0.00/0.07 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.08 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.rpNi3nTvJK 0.07/0.27 % Computer : n011.cluster.edu 0.07/0.27 % Model : x86_64 x86_64 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.07/0.27 % Memory : 8042.1875MB 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64 0.07/0.27 % CPULimit : 960 0.07/0.27 % DateTime : Thu Jul 2 08:40:16 EDT 2020 0.07/0.27 % CPUTime : 0.07/0.27 % Running portfolio for 120 s 0.07/0.27 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.07/0.27 % Number of cores: 8 0.07/0.28 % Python version: Python 3.6.8 0.07/0.28 % Running in HO mode 0.13/0.52 % Estimated wc time : 1286 0.13/0.52 % Estimated cpu time (7 cpus) : 183.71428571428572 1.01/0.63 % /export/starexec/sandbox2/solver/bin/lams/s6.sh running for 21s 1.09/0.63 % /export/starexec/sandbox2/solver/bin/lams/new_b3.2.norw.sh running for 15s 1.09/0.64 % /export/starexec/sandbox2/solver/bin/lams/b.rpo.sh running for 21s 1.09/0.64 % /export/starexec/sandbox2/solver/bin/lams/s6.ds.sh running for 10s 1.09/0.67 % /export/starexec/sandbox2/solver/bin/lams/c.s.2.sh running for 68s 1.09/0.67 % /export/starexec/sandbox2/solver/bin/lams/c.easy.sh running for 26s 1.09/0.69 % /export/starexec/sandbox2/solver/bin/lams/old_b3.avatar.sh running for 15s 69.39/10.51 % /export/starexec/sandbox2/solver/bin/lams/old_sp2.sh running for 17s 105.68/15.80 % /export/starexec/sandbox2/solver/bin/lams/b.sh running for 31s 105.68/15.83 % /export/starexec/sandbox2/solver/bin/lams/sh1.sh running for 26s 144.62/21.59 % /export/starexec/sandbox2/solver/bin/lams/b.lsimp.sh running for 17s 146.33/21.81 % /export/starexec/sandbox2/solver/bin/lams/b.split.sh running for 31s 179.31/26.56 % /export/starexec/sandbox2/solver/bin/lams/s4.sh running for 15s 186.11/27.59 % /export/starexec/sandbox2/solver/bin/lams/b.rw.sh running for 26s 186.55/27.76 % /export/starexec/sandbox2/solver/bin/lams/c_ic.sh running for 42s 262.65/38.68 % /export/starexec/sandbox2/solver/bin/lams/s1.f.sh running for 15s 281.38/41.41 % /export/starexec/sandbox2/solver/bin/lams/c.preprocess2.sh running for 21s 317.10/46.64 % /export/starexec/sandbox2/solver/bin/lams/sh.or.sh running for 26s 358.82/52.65 % /export/starexec/sandbox2/solver/bin/lams/new.cs3.comb.sh running for 18s 364.57/53.45 % /export/starexec/sandbox2/solver/bin/lams/old_b2.sh running for 31s 365.00/53.58 % /export/starexec/sandbox2/solver/bin/lams/sp5.sh running for 36s 426.95/62.59 % /export/starexec/sandbox2/solver/bin/lams/b2.sh running for 15s 469.45/68.67 % /export/starexec/sandbox2/solver/bin/lams/b.lcnf.od.sh running for 26s 477.40/69.78 % /export/starexec/sandbox2/solver/bin/lams/c.s.sh running for 36s 481.91/70.46 % /export/starexec/sandbox2/solver/bin/lams/b3.sh running for 26s 497.22/72.75 % /export/starexec/sandbox2/solver/bin/lams/cmb.lcnf.sh running for 10s 529.74/77.52 % /export/starexec/sandbox2/solver/bin/lams/sh.eqenc.sh running for 17s 535.87/78.32 % Solved by lams/sh.eqenc.sh. 535.87/78.32 % done 2565 iterations in 0.738s 535.87/78.32 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 535.87/78.32 % SZS output start Refutation 535.87/78.32 tff(cSIX_THEOREM_pme, conjecture, 535.87/78.32 (![R:(($i * $i) > $o),A,B,C,D,E,F]: 535.87/78.32 (((![Xx,Xy]: (R(Xx,Xy) => R(Xy,Xx))) & (A != B) & (A != D) & (A != F) & 535.87/78.32 (B != C) & (B != E) & (C != F) & (E != F) & (D != F) & (D != E) & 535.87/78.32 (C != E) & (C != D) & (B != F) & (B != D) & (A != E) & (A != C)) => 535.87/78.32 (?[Xa,Xb,Xc]: 535.87/78.32 ((Xa != Xb) & (Xa != Xc) & (Xb != Xc) & 535.87/78.32 ((R(Xa,Xc) & R(Xb,Xc) & R(Xa,Xb)) | 535.87/78.32 ((~R(Xa,Xb)) & (~R(Xb,Xc)) & (~R(Xa,Xc))))))))). 535.87/78.32 tff(zf_stmt_0, negated_conjecture, 535.87/78.32 (~ 535.87/78.32 (![R:(($i * $i) > $o),A,B,C,D,E,F]: 535.87/78.32 (((![Xx,Xy]: (R(Xx,Xy) => R(Xy,Xx))) & (A != B) & (A != D) & 535.87/78.32 (A != F) & (B != C) & (B != E) & (C != F) & (E != F) & (D != F) & 535.87/78.32 (D != E) & (C != E) & (C != D) & (B != F) & (B != D) & (A != E) & 535.87/78.32 (A != C)) => 535.87/78.32 (?[Xa,Xb,Xc]: 535.87/78.32 ((Xa != Xb) & (Xa != Xc) & (Xb != Xc) & 535.87/78.32 ((R(Xa,Xc) & R(Xb,Xc) & R(Xa,Xb)) | 535.87/78.32 ((~R(Xa,Xb)) & (~R(Xb,Xc)) & (~R(Xa,Xc)))))))))). 535.87/78.32 tff(zf_stmt_1, negated_conjecture, (sk_B != sk_F)).tff(zf_stmt_1, negated_conjecture, 535.87/78.32 (sk_D != sk_F)). 535.87/78.32 tff(zf_stmt_1, negated_conjecture, (sk_E != sk_F)).tff(zf_stmt_1, negated_conjecture, 535.87/78.32 (sk_C != sk_F)). 535.87/78.32 tff(zf_stmt_1, negated_conjecture, (sk_A != sk_F)).tff(zf_stmt_1, negated_conjecture, 535.87/78.32 (sk_R(Xy,Xx) 535.87/78.32 ~ sk_R(Xx,Xy))). 535.87/78.32 tff(zf_stmt_1, negated_conjecture, (sk_A != sk_B)).tff(zf_stmt_1, negated_conjecture, 535.87/78.32 (sk_A != sk_D)). 535.87/78.32 tff(zf_stmt_1, negated_conjecture, (sk_B != sk_C)).tff(zf_stmt_1, negated_conjecture, 535.87/78.32 (sk_B != sk_E)). 535.87/78.32 tff(zf_stmt_1, negated_conjecture, (sk_D != sk_E)).tff(zf_stmt_1, negated_conjecture, 535.87/78.32 (sk_C != sk_E)). 535.87/78.32 tff(zf_stmt_1, negated_conjecture, (sk_C != sk_D)).tff(zf_stmt_1, negated_conjecture, 535.87/78.32 (sk_B != sk_D)). 535.87/78.32 tff(zf_stmt_1, negated_conjecture, (sk_A != sk_E)).tff(zf_stmt_1, negated_conjecture, 535.87/78.32 (sk_A != sk_C)). 