%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG224+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 04:58:46 AM UTC 2025
% Result : Theorem 0.59s 0.77s
% Output : Proof 0.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ALG224+1 : TPTP v9.0.0. Released v3.4.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 10:51:54 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.59/0.77 % SZS status Theorem
% 0.59/0.77 % SZS output start Proof
% 0.59/0.77 tff(r1_tarski_type, type, (
% 0.59/0.77 r1_tarski: ( $i * $i ) > $o)).
% 0.59/0.77 tff(tptp_fun_E_6_type, type, (
% 0.59/0.77 tptp_fun_E_6: ( $i * $i ) > $i)).
% 0.59/0.77 tff(tptp_fun_C_2_type, type, (
% 0.59/0.77 tptp_fun_C_2: $i)).
% 0.59/0.77 tff(tptp_fun_E_4_type, type, (
% 0.59/0.77 tptp_fun_E_4: $i)).
% 0.59/0.77 tff(tptp_fun_F_5_type, type, (
% 0.59/0.77 tptp_fun_F_5: ( $i * $i ) > $i)).
% 0.59/0.77 tff(tptp_fun_D_3_type, type, (
% 0.59/0.77 tptp_fun_D_3: $i)).
% 0.59/0.77 tff(r2_hidden_type, type, (
% 0.59/0.77 r2_hidden: ( $i * $i ) > $o)).
% 0.59/0.77 tff(r2_closure3_type, type, (
% 0.59/0.77 r2_closure3: ( $i * $i * $i * $i ) > $o)).
% 0.59/0.77 tff(tptp_fun_B_0_type, type, (
% 0.59/0.77 tptp_fun_B_0: $i)).
% 0.59/0.77 tff(tptp_fun_A_1_type, type, (
% 0.59/0.77 tptp_fun_A_1: $i)).
% 0.59/0.77 tff(m1_subset_1_type, type, (
% 0.59/0.77 m1_subset_1: ( $i * $i ) > $o)).
% 0.59/0.77 tff(k1_zfmisc_1_type, type, (
% 0.59/0.77 k1_zfmisc_1: $i > $i)).
% 0.59/0.77 tff(k1_closure2_type, type, (
% 0.59/0.77 k1_closure2: ( $i * $i ) > $i)).
% 0.59/0.77 tff(m1_pboole_type, type, (
% 0.59/0.77 m1_pboole: ( $i * $i ) > $o)).
% 0.59/0.77 tff(1,plain,
% 0.59/0.77 (^[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)))) | (~((~((~r2_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C)))))))))))))) <=> ((~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)))) | (~((~((~r2_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C)))))))))))))))),
% 0.59/0.77 inference(bind,[status(th)],[])).
% 0.59/0.77 tff(2,plain,
% 0.59/0.77 (![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)))) | (~((~((~r2_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, 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)))) | (~((~((~r2_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C))))))))))))))),
% 0.59/0.77 inference(quant_intro,[status(thm)],[1])).
% 0.59/0.77 tff(3,plain,
% 0.59/0.77 (^[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)))) | (~((~((~r2_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C)))))))))))))) <=> ((~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)))) | (~((~((~r2_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C)))))))))))))))),
% 0.59/0.77 inference(bind,[status(th)],[])).
% 0.59/0.77 tff(4,plain,
% 0.59/0.77 (![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)))) | (~((~((~r2_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, 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)))) | (~((~((~r2_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C))))))))))))))),
% 0.59/0.77 inference(quant_intro,[status(thm)],[3])).
% 0.59/0.77 tff(5,plain,
% 0.59/0.77 (![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)))) | (~((~((~r2_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, 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)))) | (~((~((~r2_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C))))))))))))))),
% 0.59/0.77 inference(transitivity,[status(thm)],[4, 2])).
% 0.59/0.77 tff(6,plain,
% 0.59/0.77 (^[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)))) | (((~r2_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (r2_hidden(tptp_fun_F_5(E, D), D) & r1_tarski(tptp_fun_F_5(E, D), E)))) & (r2_closure3(A, B, C, D) | (r2_hidden(tptp_fun_E_6(D, C), C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, tptp_fun_E_6(D, C)))))))))) <=> ((~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)))) | (~((~((~r2_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C)))))))))))))))),
% 0.59/0.77 inference(bind,[status(th)],[])).
% 0.59/0.77 tff(7,plain,
% 0.59/0.77 (![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)))) | (((~r2_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (r2_hidden(tptp_fun_F_5(E, D), D) & r1_tarski(tptp_fun_F_5(E, D), E)))) & (r2_closure3(A, B, C, D) | (r2_hidden(tptp_fun_E_6(D, C), C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, tptp_fun_E_6(D, 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)))) | (~((~((~r2_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C))))))))))))))),
% 0.59/0.77 inference(quant_intro,[status(thm)],[6])).
% 0.59/0.77 tff(8,plain,
% 0.59/0.77 (![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)))) | (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E))))))))) <=> ![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)))) | (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E)))))))))),
% 0.59/0.77 inference(rewrite,[status(thm)],[])).
% 0.59/0.77 tff(9,plain,
% 0.59/0.77 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite((r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E)))))) <=> (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E))))))), ((m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B))) => (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E))))))) <=> (m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B))) => (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E))))))))), rewrite((m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B))) => (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E))))))) <=> ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E)))))))), ((m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B))) => (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E))))))) <=> ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E)))))))))), (![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B))) => (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E))))))) <=> ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E))))))))), ((m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B))) => (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E)))))))) <=> (m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B))) => ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E)))))))))), 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)))) | (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E)))))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E))))))))), ((m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B))) => (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E)))))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B)))) | (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E))))))))))), (![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))) => (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E)))))))) <=> ![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)))) | (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E)))))))))), ((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))) => (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E))))))))) <=> (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)))) | (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E))))))))))), 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)))) | (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E))))))))) <=> ((~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)))) | (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E)))))))))), ((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))) => (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E))))))))) <=> ((~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)))) | (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E)))))))))))),
% 0.59/0.77 inference(bind,[status(th)],[])).
