TSTP Solution File: ALG223+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG223+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 6 16:09:20 EDT 2022
% Result : Theorem 0.65s 0.73s
% Output : Proof 0.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG223+1 : TPTP v8.1.0. Released v3.4.0.
% 0.12/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 29 13:58:15 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.65/0.73 % SZS status Theorem
% 0.65/0.73 % SZS output start Proof
% 0.65/0.73 tff(r1_tarski_type, type, (
% 0.65/0.73 r1_tarski: ( $i * $i ) > $o)).
% 0.65/0.73 tff(tptp_fun_F_5_type, type, (
% 0.65/0.73 tptp_fun_F_5: ( $i * $i ) > $i)).
% 0.65/0.73 tff(tptp_fun_E_4_type, type, (
% 0.65/0.73 tptp_fun_E_4: $i)).
% 0.65/0.73 tff(tptp_fun_D_3_type, type, (
% 0.65/0.73 tptp_fun_D_3: $i)).
% 0.65/0.73 tff(tptp_fun_E_6_type, type, (
% 0.65/0.73 tptp_fun_E_6: ( $i * $i ) > $i)).
% 0.65/0.73 tff(tptp_fun_C_2_type, type, (
% 0.65/0.73 tptp_fun_C_2: $i)).
% 0.65/0.73 tff(r2_hidden_type, type, (
% 0.65/0.73 r2_hidden: ( $i * $i ) > $o)).
% 0.65/0.73 tff(r1_closure3_type, type, (
% 0.65/0.73 r1_closure3: ( $i * $i * $i * $i ) > $o)).
% 0.65/0.73 tff(tptp_fun_B_0_type, type, (
% 0.65/0.73 tptp_fun_B_0: $i)).
% 0.65/0.73 tff(tptp_fun_A_1_type, type, (
% 0.65/0.73 tptp_fun_A_1: $i)).
% 0.65/0.73 tff(m1_subset_1_type, type, (
% 0.65/0.73 m1_subset_1: ( $i * $i ) > $o)).
% 0.65/0.73 tff(k1_zfmisc_1_type, type, (
% 0.65/0.73 k1_zfmisc_1: $i > $i)).
% 0.65/0.73 tff(k1_closure2_type, type, (
% 0.65/0.73 k1_closure2: ( $i * $i ) > $i)).
% 0.65/0.73 tff(m1_pboole_type, type, (
% 0.65/0.73 m1_pboole: ( $i * $i ) > $o)).
% 0.65/0.73 tff(1,plain,
% 0.65/0.73 (^[A: $i, B: $i] : refl(((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (~((~((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~(r1_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F))))))))))))) <=> ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (~((~((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~(r1_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F))))))))))))))),
% 0.65/0.73 inference(bind,[status(th)],[])).
% 0.65/0.73 tff(2,plain,
% 0.65/0.73 (![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (~((~((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~(r1_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F))))))))))))) <=> ![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (~((~((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~(r1_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))))))))))),
% 0.65/0.73 inference(quant_intro,[status(thm)],[1])).
% 0.65/0.73 tff(3,plain,
% 0.65/0.73 (^[A: $i, B: $i] : rewrite(((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (~((~((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~(r1_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F))))))))))))) <=> ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (~((~((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~(r1_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F))))))))))))))),
% 0.65/0.73 inference(bind,[status(th)],[])).
% 0.65/0.73 tff(4,plain,
% 0.65/0.73 (![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (~((~((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~(r1_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F))))))))))))) <=> ![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (~((~((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~(r1_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))))))))))),
% 0.65/0.73 inference(quant_intro,[status(thm)],[3])).
% 0.65/0.73 tff(5,plain,
% 0.65/0.73 (![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (~((~((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~(r1_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F))))))))))))) <=> ![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (~((~((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~(r1_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))))))))))),
% 0.65/0.73 inference(transitivity,[status(thm)],[4, 2])).
% 0.65/0.73 tff(6,plain,
% 0.65/0.73 (^[A: $i, B: $i] : rewrite(((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (r2_hidden(tptp_fun_F_5(E, C), C) & r1_tarski(E, tptp_fun_F_5(E, C))))) & (r1_closure3(A, B, C, D) | (r2_hidden(tptp_fun_E_6(D, C), D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(tptp_fun_E_6(D, C), F))))))))) <=> ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (~((~((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~(r1_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F))))))))))))))),
% 0.65/0.73 inference(bind,[status(th)],[])).
% 0.65/0.73 tff(7,plain,
% 0.65/0.73 (![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (r2_hidden(tptp_fun_F_5(E, C), C) & r1_tarski(E, tptp_fun_F_5(E, C))))) & (r1_closure3(A, B, C, D) | (r2_hidden(tptp_fun_E_6(D, C), D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(tptp_fun_E_6(D, C), F))))))))) <=> ![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (~((~((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~(r1_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))))))))))),
% 0.65/0.73 inference(quant_intro,[status(thm)],[6])).
% 0.65/0.73 tff(8,plain,
% 0.65/0.73 (^[A: $i, B: $i] : rewrite(((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~(~(r2_hidden(tptp_fun_F_5(E, C), C) & r1_tarski(E, tptp_fun_F_5(E, C))))))) & (r1_closure3(A, B, C, D) | (r2_hidden(tptp_fun_E_6(D, C), D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(tptp_fun_E_6(D, C), F))))))))) <=> ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (r2_hidden(tptp_fun_F_5(E, C), C) & r1_tarski(E, tptp_fun_F_5(E, C))))) & (r1_closure3(A, B, C, D) | (r2_hidden(tptp_fun_E_6(D, C), D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(tptp_fun_E_6(D, C), F))))))))))),
% 0.65/0.74 inference(bind,[status(th)],[])).
% 0.65/0.74 tff(9,plain,
% 0.65/0.74 (![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~(~(r2_hidden(tptp_fun_F_5(E, C), C) & r1_tarski(E, tptp_fun_F_5(E, C))))))) & (r1_closure3(A, B, C, D) | (r2_hidden(tptp_fun_E_6(D, C), D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(tptp_fun_E_6(D, C), F))))))))) <=> ![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (r2_hidden(tptp_fun_F_5(E, C), C) & r1_tarski(E, tptp_fun_F_5(E, C))))) & (r1_closure3(A, B, C, D) | (r2_hidden(tptp_fun_E_6(D, C), D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(tptp_fun_E_6(D, C), F)))))))))),
% 0.65/0.74 inference(quant_intro,[status(thm)],[8])).
