!15))) | ![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~(F = G!20)) | (~related(B!15, F!19, G!20))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.21/0.52 tff(160,plain,
% 0.21/0.52 (![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~(F = G!20)) | (~related(B!15, F!19, G!20))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[159, 153, 149])).
% 0.21/0.52 tff(161,plain,
% 0.21/0.52 (element(F!19, the_carrier(C!16))),
% 0.21/0.52 inference(and_elim,[status(thm)],[32])).
% 0.21/0.52 tff(162,plain,
% 0.21/0.52 (((~![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~(F = G!20)) | (~related(B!15, F!19, G!20))))) | ((~element(F!19, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, F!19, F) | (~in(F, the_carrier(C!16))) | (~in(F!19, the_carrier(C!16))) | (~(F = G!20)) | (~related(B!15, F!19, G!20))))) <=> ((~![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~(F = G!20)) | (~related(B!15, F!19, G!20))))) | (~element(F!19, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, F!19, F) | (~in(F, the_carrier(C!16))) | (~in(F!19, the_carrier(C!16))) | (~(F = G!20)) | (~related(B!15, F!19, G!20))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(163,plain,
% 0.21/0.52 (((~element(F!19, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, F!19, F) | (~in(F!19, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(F!19 = F!19)) | (~(F = G!20)) | (~related(B!15, F!19, G!20)))) <=> ((~element(F!19, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, F!19, F) | (~in(F, the_carrier(C!16))) | (~in(F!19, the_carrier(C!16))) | (~(F = G!20)) | (~related(B!15, F!19, G!20))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(164,plain,
% 0.21/0.52 (((~![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~(F = G!20)) | (~related(B!15, F!19, G!20))))) | ((~element(F!19, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, F!19, F) | (~in(F!19, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(F!19 = F!19)) | (~(F = G!20)) | (~related(B!15, F!19, G!20))))) <=> ((~![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~(F = G!20)) | (~related(B!15, F!19, G!20))))) | ((~element(F!19, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, F!19, F) | (~in(F, the_carrier(C!16))) | (~in(F!19, the_carrier(C!16))) | (~(F = G!20)) | (~related(B!15, F!19, G!20)))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[163])).
% 0.21/0.52 tff(165,plain,
% 0.21/0.52 (((~![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~(F = G!20)) | (~related(B!15, F!19, G!20))))) | ((~element(F!19, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, F!19, F) | (~in(F!19, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(F!19 = F!19)) | (~(F = G!20)) | (~related(B!15, F!19, G!20))))) <=> ((~![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~(F = G!20)) | (~related(B!15, F!19, G!20))))) | (~element(F!19, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, F!19, F) | (~in(F, the_carrier(C!16))) | (~in(F!19, the_carrier(C!16))) | (~(F = G!20)) | (~related(B!15, F!19, G!20))))),
% 0.21/0.52 inference(transitivity,[status(thm)],[164, 162])).
% 0.21/0.52 tff(166,plain,
% 0.21/0.52 ((~![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~(F = G!20)) | (~related(B!15, F!19, G!20))))) | ((~element(F!19, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, F!19, F) | (~in(F!19, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(F!19 = F!19)) | (~(F = G!20)) | (~related(B!15, F!19, G!20))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(167,plain,
% 0.21/0.52 ((~![E: $i] : ((~element(E, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, E, F) | (~in(E, the_carrier(C!16))) | (~in(F, the_carrier(C!16))) | (~(E = F!19)) | (~(F = G!20)) | (~related(B!15, F!19, G!20))))) | (~element(F!19, the_carrier(C!16))) | ![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, F!19, F) | (~in(F, the_carrier(C!16))) | (~in(F!19, the_carrier(C!16))) | (~(F = G!20)) | (~related(B!15, F!19, G!20)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.21/0.53 tff(168,plain,
% 0.21/0.53 (![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, F!19, F) | (~in(F, the_carrier(C!16))) | (~in(F!19, the_carrier(C!16))) | (~(F = G!20)) | (~related(B!15, F!19, G!20)))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[167, 161, 160])).