535.87/78.32 tff(zf_stmt_1, negated_conjecture, 535.87/78.32 (Xa = Xb sk_R(Xa,Xc) sk_R(Xb,Xc) sk_R(Xa,Xb) Xb = Xc 535.87/78.32 Xa = Xc)).tff(zf_stmt_1, negated_conjecture, 535.87/78.32 (Xa = Xb ~ sk_R(Xa,Xb) ~ sk_R(Xb,Xc) 535.87/78.32 ~ sk_R(Xa,Xc) Xb = Xc Xa = Xc)). 535.87/78.32 tff('0', plain, 535.87/78.32 ![X5, X6, X7]: 535.87/78.32 ( '$_eq_proxy'($i, X5, X6) 535.87/78.32 | sk_R(X5, X7) 535.87/78.32 | sk_R(X6, X7) 535.87/78.32 | sk_R(X5, X6) 535.87/78.32 | '$_eq_proxy'($i, X6, X7) 535.87/78.32 | '$_eq_proxy'($i, X5, X7)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('1', plain, ~ '$_eq_proxy'($i, sk_A, sk_E), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('2', plain, 535.87/78.32 ![X0]: 535.87/78.32 ( '$_eq_proxy'($i, sk_A, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0) 535.87/78.32 | sk_R(sk_A, sk_E) 535.87/78.32 | sk_R(sk_E, X0) 535.87/78.32 | sk_R(sk_A, X0)), 535.87/78.32 inference('sup-', [status(thm)], ['0', '1'])). 535.87/78.32 tff('3', plain, ( sk_R(sk_A, sk_E)) <= (( sk_R(sk_A, sk_E))), 535.87/78.32 inference('split', [status(esa)], ['2'])). 535.87/78.32 tff('4', plain, 535.87/78.32 ![X5, X6, X7]: 535.87/78.32 ( '$_eq_proxy'($i, X5, X6) 535.87/78.32 | sk_R(X5, X7) 535.87/78.32 | sk_R(X6, X7) 535.87/78.32 | sk_R(X5, X6) 535.87/78.32 | '$_eq_proxy'($i, X6, X7) 535.87/78.32 | '$_eq_proxy'($i, X5, X7)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('5', plain, ~ '$_eq_proxy'($i, sk_A, sk_D), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('6', plain, 535.87/78.32 ![X0]: 535.87/78.32 ( '$_eq_proxy'($i, sk_A, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_D, X0) 535.87/78.32 | sk_R(sk_A, sk_D) 535.87/78.32 | sk_R(sk_D, X0) 535.87/78.32 | sk_R(sk_A, X0)), 535.87/78.32 inference('sup-', [status(thm)], ['4', '5'])). 535.87/78.32 tff('7', plain, ( sk_R(sk_A, sk_D)) <= (( sk_R(sk_A, sk_D))), 535.87/78.32 inference('split', [status(esa)], ['6'])). 535.87/78.32 tff('8', plain, 535.87/78.32 ![X5, X6, X7]: 535.87/78.32 ( '$_eq_proxy'($i, X5, X6) 535.87/78.32 | ~ sk_R(X5, X6) 535.87/78.32 | ~ sk_R(X6, X7) 535.87/78.32 | ~ sk_R(X5, X7) 535.87/78.32 | '$_eq_proxy'($i, X6, X7) 535.87/78.32 | '$_eq_proxy'($i, X5, X7)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('9', plain, 535.87/78.32 (![X0]: 535.87/78.32 ( '$_eq_proxy'($i, sk_A, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_D, X0) 535.87/78.32 | ~ sk_R(sk_A, X0) 535.87/78.32 | ~ sk_R(sk_D, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_A, sk_D))) 535.87/78.32 <= (( sk_R(sk_A, sk_D))), 535.87/78.32 inference('sup-', [status(thm)], ['7', '8'])). 535.87/78.32 tff('10', plain, 535.87/78.32 (![X0]: 535.87/78.32 (~ sk_R(sk_A, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.32 | ~ sk_R(sk_D, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_D, X0))) 535.87/78.32 <= ((![X0]: 535.87/78.32 (~ sk_R(sk_A, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.32 | ~ sk_R(sk_D, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_D, X0)))), 535.87/78.32 inference('split', [status(esa)], ['9'])). 535.87/78.32 tff('11', plain, 535.87/78.32 (( '$_eq_proxy'($i, sk_D, sk_E) 535.87/78.32 | ~ sk_R(sk_D, sk_E) 535.87/78.32 | '$_eq_proxy'($i, sk_A, sk_E))) 535.87/78.32 <= (( sk_R(sk_A, sk_E)) & 535.87/78.32 (![X0]: 535.87/78.32 (~ sk_R(sk_A, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.32 | ~ sk_R(sk_D, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_D, X0)))), 535.87/78.32 inference('sup-', [status(thm)], ['3', '10'])). 535.87/78.32 tff('12', plain, 535.87/78.32 ( '$_eq_proxy'($i, sk_D, sk_E)) | ( '$_eq_proxy'($i, sk_A, sk_E)) | 535.87/78.32 ~ ( sk_R(sk_A, sk_E)) | ~ ( sk_R(sk_D, sk_E)) | 535.87/78.32 ~ 535.87/78.32 (![X0]: 535.87/78.32 (~ sk_R(sk_A, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.32 | ~ sk_R(sk_D, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_D, X0))), 535.87/78.32 inference('split', [status(esa)], ['11'])). 535.87/78.32 tff('13', plain, 535.87/78.32 ![X5, X6, X7]: 535.87/78.32 ( '$_eq_proxy'($i, X5, X6) 535.87/78.32 | sk_R(X5, X7) 535.87/78.32 | sk_R(X6, X7) 535.87/78.32 | sk_R(X5, X6) 535.87/78.32 | '$_eq_proxy'($i, X6, X7) 535.87/78.32 | '$_eq_proxy'($i, X5, X7)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('14', plain, ~ '$_eq_proxy'($i, sk_B, sk_F), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('15', plain, 535.87/78.32 ![X0]: 535.87/78.32 ( '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_F, X0) 535.87/78.32 | sk_R(sk_B, sk_F) 535.87/78.32 | sk_R(sk_F, X0) 535.87/78.32 | sk_R(sk_B, X0)), 535.87/78.32 inference('sup-', [status(thm)], ['13', '14'])). 535.87/78.32 tff('16', plain, ( sk_R(sk_B, sk_F)) <= (( sk_R(sk_B, sk_F))), 535.87/78.32 inference('split', [status(esa)], ['15'])). 535.87/78.32 tff('17', plain, 535.87/78.32 ![X5, X6, X7]: 535.87/78.32 ( '$_eq_proxy'($i, X5, X6) 535.87/78.32 | sk_R(X5, X7) 535.87/78.32 | sk_R(X6, X7) 535.87/78.32 | sk_R(X5, X6) 535.87/78.32 | '$_eq_proxy'($i, X6, X7) 535.87/78.32 | '$_eq_proxy'($i, X5, X7)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('18', plain, ~ '$_eq_proxy'($i, sk_B, sk_E), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('19', plain, 535.87/78.32 ![X0]: 535.87/78.32 ( '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0) 535.87/78.32 | sk_R(sk_B, sk_E) 535.87/78.32 | sk_R(sk_E, X0) 535.87/78.32 | sk_R(sk_B, X0)), 535.87/78.32 inference('sup-', [status(thm)], ['17', '18'])). 