% 0.65/0.74 tff(10,plain,
% 0.65/0.74 (![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F))))))))) <=> ![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F)))))))))),
% 0.65/0.74 inference(rewrite,[status(thm)],[])).
% 0.65/0.74 tff(11,plain,
% 0.65/0.74 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite((r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F)))))) <=> (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F))))))), ((m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B))) => (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F))))))) <=> (m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B))) => (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F))))))))), rewrite((m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B))) => (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F))))))) <=> ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F)))))))), ((m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B))) => (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F))))))) <=> ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F)))))))))), (![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B))) => (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F))))))) <=> ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F))))))))), ((m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B))) => (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F)))))))) <=> (m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B))) => ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F)))))))))), rewrite((m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B))) => ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F)))))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F))))))))), ((m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B))) => (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F)))))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F))))))))))), (![C: $i] : (m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B))) => (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F)))))))) <=> ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F)))))))))), ((m1_pboole(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B))) => (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F))))))))) <=> (m1_pboole(B, A) => ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F))))))))))), rewrite((m1_pboole(B, A) => ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F))))))))) <=> ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F)))))))))), ((m1_pboole(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B))) => (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F))))))))) <=> ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F)))))))))))),
% 0.65/0.74 inference(bind,[status(th)],[])).
% 0.65/0.74 tff(12,plain,
% 0.65/0.74 (![A: $i, B: $i] : (m1_pboole(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B))) => (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F))))))))) <=> ![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F)))))))))),
% 0.65/0.74 inference(quant_intro,[status(thm)],[11])).
% 0.65/0.74 tff(13,axiom,(![A: $i, B: $i] : (m1_pboole(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B))) => (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_closure3')).
% 0.65/0.74 tff(14,plain,
% 0.65/0.74 (![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F)))))))))),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.65/0.74 tff(15,plain,
% 0.65/0.74 (![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (r1_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(E, F)))))))))),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.65/0.74 tff(16,plain,(
% 0.65/0.74 ![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~(~(r2_hidden(tptp_fun_F_5(E, C), C) & r1_tarski(E, tptp_fun_F_5(E, C))))))) & (r1_closure3(A, B, C, D) | (r2_hidden(tptp_fun_E_6(D, C), D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(tptp_fun_E_6(D, C), F)))))))))),
% 0.65/0.74 inference(skolemize,[status(sab)],[15])).
% 0.65/0.74 tff(17,plain,
% 0.65/0.74 (![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (r2_hidden(tptp_fun_F_5(E, C), C) & r1_tarski(E, tptp_fun_F_5(E, C))))) & (r1_closure3(A, B, C, D) | (r2_hidden(tptp_fun_E_6(D, C), D) & ![F: $i] : (~(r2_hidden(F, C) & r1_tarski(tptp_fun_E_6(D, C), F)))))))))),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.65/0.74 tff(18,plain,
% 0.65/0.74 (![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (~((~((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~(r1_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))))))))))),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[17, 7])).
% 0.65/0.74 tff(19,plain,
% 0.65/0.74 (![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (~((~((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~(r1_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))))))))))),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[18, 5])).
% 0.65/0.74 tff(20,plain,
% 0.65/0.74 ((m1_pboole(B!0, A!1) & (m1_subset_1(C!2, k1_zfmisc_1(k1_closure2(A!1, B!0))) & m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0))) & (~(r1_closure3(A!1, B!0, E!4, C!2) | (~(r1_closure3(A!1, B!0, D!3, C!2) & r1_closure3(A!1, B!0, E!4, D!3))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))))))) <=> (m1_pboole(B!0, A!1) & m1_subset_1(C!2, k1_zfmisc_1(k1_closure2(A!1, B!0))) & m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0))) & (~(r1_closure3(A!1, B!0, E!4, C!2) | (~(r1_closure3(A!1, B!0, D!3, C!2) & r1_closure3(A!1, B!0, E!4, D!3))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))))))),
% 0.65/0.74 inference(rewrite,[status(thm)],[])).
% 0.65/0.74 tff(21,plain,
% 0.65/0.74 ((m1_subset_1(C!2, k1_zfmisc_1(k1_closure2(A!1, B!0))) & (m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0))) & (~(r1_closure3(A!1, B!0, E!4, C!2) | (~(r1_closure3(A!1, B!0, D!3, C!2) & r1_closure3(A!1, B!0, E!4, D!3))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))))))) <=> (m1_subset_1(C!2, k1_zfmisc_1(k1_closure2(A!1, B!0))) & m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0))) & (~(r1_closure3(A!1, B!0, E!4, C!2) | (~(r1_closure3(A!1, B!0, D!3, C!2) & r1_closure3(A!1, B!0, E!4, D!3))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))))))),
% 0.81/0.74 inference(rewrite,[status(thm)],[])).
% 0.81/0.74 tff(22,plain,
% 0.81/0.74 (((~(~m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0))))) & (~(r1_closure3(A!1, B!0, E!4, C!2) | (~(r1_closure3(A!1, B!0, D!3, C!2) & r1_closure3(A!1, B!0, E!4, D!3))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0))))))) <=> (m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0))) & (~(r1_closure3(A!1, B!0, E!4, C!2) | (~(r1_closure3(A!1, B!0, D!3, C!2) & r1_closure3(A!1, B!0, E!4, D!3))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))))))),
% 0.81/0.74 inference(rewrite,[status(thm)],[])).
% 0.81/0.74 tff(23,plain,
% 0.81/0.74 ((~(~m1_subset_1(C!2, k1_zfmisc_1(k1_closure2(A!1, B!0))))) <=> m1_subset_1(C!2, k1_zfmisc_1(k1_closure2(A!1, B!0)))),
% 0.81/0.74 inference(rewrite,[status(thm)],[])).
% 0.81/0.74 tff(24,plain,
% 0.81/0.74 (((~(~m1_subset_1(C!2, k1_zfmisc_1(k1_closure2(A!1, B!0))))) & ((~(~m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0))))) & (~(r1_closure3(A!1, B!0, E!4, C!2) | (~(r1_closure3(A!1, B!0, D!3, C!2) & r1_closure3(A!1, B!0, E!4, D!3))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))))))) <=> (m1_subset_1(C!2, k1_zfmisc_1(k1_closure2(A!1, B!0))) & (m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0))) & (~(r1_closure3(A!1, B!0, E!4, C!2) | (~(r1_closure3(A!1, B!0, D!3, C!2) & r1_closure3(A!1, B!0, E!4, D!3))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0))))))))),
% 0.81/0.74 inference(monotonicity,[status(thm)],[23, 22])).