% 0.21/0.53 tff(169,plain,
% 0.21/0.53 (^[A: $i, B: $i] : rewrite(((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)) | (~one_sorted_str(A))) <=> ((~net_str(B, A)) | (~one_sorted_str(A)) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(170,plain,
% 0.21/0.53 (![A: $i, B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)) | (~one_sorted_str(A))) <=> ![A: $i, B: $i] : ((~net_str(B, A)) | (~one_sorted_str(A)) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[169])).
% 0.21/0.53 tff(171,plain,
% 0.21/0.53 (^[A: $i, B: $i] : refl(((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)) | (~one_sorted_str(A))) <=> ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)) | (~one_sorted_str(A))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(172,plain,
% 0.21/0.53 (![A: $i, B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)) | (~one_sorted_str(A))) <=> ![A: $i, B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)) | (~one_sorted_str(A)))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[171])).
% 0.21/0.53 tff(173,plain,
% 0.21/0.53 (^[A: $i, B: $i] : rewrite(((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)) | (~one_sorted_str(A))) <=> ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)) | (~one_sorted_str(A))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(174,plain,
% 0.21/0.53 (![A: $i, B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)) | (~one_sorted_str(A))) <=> ![A: $i, B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)) | (~one_sorted_str(A)))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[173])).
% 0.21/0.53 tff(175,plain,
% 0.21/0.53 (![A: $i, B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)) | (~one_sorted_str(A))) <=> ![A: $i, B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)) | (~one_sorted_str(A)))),
% 0.21/0.53 inference(transitivity,[status(thm)],[174, 172])).
% 0.21/0.53 tff(176,plain,
% 0.21/0.53 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((one_sorted_str(A) & net_str(B, A)) <=> (~((~one_sorted_str(A)) | (~net_str(B, A))))), ((~(one_sorted_str(A) & net_str(B, A))) <=> (~(~((~one_sorted_str(A)) | (~net_str(B, A))))))), rewrite((~(~((~one_sorted_str(A)) | (~net_str(B, A))))) <=> ((~one_sorted_str(A)) | (~net_str(B, A)))), ((~(one_sorted_str(A) & net_str(B, A))) <=> ((~one_sorted_str(A)) | (~net_str(B, A))))), (((~(one_sorted_str(A) & net_str(B, A))) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A))) <=> (((~one_sorted_str(A)) | (~net_str(B, A))) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A))))), rewrite((((~one_sorted_str(A)) | (~net_str(B, A))) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A))) <=> ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)) | (~one_sorted_str(A)))), (((~(one_sorted_str(A) & net_str(B, A))) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A))) <=> ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)) | (~one_sorted_str(A)))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(177,plain,
% 0.21/0.53 (![A: $i, B: $i] : ((~(one_sorted_str(A) & net_str(B, A))) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A))) <=> ![A: $i, B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)) | (~one_sorted_str(A)))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[176])).
% 0.21/0.53 tff(178,plain,
% 0.21/0.53 (![A: $i, B: $i] : ((~(one_sorted_str(A) & net_str(B, A))) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A))) <=> ![A: $i, B: $i] : ((~(one_sorted_str(A) & net_str(B, A))) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(179,plain,
% 0.21/0.53 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((subnetstr(C, A, B) => net_str(C, A)) <=> ((~subnetstr(C, A, B)) | net_str(C, A)))), (![C: $i] : (subnetstr(C, A, B) => net_str(C, A)) <=> ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)))), (((one_sorted_str(A) & net_str(B, A)) => ![C: $i] : (subnetstr(C, A, B) => net_str(C, A))) <=> ((one_sorted_str(A) & net_str(B, A)) => ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A))))), rewrite(((one_sorted_str(A) & net_str(B, A)) => ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A))) <=> ((~(one_sorted_str(A) & net_str(B, A))) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)))), (((one_sorted_str(A) & net_str(B, A)) => ![C: $i] : (subnetstr(C, A, B) => net_str(C, A))) <=> ((~(one_sorted_str(A) & net_str(B, A))) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(180,plain,
% 0.21/0.53 (![A: $i, B: $i] : ((one_sorted_str(A) & net_str(B, A)) => ![C: $i] : (subnetstr(C, A, B) => net_str(C, A))) <=> ![A: $i, B: $i] : ((~(one_sorted_str(A) & net_str(B, A))) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[179])).