% 0.59/0.77 tff(10,plain,
% 0.59/0.77 (![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))) => (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E))))))))) <=> ![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)))) | (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E)))))))))),
% 0.59/0.77 inference(quant_intro,[status(thm)],[9])).
% 0.59/0.77 tff(11,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))) => (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_closure3')).
% 0.59/0.77 tff(12,plain,
% 0.59/0.77 (![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)))) | (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E)))))))))),
% 0.59/0.77 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.59/0.77 tff(13,plain,
% 0.59/0.77 (![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)))) | (r2_closure3(A, B, C, D) <=> ![E: $i] : (~(r2_hidden(E, C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, E)))))))))),
% 0.59/0.77 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.59/0.77 tff(14,plain,(
% 0.59/0.77 ![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)))) | (((~r2_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (r2_hidden(tptp_fun_F_5(E, D), D) & r1_tarski(tptp_fun_F_5(E, D), E)))) & (r2_closure3(A, B, C, D) | (r2_hidden(tptp_fun_E_6(D, C), C) & ![F: $i] : (~(r2_hidden(F, D) & r1_tarski(F, tptp_fun_E_6(D, C))))))))))),
% 0.59/0.77 inference(skolemize,[status(sab)],[13])).
% 0.59/0.77 tff(15,plain,
% 0.59/0.77 (![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)))) | (~((~((~r2_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C))))))))))))))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.59/0.78 tff(16,plain,
% 0.59/0.78 (![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)))) | (~((~((~r2_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C))))))))))))))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.59/0.78 tff(17,plain,
% 0.59/0.78 ((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))) & (~(r2_closure3(A!1, B!0, C!2, E!4) | (~(r2_closure3(A!1, B!0, C!2, D!3) & r2_closure3(A!1, B!0, D!3, E!4))) | (~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))) & (~(r2_closure3(A!1, B!0, C!2, E!4) | (~(r2_closure3(A!1, B!0, C!2, D!3) & r2_closure3(A!1, B!0, D!3, E!4))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))))))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(18,plain,
% 0.59/0.78 ((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))) & (~(r2_closure3(A!1, B!0, C!2, E!4) | (~(r2_closure3(A!1, B!0, C!2, D!3) & r2_closure3(A!1, B!0, D!3, E!4))) | (~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))) & (~(r2_closure3(A!1, B!0, C!2, E!4) | (~(r2_closure3(A!1, B!0, C!2, D!3) & r2_closure3(A!1, B!0, D!3, E!4))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))))))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(19,plain,
% 0.59/0.78 ((~(r2_closure3(A!1, B!0, C!2, E!4) | (~(r2_closure3(A!1, B!0, C!2, D!3) & r2_closure3(A!1, B!0, D!3, E!4))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))))) <=> (~(r2_closure3(A!1, B!0, C!2, E!4) | (~(r2_closure3(A!1, B!0, C!2, D!3) & r2_closure3(A!1, B!0, D!3, E!4))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0))))))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(20,plain,
% 0.59/0.78 ((m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0))) & (~(r2_closure3(A!1, B!0, C!2, E!4) | (~(r2_closure3(A!1, B!0, C!2, D!3) & r2_closure3(A!1, B!0, D!3, E!4))) | (~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))) & (~(r2_closure3(A!1, B!0, C!2, E!4) | (~(r2_closure3(A!1, B!0, C!2, D!3) & r2_closure3(A!1, B!0, D!3, E!4))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))))))),
% 0.59/0.78 inference(monotonicity,[status(thm)],[19])).
% 0.59/0.78 tff(21,plain,
% 0.59/0.78 ((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))) & (~(r2_closure3(A!1, B!0, C!2, E!4) | (~(r2_closure3(A!1, B!0, C!2, D!3) & r2_closure3(A!1, B!0, D!3, E!4))) | (~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))) & (~(r2_closure3(A!1, B!0, C!2, E!4) | (~(r2_closure3(A!1, B!0, C!2, D!3) & r2_closure3(A!1, B!0, D!3, E!4))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0))))))))),
% 0.59/0.78 inference(monotonicity,[status(thm)],[20])).
% 0.59/0.78 tff(22,plain,
% 0.59/0.78 ((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))) & (~(r2_closure3(A!1, B!0, C!2, E!4) | (~(r2_closure3(A!1, B!0, C!2, D!3) & r2_closure3(A!1, B!0, D!3, E!4))) | (~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))) & (~(r2_closure3(A!1, B!0, C!2, E!4) | (~(r2_closure3(A!1, B!0, C!2, D!3) & r2_closure3(A!1, B!0, D!3, E!4))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))))))),
% 0.59/0.78 inference(transitivity,[status(thm)],[21, 18])).
% 0.59/0.78 tff(23,plain,
% 0.59/0.78 ((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))) & (~(r2_closure3(A!1, B!0, C!2, E!4) | (~(r2_closure3(A!1, B!0, C!2, D!3) & r2_closure3(A!1, B!0, D!3, E!4))) | (~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))) & (~(r2_closure3(A!1, B!0, C!2, E!4) | (~(r2_closure3(A!1, B!0, C!2, D!3) & r2_closure3(A!1, B!0, D!3, E!4))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0))))))))),
% 0.59/0.78 inference(monotonicity,[status(thm)],[22])).