% 0.81/0.74 tff(25,plain,
% 0.81/0.74 (((~(~m1_subset_1(C!2, k1_zfmisc_1(k1_closure2(A!1, B!0))))) & ((~(~m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0))))) & (~(r1_closure3(A!1, B!0, E!4, C!2) | (~(r1_closure3(A!1, B!0, D!3, C!2) & r1_closure3(A!1, B!0, E!4, D!3))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))))))) <=> (m1_subset_1(C!2, k1_zfmisc_1(k1_closure2(A!1, B!0))) & m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0))) & (~(r1_closure3(A!1, B!0, E!4, C!2) | (~(r1_closure3(A!1, B!0, D!3, C!2) & r1_closure3(A!1, B!0, E!4, D!3))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))))))),
% 0.81/0.74 inference(transitivity,[status(thm)],[24, 21])).
% 0.81/0.74 tff(26,plain,
% 0.81/0.74 ((~(~m1_pboole(B!0, A!1))) <=> m1_pboole(B!0, A!1)),
% 0.81/0.74 inference(rewrite,[status(thm)],[])).
% 0.81/0.74 tff(27,plain,
% 0.81/0.74 (((~(~m1_pboole(B!0, A!1))) & ((~(~m1_subset_1(C!2, k1_zfmisc_1(k1_closure2(A!1, B!0))))) & ((~(~m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0))))) & (~(r1_closure3(A!1, B!0, E!4, C!2) | (~(r1_closure3(A!1, B!0, D!3, C!2) & r1_closure3(A!1, B!0, E!4, D!3))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0))))))))) <=> (m1_pboole(B!0, A!1) & (m1_subset_1(C!2, k1_zfmisc_1(k1_closure2(A!1, B!0))) & m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0))) & (~(r1_closure3(A!1, B!0, E!4, C!2) | (~(r1_closure3(A!1, B!0, D!3, C!2) & r1_closure3(A!1, B!0, E!4, D!3))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0))))))))),
% 0.81/0.74 inference(monotonicity,[status(thm)],[26, 25])).
% 0.81/0.74 tff(28,plain,
% 0.81/0.74 (((~(~m1_pboole(B!0, A!1))) & ((~(~m1_subset_1(C!2, k1_zfmisc_1(k1_closure2(A!1, B!0))))) & ((~(~m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0))))) & (~(r1_closure3(A!1, B!0, E!4, C!2) | (~(r1_closure3(A!1, B!0, D!3, C!2) & r1_closure3(A!1, B!0, E!4, D!3))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0))))))))) <=> (m1_pboole(B!0, A!1) & m1_subset_1(C!2, k1_zfmisc_1(k1_closure2(A!1, B!0))) & m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0))) & (~(r1_closure3(A!1, B!0, E!4, C!2) | (~(r1_closure3(A!1, B!0, D!3, C!2) & r1_closure3(A!1, B!0, E!4, D!3))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))))))),
% 0.81/0.74 inference(transitivity,[status(thm)],[27, 20])).
% 0.81/0.74 tff(29,plain,
% 0.81/0.74 ((~![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | ![E: $i] : (r1_closure3(A, B, E, C) | (~(r1_closure3(A, B, D, C) & r1_closure3(A, B, E, D))) | (~m1_subset_1(E, k1_zfmisc_1(k1_closure2(A, B))))))))) <=> (~![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | ![E: $i] : (r1_closure3(A, B, E, C) | (~(r1_closure3(A, B, D, C) & r1_closure3(A, B, E, D))) | (~m1_subset_1(E, k1_zfmisc_1(k1_closure2(A, B)))))))))),
% 0.81/0.74 inference(rewrite,[status(thm)],[])).
% 0.81/0.74 tff(30,plain,
% 0.81/0.74 ((~![A: $i, B: $i] : (m1_pboole(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B))) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k1_closure2(A, B))) => ((r1_closure3(A, B, D, C) & r1_closure3(A, B, E, D)) => r1_closure3(A, B, E, C))))))) <=> (~![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | ![E: $i] : (r1_closure3(A, B, E, C) | (~(r1_closure3(A, B, D, C) & r1_closure3(A, B, E, D))) | (~m1_subset_1(E, k1_zfmisc_1(k1_closure2(A, B)))))))))),
% 0.81/0.74 inference(rewrite,[status(thm)],[])).
% 0.81/0.74 tff(31,axiom,(~![A: $i, B: $i] : (m1_pboole(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B))) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(k1_closure2(A, B))) => ((r1_closure3(A, B, D, C) & r1_closure3(A, B, E, D)) => r1_closure3(A, B, E, C))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t4_closure3')).
% 0.81/0.74 tff(32,plain,
% 0.81/0.74 (~![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | ![E: $i] : (r1_closure3(A, B, E, C) | (~(r1_closure3(A, B, D, C) & r1_closure3(A, B, E, D))) | (~m1_subset_1(E, k1_zfmisc_1(k1_closure2(A, B))))))))),
% 0.81/0.74 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.81/0.74 tff(33,plain,
% 0.81/0.74 (~![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | ![E: $i] : (r1_closure3(A, B, E, C) | (~(r1_closure3(A, B, D, C) & r1_closure3(A, B, E, D))) | (~m1_subset_1(E, k1_zfmisc_1(k1_closure2(A, B))))))))),
% 0.81/0.74 inference(modus_ponens,[status(thm)],[32, 29])).
% 0.81/0.74 tff(34,plain,
% 0.81/0.74 (~![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | ![E: $i] : (r1_closure3(A, B, E, C) | (~(r1_closure3(A, B, D, C) & r1_closure3(A, B, E, D))) | (~m1_subset_1(E, k1_zfmisc_1(k1_closure2(A, B))))))))),
% 0.81/0.74 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.81/0.74 tff(35,plain,
% 0.81/0.74 (~![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | ![E: $i] : (r1_closure3(A, B, E, C) | (~(r1_closure3(A, B, D, C) & r1_closure3(A, B, E, D))) | (~m1_subset_1(E, k1_zfmisc_1(k1_closure2(A, B))))))))),
% 0.81/0.74 inference(modus_ponens,[status(thm)],[34, 29])).
% 0.81/0.74 tff(36,plain,
% 0.81/0.74 (~![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | ![E: $i] : (r1_closure3(A, B, E, C) | (~(r1_closure3(A, B, D, C) & r1_closure3(A, B, E, D))) | (~m1_subset_1(E, k1_zfmisc_1(k1_closure2(A, B))))))))),
% 0.81/0.74 inference(modus_ponens,[status(thm)],[35, 29])).