535.87/78.32 tff('20', plain, ( sk_R(sk_B, sk_E)) <= (( sk_R(sk_B, sk_E))), 535.87/78.32 inference('split', [status(esa)], ['19'])). 535.87/78.32 tff('21', plain, 535.87/78.32 ![X5, X6, X7]: 535.87/78.32 ( '$_eq_proxy'($i, X5, X6) 535.87/78.32 | ~ sk_R(X5, X6) 535.87/78.32 | ~ sk_R(X6, X7) 535.87/78.32 | ~ sk_R(X5, X7) 535.87/78.32 | '$_eq_proxy'($i, X6, X7) 535.87/78.32 | '$_eq_proxy'($i, X5, X7)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('22', plain, 535.87/78.32 (![X0]: 535.87/78.32 ( '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0) 535.87/78.32 | ~ sk_R(sk_B, X0) 535.87/78.32 | ~ sk_R(sk_E, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, sk_E))) 535.87/78.32 <= (( sk_R(sk_B, sk_E))), 535.87/78.32 inference('sup-', [status(thm)], ['20', '21'])). 535.87/78.32 tff('23', plain, 535.87/78.32 (![X0]: 535.87/78.32 (~ sk_R(sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | ~ sk_R(sk_E, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0))) 535.87/78.32 <= ((![X0]: 535.87/78.32 (~ sk_R(sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | ~ sk_R(sk_E, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0)))), 535.87/78.32 inference('split', [status(esa)], ['22'])). 535.87/78.32 tff('24', plain, 535.87/78.32 (( '$_eq_proxy'($i, sk_E, sk_F) 535.87/78.32 | ~ sk_R(sk_E, sk_F) 535.87/78.32 | '$_eq_proxy'($i, sk_B, sk_F))) 535.87/78.32 <= (( sk_R(sk_B, sk_F)) & 535.87/78.32 (![X0]: 535.87/78.32 (~ sk_R(sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | ~ sk_R(sk_E, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0)))), 535.87/78.32 inference('sup-', [status(thm)], ['16', '23'])). 535.87/78.32 tff('25', plain, 535.87/78.32 ( '$_eq_proxy'($i, sk_E, sk_F)) | ( '$_eq_proxy'($i, sk_B, sk_F)) | 535.87/78.32 ~ ( sk_R(sk_B, sk_F)) | ~ ( sk_R(sk_E, sk_F)) | 535.87/78.32 ~ 535.87/78.32 (![X0]: 535.87/78.32 (~ sk_R(sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | ~ sk_R(sk_E, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0))), 535.87/78.32 inference('split', [status(esa)], ['24'])). 535.87/78.32 tff('26', plain, 535.87/78.32 ![X5, X6, X7]: 535.87/78.32 ( '$_eq_proxy'($i, X5, X6) 535.87/78.32 | sk_R(X5, X7) 535.87/78.32 | sk_R(X6, X7) 535.87/78.32 | sk_R(X5, X6) 535.87/78.32 | '$_eq_proxy'($i, X6, X7) 535.87/78.32 | '$_eq_proxy'($i, X5, X7)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('27', plain, ~ '$_eq_proxy'($i, sk_C, sk_E), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('28', plain, 535.87/78.32 ![X0]: 535.87/78.32 ( '$_eq_proxy'($i, X0, sk_E) 535.87/78.32 | sk_R(X0, sk_C) 535.87/78.32 | sk_R(sk_C, sk_E) 535.87/78.32 | sk_R(X0, sk_E) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_C)), 535.87/78.32 inference('sup-', [status(thm)], ['26', '27'])). 535.87/78.32 tff('29', plain, 535.87/78.32 (![X0]: 535.87/78.32 ( sk_R(X0, sk_C) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_C) 535.87/78.32 | sk_R(X0, sk_E) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_E))) 535.87/78.32 <= ((![X0]: 535.87/78.32 ( sk_R(X0, sk_C) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_C) 535.87/78.32 | sk_R(X0, sk_E) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_E)))), 535.87/78.32 inference('split', [status(esa)], ['28'])). 535.87/78.32 tff('30', plain, ~ '$_eq_proxy'($i, sk_B, sk_E), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('31', plain, 535.87/78.32 (( sk_R(sk_B, sk_E) | '$_eq_proxy'($i, sk_B, sk_C) | sk_R(sk_B, sk_C))) 535.87/78.32 <= ((![X0]: 535.87/78.32 ( sk_R(X0, sk_C) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_C) 535.87/78.32 | sk_R(X0, sk_E) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_E)))), 535.87/78.32 inference('sup-', [status(thm)], ['29', '30'])). 535.87/78.32 tff('32', plain, 535.87/78.32 ( sk_R(sk_B, sk_C)) | ( sk_R(sk_B, sk_E)) | 535.87/78.32 ~ 535.87/78.32 (![X0]: 535.87/78.32 ( sk_R(X0, sk_C) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_C) 535.87/78.32 | sk_R(X0, sk_E) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_E))) | 535.87/78.32 ( '$_eq_proxy'($i, sk_B, sk_C)), 535.87/78.32 inference('split', [status(esa)], ['31'])). 535.87/78.32 tff('33', plain, 535.87/78.32 (![X0]: 535.87/78.32 ( sk_R(X0, sk_C) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_C) 535.87/78.32 | sk_R(X0, sk_E) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_E))) | 535.87/78.32 ( sk_R(sk_C, sk_E)), inference('split', [status(esa)], ['28'])). 535.87/78.32 tff('34', plain, 535.87/78.32 ![X5, X6, X7]: 535.87/78.32 ( '$_eq_proxy'($i, X5, X6) 535.87/78.32 | sk_R(X5, X7) 535.87/78.32 | sk_R(X6, X7) 535.87/78.32 | sk_R(X5, X6) 535.87/78.32 | '$_eq_proxy'($i, X6, X7) 535.87/78.32 | '$_eq_proxy'($i, X5, X7)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('35', plain, 535.87/78.32 ![X0 : $tType, X1 : X0, X2 : X0]: 535.87/78.32 (~ '$_eq_proxy'(X0, X1, X2) | '$_eq_proxy'(X0, X2, X1)), 535.87/78.32 trivial([status(thm)])). 535.87/78.32 tff('36', plain, 535.87/78.32 ![X0, X1, X2]: 535.87/78.32 ( '$_eq_proxy'($i, X1, X2) 535.87/78.32 | '$_eq_proxy'($i, X0, X2) 535.87/78.32 | sk_R(X1, X0) 535.87/78.32 | sk_R(X0, X2) 535.87/78.32 | sk_R(X1, X2) 535.87/78.32 | '$_eq_proxy'($i, X0, X1)), 535.87/78.32 inference('sup-', [status(thm)], ['34', '35'])). 