% 0.59/0.78 tff(24,plain,
% 0.59/0.78 ((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))) & (~(r2_closure3(A!1, B!0, C!2, E!4) | (~(r2_closure3(A!1, B!0, C!2, D!3) & r2_closure3(A!1, B!0, D!3, E!4))) | (~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))) & (~(r2_closure3(A!1, B!0, C!2, E!4) | (~(r2_closure3(A!1, B!0, C!2, D!3) & r2_closure3(A!1, B!0, D!3, E!4))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))))))),
% 0.59/0.78 inference(transitivity,[status(thm)],[23, 17])).
% 0.59/0.78 tff(25,plain,
% 0.59/0.78 ((~![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] : (r2_closure3(A, B, C, E) | (~(r2_closure3(A, B, C, D) & r2_closure3(A, B, D, E))) | (~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] : (r2_closure3(A, B, C, E) | (~(r2_closure3(A, B, C, D) & r2_closure3(A, B, D, E))) | (~m1_subset_1(E, k1_zfmisc_1(k1_closure2(A, B)))))))))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(26,plain,
% 0.59/0.78 ((~![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))) => ((r2_closure3(A, B, C, D) & r2_closure3(A, B, D, E)) => r2_closure3(A, B, C, E))))))) <=> (~![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] : (r2_closure3(A, B, C, E) | (~(r2_closure3(A, B, C, D) & r2_closure3(A, B, D, E))) | (~m1_subset_1(E, k1_zfmisc_1(k1_closure2(A, B)))))))))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(27,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))) => ((r2_closure3(A, B, C, D) & r2_closure3(A, B, D, E)) => r2_closure3(A, B, C, E))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t5_closure3')).
% 0.59/0.78 tff(28,plain,
% 0.59/0.78 (~![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] : (r2_closure3(A, B, C, E) | (~(r2_closure3(A, B, C, D) & r2_closure3(A, B, D, E))) | (~m1_subset_1(E, k1_zfmisc_1(k1_closure2(A, B))))))))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.59/0.78 tff(29,plain,
% 0.59/0.78 (~![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] : (r2_closure3(A, B, C, E) | (~(r2_closure3(A, B, C, D) & r2_closure3(A, B, D, E))) | (~m1_subset_1(E, k1_zfmisc_1(k1_closure2(A, B))))))))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.59/0.78 tff(30,plain,
% 0.59/0.78 (~![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] : (r2_closure3(A, B, C, E) | (~(r2_closure3(A, B, C, D) & r2_closure3(A, B, D, E))) | (~m1_subset_1(E, k1_zfmisc_1(k1_closure2(A, B))))))))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.59/0.78 tff(31,plain,
% 0.59/0.78 (~![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] : (r2_closure3(A, B, C, E) | (~(r2_closure3(A, B, C, D) & r2_closure3(A, B, D, E))) | (~m1_subset_1(E, k1_zfmisc_1(k1_closure2(A, B))))))))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[30, 25])).
% 0.59/0.78 tff(32,plain,
% 0.59/0.78 (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))) & (~(r2_closure3(A!1, B!0, C!2, E!4) | (~(r2_closure3(A!1, B!0, C!2, D!3) & r2_closure3(A!1, B!0, D!3, E!4))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0))))))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.59/0.78 tff(33,plain,
% 0.59/0.78 (m1_pboole(B!0, A!1)),
% 0.59/0.78 inference(and_elim,[status(thm)],[32])).
% 0.59/0.78 tff(34,plain,
% 0.59/0.78 (((~![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)))) | (~((~((~r2_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C))))))))))))))) | ((~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)))) | (~((~((~r2_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, 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)))) | (~((~((~r2_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C))))))))))))))) | (~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)))) | (~((~((~r2_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C))))))))))))))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(35,plain,
% 0.59/0.78 ((~![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)))) | (~((~((~r2_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C))))))))))))))) | ((~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)))) | (~((~((~r2_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C))))))))))))))),
% 0.59/0.78 inference(quant_inst,[status(thm)],[])).
% 0.59/0.78 tff(36,plain,
% 0.59/0.78 ((~![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)))) | (~((~((~r2_closure3(A, B, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A, B, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C))))))))))))))) | (~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)))) | (~((~((~r2_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C)))))))))))))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.59/0.78 tff(37,plain,
% 0.59/0.78 (![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)))) | (~((~((~r2_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C)))))))))))))),
% 0.59/0.78 inference(unit_resolution,[status(thm)],[36, 33, 16])).
% 0.59/0.78 tff(38,plain,
% 0.59/0.78 (m1_subset_1(C!2, k1_zfmisc_1(k1_closure2(A!1, B!0)))),
% 0.59/0.78 inference(and_elim,[status(thm)],[32])).
% 0.59/0.78 tff(39,plain,
% 0.59/0.78 (((~![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)))) | (~((~((~r2_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C)))))))))))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, C!2, D)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, C!2, D) | (~((~r2_hidden(tptp_fun_E_6(D, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C!2)))))))))))))) <=> ((~![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)))) | (~((~((~r2_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C)))))))))))))) | (~m1_subset_1(C!2, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, C!2, D)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, C!2, D) | (~((~r2_hidden(tptp_fun_E_6(D, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C!2)))))))))))))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(40,plain,
% 0.59/0.78 ((~![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)))) | (~((~((~r2_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C)))))))))))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, C!2, D)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, C!2, D) | (~((~r2_hidden(tptp_fun_E_6(D, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C!2)))))))))))))),
% 0.59/0.78 inference(quant_inst,[status(thm)],[])).