% 0.21/0.53 tff(181,axiom,(![A: $i, B: $i] : ((one_sorted_str(A) & net_str(B, A)) => ![C: $i] : (subnetstr(C, A, B) => net_str(C, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m1_yellow_6')).
% 0.21/0.53 tff(182,plain,
% 0.21/0.53 (![A: $i, B: $i] : ((~(one_sorted_str(A) & net_str(B, A))) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.21/0.53 tff(183,plain,
% 0.21/0.53 (![A: $i, B: $i] : ((~(one_sorted_str(A) & net_str(B, A))) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[182, 178])).
% 0.21/0.53 tff(184,plain,(
% 0.21/0.53 ![A: $i, B: $i] : ((~(one_sorted_str(A) & net_str(B, A))) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)))),
% 0.21/0.53 inference(skolemize,[status(sab)],[183])).
% 0.21/0.53 tff(185,plain,
% 0.21/0.53 (![A: $i, B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)) | (~one_sorted_str(A)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[184, 177])).
% 0.21/0.53 tff(186,plain,
% 0.21/0.53 (![A: $i, B: $i] : ((~net_str(B, A)) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)) | (~one_sorted_str(A)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[185, 175])).
% 0.21/0.53 tff(187,plain,
% 0.21/0.53 (![A: $i, B: $i] : ((~net_str(B, A)) | (~one_sorted_str(A)) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[186, 170])).
% 0.21/0.53 tff(188,plain,
% 0.21/0.53 (((~![A: $i, B: $i] : ((~net_str(B, A)) | (~one_sorted_str(A)) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)))) | ((~one_sorted_str(A!14)) | (~net_str(B!15, A!14)) | ![C: $i] : ((~subnetstr(C, A!14, B!15)) | net_str(C, A!14)))) <=> ((~![A: $i, B: $i] : ((~net_str(B, A)) | (~one_sorted_str(A)) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)))) | (~one_sorted_str(A!14)) | (~net_str(B!15, A!14)) | ![C: $i] : ((~subnetstr(C, A!14, B!15)) | net_str(C, A!14)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(189,plain,
% 0.21/0.53 (((~net_str(B!15, A!14)) | (~one_sorted_str(A!14)) | ![C: $i] : ((~subnetstr(C, A!14, B!15)) | net_str(C, A!14))) <=> ((~one_sorted_str(A!14)) | (~net_str(B!15, A!14)) | ![C: $i] : ((~subnetstr(C, A!14, B!15)) | net_str(C, A!14)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(190,plain,
% 0.21/0.53 (((~![A: $i, B: $i] : ((~net_str(B, A)) | (~one_sorted_str(A)) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)))) | ((~net_str(B!15, A!14)) | (~one_sorted_str(A!14)) | ![C: $i] : ((~subnetstr(C, A!14, B!15)) | net_str(C, A!14)))) <=> ((~![A: $i, B: $i] : ((~net_str(B, A)) | (~one_sorted_str(A)) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)))) | ((~one_sorted_str(A!14)) | (~net_str(B!15, A!14)) | ![C: $i] : ((~subnetstr(C, A!14, B!15)) | net_str(C, A!14))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[189])).
% 0.21/0.53 tff(191,plain,
% 0.21/0.53 (((~![A: $i, B: $i] : ((~net_str(B, A)) | (~one_sorted_str(A)) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)))) | ((~net_str(B!15, A!14)) | (~one_sorted_str(A!14)) | ![C: $i] : ((~subnetstr(C, A!14, B!15)) | net_str(C, A!14)))) <=> ((~![A: $i, B: $i] : ((~net_str(B, A)) | (~one_sorted_str(A)) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)))) | (~one_sorted_str(A!14)) | (~net_str(B!15, A!14)) | ![C: $i] : ((~subnetstr(C, A!14, B!15)) | net_str(C, A!14)))),
% 0.21/0.53 inference(transitivity,[status(thm)],[190, 188])).