% 0.81/0.74 tff(37,plain,
% 0.81/0.74 (~![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | ![E: $i] : (r1_closure3(A, B, E, C) | (~(r1_closure3(A, B, D, C) & r1_closure3(A, B, E, D))) | (~m1_subset_1(E, k1_zfmisc_1(k1_closure2(A, B))))))))),
% 0.81/0.74 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.81/0.74 tff(38,plain,
% 0.81/0.74 (~![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | ![E: $i] : (r1_closure3(A, B, E, C) | (~(r1_closure3(A, B, D, C) & r1_closure3(A, B, E, D))) | (~m1_subset_1(E, k1_zfmisc_1(k1_closure2(A, B))))))))),
% 0.81/0.74 inference(modus_ponens,[status(thm)],[37, 29])).
% 0.81/0.74 tff(39,plain,
% 0.81/0.74 (m1_pboole(B!0, A!1) & m1_subset_1(C!2, k1_zfmisc_1(k1_closure2(A!1, B!0))) & m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0))) & (~(r1_closure3(A!1, B!0, E!4, C!2) | (~(r1_closure3(A!1, B!0, D!3, C!2) & r1_closure3(A!1, B!0, E!4, D!3))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0))))))),
% 0.81/0.74 inference(modus_ponens,[status(thm)],[38, 28])).
% 0.81/0.74 tff(40,plain,
% 0.81/0.74 (m1_pboole(B!0, A!1)),
% 0.81/0.74 inference(and_elim,[status(thm)],[39])).
% 0.81/0.74 tff(41,plain,
% 0.81/0.74 (((~![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (~((~((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~(r1_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))))))))))) | ((~m1_pboole(B!0, A!1)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))) | r1_closure3(A!1, B!0, C, D))))))))) <=> ((~![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (~((~((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~(r1_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))))))))))) | (~m1_pboole(B!0, A!1)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))) | r1_closure3(A!1, B!0, C, D))))))))),
% 0.81/0.74 inference(rewrite,[status(thm)],[])).
% 0.81/0.74 tff(42,plain,
% 0.81/0.74 (((~m1_pboole(B!0, A!1)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~(r1_closure3(A!1, B!0, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F))))))))))))) <=> ((~m1_pboole(B!0, A!1)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))) | r1_closure3(A!1, B!0, C, D))))))))),
% 0.81/0.74 inference(rewrite,[status(thm)],[])).
% 0.81/0.74 tff(43,plain,
% 0.81/0.74 (((~![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (~((~((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~(r1_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))))))))))) | ((~m1_pboole(B!0, A!1)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~(r1_closure3(A!1, B!0, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))))))))))) <=> ((~![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (~((~((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~(r1_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))))))))))) | ((~m1_pboole(B!0, A!1)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))) | r1_closure3(A!1, B!0, C, D)))))))))),
% 0.81/0.74 inference(monotonicity,[status(thm)],[42])).
% 0.81/0.74 tff(44,plain,
% 0.81/0.74 (((~![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (~((~((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~(r1_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))))))))))) | ((~m1_pboole(B!0, A!1)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~(r1_closure3(A!1, B!0, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))))))))))) <=> ((~![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (~((~((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~(r1_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))))))))))) | (~m1_pboole(B!0, A!1)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))) | r1_closure3(A!1, B!0, C, D))))))))),
% 0.81/0.74 inference(transitivity,[status(thm)],[43, 41])).
% 0.81/0.74 tff(45,plain,
% 0.81/0.74 ((~![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (~((~((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~(r1_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))))))))))) | ((~m1_pboole(B!0, A!1)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~(r1_closure3(A!1, B!0, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))))))))))),
% 0.81/0.75 inference(quant_inst,[status(thm)],[])).
% 0.81/0.75 tff(46,plain,
% 0.81/0.75 ((~![A: $i, B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (~((~((~r1_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~(r1_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))))))))))) | (~m1_pboole(B!0, A!1)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))) | r1_closure3(A!1, B!0, C, D)))))))),
% 0.81/0.75 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.81/0.75 tff(47,plain,
% 0.81/0.75 (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))) | r1_closure3(A!1, B!0, C, D)))))))),
% 0.81/0.75 inference(unit_resolution,[status(thm)],[46, 40, 19])).
% 0.81/0.75 tff(48,plain,
% 0.81/0.75 (m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0)))),
% 0.81/0.75 inference(and_elim,[status(thm)],[39])).
% 0.81/0.75 tff(49,plain,
% 0.81/0.75 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))) | r1_closure3(A!1, B!0, C, D)))))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, D!3, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(E, tptp_fun_F_5(E, D!3)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, D!3), D)) | (~![F: $i] : ((~r2_hidden(F, D!3)) | (~r1_tarski(tptp_fun_E_6(D, D!3), F)))))) | r1_closure3(A!1, B!0, D!3, D)))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))) | r1_closure3(A!1, B!0, C, D)))))))) | (~m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, D!3, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(E, tptp_fun_F_5(E, D!3)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, D!3), D)) | (~![F: $i] : ((~r2_hidden(F, D!3)) | (~r1_tarski(tptp_fun_E_6(D, D!3), F)))))) | r1_closure3(A!1, B!0, D!3, D)))))))),
% 0.81/0.75 inference(rewrite,[status(thm)],[])).
% 0.81/0.75 tff(50,plain,
% 0.81/0.75 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))) | r1_closure3(A!1, B!0, C, D)))))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, D!3, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(E, tptp_fun_F_5(E, D!3)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, D!3), D)) | (~![F: $i] : ((~r2_hidden(F, D!3)) | (~r1_tarski(tptp_fun_E_6(D, D!3), F)))))) | r1_closure3(A!1, B!0, D!3, D)))))))),
% 0.81/0.75 inference(quant_inst,[status(thm)],[])).
% 0.81/0.75 tff(51,plain,
% 0.81/0.75 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))) | r1_closure3(A!1, B!0, C, D)))))))) | (~m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, D!3, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(E, tptp_fun_F_5(E, D!3)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, D!3), D)) | (~![F: $i] : ((~r2_hidden(F, D!3)) | (~r1_tarski(tptp_fun_E_6(D, D!3), F)))))) | r1_closure3(A!1, B!0, D!3, D))))))),
% 0.81/0.75 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.81/0.75 tff(52,plain,
% 0.81/0.75 (![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, D!3, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(E, tptp_fun_F_5(E, D!3)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, D!3), D)) | (~![F: $i] : ((~r2_hidden(F, D!3)) | (~r1_tarski(tptp_fun_E_6(D, D!3), F)))))) | r1_closure3(A!1, B!0, D!3, D))))))),
% 0.81/0.75 inference(unit_resolution,[status(thm)],[51, 48, 47])).