% 0.59/0.78 tff(41,plain,
% 0.59/0.78 ((~![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)))) | (~((~((~r2_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C)))))))))))))) | (~m1_subset_1(C!2, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, C!2, D)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, C!2, D) | (~((~r2_hidden(tptp_fun_E_6(D, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C!2))))))))))))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.59/0.78 tff(42,plain,
% 0.59/0.78 (![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, C!2, D)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, C!2, D) | (~((~r2_hidden(tptp_fun_E_6(D, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C!2))))))))))))),
% 0.59/0.78 inference(unit_resolution,[status(thm)],[41, 38, 37])).
% 0.59/0.78 tff(43,plain,
% 0.59/0.78 (~(r2_closure3(A!1, B!0, C!2, E!4) | (~(r2_closure3(A!1, B!0, C!2, D!3) & r2_closure3(A!1, B!0, D!3, E!4))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))))),
% 0.59/0.78 inference(and_elim,[status(thm)],[32])).
% 0.59/0.78 tff(44,plain,
% 0.59/0.78 (m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))),
% 0.59/0.78 inference(or_elim,[status(thm)],[43])).
% 0.59/0.78 tff(45,plain,
% 0.59/0.78 (((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, C!2, D)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, C!2, D) | (~((~r2_hidden(tptp_fun_E_6(D, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C!2))))))))))))) | ((~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, C!2, E!4)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(E, E!4), E))))))) | (~(r2_closure3(A!1, B!0, C!2, E!4) | (~((~r2_hidden(tptp_fun_E_6(E!4, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(F, tptp_fun_E_6(E!4, C!2))))))))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, C!2, D)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, C!2, D) | (~((~r2_hidden(tptp_fun_E_6(D, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C!2))))))))))))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, C!2, E!4)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(E, E!4), E))))))) | (~(r2_closure3(A!1, B!0, C!2, E!4) | (~((~r2_hidden(tptp_fun_E_6(E!4, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(F, tptp_fun_E_6(E!4, C!2))))))))))))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(46,plain,
% 0.59/0.79 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, C!2, D)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, C!2, D) | (~((~r2_hidden(tptp_fun_E_6(D, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C!2))))))))))))) | ((~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, C!2, E!4)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(E, E!4), E))))))) | (~(r2_closure3(A!1, B!0, C!2, E!4) | (~((~r2_hidden(tptp_fun_E_6(E!4, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(F, tptp_fun_E_6(E!4, C!2))))))))))))),
% 0.59/0.79 inference(quant_inst,[status(thm)],[])).
% 0.59/0.79 tff(47,plain,
% 0.59/0.79 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, C!2, D)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, C!2, D) | (~((~r2_hidden(tptp_fun_E_6(D, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C!2))))))))))))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, C!2, E!4)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(E, E!4), E))))))) | (~(r2_closure3(A!1, B!0, C!2, E!4) | (~((~r2_hidden(tptp_fun_E_6(E!4, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(F, tptp_fun_E_6(E!4, C!2)))))))))))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.59/0.79 tff(48,plain,
% 0.59/0.79 (~((~((~r2_closure3(A!1, B!0, C!2, E!4)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(E, E!4), E))))))) | (~(r2_closure3(A!1, B!0, C!2, E!4) | (~((~r2_hidden(tptp_fun_E_6(E!4, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(F, tptp_fun_E_6(E!4, C!2))))))))))),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[47, 44, 42])).
% 0.59/0.79 tff(49,plain,
% 0.59/0.79 (((~((~r2_closure3(A!1, B!0, C!2, E!4)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(E, E!4), E))))))) | (~(r2_closure3(A!1, B!0, C!2, E!4) | (~((~r2_hidden(tptp_fun_E_6(E!4, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(F, tptp_fun_E_6(E!4, C!2)))))))))) | (r2_closure3(A!1, B!0, C!2, E!4) | (~((~r2_hidden(tptp_fun_E_6(E!4, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(F, tptp_fun_E_6(E!4, C!2))))))))),
% 0.59/0.79 inference(tautology,[status(thm)],[])).
% 0.59/0.79 tff(50,plain,
% 0.59/0.79 (r2_closure3(A!1, B!0, C!2, E!4) | (~((~r2_hidden(tptp_fun_E_6(E!4, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(F, tptp_fun_E_6(E!4, C!2)))))))),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.59/0.79 tff(51,plain,
% 0.59/0.79 (~r2_closure3(A!1, B!0, C!2, E!4)),
% 0.59/0.79 inference(or_elim,[status(thm)],[43])).
% 0.59/0.79 tff(52,plain,
% 0.59/0.79 ((~(r2_closure3(A!1, B!0, C!2, E!4) | (~((~r2_hidden(tptp_fun_E_6(E!4, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(F, tptp_fun_E_6(E!4, C!2))))))))) | r2_closure3(A!1, B!0, C!2, E!4) | (~((~r2_hidden(tptp_fun_E_6(E!4, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(F, tptp_fun_E_6(E!4, C!2)))))))),
% 0.59/0.79 inference(tautology,[status(thm)],[])).
% 0.59/0.79 tff(53,plain,
% 0.59/0.79 ((~(r2_closure3(A!1, B!0, C!2, E!4) | (~((~r2_hidden(tptp_fun_E_6(E!4, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(F, tptp_fun_E_6(E!4, C!2))))))))) | (~((~r2_hidden(tptp_fun_E_6(E!4, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(F, tptp_fun_E_6(E!4, C!2)))))))),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.59/0.79 tff(54,plain,
% 0.59/0.79 (~((~r2_hidden(tptp_fun_E_6(E!4, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(F, tptp_fun_E_6(E!4, C!2))))))),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[53, 50])).