% 0.21/0.53 tff(192,plain,
% 0.21/0.53 ((~![A: $i, B: $i] : ((~net_str(B, A)) | (~one_sorted_str(A)) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)))) | ((~net_str(B!15, A!14)) | (~one_sorted_str(A!14)) | ![C: $i] : ((~subnetstr(C, A!14, B!15)) | net_str(C, A!14)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(193,plain,
% 0.21/0.53 ((~![A: $i, B: $i] : ((~net_str(B, A)) | (~one_sorted_str(A)) | ![C: $i] : ((~subnetstr(C, A, B)) | net_str(C, A)))) | (~one_sorted_str(A!14)) | (~net_str(B!15, A!14)) | ![C: $i] : ((~subnetstr(C, A!14, B!15)) | net_str(C, A!14))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.21/0.53 tff(194,plain,
% 0.21/0.53 (![C: $i] : ((~subnetstr(C, A!14, B!15)) | net_str(C, A!14))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[193, 187, 43, 64])).
% 0.21/0.53 tff(195,plain,
% 0.21/0.53 (((~![C: $i] : ((~subnetstr(C, A!14, B!15)) | net_str(C, A!14))) | ((~subnetstr(C!16, A!14, B!15)) | net_str(C!16, A!14))) <=> ((~![C: $i] : ((~subnetstr(C, A!14, B!15)) | net_str(C, A!14))) | (~subnetstr(C!16, A!14, B!15)) | net_str(C!16, A!14))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(196,plain,
% 0.21/0.53 ((~![C: $i] : ((~subnetstr(C, A!14, B!15)) | net_str(C, A!14))) | ((~subnetstr(C!16, A!14, B!15)) | net_str(C!16, A!14))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(197,plain,
% 0.21/0.53 ((~![C: $i] : ((~subnetstr(C, A!14, B!15)) | net_str(C, A!14))) | (~subnetstr(C!16, A!14, B!15)) | net_str(C!16, A!14)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.21/0.53 tff(198,plain,
% 0.21/0.53 (net_str(C!16, A!14)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[197, 69, 194])).
% 0.21/0.53 tff(199,plain,
% 0.21/0.53 (((~![B: $i] : (rel_str(B) | (~net_str(B, A!14)))) | (rel_str(C!16) | (~net_str(C!16, A!14)))) <=> ((~![B: $i] : (rel_str(B) | (~net_str(B, A!14)))) | rel_str(C!16) | (~net_str(C!16, A!14)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(200,plain,
% 0.21/0.53 ((~![B: $i] : (rel_str(B) | (~net_str(B, A!14)))) | (rel_str(C!16) | (~net_str(C!16, A!14)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(201,plain,
% 0.21/0.53 ((~![B: $i] : (rel_str(B) | (~net_str(B, A!14)))) | rel_str(C!16) | (~net_str(C!16, A!14))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.21/0.53 tff(202,plain,
% 0.21/0.53 (rel_str(C!16)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[201, 98, 198])).
% 0.21/0.53 tff(203,plain,
% 0.21/0.53 (^[A: $i] : refl((one_sorted_str(A) | (~rel_str(A))) <=> (one_sorted_str(A) | (~rel_str(A))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(204,plain,
% 0.21/0.53 (![A: $i] : (one_sorted_str(A) | (~rel_str(A))) <=> ![A: $i] : (one_sorted_str(A) | (~rel_str(A)))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[203])).
% 0.21/0.53 tff(205,plain,
% 0.21/0.53 (![A: $i] : (one_sorted_str(A) | (~rel_str(A))) <=> ![A: $i] : (one_sorted_str(A) | (~rel_str(A)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(206,plain,
% 0.21/0.53 (^[A: $i] : rewrite((rel_str(A) => one_sorted_str(A)) <=> (one_sorted_str(A) | (~rel_str(A))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(207,plain,
% 0.21/0.53 (![A: $i] : (rel_str(A) => one_sorted_str(A)) <=> ![A: $i] : (one_sorted_str(A) | (~rel_str(A)))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[206])).
% 0.21/0.53 tff(208,axiom,(![A: $i] : (rel_str(A) => one_sorted_str(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_orders_2')).
% 0.21/0.53 tff(209,plain,
% 0.21/0.53 (![A: $i] : (one_sorted_str(A) | (~rel_str(A)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.21/0.53 tff(210,plain,
% 0.21/0.53 (![A: $i] : (one_sorted_str(A) | (~rel_str(A)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[209, 205])).