535.87/78.32 tff('37', plain, ~ '$_eq_proxy'($i, sk_C, sk_E), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('38', plain, 535.87/78.32 ![X0]: 535.87/78.32 ( sk_R(sk_E, X0) 535.87/78.32 | sk_R(sk_C, X0) 535.87/78.32 | sk_R(sk_E, sk_C) 535.87/78.32 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0)), 535.87/78.32 inference('sup-', [status(thm)], ['36', '37'])). 535.87/78.32 tff('39', plain, ( sk_R(sk_E, sk_C)) <= (( sk_R(sk_E, sk_C))), 535.87/78.32 inference('split', [status(esa)], ['38'])). 535.87/78.32 tff('40', plain, 535.87/78.32 ![X5, X6, X7]: 535.87/78.32 ( '$_eq_proxy'($i, X5, X6) 535.87/78.32 | ~ sk_R(X5, X6) 535.87/78.32 | ~ sk_R(X6, X7) 535.87/78.32 | ~ sk_R(X5, X7) 535.87/78.32 | '$_eq_proxy'($i, X6, X7) 535.87/78.32 | '$_eq_proxy'($i, X5, X7)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('41', plain, 535.87/78.32 (![X0]: 535.87/78.32 ( '$_eq_proxy'($i, sk_E, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.32 | ~ sk_R(sk_E, X0) 535.87/78.32 | ~ sk_R(sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, sk_C))) 535.87/78.32 <= (( sk_R(sk_E, sk_C))), 535.87/78.32 inference('sup-', [status(thm)], ['39', '40'])). 535.87/78.32 tff('42', plain, 535.87/78.32 ( '$_eq_proxy'($i, sk_E, sk_C)) <= (( '$_eq_proxy'($i, sk_E, sk_C))), 535.87/78.32 inference('split', [status(esa)], ['41'])). 535.87/78.32 tff('43', plain, 535.87/78.32 ![X0 : $tType, X1 : X0, X2 : X0]: 535.87/78.32 (~ '$_eq_proxy'(X0, X1, X2) | '$_eq_proxy'(X0, X2, X1)), 535.87/78.32 trivial([status(thm)])). 535.87/78.32 tff('44', plain, 535.87/78.32 ( '$_eq_proxy'($i, sk_C, sk_E)) <= (( '$_eq_proxy'($i, sk_E, sk_C))), 535.87/78.32 inference('sup-', [status(thm)], ['42', '43'])). 535.87/78.32 tff('45', plain, ~ '$_eq_proxy'($i, sk_C, sk_E), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('46', plain, ~ ( '$_eq_proxy'($i, sk_E, sk_C)), 535.87/78.32 inference('sup-', [status(thm)], ['44', '45'])). 535.87/78.32 tff('47', plain, 535.87/78.32 ![X5, X6, X7]: 535.87/78.32 ( '$_eq_proxy'($i, X5, X6) 535.87/78.32 | sk_R(X5, X7) 535.87/78.32 | sk_R(X6, X7) 535.87/78.32 | sk_R(X5, X6) 535.87/78.32 | '$_eq_proxy'($i, X6, X7) 535.87/78.32 | '$_eq_proxy'($i, X5, X7)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('48', plain, ~ '$_eq_proxy'($i, sk_B, sk_D), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('49', plain, 535.87/78.32 ![X0]: 535.87/78.32 ( '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_D, X0) 535.87/78.32 | sk_R(sk_B, sk_D) 535.87/78.32 | sk_R(sk_D, X0) 535.87/78.32 | sk_R(sk_B, X0)), 535.87/78.32 inference('sup-', [status(thm)], ['47', '48'])). 535.87/78.32 tff('50', plain, ( sk_R(sk_B, sk_D)) <= (( sk_R(sk_B, sk_D))), 535.87/78.32 inference('split', [status(esa)], ['49'])). 535.87/78.32 tff('51', plain, ( sk_R(sk_B, sk_F)) <= (( sk_R(sk_B, sk_F))), 535.87/78.32 inference('split', [status(esa)], ['15'])). 535.87/78.32 tff('52', plain, 535.87/78.32 ![X5, X6, X7]: 535.87/78.32 ( '$_eq_proxy'($i, X5, X6) 535.87/78.32 | ~ sk_R(X5, X6) 535.87/78.32 | ~ sk_R(X6, X7) 535.87/78.32 | ~ sk_R(X5, X7) 535.87/78.32 | '$_eq_proxy'($i, X6, X7) 535.87/78.32 | '$_eq_proxy'($i, X5, X7)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('53', plain, 535.87/78.32 (![X0]: 535.87/78.32 ( '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_F, X0) 535.87/78.32 | ~ sk_R(sk_B, X0) 535.87/78.32 | ~ sk_R(sk_F, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, sk_F))) 535.87/78.32 <= (( sk_R(sk_B, sk_F))), 535.87/78.32 inference('sup-', [status(thm)], ['51', '52'])). 535.87/78.32 tff('54', plain, 535.87/78.32 (![X0]: 535.87/78.32 (~ sk_R(sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | ~ sk_R(sk_F, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_F, X0))) 535.87/78.32 <= ((![X0]: 535.87/78.32 (~ sk_R(sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | ~ sk_R(sk_F, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_F, X0)))), 535.87/78.32 inference('split', [status(esa)], ['53'])). 535.87/78.32 tff('55', plain, 535.87/78.32 (( '$_eq_proxy'($i, sk_F, sk_D) 535.87/78.32 | ~ sk_R(sk_F, sk_D) 535.87/78.32 | '$_eq_proxy'($i, sk_B, sk_D))) 535.87/78.32 <= (( sk_R(sk_B, sk_D)) & 535.87/78.32 (![X0]: 535.87/78.32 (~ sk_R(sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | ~ sk_R(sk_F, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_F, X0)))), 535.87/78.32 inference('sup-', [status(thm)], ['50', '54'])). 535.87/78.32 tff('56', plain, 535.87/78.32 ( '$_eq_proxy'($i, sk_F, sk_D)) | ( '$_eq_proxy'($i, sk_B, sk_D)) | 535.87/78.32 ~ ( sk_R(sk_B, sk_D)) | ~ ( sk_R(sk_F, sk_D)) | 535.87/78.32 ~ 535.87/78.32 (![X0]: 535.87/78.32 (~ sk_R(sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | ~ sk_R(sk_F, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_F, X0))), 535.87/78.32 inference('split', [status(esa)], ['55'])). 535.87/78.32 tff('57', plain, 535.87/78.32 ![X0, X1, X2]: 535.87/78.32 ( '$_eq_proxy'($i, X1, X2) 535.87/78.32 | '$_eq_proxy'($i, X0, X2) 535.87/78.32 | sk_R(X1, X0) 535.87/78.32 | sk_R(X0, X2) 535.87/78.32 | sk_R(X1, X2) 535.87/78.32 | '$_eq_proxy'($i, X0, X1)), 535.87/78.32 inference('sup-', [status(thm)], ['34', '35'])). 