% 0.59/0.79 tff(55,plain,
% 0.59/0.79 (((~r2_hidden(tptp_fun_E_6(E!4, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(F, tptp_fun_E_6(E!4, C!2)))))) | r2_hidden(tptp_fun_E_6(E!4, C!2), C!2)),
% 0.59/0.79 inference(tautology,[status(thm)],[])).
% 0.59/0.79 tff(56,plain,
% 0.59/0.79 (r2_hidden(tptp_fun_E_6(E!4, C!2), C!2)),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.59/0.79 tff(57,plain,
% 0.59/0.79 (m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0)))),
% 0.59/0.79 inference(and_elim,[status(thm)],[32])).
% 0.59/0.79 tff(58,plain,
% 0.59/0.79 (((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, C!2, D)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, C!2, D) | (~((~r2_hidden(tptp_fun_E_6(D, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C!2))))))))))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, C!2, D!3)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(tptp_fun_F_5(E, D!3), E))))))) | (~(r2_closure3(A!1, B!0, C!2, D!3) | (~((~r2_hidden(tptp_fun_E_6(D!3, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, D!3)) | (~r1_tarski(F, tptp_fun_E_6(D!3, C!2))))))))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, C!2, D)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, C!2, D) | (~((~r2_hidden(tptp_fun_E_6(D, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C!2))))))))))))) | (~m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, C!2, D!3)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(tptp_fun_F_5(E, D!3), E))))))) | (~(r2_closure3(A!1, B!0, C!2, D!3) | (~((~r2_hidden(tptp_fun_E_6(D!3, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, D!3)) | (~r1_tarski(F, tptp_fun_E_6(D!3, C!2))))))))))))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(59,plain,
% 0.59/0.79 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, C!2, D)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, C!2, D) | (~((~r2_hidden(tptp_fun_E_6(D, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C!2))))))))))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, C!2, D!3)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(tptp_fun_F_5(E, D!3), E))))))) | (~(r2_closure3(A!1, B!0, C!2, D!3) | (~((~r2_hidden(tptp_fun_E_6(D!3, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, D!3)) | (~r1_tarski(F, tptp_fun_E_6(D!3, C!2))))))))))))),
% 0.59/0.79 inference(quant_inst,[status(thm)],[])).
% 0.59/0.79 tff(60,plain,
% 0.59/0.79 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, C!2, D)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, C!2, D) | (~((~r2_hidden(tptp_fun_E_6(D, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C!2))))))))))))) | (~m1_subset_1(D!3, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, C!2, D!3)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(tptp_fun_F_5(E, D!3), E))))))) | (~(r2_closure3(A!1, B!0, C!2, D!3) | (~((~r2_hidden(tptp_fun_E_6(D!3, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, D!3)) | (~r1_tarski(F, tptp_fun_E_6(D!3, C!2)))))))))))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.59/0.79 tff(61,plain,
% 0.59/0.79 (~((~((~r2_closure3(A!1, B!0, C!2, D!3)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(tptp_fun_F_5(E, D!3), E))))))) | (~(r2_closure3(A!1, B!0, C!2, D!3) | (~((~r2_hidden(tptp_fun_E_6(D!3, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, D!3)) | (~r1_tarski(F, tptp_fun_E_6(D!3, C!2))))))))))),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[60, 57, 42])).
% 0.59/0.79 tff(62,plain,
% 0.59/0.79 (((~((~r2_closure3(A!1, B!0, C!2, D!3)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(tptp_fun_F_5(E, D!3), E))))))) | (~(r2_closure3(A!1, B!0, C!2, D!3) | (~((~r2_hidden(tptp_fun_E_6(D!3, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, D!3)) | (~r1_tarski(F, tptp_fun_E_6(D!3, C!2)))))))))) | ((~r2_closure3(A!1, B!0, C!2, D!3)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(tptp_fun_F_5(E, D!3), E))))))),
% 0.59/0.79 inference(tautology,[status(thm)],[])).
% 0.59/0.79 tff(63,plain,
% 0.59/0.79 ((~r2_closure3(A!1, B!0, C!2, D!3)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(tptp_fun_F_5(E, D!3), E)))))),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.59/0.79 tff(64,plain,
% 0.59/0.79 (r2_closure3(A!1, B!0, C!2, D!3) & r2_closure3(A!1, B!0, D!3, E!4)),
% 0.59/0.79 inference(or_elim,[status(thm)],[43])).
% 0.59/0.79 tff(65,plain,
% 0.59/0.79 (r2_closure3(A!1, B!0, C!2, D!3)),
% 0.59/0.79 inference(and_elim,[status(thm)],[64])).
% 0.59/0.79 tff(66,plain,
% 0.59/0.79 ((~((~r2_closure3(A!1, B!0, C!2, D!3)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(tptp_fun_F_5(E, D!3), E))))))) | (~r2_closure3(A!1, B!0, C!2, D!3)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(tptp_fun_F_5(E, D!3), E)))))),
% 0.59/0.79 inference(tautology,[status(thm)],[])).
% 0.59/0.79 tff(67,plain,
% 0.59/0.79 ((~((~r2_closure3(A!1, B!0, C!2, D!3)) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(tptp_fun_F_5(E, D!3), E))))))) | ![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(tptp_fun_F_5(E, D!3), E)))))),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.59/0.79 tff(68,plain,
% 0.59/0.79 (![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(tptp_fun_F_5(E, D!3), E)))))),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[67, 63])).