% 0.21/0.53 tff(211,plain,(
% 0.21/0.53 ![A: $i] : (one_sorted_str(A) | (~rel_str(A)))),
% 0.21/0.53 inference(skolemize,[status(sab)],[210])).
% 0.21/0.53 tff(212,plain,
% 0.21/0.53 (![A: $i] : (one_sorted_str(A) | (~rel_str(A)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[211, 204])).
% 0.21/0.53 tff(213,plain,
% 0.21/0.53 (((~![A: $i] : (one_sorted_str(A) | (~rel_str(A)))) | (one_sorted_str(C!16) | (~rel_str(C!16)))) <=> ((~![A: $i] : (one_sorted_str(A) | (~rel_str(A)))) | one_sorted_str(C!16) | (~rel_str(C!16)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(214,plain,
% 0.21/0.53 ((~![A: $i] : (one_sorted_str(A) | (~rel_str(A)))) | (one_sorted_str(C!16) | (~rel_str(C!16)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(215,plain,
% 0.21/0.53 ((~![A: $i] : (one_sorted_str(A) | (~rel_str(A)))) | one_sorted_str(C!16) | (~rel_str(C!16))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.21/0.53 tff(216,plain,
% 0.21/0.53 (one_sorted_str(C!16)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[215, 212, 202])).
% 0.21/0.53 tff(217,plain,
% 0.21/0.53 (~empty_carrier(C!16)),
% 0.21/0.53 inference(and_elim,[status(thm)],[32])).
% 0.21/0.53 tff(218,plain,
% 0.21/0.53 (^[A: $i] : refl((empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A))) <=> (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(219,plain,
% 0.21/0.53 (![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A))) <=> ![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[218])).
% 0.21/0.53 tff(220,plain,
% 0.21/0.53 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & one_sorted_str(A)) <=> (~(empty_carrier(A) | (~one_sorted_str(A))))), ((~((~empty_carrier(A)) & one_sorted_str(A))) <=> (~(~(empty_carrier(A) | (~one_sorted_str(A))))))), rewrite((~(~(empty_carrier(A) | (~one_sorted_str(A))))) <=> (empty_carrier(A) | (~one_sorted_str(A)))), ((~((~empty_carrier(A)) & one_sorted_str(A))) <=> (empty_carrier(A) | (~one_sorted_str(A))))), (((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> ((~empty(the_carrier(A))) | (empty_carrier(A) | (~one_sorted_str(A)))))), rewrite(((~empty(the_carrier(A))) | (empty_carrier(A) | (~one_sorted_str(A)))) <=> (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))), (((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(221,plain,
% 0.21/0.53 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> ![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[220])).
% 0.21/0.53 tff(222,plain,
% 0.21/0.53 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> ![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(223,plain,
% 0.21/0.53 (^[A: $i] : rewrite((((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(the_carrier(A)))) <=> ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(224,plain,
% 0.21/0.53 (![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(the_carrier(A)))) <=> ![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[223])).
% 0.21/0.53 tff(225,axiom,(![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(the_carrier(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_struct_0')).
% 0.21/0.53 tff(226,plain,
% 0.21/0.53 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.21/0.53 tff(227,plain,
% 0.21/0.53 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[226, 222])).
% 0.21/0.53 tff(228,plain,(
% 0.21/0.53 ![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 0.21/0.53 inference(skolemize,[status(sab)],[227])).
% 0.21/0.53 tff(229,plain,
% 0.21/0.53 (![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[228, 221])).
% 0.21/0.53 tff(230,plain,
% 0.21/0.53 (![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[229, 219])).
% 0.21/0.53 tff(231,plain,
% 0.21/0.53 (((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | (empty_carrier(C!16) | (~empty(the_carrier(C!16))) | (~one_sorted_str(C!16)))) <=> ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | empty_carrier(C!16) | (~empty(the_carrier(C!16))) | (~one_sorted_str(C!16)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(232,plain,
% 0.21/0.53 ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | (empty_carrier(C!16) | (~empty(the_carrier(C!16))) | (~one_sorted_str(C!16)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(233,plain,
% 0.21/0.53 ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | empty_carrier(C!16) | (~empty(the_carrier(C!16))) | (~one_sorted_str(C!16))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.21/0.53 tff(234,plain,
% 0.21/0.53 ((~empty(the_carrier(C!16))) | (~one_sorted_str(C!16))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[233, 230, 217])).