535.87/78.32 tff('58', plain, ~ '$_eq_proxy'($i, sk_C, sk_F), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('59', plain, 535.87/78.32 ![X0]: 535.87/78.32 ( '$_eq_proxy'($i, X0, sk_C) 535.87/78.32 | sk_R(sk_C, sk_F) 535.87/78.32 | sk_R(X0, sk_F) 535.87/78.32 | sk_R(sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_F)), 535.87/78.32 inference('sup-', [status(thm)], ['57', '58'])). 535.87/78.32 tff('60', plain, 535.87/78.32 (![X0]: 535.87/78.32 ( sk_R(sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_C) 535.87/78.32 | sk_R(X0, sk_F) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_F))) 535.87/78.32 <= ((![X0]: 535.87/78.32 ( sk_R(sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_C) 535.87/78.32 | sk_R(X0, sk_F) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.32 inference('split', [status(esa)], ['59'])). 535.87/78.32 tff('61', plain, ~ '$_eq_proxy'($i, sk_D, sk_F), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('62', plain, 535.87/78.32 (( sk_R(sk_D, sk_F) | '$_eq_proxy'($i, sk_D, sk_C) | sk_R(sk_C, sk_D))) 535.87/78.32 <= ((![X0]: 535.87/78.32 ( sk_R(sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_C) 535.87/78.32 | sk_R(X0, sk_F) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.32 inference('sup-', [status(thm)], ['60', '61'])). 535.87/78.32 tff('63', plain, 535.87/78.32 ( sk_R(sk_D, sk_F)) | ( sk_R(sk_C, sk_D)) | 535.87/78.32 ( '$_eq_proxy'($i, sk_D, sk_C)) | 535.87/78.32 ~ 535.87/78.32 (![X0]: 535.87/78.32 ( sk_R(sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_C) 535.87/78.32 | sk_R(X0, sk_F) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_F))), 535.87/78.32 inference('split', [status(esa)], ['62'])). 535.87/78.32 tff('64', plain, 535.87/78.32 (![X0]: 535.87/78.32 ( sk_R(sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_C) 535.87/78.32 | sk_R(X0, sk_F) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_F))) | 535.87/78.32 ( sk_R(sk_C, sk_F)), inference('split', [status(esa)], ['59'])). 535.87/78.32 tff('65', plain, ( sk_R(sk_E, sk_C)) <= (( sk_R(sk_E, sk_C))), 535.87/78.32 inference('split', [status(esa)], ['38'])). 535.87/78.32 tff('66', plain, ![X3, X4]: ( sk_R(X3, X4) | ~ sk_R(X4, X3)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('67', plain, ( sk_R(sk_C, sk_E)) <= (( sk_R(sk_E, sk_C))), 535.87/78.32 inference('sup-', [status(thm)], ['65', '66'])). 535.87/78.32 tff('68', plain, 535.87/78.32 ![X5, X6, X7]: 535.87/78.32 ( '$_eq_proxy'($i, X5, X6) 535.87/78.32 | sk_R(X5, X7) 535.87/78.32 | sk_R(X6, X7) 535.87/78.32 | sk_R(X5, X6) 535.87/78.32 | '$_eq_proxy'($i, X6, X7) 535.87/78.32 | '$_eq_proxy'($i, X5, X7)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('69', plain, ~ '$_eq_proxy'($i, sk_C, sk_D), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('70', plain, 535.87/78.32 ![X0]: 535.87/78.32 ( '$_eq_proxy'($i, sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_D, X0) 535.87/78.32 | sk_R(sk_C, sk_D) 535.87/78.32 | sk_R(sk_D, X0) 535.87/78.32 | sk_R(sk_C, X0)), 535.87/78.32 inference('sup-', [status(thm)], ['68', '69'])). 535.87/78.32 tff('71', plain, ( sk_R(sk_C, sk_D)) <= (( sk_R(sk_C, sk_D))), 535.87/78.32 inference('split', [status(esa)], ['70'])). 535.87/78.32 tff('72', plain, 535.87/78.32 ![X5, X6, X7]: 535.87/78.32 ( '$_eq_proxy'($i, X5, X6) 535.87/78.32 | ~ sk_R(X5, X6) 535.87/78.32 | ~ sk_R(X6, X7) 535.87/78.32 | ~ sk_R(X5, X7) 535.87/78.32 | '$_eq_proxy'($i, X6, X7) 535.87/78.32 | '$_eq_proxy'($i, X5, X7)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('73', plain, 535.87/78.32 (![X0]: 535.87/78.32 ( '$_eq_proxy'($i, sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_D, X0) 535.87/78.32 | ~ sk_R(sk_C, X0) 535.87/78.32 | ~ sk_R(sk_D, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_C, sk_D))) 535.87/78.32 <= (( sk_R(sk_C, sk_D))), 535.87/78.32 inference('sup-', [status(thm)], ['71', '72'])). 535.87/78.32 tff('74', plain, 535.87/78.32 (![X0]: 535.87/78.32 (~ sk_R(sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.32 | ~ sk_R(sk_D, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_D, X0))) 535.87/78.32 <= ((![X0]: 535.87/78.32 (~ sk_R(sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.32 | ~ sk_R(sk_D, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_D, X0)))), 535.87/78.32 inference('split', [status(esa)], ['73'])). 535.87/78.32 tff('75', plain, 535.87/78.32 (( '$_eq_proxy'($i, sk_D, sk_E) 535.87/78.32 | ~ sk_R(sk_D, sk_E) 535.87/78.32 | '$_eq_proxy'($i, sk_C, sk_E))) 535.87/78.32 <= (( sk_R(sk_E, sk_C)) & 535.87/78.32 (![X0]: 535.87/78.32 (~ sk_R(sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.32 | ~ sk_R(sk_D, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_D, X0)))), 535.87/78.32 inference('sup-', [status(thm)], ['67', '74'])). 535.87/78.32 tff('76', plain, 535.87/78.32 ( '$_eq_proxy'($i, sk_D, sk_E)) | ( '$_eq_proxy'($i, sk_C, sk_E)) | 535.87/78.32 ~ ( sk_R(sk_D, sk_E)) | ~ ( sk_R(sk_E, sk_C)) | 535.87/78.32 ~ 535.87/78.32 (![X0]: 535.87/78.32 (~ sk_R(sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.32 | ~ sk_R(sk_D, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_D, X0))), 535.87/78.32 inference('split', [status(esa)], ['75'])). 