% 0.59/0.79 tff(69,plain,
% 0.59/0.79 (((~![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(tptp_fun_F_5(E, D!3), E)))))) | ((~r2_hidden(tptp_fun_E_6(E!4, C!2), C!2)) | (~((~r2_hidden(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), D!3)) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), tptp_fun_E_6(E!4, C!2))))))) <=> ((~![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(tptp_fun_F_5(E, D!3), E)))))) | (~r2_hidden(tptp_fun_E_6(E!4, C!2), C!2)) | (~((~r2_hidden(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), D!3)) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), tptp_fun_E_6(E!4, C!2))))))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(70,plain,
% 0.59/0.79 ((~![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(tptp_fun_F_5(E, D!3), E)))))) | ((~r2_hidden(tptp_fun_E_6(E!4, C!2), C!2)) | (~((~r2_hidden(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), D!3)) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), tptp_fun_E_6(E!4, C!2))))))),
% 0.59/0.79 inference(quant_inst,[status(thm)],[])).
% 0.59/0.79 tff(71,plain,
% 0.59/0.79 ((~![E: $i] : ((~r2_hidden(E, C!2)) | (~((~r2_hidden(tptp_fun_F_5(E, D!3), D!3)) | (~r1_tarski(tptp_fun_F_5(E, D!3), E)))))) | (~r2_hidden(tptp_fun_E_6(E!4, C!2), C!2)) | (~((~r2_hidden(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), D!3)) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), tptp_fun_E_6(E!4, C!2)))))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.59/0.79 tff(72,plain,
% 0.59/0.79 (~((~r2_hidden(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), D!3)) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), tptp_fun_E_6(E!4, C!2))))),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[71, 68, 56])).
% 0.59/0.79 tff(73,plain,
% 0.59/0.79 (((~r2_hidden(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), D!3)) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), tptp_fun_E_6(E!4, C!2)))) | r2_hidden(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), D!3)),
% 0.59/0.79 inference(tautology,[status(thm)],[])).
% 0.59/0.79 tff(74,plain,
% 0.59/0.79 (r2_hidden(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), D!3)),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.59/0.79 tff(75,plain,
% 0.59/0.79 (((~![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)))) | (~((~((~r2_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C)))))))))))))) | ((~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)))) | (~((~((~r2_closure3(A!1, B!0, D!3, D)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, D!3, D) | (~((~r2_hidden(tptp_fun_E_6(D, D!3), D!3)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, D!3)))))))))))))) <=> ((~![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)))) | (~((~((~r2_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C)))))))))))))) | (~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)))) | (~((~((~r2_closure3(A!1, B!0, D!3, D)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, D!3, D) | (~((~r2_hidden(tptp_fun_E_6(D, D!3), D!3)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, D!3)))))))))))))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(76,plain,
% 0.59/0.79 ((~![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)))) | (~((~((~r2_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C)))))))))))))) | ((~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)))) | (~((~((~r2_closure3(A!1, B!0, D!3, D)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, D!3, D) | (~((~r2_hidden(tptp_fun_E_6(D, D!3), D!3)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, D!3)))))))))))))),
% 0.59/0.79 inference(quant_inst,[status(thm)],[])).
% 0.59/0.79 tff(77,plain,
% 0.59/0.79 ((~![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)))) | (~((~((~r2_closure3(A!1, B!0, C, D)) | ![E: $i] : ((~r2_hidden(E, C)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, C, D) | (~((~r2_hidden(tptp_fun_E_6(D, C), C)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, C)))))))))))))) | (~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)))) | (~((~((~r2_closure3(A!1, B!0, D!3, D)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, D!3, D) | (~((~r2_hidden(tptp_fun_E_6(D, D!3), D!3)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, D!3))))))))))))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.59/0.79 tff(78,plain,
% 0.59/0.79 (![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, D!3, D)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, D!3, D) | (~((~r2_hidden(tptp_fun_E_6(D, D!3), D!3)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, D!3))))))))))))),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[77, 57, 37])).
% 0.59/0.79 tff(79,plain,
% 0.59/0.79 (((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, D!3, D)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, D!3, D) | (~((~r2_hidden(tptp_fun_E_6(D, D!3), D!3)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, D!3))))))))))))) | ((~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, D!3, E!4)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(E, E!4), E))))))) | (~(r2_closure3(A!1, B!0, D!3, E!4) | (~((~r2_hidden(tptp_fun_E_6(E!4, D!3), D!3)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(F, tptp_fun_E_6(E!4, D!3))))))))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, D!3, D)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, D!3, D) | (~((~r2_hidden(tptp_fun_E_6(D, D!3), D!3)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, D!3))))))))))))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, D!3, E!4)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(E, E!4), E))))))) | (~(r2_closure3(A!1, B!0, D!3, E!4) | (~((~r2_hidden(tptp_fun_E_6(E!4, D!3), D!3)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(F, tptp_fun_E_6(E!4, D!3))))))))))))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(80,plain,
% 0.59/0.79 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, D!3, D)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, D!3, D) | (~((~r2_hidden(tptp_fun_E_6(D, D!3), D!3)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, D!3))))))))))))) | ((~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, D!3, E!4)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(E, E!4), E))))))) | (~(r2_closure3(A!1, B!0, D!3, E!4) | (~((~r2_hidden(tptp_fun_E_6(E!4, D!3), D!3)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(F, tptp_fun_E_6(E!4, D!3))))))))))))),
% 0.59/0.79 inference(quant_inst,[status(thm)],[])).