% 0.21/0.53 tff(235,plain,
% 0.21/0.53 (~empty(the_carrier(C!16))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[234, 216])).
% 0.21/0.53 tff(236,plain,
% 0.21/0.53 (^[A: $i, B: $i] : refl((empty(B) | in(A, B) | (~element(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(237,plain,
% 0.21/0.53 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[236])).
% 0.21/0.53 tff(238,plain,
% 0.21/0.53 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(239,plain,
% 0.21/0.53 (^[A: $i, B: $i] : rewrite((element(A, B) => (empty(B) | in(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(240,plain,
% 0.21/0.53 (![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[239])).
% 0.21/0.53 tff(241,axiom,(![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_subset')).
% 0.21/0.53 tff(242,plain,
% 0.21/0.53 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.21/0.53 tff(243,plain,
% 0.21/0.53 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[242, 238])).
% 0.21/0.53 tff(244,plain,(
% 0.21/0.53 ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.21/0.53 inference(skolemize,[status(sab)],[243])).
% 0.21/0.53 tff(245,plain,
% 0.21/0.53 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[244, 237])).
% 0.21/0.53 tff(246,plain,
% 0.21/0.53 (element(G!20, the_carrier(C!16))),
% 0.21/0.53 inference(or_elim,[status(thm)],[33])).
% 0.21/0.53 tff(247,plain,
% 0.21/0.53 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | ((~element(G!20, the_carrier(C!16))) | empty(the_carrier(C!16)) | in(G!20, the_carrier(C!16)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (~element(G!20, the_carrier(C!16))) | empty(the_carrier(C!16)) | in(G!20, the_carrier(C!16)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(248,plain,
% 0.21/0.53 ((empty(the_carrier(C!16)) | in(G!20, the_carrier(C!16)) | (~element(G!20, the_carrier(C!16)))) <=> ((~element(G!20, the_carrier(C!16))) | empty(the_carrier(C!16)) | in(G!20, the_carrier(C!16)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(249,plain,
% 0.21/0.53 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(the_carrier(C!16)) | in(G!20, the_carrier(C!16)) | (~element(G!20, the_carrier(C!16))))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | ((~element(G!20, the_carrier(C!16))) | empty(the_carrier(C!16)) | in(G!20, the_carrier(C!16))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[248])).
% 0.21/0.53 tff(250,plain,
% 0.21/0.53 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(the_carrier(C!16)) | in(G!20, the_carrier(C!16)) | (~element(G!20, the_carrier(C!16))))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (~element(G!20, the_carrier(C!16))) | empty(the_carrier(C!16)) | in(G!20, the_carrier(C!16)))),
% 0.21/0.53 inference(transitivity,[status(thm)],[249, 247])).
% 0.21/0.53 tff(251,plain,
% 0.21/0.53 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(the_carrier(C!16)) | in(G!20, the_carrier(C!16)) | (~element(G!20, the_carrier(C!16))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(252,plain,
% 0.21/0.53 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (~element(G!20, the_carrier(C!16))) | empty(the_carrier(C!16)) | in(G!20, the_carrier(C!16))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.21/0.53 tff(253,plain,
% 0.21/0.53 (empty(the_carrier(C!16)) | in(G!20, the_carrier(C!16))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[252, 246, 245])).
% 0.21/0.53 tff(254,plain,
% 0.21/0.53 (in(G!20, the_carrier(C!16))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[253, 235])).
% 0.21/0.53 tff(255,plain,
% 0.21/0.53 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | ((~element(F!19, the_carrier(C!16))) | empty(the_carrier(C!16)) | in(F!19, the_carrier(C!16)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (~element(F!19, the_carrier(C!16))) | empty(the_carrier(C!16)) | in(F!19, the_carrier(C!16)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(256,plain,
% 0.21/0.53 ((empty(the_carrier(C!16)) | in(F!19, the_carrier(C!16)) | (~element(F!19, the_carrier(C!16)))) <=> ((~element(F!19, the_carrier(C!16))) | empty(the_carrier(C!16)) | in(F!19, the_carrier(C!16)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(257,plain,
% 0.21/0.53 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(the_carrier(C!16)) | in(F!19, the_carrier(C!16)) | (~element(F!19, the_carrier(C!16))))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | ((~element(F!19, the_carrier(C!16))) | empty(the_carrier(C!16)) | in(F!19, the_carrier(C!16))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[256])).