% 0.81/0.75 tff(53,plain,
% 0.81/0.75 (m1_subset_1(C!2, k1_zfmisc_1(k1_closure2(A!1, B!0)))),
% 0.81/0.75 inference(and_elim,[status(thm)],[39])).
% 0.81/0.75 tff(54,plain,
% 0.81/0.75 (((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, D!3, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(E, tptp_fun_F_5(E, D!3)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, D!3), D)) | (~![F: $i] : ((~r2_hidden(F, D!3)) | (~r1_tarski(tptp_fun_E_6(D, D!3), F)))))) | r1_closure3(A!1, B!0, D!3, D))))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, D!3, C!2)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(E, tptp_fun_F_5(E, D!3)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(C!2, D!3), C!2)) | (~![F: $i] : ((~r2_hidden(F, D!3)) | (~r1_tarski(tptp_fun_E_6(C!2, D!3), F)))))) | r1_closure3(A!1, B!0, D!3, C!2))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, D!3, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(E, tptp_fun_F_5(E, D!3)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, D!3), D)) | (~![F: $i] : ((~r2_hidden(F, D!3)) | (~r1_tarski(tptp_fun_E_6(D, D!3), F)))))) | r1_closure3(A!1, B!0, D!3, D))))))) | (~m1_subset_1(C!2, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, D!3, C!2)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(E, tptp_fun_F_5(E, D!3)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(C!2, D!3), C!2)) | (~![F: $i] : ((~r2_hidden(F, D!3)) | (~r1_tarski(tptp_fun_E_6(C!2, D!3), F)))))) | r1_closure3(A!1, B!0, D!3, C!2))))))),
% 0.81/0.75 inference(rewrite,[status(thm)],[])).
% 0.81/0.75 tff(55,plain,
% 0.81/0.75 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, D!3, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(E, tptp_fun_F_5(E, D!3)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, D!3), D)) | (~![F: $i] : ((~r2_hidden(F, D!3)) | (~r1_tarski(tptp_fun_E_6(D, D!3), F)))))) | r1_closure3(A!1, B!0, D!3, D))))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, D!3, C!2)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(E, tptp_fun_F_5(E, D!3)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(C!2, D!3), C!2)) | (~![F: $i] : ((~r2_hidden(F, D!3)) | (~r1_tarski(tptp_fun_E_6(C!2, D!3), F)))))) | r1_closure3(A!1, B!0, D!3, C!2))))))),
% 0.81/0.75 inference(quant_inst,[status(thm)],[])).
% 0.81/0.75 tff(56,plain,
% 0.81/0.75 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, D!3, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(E, tptp_fun_F_5(E, D!3)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, D!3), D)) | (~![F: $i] : ((~r2_hidden(F, D!3)) | (~r1_tarski(tptp_fun_E_6(D, D!3), F)))))) | r1_closure3(A!1, B!0, D!3, D))))))) | (~m1_subset_1(C!2, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, D!3, C!2)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(E, tptp_fun_F_5(E, D!3)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(C!2, D!3), C!2)) | (~![F: $i] : ((~r2_hidden(F, D!3)) | (~r1_tarski(tptp_fun_E_6(C!2, D!3), F)))))) | r1_closure3(A!1, B!0, D!3, C!2)))))),
% 0.81/0.75 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.81/0.75 tff(57,plain,
% 0.81/0.75 (~((~((~r1_closure3(A!1, B!0, D!3, C!2)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(E, tptp_fun_F_5(E, D!3)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(C!2, D!3), C!2)) | (~![F: $i] : ((~r2_hidden(F, D!3)) | (~r1_tarski(tptp_fun_E_6(C!2, D!3), F)))))) | r1_closure3(A!1, B!0, D!3, C!2))))),
% 0.81/0.75 inference(unit_resolution,[status(thm)],[56, 53, 52])).
% 0.81/0.75 tff(58,plain,
% 0.81/0.75 (((~((~r1_closure3(A!1, B!0, D!3, C!2)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(E, tptp_fun_F_5(E, D!3)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(C!2, D!3), C!2)) | (~![F: $i] : ((~r2_hidden(F, D!3)) | (~r1_tarski(tptp_fun_E_6(C!2, D!3), F)))))) | r1_closure3(A!1, B!0, D!3, C!2)))) | ((~r1_closure3(A!1, B!0, D!3, C!2)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(E, tptp_fun_F_5(E, D!3)))))))),
% 0.81/0.75 inference(tautology,[status(thm)],[])).
% 0.81/0.75 tff(59,plain,
% 0.81/0.75 ((~r1_closure3(A!1, B!0, D!3, C!2)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(E, tptp_fun_F_5(E, D!3))))))),
% 0.81/0.75 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.81/0.75 tff(60,plain,
% 0.81/0.75 (~(r1_closure3(A!1, B!0, E!4, C!2) | (~(r1_closure3(A!1, B!0, D!3, C!2) & r1_closure3(A!1, B!0, E!4, D!3))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))))),
% 0.81/0.75 inference(and_elim,[status(thm)],[39])).
% 0.81/0.75 tff(61,plain,
% 0.81/0.75 (r1_closure3(A!1, B!0, D!3, C!2) & r1_closure3(A!1, B!0, E!4, D!3)),
% 0.81/0.75 inference(or_elim,[status(thm)],[60])).
% 0.81/0.75 tff(62,plain,
% 0.81/0.75 (r1_closure3(A!1, B!0, D!3, C!2)),
% 0.81/0.75 inference(and_elim,[status(thm)],[61])).
% 0.81/0.75 tff(63,plain,
% 0.81/0.75 ((~((~r1_closure3(A!1, B!0, D!3, C!2)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(E, tptp_fun_F_5(E, D!3)))))))) | (~r1_closure3(A!1, B!0, D!3, C!2)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(E, tptp_fun_F_5(E, D!3))))))),
% 0.81/0.75 inference(tautology,[status(thm)],[])).
% 0.81/0.75 tff(64,plain,
% 0.81/0.75 ((~((~r1_closure3(A!1, B!0, D!3, C!2)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(E, tptp_fun_F_5(E, D!3)))))))) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(E, tptp_fun_F_5(E, D!3))))))),
% 0.81/0.75 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.81/0.75 tff(65,plain,
% 0.81/0.75 (![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(E, tptp_fun_F_5(E, D!3))))))),
% 0.81/0.75 inference(unit_resolution,[status(thm)],[64, 59])).