535.87/78.32 tff('77', plain, 535.87/78.32 ![X5, X6, X7]: 535.87/78.32 ( '$_eq_proxy'($i, X5, X6) 535.87/78.32 | sk_R(X5, X7) 535.87/78.32 | sk_R(X6, X7) 535.87/78.32 | sk_R(X5, X6) 535.87/78.32 | '$_eq_proxy'($i, X6, X7) 535.87/78.32 | '$_eq_proxy'($i, X5, X7)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('78', plain, ~ '$_eq_proxy'($i, sk_A, sk_E), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('79', plain, 535.87/78.32 ![X0]: 535.87/78.32 ( '$_eq_proxy'($i, X0, sk_E) 535.87/78.32 | sk_R(sk_A, X0) 535.87/78.32 | sk_R(X0, sk_E) 535.87/78.32 | sk_R(sk_A, sk_E) 535.87/78.32 | '$_eq_proxy'($i, sk_A, X0)), 535.87/78.32 inference('sup-', [status(thm)], ['77', '78'])). 535.87/78.32 tff('80', plain, 535.87/78.32 (![X0]: 535.87/78.32 ( sk_R(sk_A, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.32 | sk_R(X0, sk_E) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_E))) 535.87/78.32 <= ((![X0]: 535.87/78.32 ( sk_R(sk_A, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.32 | sk_R(X0, sk_E) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_E)))), 535.87/78.32 inference('split', [status(esa)], ['79'])). 535.87/78.32 tff('81', plain, ~ '$_eq_proxy'($i, sk_D, sk_E), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('82', plain, 535.87/78.32 (( sk_R(sk_D, sk_E) | '$_eq_proxy'($i, sk_A, sk_D) | sk_R(sk_A, sk_D))) 535.87/78.32 <= ((![X0]: 535.87/78.32 ( sk_R(sk_A, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.32 | sk_R(X0, sk_E) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_E)))), 535.87/78.32 inference('sup-', [status(thm)], ['80', '81'])). 535.87/78.32 tff('83', plain, 535.87/78.32 ( '$_eq_proxy'($i, sk_A, sk_D)) | ( sk_R(sk_D, sk_E)) | 535.87/78.32 ( sk_R(sk_A, sk_D)) | 535.87/78.32 ~ 535.87/78.32 (![X0]: 535.87/78.32 ( sk_R(sk_A, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.32 | sk_R(X0, sk_E) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_E))), 535.87/78.32 inference('split', [status(esa)], ['82'])). 535.87/78.32 tff('84', plain, 535.87/78.32 ![X5, X6, X7]: 535.87/78.32 ( '$_eq_proxy'($i, X5, X6) 535.87/78.32 | sk_R(X5, X7) 535.87/78.32 | sk_R(X6, X7) 535.87/78.32 | sk_R(X5, X6) 535.87/78.32 | '$_eq_proxy'($i, X6, X7) 535.87/78.32 | '$_eq_proxy'($i, X5, X7)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('85', plain, ~ '$_eq_proxy'($i, sk_C, sk_F), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('86', plain, 535.87/78.32 ![X0]: 535.87/78.32 ( '$_eq_proxy'($i, X0, sk_F) 535.87/78.32 | sk_R(X0, sk_C) 535.87/78.32 | sk_R(sk_C, sk_F) 535.87/78.32 | sk_R(X0, sk_F) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_C)), 535.87/78.32 inference('sup-', [status(thm)], ['84', '85'])). 535.87/78.32 tff('87', plain, 535.87/78.32 (![X0]: 535.87/78.32 ( sk_R(X0, sk_C) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_C) 535.87/78.32 | sk_R(X0, sk_F) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_F))) 535.87/78.32 <= ((![X0]: 535.87/78.32 ( sk_R(X0, sk_C) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_C) 535.87/78.32 | sk_R(X0, sk_F) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.32 inference('split', [status(esa)], ['86'])). 535.87/78.32 tff('88', plain, ~ '$_eq_proxy'($i, sk_B, sk_F), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('89', plain, 535.87/78.32 (( sk_R(sk_B, sk_F) | '$_eq_proxy'($i, sk_B, sk_C) | sk_R(sk_B, sk_C))) 535.87/78.32 <= ((![X0]: 535.87/78.32 ( sk_R(X0, sk_C) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_C) 535.87/78.32 | sk_R(X0, sk_F) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.32 inference('sup-', [status(thm)], ['87', '88'])). 535.87/78.32 tff('90', plain, 535.87/78.32 ( sk_R(sk_B, sk_C)) | ( sk_R(sk_B, sk_F)) | 535.87/78.32 ~ 535.87/78.32 (![X0]: 535.87/78.32 ( sk_R(X0, sk_C) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_C) 535.87/78.32 | sk_R(X0, sk_F) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_F))) | 535.87/78.32 ( '$_eq_proxy'($i, sk_B, sk_C)), 535.87/78.32 inference('split', [status(esa)], ['89'])). 535.87/78.32 tff('91', plain, ( sk_R(sk_B, sk_D)) <= (( sk_R(sk_B, sk_D))), 535.87/78.32 inference('split', [status(esa)], ['49'])). 535.87/78.32 tff('92', plain, 535.87/78.32 (![X0]: 535.87/78.32 (~ sk_R(sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | ~ sk_R(sk_E, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0))) 535.87/78.32 <= ((![X0]: 535.87/78.32 (~ sk_R(sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | ~ sk_R(sk_E, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0)))), 535.87/78.32 inference('split', [status(esa)], ['22'])). 535.87/78.32 tff('93', plain, 535.87/78.32 (( '$_eq_proxy'($i, sk_E, sk_D) 535.87/78.32 | ~ sk_R(sk_E, sk_D) 535.87/78.32 | '$_eq_proxy'($i, sk_B, sk_D))) 535.87/78.32 <= (( sk_R(sk_B, sk_D)) & 535.87/78.32 (![X0]: 535.87/78.32 (~ sk_R(sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | ~ sk_R(sk_E, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0)))), 535.87/78.32 inference('sup-', [status(thm)], ['91', '92'])). 535.87/78.32 tff('94', plain, 535.87/78.32 ( '$_eq_proxy'($i, sk_E, sk_D)) | ( '$_eq_proxy'($i, sk_B, sk_D)) | 535.87/78.32 ~ ( sk_R(sk_B, sk_D)) | ~ ( sk_R(sk_E, sk_D)) | 535.87/78.32 ~ 535.87/78.32 (![X0]: 535.87/78.32 (~ sk_R(sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | ~ sk_R(sk_E, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0))), 535.87/78.32 inference('split', [status(esa)], ['93'])). 