% 0.59/0.79 tff(81,plain,
% 0.59/0.79 ((~![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, D!3, D)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, D), D)) | (~r1_tarski(tptp_fun_F_5(E, D), E))))))) | (~(r2_closure3(A!1, B!0, D!3, D) | (~((~r2_hidden(tptp_fun_E_6(D, D!3), D!3)) | (~![F: $i] : ((~r2_hidden(F, D)) | (~r1_tarski(F, tptp_fun_E_6(D, D!3))))))))))))) | (~m1_subset_1(E!4, k1_zfmisc_1(k1_closure2(A!1, B!0)))) | (~((~((~r2_closure3(A!1, B!0, D!3, E!4)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(E, E!4), E))))))) | (~(r2_closure3(A!1, B!0, D!3, E!4) | (~((~r2_hidden(tptp_fun_E_6(E!4, D!3), D!3)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(F, tptp_fun_E_6(E!4, D!3)))))))))))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.59/0.79 tff(82,plain,
% 0.59/0.79 (~((~((~r2_closure3(A!1, B!0, D!3, E!4)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(E, E!4), E))))))) | (~(r2_closure3(A!1, B!0, D!3, E!4) | (~((~r2_hidden(tptp_fun_E_6(E!4, D!3), D!3)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(F, tptp_fun_E_6(E!4, D!3))))))))))),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[81, 44, 78])).
% 0.59/0.79 tff(83,plain,
% 0.59/0.79 (((~((~r2_closure3(A!1, B!0, D!3, E!4)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(E, E!4), E))))))) | (~(r2_closure3(A!1, B!0, D!3, E!4) | (~((~r2_hidden(tptp_fun_E_6(E!4, D!3), D!3)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(F, tptp_fun_E_6(E!4, D!3)))))))))) | ((~r2_closure3(A!1, B!0, D!3, E!4)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(E, E!4), E))))))),
% 0.59/0.80 inference(tautology,[status(thm)],[])).
% 0.59/0.80 tff(84,plain,
% 0.59/0.80 ((~r2_closure3(A!1, B!0, D!3, E!4)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(E, E!4), E)))))),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.59/0.80 tff(85,plain,
% 0.59/0.80 (r2_closure3(A!1, B!0, D!3, E!4)),
% 0.59/0.80 inference(and_elim,[status(thm)],[64])).
% 0.59/0.80 tff(86,plain,
% 0.59/0.80 ((~((~r2_closure3(A!1, B!0, D!3, E!4)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(E, E!4), E))))))) | (~r2_closure3(A!1, B!0, D!3, E!4)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(E, E!4), E)))))),
% 0.59/0.80 inference(tautology,[status(thm)],[])).
% 0.59/0.80 tff(87,plain,
% 0.59/0.80 ((~((~r2_closure3(A!1, B!0, D!3, E!4)) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(E, E!4), E))))))) | ![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(E, E!4), E)))))),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.59/0.80 tff(88,plain,
% 0.59/0.80 (![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(E, E!4), E)))))),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[87, 84])).
% 0.59/0.80 tff(89,plain,
% 0.59/0.80 (((~![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(E, E!4), E)))))) | ((~r2_hidden(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), D!3)) | (~((~r2_hidden(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3))))))) <=> ((~![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(E, E!4), E)))))) | (~r2_hidden(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), D!3)) | (~((~r2_hidden(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3))))))),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(90,plain,
% 0.59/0.80 ((~![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(E, E!4), E)))))) | ((~r2_hidden(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), D!3)) | (~((~r2_hidden(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3))))))),
% 0.59/0.80 inference(quant_inst,[status(thm)],[])).
% 0.59/0.80 tff(91,plain,
% 0.59/0.80 ((~![E: $i] : ((~r2_hidden(E, D!3)) | (~((~r2_hidden(tptp_fun_F_5(E, E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(E, E!4), E)))))) | (~r2_hidden(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), D!3)) | (~((~r2_hidden(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3)))))),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.59/0.80 tff(92,plain,
% 0.59/0.80 (~((~r2_hidden(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3))))),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[91, 88, 74])).
% 0.59/0.80 tff(93,plain,
% 0.59/0.80 (((~r2_hidden(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3)))) | r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3))),
% 0.59/0.80 inference(tautology,[status(thm)],[])).
% 0.59/0.80 tff(94,plain,
% 0.59/0.80 (r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3))),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.59/0.80 tff(95,plain,
% 0.59/0.80 (((~r2_hidden(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), D!3)) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), tptp_fun_E_6(E!4, C!2)))) | r1_tarski(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), tptp_fun_E_6(E!4, C!2))),
% 0.59/0.80 inference(tautology,[status(thm)],[])).
% 0.59/0.80 tff(96,plain,
% 0.59/0.80 (r1_tarski(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), tptp_fun_E_6(E!4, C!2))),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[95, 72])).
% 0.59/0.80 tff(97,plain,
% 0.59/0.80 (![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)))),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(98,plain,
% 0.59/0.80 (^[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)))))),
% 0.59/0.80 inference(bind,[status(th)],[])).
% 0.59/0.80 tff(99,plain,
% 0.59/0.80 (![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)))),
% 0.59/0.80 inference(quant_intro,[status(thm)],[98])).
% 0.59/0.80 tff(100,plain,
% 0.59/0.80 (![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))),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(101,plain,
% 0.59/0.80 (^[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)))),
% 0.59/0.80 inference(bind,[status(th)],[])).
% 0.59/0.80 tff(102,plain,
% 0.59/0.80 (![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))),
% 0.59/0.80 inference(quant_intro,[status(thm)],[101])).
% 0.59/0.80 tff(103,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')).