% 0.21/0.53 tff(258,plain,
% 0.21/0.53 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(the_carrier(C!16)) | in(F!19, the_carrier(C!16)) | (~element(F!19, the_carrier(C!16))))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (~element(F!19, the_carrier(C!16))) | empty(the_carrier(C!16)) | in(F!19, the_carrier(C!16)))),
% 0.21/0.53 inference(transitivity,[status(thm)],[257, 255])).
% 0.21/0.53 tff(259,plain,
% 0.21/0.53 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(the_carrier(C!16)) | in(F!19, the_carrier(C!16)) | (~element(F!19, the_carrier(C!16))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(260,plain,
% 0.21/0.53 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (~element(F!19, the_carrier(C!16))) | empty(the_carrier(C!16)) | in(F!19, the_carrier(C!16))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.21/0.53 tff(261,plain,
% 0.21/0.53 (empty(the_carrier(C!16)) | in(F!19, the_carrier(C!16))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[260, 161, 245])).
% 0.21/0.53 tff(262,plain,
% 0.21/0.53 (in(F!19, the_carrier(C!16))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[261, 235])).
% 0.21/0.53 tff(263,plain,
% 0.21/0.53 (~related(C!16, F!19, G!20)),
% 0.21/0.53 inference(or_elim,[status(thm)],[33])).
% 0.21/0.53 tff(264,plain,
% 0.21/0.53 (((~![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, F!19, F) | (~in(F, the_carrier(C!16))) | (~in(F!19, the_carrier(C!16))) | (~(F = G!20)) | (~related(B!15, F!19, G!20)))) | (related(C!16, F!19, G!20) | (~element(G!20, the_carrier(C!16))) | (~in(F!19, the_carrier(C!16))) | (~in(G!20, the_carrier(C!16))) | (~related(B!15, F!19, G!20)))) <=> ((~![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, F!19, F) | (~in(F, the_carrier(C!16))) | (~in(F!19, the_carrier(C!16))) | (~(F = G!20)) | (~related(B!15, F!19, G!20)))) | related(C!16, F!19, G!20) | (~element(G!20, the_carrier(C!16))) | (~in(F!19, the_carrier(C!16))) | (~in(G!20, the_carrier(C!16))) | (~related(B!15, F!19, G!20)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(265,plain,
% 0.21/0.53 (((~element(G!20, the_carrier(C!16))) | related(C!16, F!19, G!20) | (~in(G!20, the_carrier(C!16))) | (~in(F!19, the_carrier(C!16))) | $false | (~related(B!15, F!19, G!20))) <=> (related(C!16, F!19, G!20) | (~element(G!20, the_carrier(C!16))) | (~in(F!19, the_carrier(C!16))) | (~in(G!20, the_carrier(C!16))) | (~related(B!15, F!19, G!20)))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(266,plain,
% 0.21/0.54 ((~$true) <=> $false),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(267,plain,
% 0.21/0.54 ((G!20 = G!20) <=> $true),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(268,plain,
% 0.21/0.54 ((~(G!20 = G!20)) <=> (~$true)),
% 0.21/0.54 inference(monotonicity,[status(thm)],[267])).
% 0.21/0.54 tff(269,plain,
% 0.21/0.54 ((~(G!20 = G!20)) <=> $false),
% 0.21/0.54 inference(transitivity,[status(thm)],[268, 266])).
% 0.21/0.54 tff(270,plain,
% 0.21/0.54 (((~element(G!20, the_carrier(C!16))) | related(C!16, F!19, G!20) | (~in(G!20, the_carrier(C!16))) | (~in(F!19, the_carrier(C!16))) | (~(G!20 = G!20)) | (~related(B!15, F!19, G!20))) <=> ((~element(G!20, the_carrier(C!16))) | related(C!16, F!19, G!20) | (~in(G!20, the_carrier(C!16))) | (~in(F!19, the_carrier(C!16))) | $false | (~related(B!15, F!19, G!20)))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[269])).