% 0.81/0.75 tff(66,plain,
% 0.81/0.75 (m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))),
% 0.81/0.75 inference(or_elim,[status(thm)],[60])).
% 0.81/0.75 tff(67,plain,
% 0.81/0.75 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))) | r1_closure3(A!1, B!0, C, D)))))))) | ((~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, E!4, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, E!4), D)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(D, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, D)))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))) | r1_closure3(A!1, B!0, C, D)))))))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, E!4, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, E!4), D)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(D, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, D)))))))),
% 0.81/0.75 inference(rewrite,[status(thm)],[])).
% 0.81/0.75 tff(68,plain,
% 0.81/0.75 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))) | r1_closure3(A!1, B!0, C, D)))))))) | ((~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, E!4, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, E!4), D)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(D, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, D)))))))),
% 0.81/0.75 inference(quant_inst,[status(thm)],[])).
% 0.81/0.75 tff(69,plain,
% 0.81/0.75 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, C), C)) | (~r1_tarski(E, tptp_fun_F_5(E, C)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, C), D)) | (~![F: $i] : ((~r2_hidden(F, C)) | (~r1_tarski(tptp_fun_E_6(D, C), F)))))) | r1_closure3(A!1, B!0, C, D)))))))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, E!4, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, E!4), D)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(D, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, D))))))),
% 0.81/0.75 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.81/0.75 tff(70,plain,
% 0.81/0.75 (![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, E!4, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, E!4), D)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(D, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, D))))))),
% 0.81/0.75 inference(unit_resolution,[status(thm)],[69, 66, 47])).
% 0.81/0.75 tff(71,plain,
% 0.81/0.75 (((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, E!4, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, E!4), D)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(D, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, D))))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, E!4, C!2)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(C!2, E!4), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, C!2))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, E!4, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, E!4), D)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(D, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, D))))))) | (~m1_subset_1(C!2, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, E!4, C!2)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(C!2, E!4), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, C!2))))))),
% 0.81/0.75 inference(rewrite,[status(thm)],[])).
% 0.81/0.75 tff(72,plain,
% 0.81/0.75 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, E!4, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, E!4), D)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(D, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, D))))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, E!4, C!2)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(C!2, E!4), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, C!2))))))),
% 0.81/0.75 inference(quant_inst,[status(thm)],[])).
% 0.81/0.75 tff(73,plain,
% 0.81/0.75 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, E!4, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, E!4), D)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(D, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, D))))))) | (~m1_subset_1(C!2, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, E!4, C!2)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(C!2, E!4), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, C!2)))))),
% 0.81/0.75 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.81/0.76 tff(74,plain,
% 0.81/0.76 (~((~((~r1_closure3(A!1, B!0, E!4, C!2)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(C!2, E!4), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, C!2))))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[73, 53, 70])).
% 0.81/0.76 tff(75,plain,
% 0.81/0.76 (((~((~r1_closure3(A!1, B!0, E!4, C!2)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(C!2, E!4), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, C!2)))) | ((~((~r2_hidden(tptp_fun_E_6(C!2, E!4), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, C!2))),
% 0.81/0.76 inference(tautology,[status(thm)],[])).
% 0.81/0.76 tff(76,plain,
% 0.81/0.76 ((~((~r2_hidden(tptp_fun_E_6(C!2, E!4), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, C!2)),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.81/0.76 tff(77,plain,
% 0.81/0.76 (~r1_closure3(A!1, B!0, E!4, C!2)),
% 0.81/0.76 inference(or_elim,[status(thm)],[60])).
% 0.81/0.76 tff(78,plain,
% 0.81/0.76 ((~((~((~r2_hidden(tptp_fun_E_6(C!2, E!4), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, C!2))) | (~((~r2_hidden(tptp_fun_E_6(C!2, E!4), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, C!2)),
% 0.81/0.76 inference(tautology,[status(thm)],[])).
% 0.81/0.76 tff(79,plain,
% 0.81/0.76 ((~((~((~r2_hidden(tptp_fun_E_6(C!2, E!4), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, C!2))) | (~((~r2_hidden(tptp_fun_E_6(C!2, E!4), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), F))))))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.81/0.76 tff(80,plain,
% 0.81/0.76 (~((~r2_hidden(tptp_fun_E_6(C!2, E!4), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), F)))))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[79, 76])).
% 0.81/0.76 tff(81,plain,
% 0.81/0.76 (((~r2_hidden(tptp_fun_E_6(C!2, E!4), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), F))))) | r2_hidden(tptp_fun_E_6(C!2, E!4), C!2)),
% 0.81/0.76 inference(tautology,[status(thm)],[])).
% 0.81/0.76 tff(82,plain,
% 0.81/0.76 (r2_hidden(tptp_fun_E_6(C!2, E!4), C!2)),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.81/0.76 tff(83,plain,
% 0.81/0.76 (((~![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(E, tptp_fun_F_5(E, D!3))))))) | ((~r2_hidden(tptp_fun_E_6(C!2, E!4), C!2)) | (~((~r2_hidden(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), D!3)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3))))))) <=> ((~![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(E, tptp_fun_F_5(E, D!3))))))) | (~r2_hidden(tptp_fun_E_6(C!2, E!4), C!2)) | (~((~r2_hidden(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), D!3)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3))))))),
% 0.81/0.76 inference(rewrite,[status(thm)],[])).
% 0.81/0.76 tff(84,plain,
% 0.81/0.76 ((~![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(E, tptp_fun_F_5(E, D!3))))))) | ((~r2_hidden(tptp_fun_E_6(C!2, E!4), C!2)) | (~((~r2_hidden(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), D!3)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3))))))),
% 0.81/0.76 inference(quant_inst,[status(thm)],[])).
% 0.81/0.76 tff(85,plain,
% 0.81/0.76 ((~![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(E, tptp_fun_F_5(E, D!3))))))) | (~r2_hidden(tptp_fun_E_6(C!2, E!4), C!2)) | (~((~r2_hidden(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), D!3)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3)))))),
% 0.81/0.76 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.81/0.76 tff(86,plain,
% 0.81/0.76 (~((~r2_hidden(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), D!3)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3))))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[85, 82, 65])).