535.87/78.32 tff('95', plain, 535.87/78.32 ![X5, X6, X7]: 535.87/78.32 ( '$_eq_proxy'($i, X5, X6) 535.87/78.32 | sk_R(X5, X7) 535.87/78.32 | sk_R(X6, X7) 535.87/78.32 | sk_R(X5, X6) 535.87/78.32 | '$_eq_proxy'($i, X6, X7) 535.87/78.32 | '$_eq_proxy'($i, X5, X7)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('96', plain, ~ '$_eq_proxy'($i, sk_D, sk_E), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('97', plain, 535.87/78.32 ![X0]: 535.87/78.32 ( '$_eq_proxy'($i, X0, sk_E) 535.87/78.32 | sk_R(X0, sk_D) 535.87/78.32 | sk_R(sk_D, sk_E) 535.87/78.32 | sk_R(X0, sk_E) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_D)), 535.87/78.32 inference('sup-', [status(thm)], ['95', '96'])). 535.87/78.32 tff('98', plain, 535.87/78.32 (![X0]: 535.87/78.32 ( sk_R(X0, sk_D) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_D) 535.87/78.32 | sk_R(X0, sk_E) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_E))) 535.87/78.32 <= ((![X0]: 535.87/78.32 ( sk_R(X0, sk_D) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_D) 535.87/78.32 | sk_R(X0, sk_E) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_E)))), 535.87/78.32 inference('split', [status(esa)], ['97'])). 535.87/78.32 tff('99', plain, ~ '$_eq_proxy'($i, sk_C, sk_D), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('100', plain, 535.87/78.32 (( '$_eq_proxy'($i, sk_C, sk_E) | sk_R(sk_C, sk_E) | sk_R(sk_C, sk_D))) 535.87/78.32 <= ((![X0]: 535.87/78.32 ( sk_R(X0, sk_D) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_D) 535.87/78.32 | sk_R(X0, sk_E) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_E)))), 535.87/78.32 inference('sup-', [status(thm)], ['98', '99'])). 535.87/78.32 tff('101', plain, 535.87/78.32 ~ 535.87/78.32 (![X0]: 535.87/78.32 ( sk_R(X0, sk_D) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_D) 535.87/78.32 | sk_R(X0, sk_E) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_E))) | 535.87/78.32 ( sk_R(sk_C, sk_D)) | ( sk_R(sk_C, sk_E)) | 535.87/78.32 ( '$_eq_proxy'($i, sk_C, sk_E)), 535.87/78.32 inference('split', [status(esa)], ['100'])). 535.87/78.32 tff('102', plain, 535.87/78.32 ![X5, X6, X7]: 535.87/78.32 ( '$_eq_proxy'($i, X5, X6) 535.87/78.32 | sk_R(X5, X7) 535.87/78.32 | sk_R(X6, X7) 535.87/78.32 | sk_R(X5, X6) 535.87/78.32 | '$_eq_proxy'($i, X6, X7) 535.87/78.32 | '$_eq_proxy'($i, X5, X7)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('103', plain, ~ '$_eq_proxy'($i, sk_A, sk_F), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('104', plain, 535.87/78.32 ![X0]: 535.87/78.32 ( '$_eq_proxy'($i, X0, sk_F) 535.87/78.32 | sk_R(sk_A, X0) 535.87/78.32 | sk_R(X0, sk_F) 535.87/78.32 | sk_R(sk_A, sk_F) 535.87/78.32 | '$_eq_proxy'($i, sk_A, X0)), 535.87/78.32 inference('sup-', [status(thm)], ['102', '103'])). 535.87/78.32 tff('105', plain, 535.87/78.32 (![X0]: 535.87/78.32 ( sk_R(sk_A, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.32 | sk_R(X0, sk_F) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_F))) 535.87/78.32 <= ((![X0]: 535.87/78.32 ( sk_R(sk_A, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.32 | sk_R(X0, sk_F) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.32 inference('split', [status(esa)], ['104'])). 535.87/78.32 tff('106', plain, ~ '$_eq_proxy'($i, sk_D, sk_F), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('107', plain, 535.87/78.32 (( sk_R(sk_D, sk_F) | '$_eq_proxy'($i, sk_A, sk_D) | sk_R(sk_A, sk_D))) 535.87/78.32 <= ((![X0]: 535.87/78.32 ( sk_R(sk_A, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.32 | sk_R(X0, sk_F) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.32 inference('sup-', [status(thm)], ['105', '106'])). 535.87/78.32 tff('108', plain, 535.87/78.32 ( '$_eq_proxy'($i, sk_A, sk_D)) | ( sk_R(sk_D, sk_F)) | 535.87/78.32 ( sk_R(sk_A, sk_D)) | 535.87/78.32 ~ 535.87/78.32 (![X0]: 535.87/78.32 ( sk_R(sk_A, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.32 | sk_R(X0, sk_F) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_F))), 535.87/78.32 inference('split', [status(esa)], ['107'])). 535.87/78.32 tff('109', plain, 535.87/78.32 ![X0, X1, X2]: 535.87/78.32 ( '$_eq_proxy'($i, X1, X2) 535.87/78.32 | '$_eq_proxy'($i, X0, X2) 535.87/78.32 | sk_R(X1, X0) 535.87/78.32 | sk_R(X0, X2) 535.87/78.32 | sk_R(X1, X2) 535.87/78.32 | '$_eq_proxy'($i, X0, X1)), 535.87/78.32 inference('sup-', [status(thm)], ['34', '35'])). 535.87/78.32 tff('110', plain, ~ '$_eq_proxy'($i, sk_C, sk_F), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('111', plain, 535.87/78.32 ![X0]: 535.87/78.32 ( sk_R(sk_F, X0) 535.87/78.32 | sk_R(sk_C, X0) 535.87/78.32 | sk_R(sk_F, sk_C) 535.87/78.32 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_F, X0)), 535.87/78.32 inference('sup-', [status(thm)], ['109', '110'])). 535.87/78.32 tff('112', plain, ( sk_R(sk_F, sk_C)) <= (( sk_R(sk_F, sk_C))), 535.87/78.32 inference('split', [status(esa)], ['111'])). 535.87/78.32 tff('113', plain, 535.87/78.32 ![X5, X6, X7]: 535.87/78.32 ( '$_eq_proxy'($i, X5, X6) 535.87/78.32 | ~ sk_R(X5, X6) 535.87/78.32 | ~ sk_R(X6, X7) 535.87/78.32 | ~ sk_R(X5, X7) 535.87/78.32 | '$_eq_proxy'($i, X6, X7) 535.87/78.32 | '$_eq_proxy'($i, X5, X7)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('114', plain, 535.87/78.32 (![X0]: 535.87/78.32 ( '$_eq_proxy'($i, sk_F, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.32 | ~ sk_R(sk_F, X0) 535.87/78.32 | ~ sk_R(sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_F, sk_C))) 535.87/78.32 <= (( sk_R(sk_F, sk_C))), 535.87/78.32 inference('sup-', [status(thm)], ['112', '113'])). 