% 0.21/0.54 tff(271,plain,
% 0.21/0.54 (((~element(G!20, the_carrier(C!16))) | related(C!16, F!19, G!20) | (~in(G!20, the_carrier(C!16))) | (~in(F!19, the_carrier(C!16))) | (~(G!20 = G!20)) | (~related(B!15, F!19, G!20))) <=> (related(C!16, F!19, G!20) | (~element(G!20, the_carrier(C!16))) | (~in(F!19, the_carrier(C!16))) | (~in(G!20, the_carrier(C!16))) | (~related(B!15, F!19, G!20)))),
% 0.21/0.54 inference(transitivity,[status(thm)],[270, 265])).
% 0.21/0.54 tff(272,plain,
% 0.21/0.54 (((~![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, F!19, F) | (~in(F, the_carrier(C!16))) | (~in(F!19, the_carrier(C!16))) | (~(F = G!20)) | (~related(B!15, F!19, G!20)))) | ((~element(G!20, the_carrier(C!16))) | related(C!16, F!19, G!20) | (~in(G!20, the_carrier(C!16))) | (~in(F!19, the_carrier(C!16))) | (~(G!20 = G!20)) | (~related(B!15, F!19, G!20)))) <=> ((~![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, F!19, F) | (~in(F, the_carrier(C!16))) | (~in(F!19, the_carrier(C!16))) | (~(F = G!20)) | (~related(B!15, F!19, G!20)))) | (related(C!16, F!19, G!20) | (~element(G!20, the_carrier(C!16))) | (~in(F!19, the_carrier(C!16))) | (~in(G!20, the_carrier(C!16))) | (~related(B!15, F!19, G!20))))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[271])).
% 0.21/0.54 tff(273,plain,
% 0.21/0.54 (((~![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, F!19, F) | (~in(F, the_carrier(C!16))) | (~in(F!19, the_carrier(C!16))) | (~(F = G!20)) | (~related(B!15, F!19, G!20)))) | ((~element(G!20, the_carrier(C!16))) | related(C!16, F!19, G!20) | (~in(G!20, the_carrier(C!16))) | (~in(F!19, the_carrier(C!16))) | (~(G!20 = G!20)) | (~related(B!15, F!19, G!20)))) <=> ((~![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, F!19, F) | (~in(F, the_carrier(C!16))) | (~in(F!19, the_carrier(C!16))) | (~(F = G!20)) | (~related(B!15, F!19, G!20)))) | related(C!16, F!19, G!20) | (~element(G!20, the_carrier(C!16))) | (~in(F!19, the_carrier(C!16))) | (~in(G!20, the_carrier(C!16))) | (~related(B!15, F!19, G!20)))),
% 0.21/0.54 inference(transitivity,[status(thm)],[272, 264])).
% 0.21/0.54 tff(274,plain,
% 0.21/0.54 ((~![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, F!19, F) | (~in(F, the_carrier(C!16))) | (~in(F!19, the_carrier(C!16))) | (~(F = G!20)) | (~related(B!15, F!19, G!20)))) | ((~element(G!20, the_carrier(C!16))) | related(C!16, F!19, G!20) | (~in(G!20, the_carrier(C!16))) | (~in(F!19, the_carrier(C!16))) | (~(G!20 = G!20)) | (~related(B!15, F!19, G!20)))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(275,plain,
% 0.21/0.54 ((~![F: $i] : ((~element(F, the_carrier(C!16))) | related(C!16, F!19, F) | (~in(F, the_carrier(C!16))) | (~in(F!19, the_carrier(C!16))) | (~(F = G!20)) | (~related(B!15, F!19, G!20)))) | related(C!16, F!19, G!20) | (~element(G!20, the_carrier(C!16))) | (~in(F!19, the_carrier(C!16))) | (~in(G!20, the_carrier(C!16))) | (~related(B!15, F!19, G!20))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.21/0.54 tff(276,plain,
% 0.21/0.54 (~related(B!15, F!19, G!20)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[275, 263, 246, 262, 254, 168])).
% 0.21/0.54 tff(277,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[276, 42])).
% 0.21/0.54 % SZS output end Proof
%------------------------------------------------------------------------------