% 0.81/0.76 tff(87,plain,
% 0.81/0.76 (((~r2_hidden(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), D!3)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3)))) | r2_hidden(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), D!3)),
% 0.81/0.76 inference(tautology,[status(thm)],[])).
% 0.81/0.76 tff(88,plain,
% 0.81/0.76 (r2_hidden(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), D!3)),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.81/0.76 tff(89,plain,
% 0.81/0.76 (((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, E!4, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, E!4), D)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(D, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, D))))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, E!4, D!3)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D!3, E!4), D!3)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(D!3, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, D!3))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, E!4, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, E!4), D)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(D, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, D))))))) | (~m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, E!4, D!3)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D!3, E!4), D!3)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(D!3, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, D!3))))))),
% 0.81/0.76 inference(rewrite,[status(thm)],[])).
% 0.81/0.76 tff(90,plain,
% 0.81/0.76 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, E!4, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, E!4), D)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(D, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, D))))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, E!4, D!3)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D!3, E!4), D!3)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(D!3, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, D!3))))))),
% 0.81/0.76 inference(quant_inst,[status(thm)],[])).
% 0.81/0.76 tff(91,plain,
% 0.81/0.76 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, E!4, D)) | ![E: $i] : ((~r2_hidden(E, D)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D, E!4), D)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(D, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, D))))))) | (~m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r1_closure3(A!1, B!0, E!4, D!3)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D!3, E!4), D!3)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(D!3, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, D!3)))))),
% 0.81/0.76 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.81/0.76 tff(92,plain,
% 0.81/0.76 (~((~((~r1_closure3(A!1, B!0, E!4, D!3)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D!3, E!4), D!3)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(D!3, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, D!3))))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[91, 48, 70])).
% 0.81/0.76 tff(93,plain,
% 0.81/0.76 (((~((~r1_closure3(A!1, B!0, E!4, D!3)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4)))))))) | (~((~((~r2_hidden(tptp_fun_E_6(D!3, E!4), D!3)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(D!3, E!4), F)))))) | r1_closure3(A!1, B!0, E!4, D!3)))) | ((~r1_closure3(A!1, B!0, E!4, D!3)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4)))))))),
% 0.81/0.76 inference(tautology,[status(thm)],[])).
% 0.81/0.76 tff(94,plain,
% 0.81/0.76 ((~r1_closure3(A!1, B!0, E!4, D!3)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4))))))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.81/0.76 tff(95,plain,
% 0.81/0.76 (r1_closure3(A!1, B!0, E!4, D!3)),
% 0.81/0.76 inference(and_elim,[status(thm)],[61])).
% 0.81/0.76 tff(96,plain,
% 0.81/0.76 ((~((~r1_closure3(A!1, B!0, E!4, D!3)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4)))))))) | (~r1_closure3(A!1, B!0, E!4, D!3)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4))))))),
% 0.81/0.76 inference(tautology,[status(thm)],[])).
% 0.81/0.76 tff(97,plain,
% 0.81/0.76 ((~((~r1_closure3(A!1, B!0, E!4, D!3)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4)))))))) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4))))))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.81/0.76 tff(98,plain,
% 0.81/0.76 (![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4))))))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[97, 94])).
% 0.81/0.76 tff(99,plain,
% 0.81/0.76 (((~![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4))))))) | ((~r2_hidden(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), D!3)) | (~((~r2_hidden(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4))))))) <=> ((~![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4))))))) | (~r2_hidden(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), D!3)) | (~((~r2_hidden(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4))))))),
% 0.81/0.76 inference(rewrite,[status(thm)],[])).
% 0.81/0.76 tff(100,plain,
% 0.81/0.76 ((~![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4))))))) | ((~r2_hidden(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), D!3)) | (~((~r2_hidden(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4))))))),
% 0.81/0.76 inference(quant_inst,[status(thm)],[])).
% 0.81/0.76 tff(101,plain,
% 0.81/0.76 ((~![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(E, tptp_fun_F_5(E, E!4))))))) | (~r2_hidden(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), D!3)) | (~((~r2_hidden(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4)))))),
% 0.81/0.76 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.81/0.76 tff(102,plain,
% 0.81/0.76 (~((~r2_hidden(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4))))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[101, 98, 88])).
% 0.81/0.76 tff(103,plain,
% 0.81/0.76 (((~r2_hidden(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4)))) | r1_tarski(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4))),
% 0.81/0.76 inference(tautology,[status(thm)],[])).
% 0.81/0.76 tff(104,plain,
% 0.81/0.76 (r1_tarski(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.81/0.76 tff(105,plain,
% 0.81/0.76 (((~r2_hidden(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), D!3)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3)))) | r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3))),
% 0.81/0.76 inference(tautology,[status(thm)],[])).
% 0.81/0.76 tff(106,plain,
% 0.81/0.76 (r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[105, 86])).
% 0.81/0.76 tff(107,plain,
% 0.81/0.76 (![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(A, B)) | (~r1_tarski(B, C))) <=> ![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(A, B)) | (~r1_tarski(B, C)))),
% 0.81/0.76 inference(rewrite,[status(thm)],[])).
% 0.81/0.76 tff(108,plain,
% 0.81/0.76 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((r1_tarski(A, B) & r1_tarski(B, C)) <=> (~((~r1_tarski(A, B)) | (~r1_tarski(B, C))))), ((~(r1_tarski(A, B) & r1_tarski(B, C))) <=> (~(~((~r1_tarski(A, B)) | (~r1_tarski(B, C))))))), rewrite((~(~((~r1_tarski(A, B)) | (~r1_tarski(B, C))))) <=> ((~r1_tarski(A, B)) | (~r1_tarski(B, C)))), ((~(r1_tarski(A, B) & r1_tarski(B, C))) <=> ((~r1_tarski(A, B)) | (~r1_tarski(B, C))))), (((~(r1_tarski(A, B) & r1_tarski(B, C))) | r1_tarski(A, C)) <=> (((~r1_tarski(A, B)) | (~r1_tarski(B, C))) | r1_tarski(A, C)))), rewrite((((~r1_tarski(A, B)) | (~r1_tarski(B, C))) | r1_tarski(A, C)) <=> (r1_tarski(A, C) | (~r1_tarski(A, B)) | (~r1_tarski(B, C)))), (((~(r1_tarski(A, B) & r1_tarski(B, C))) | r1_tarski(A, C)) <=> (r1_tarski(A, C) | (~r1_tarski(A, B)) | (~r1_tarski(B, C)))))),
% 0.81/0.76 inference(bind,[status(th)],[])).