% 0.59/0.80 tff(104,plain,
% 0.59/0.80 (![A: $i, B: $i, C: $i] : ((~(r1_tarski(A, B) & r1_tarski(B, C))) | r1_tarski(A, C))),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.59/0.80 tff(105,plain,
% 0.59/0.80 (![A: $i, B: $i, C: $i] : ((~(r1_tarski(A, B) & r1_tarski(B, C))) | r1_tarski(A, C))),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.59/0.80 tff(106,plain,(
% 0.59/0.80 ![A: $i, B: $i, C: $i] : ((~(r1_tarski(A, B) & r1_tarski(B, C))) | r1_tarski(A, C))),
% 0.59/0.80 inference(skolemize,[status(sab)],[105])).
% 0.59/0.80 tff(107,plain,
% 0.59/0.80 (![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(A, B)) | (~r1_tarski(B, C)))),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.59/0.80 tff(108,plain,
% 0.59/0.80 (![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(A, B)) | (~r1_tarski(B, C)))),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[107, 97])).
% 0.59/0.80 tff(109,plain,
% 0.59/0.80 (((~![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(A, B)) | (~r1_tarski(B, C)))) | ((~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), tptp_fun_E_6(E!4, C!2))) | (~r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3))) | r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_E_6(E!4, C!2)))) <=> ((~![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(A, B)) | (~r1_tarski(B, C)))) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), tptp_fun_E_6(E!4, C!2))) | (~r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3))) | r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_E_6(E!4, C!2)))),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(110,plain,
% 0.59/0.80 ((r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_E_6(E!4, C!2)) | (~r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3))) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), tptp_fun_E_6(E!4, C!2)))) <=> ((~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), tptp_fun_E_6(E!4, C!2))) | (~r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3))) | r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_E_6(E!4, C!2)))),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(111,plain,
% 0.59/0.80 (((~![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(A, B)) | (~r1_tarski(B, C)))) | (r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_E_6(E!4, C!2)) | (~r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3))) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), tptp_fun_E_6(E!4, C!2))))) <=> ((~![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(A, B)) | (~r1_tarski(B, C)))) | ((~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), tptp_fun_E_6(E!4, C!2))) | (~r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3))) | r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_E_6(E!4, C!2))))),
% 0.59/0.80 inference(monotonicity,[status(thm)],[110])).
% 0.59/0.80 tff(112,plain,
% 0.59/0.80 (((~![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(A, B)) | (~r1_tarski(B, C)))) | (r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_E_6(E!4, C!2)) | (~r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3))) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), tptp_fun_E_6(E!4, C!2))))) <=> ((~![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(A, B)) | (~r1_tarski(B, C)))) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), tptp_fun_E_6(E!4, C!2))) | (~r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3))) | r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_E_6(E!4, C!2)))),
% 0.59/0.80 inference(transitivity,[status(thm)],[111, 109])).
% 0.59/0.80 tff(113,plain,
% 0.59/0.80 ((~![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(A, B)) | (~r1_tarski(B, C)))) | (r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_E_6(E!4, C!2)) | (~r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3))) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), tptp_fun_E_6(E!4, C!2))))),
% 0.59/0.80 inference(quant_inst,[status(thm)],[])).
% 0.59/0.80 tff(114,plain,
% 0.59/0.80 ((~![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(A, B)) | (~r1_tarski(B, C)))) | (~r1_tarski(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), tptp_fun_E_6(E!4, C!2))) | (~r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3))) | r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_E_6(E!4, C!2))),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.59/0.80 tff(115,plain,
% 0.59/0.80 (r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_E_6(E!4, C!2))),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[114, 108, 96, 94])).
% 0.59/0.80 tff(116,plain,
% 0.59/0.80 (((~r2_hidden(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3)))) | r2_hidden(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), E!4)),
% 0.59/0.80 inference(tautology,[status(thm)],[])).
% 0.59/0.80 tff(117,plain,
% 0.59/0.80 (r2_hidden(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), E!4)),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[116, 92])).
% 0.59/0.80 tff(118,plain,
% 0.59/0.80 (((~r2_hidden(tptp_fun_E_6(E!4, C!2), C!2)) | (~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(F, tptp_fun_E_6(E!4, C!2)))))) | ![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(F, tptp_fun_E_6(E!4, C!2))))),
% 0.59/0.80 inference(tautology,[status(thm)],[])).
% 0.59/0.80 tff(119,plain,
% 0.59/0.80 (![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(F, tptp_fun_E_6(E!4, C!2))))),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[118, 54])).
% 0.59/0.80 tff(120,plain,
% 0.59/0.80 (((~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(F, tptp_fun_E_6(E!4, C!2))))) | ((~r2_hidden(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_E_6(E!4, C!2))))) <=> ((~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(F, tptp_fun_E_6(E!4, C!2))))) | (~r2_hidden(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_E_6(E!4, C!2))))),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(121,plain,
% 0.59/0.80 ((~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(F, tptp_fun_E_6(E!4, C!2))))) | ((~r2_hidden(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_E_6(E!4, C!2))))),
% 0.59/0.80 inference(quant_inst,[status(thm)],[])).
% 0.59/0.80 tff(122,plain,
% 0.59/0.80 ((~![F: $i] : ((~r2_hidden(F, E!4)) | (~r1_tarski(F, tptp_fun_E_6(E!4, C!2))))) | (~r2_hidden(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), E!4)) | (~r1_tarski(tptp_fun_F_5(tptp_fun_F_5(tptp_fun_E_6(E!4, C!2), D!3), E!4), tptp_fun_E_6(E!4, C!2)))),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.59/0.80 tff(123,plain,
% 0.59/0.80 ($false),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[122, 119, 117, 115])).
% 0.59/0.80 % SZS output end Proof
% 0.59/0.81 % E exiting
%------------------------------------------------------------------------------