% 0.81/0.76 tff(109,plain,
% 0.81/0.76 (![A: $i, B: $i, C: $i] : ((~(r1_tarski(A, B) & r1_tarski(B, C))) | r1_tarski(A, C)) <=> ![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(A, B)) | (~r1_tarski(B, C)))),
% 0.81/0.76 inference(quant_intro,[status(thm)],[108])).
% 0.81/0.76 tff(110,plain,
% 0.81/0.76 (![A: $i, B: $i, C: $i] : ((~(r1_tarski(A, B) & r1_tarski(B, C))) | r1_tarski(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(r1_tarski(A, B) & r1_tarski(B, C))) | r1_tarski(A, C))),
% 0.81/0.76 inference(rewrite,[status(thm)],[])).
% 0.81/0.76 tff(111,plain,
% 0.81/0.76 (^[A: $i, B: $i, C: $i] : rewrite(((r1_tarski(A, B) & r1_tarski(B, C)) => r1_tarski(A, C)) <=> ((~(r1_tarski(A, B) & r1_tarski(B, C))) | r1_tarski(A, C)))),
% 0.81/0.76 inference(bind,[status(th)],[])).
% 0.81/0.76 tff(112,plain,
% 0.81/0.76 (![A: $i, B: $i, C: $i] : ((r1_tarski(A, B) & r1_tarski(B, C)) => r1_tarski(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(r1_tarski(A, B) & r1_tarski(B, C))) | r1_tarski(A, C))),
% 0.81/0.76 inference(quant_intro,[status(thm)],[111])).
% 0.81/0.76 tff(113,axiom,(![A: $i, B: $i, C: $i] : ((r1_tarski(A, B) & r1_tarski(B, C)) => r1_tarski(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_xboole_1')).
% 0.81/0.76 tff(114,plain,
% 0.81/0.76 (![A: $i, B: $i, C: $i] : ((~(r1_tarski(A, B) & r1_tarski(B, C))) | r1_tarski(A, C))),
% 0.81/0.76 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.81/0.76 tff(115,plain,
% 0.81/0.76 (![A: $i, B: $i, C: $i] : ((~(r1_tarski(A, B) & r1_tarski(B, C))) | r1_tarski(A, C))),
% 0.81/0.76 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.81/0.76 tff(116,plain,(
% 0.81/0.76 ![A: $i, B: $i, C: $i] : ((~(r1_tarski(A, B) & r1_tarski(B, C))) | r1_tarski(A, C))),
% 0.81/0.76 inference(skolemize,[status(sab)],[115])).
% 0.81/0.76 tff(117,plain,
% 0.81/0.76 (![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(A, B)) | (~r1_tarski(B, C)))),
% 0.81/0.76 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.81/0.76 tff(118,plain,
% 0.81/0.76 (![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(A, B)) | (~r1_tarski(B, C)))),
% 0.81/0.76 inference(modus_ponens,[status(thm)],[117, 107])).
% 0.81/0.76 tff(119,plain,
% 0.81/0.76 (((~![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(A, B)) | (~r1_tarski(B, C)))) | ((~r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3))) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4))) | r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4)))) <=> ((~![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(A, B)) | (~r1_tarski(B, C)))) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3))) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4))) | r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4)))),
% 0.81/0.76 inference(rewrite,[status(thm)],[])).
% 0.81/0.76 tff(120,plain,
% 0.81/0.76 ((r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3))) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4)))) <=> ((~r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3))) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4))) | r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4)))),
% 0.81/0.76 inference(rewrite,[status(thm)],[])).
% 0.81/0.76 tff(121,plain,
% 0.81/0.76 (((~![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(A, B)) | (~r1_tarski(B, C)))) | (r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3))) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4))))) <=> ((~![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(A, B)) | (~r1_tarski(B, C)))) | ((~r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3))) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4))) | r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4))))),
% 0.81/0.76 inference(monotonicity,[status(thm)],[120])).
% 0.81/0.76 tff(122,plain,
% 0.81/0.76 (((~![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(A, B)) | (~r1_tarski(B, C)))) | (r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3))) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4))))) <=> ((~![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(A, B)) | (~r1_tarski(B, C)))) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3))) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4))) | r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4)))),
% 0.81/0.76 inference(transitivity,[status(thm)],[121, 119])).
% 0.81/0.76 tff(123,plain,
% 0.81/0.76 ((~![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(A, B)) | (~r1_tarski(B, C)))) | (r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3))) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4))))),
% 0.81/0.76 inference(quant_inst,[status(thm)],[])).
% 0.81/0.76 tff(124,plain,
% 0.81/0.76 ((~![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(A, B)) | (~r1_tarski(B, C)))) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3))) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4))) | r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4))),
% 0.81/0.77 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.81/0.77 tff(125,plain,
% 0.81/0.77 (r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4))),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[124, 118, 106, 104])).
% 0.81/0.77 tff(126,plain,
% 0.81/0.77 (((~r2_hidden(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4)))) | r2_hidden(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4), E!4)),
% 0.81/0.77 inference(tautology,[status(thm)],[])).
% 0.81/0.77 tff(127,plain,
% 0.81/0.77 (r2_hidden(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4), E!4)),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[126, 102])).
% 0.81/0.77 tff(128,plain,
% 0.81/0.77 (((~r2_hidden(tptp_fun_E_6(C!2, E!4), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), F))))) | ![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), F)))),
% 0.81/0.77 inference(tautology,[status(thm)],[])).
% 0.81/0.77 tff(129,plain,
% 0.81/0.77 (![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), F)))),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[128, 80])).
% 0.81/0.77 tff(130,plain,
% 0.81/0.77 (((~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), F)))) | ((~r2_hidden(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4), E!4)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4))))) <=> ((~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), F)))) | (~r2_hidden(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4), E!4)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4))))),
% 0.81/0.77 inference(rewrite,[status(thm)],[])).
% 0.81/0.77 tff(131,plain,
% 0.81/0.77 ((~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), F)))) | ((~r2_hidden(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4), E!4)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4))))),
% 0.81/0.77 inference(quant_inst,[status(thm)],[])).
% 0.81/0.77 tff(132,plain,
% 0.81/0.77 ((~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), F)))) | (~r2_hidden(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4), E!4)) | (~r1_tarski(tptp_fun_E_6(C!2, E!4), tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(C!2, E!4), D!3), E!4)))),
% 0.81/0.77 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.81/0.77 tff(133,plain,
% 0.81/0.77 ($false),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[132, 129, 127, 125])).
% 0.81/0.77 % SZS output end Proof
%------------------------------------------------------------------------------