535.87/78.32 tff('115', plain, 535.87/78.32 ( '$_eq_proxy'($i, sk_F, sk_C)) <= (( '$_eq_proxy'($i, sk_F, sk_C))), 535.87/78.32 inference('split', [status(esa)], ['114'])). 535.87/78.32 tff('116', plain, 535.87/78.32 ![X0 : $tType, X1 : X0, X2 : X0]: 535.87/78.32 (~ '$_eq_proxy'(X0, X1, X2) | '$_eq_proxy'(X0, X2, X1)), 535.87/78.32 trivial([status(thm)])). 535.87/78.32 tff('117', plain, 535.87/78.32 ( '$_eq_proxy'($i, sk_C, sk_F)) <= (( '$_eq_proxy'($i, sk_F, sk_C))), 535.87/78.32 inference('sup-', [status(thm)], ['115', '116'])). 535.87/78.32 tff('118', plain, ~ '$_eq_proxy'($i, sk_C, sk_F), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('119', plain, ~ ( '$_eq_proxy'($i, sk_F, sk_C)), 535.87/78.32 inference('sup-', [status(thm)], ['117', '118'])). 535.87/78.32 tff('120', plain, 535.87/78.32 ![X5, X6, X7]: 535.87/78.32 ( '$_eq_proxy'($i, X5, X6) 535.87/78.32 | sk_R(X5, X7) 535.87/78.32 | sk_R(X6, X7) 535.87/78.32 | sk_R(X5, X6) 535.87/78.32 | '$_eq_proxy'($i, X6, X7) 535.87/78.32 | '$_eq_proxy'($i, X5, X7)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('121', plain, ~ '$_eq_proxy'($i, sk_B, sk_C), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('122', plain, 535.87/78.32 ![X0]: 535.87/78.32 ( '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.32 | sk_R(sk_B, sk_C) 535.87/78.32 | sk_R(sk_C, X0) 535.87/78.32 | sk_R(sk_B, X0)), 535.87/78.32 inference('sup-', [status(thm)], ['120', '121'])). 535.87/78.32 tff('123', plain, ( sk_R(sk_B, sk_C)) <= (( sk_R(sk_B, sk_C))), 535.87/78.32 inference('split', [status(esa)], ['122'])). 535.87/78.32 tff('124', plain, 535.87/78.32 (![X0]: 535.87/78.32 (~ sk_R(sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | ~ sk_R(sk_F, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_F, X0))) 535.87/78.32 <= ((![X0]: 535.87/78.32 (~ sk_R(sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | ~ sk_R(sk_F, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_F, X0)))), 535.87/78.32 inference('split', [status(esa)], ['53'])). 535.87/78.32 tff('125', plain, 535.87/78.32 (( '$_eq_proxy'($i, sk_F, sk_C) 535.87/78.32 | ~ sk_R(sk_F, sk_C) 535.87/78.32 | '$_eq_proxy'($i, sk_B, sk_C))) 535.87/78.32 <= (( sk_R(sk_B, sk_C)) & 535.87/78.32 (![X0]: 535.87/78.32 (~ sk_R(sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | ~ sk_R(sk_F, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_F, X0)))), 535.87/78.32 inference('sup-', [status(thm)], ['123', '124'])). 535.87/78.32 tff('126', plain, 535.87/78.32 ( '$_eq_proxy'($i, sk_F, sk_C)) | ( '$_eq_proxy'($i, sk_B, sk_C)) | 535.87/78.32 ~ ( sk_R(sk_B, sk_C)) | ~ ( sk_R(sk_F, sk_C)) | 535.87/78.32 ~ 535.87/78.32 (![X0]: 535.87/78.32 (~ sk_R(sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | ~ sk_R(sk_F, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_F, X0))), 535.87/78.32 inference('split', [status(esa)], ['125'])). 535.87/78.32 tff('127', plain, 535.87/78.32 ![X5, X6, X7]: 535.87/78.32 ( '$_eq_proxy'($i, X5, X6) 535.87/78.32 | sk_R(X5, X7) 535.87/78.32 | sk_R(X6, X7) 535.87/78.32 | sk_R(X5, X6) 535.87/78.32 | '$_eq_proxy'($i, X6, X7) 535.87/78.32 | '$_eq_proxy'($i, X5, X7)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('128', plain, 535.87/78.32 ![X0 : $tType, X1 : X0, X2 : X0]: 535.87/78.32 (~ '$_eq_proxy'(X0, X1, X2) | '$_eq_proxy'(X0, X2, X1)), 535.87/78.32 trivial([status(thm)])). 535.87/78.32 tff('129', plain, 535.87/78.32 ![X0, X1, X2]: 535.87/78.32 ( '$_eq_proxy'($i, X2, X0) 535.87/78.32 | sk_R(X2, X1) 535.87/78.32 | sk_R(X1, X0) 535.87/78.32 | sk_R(X2, X0) 535.87/78.32 | '$_eq_proxy'($i, X2, X1) 535.87/78.32 | '$_eq_proxy'($i, X0, X1)), 535.87/78.32 inference('sup-', [status(thm)], ['127', '128'])). 535.87/78.32 tff('130', plain, ~ '$_eq_proxy'($i, sk_D, sk_E), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('131', plain, 535.87/78.32 ![X0]: 535.87/78.32 ( '$_eq_proxy'($i, X0, sk_E) 535.87/78.32 | sk_R(X0, sk_D) 535.87/78.32 | sk_R(sk_E, sk_D) 535.87/78.32 | sk_R(X0, sk_E) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_D)), 535.87/78.32 inference('sup-', [status(thm)], ['129', '130'])). 535.87/78.32 tff('132', plain, 535.87/78.32 ( sk_R(sk_E, sk_D)) | 535.87/78.32 (![X0]: 535.87/78.32 ( sk_R(X0, sk_D) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_D) 535.87/78.32 | sk_R(X0, sk_E) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_E))), 535.87/78.32 inference('split', [status(esa)], ['131'])). 535.87/78.32 tff('133', plain, 535.87/78.32 (![X0]: 535.87/78.32 ( sk_R(X0, sk_C) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_C) 535.87/78.32 | sk_R(X0, sk_F) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_F))) | 535.87/78.32 ( sk_R(sk_C, sk_F)), inference('split', [status(esa)], ['86'])). 535.87/78.32 tff('134', plain, 535.87/78.32 ![X0, X1, X2]: 535.87/78.32 ( '$_eq_proxy'($i, X1, X2) 535.87/78.32 | '$_eq_proxy'($i, X0, X2) 535.87/78.32 | sk_R(X1, X0) 535.87/78.32 | sk_R(X0, X2) 535.87/78.32 | sk_R(X1, X2) 535.87/78.32 | '$_eq_proxy'($i, X0, X1)), 535.87/78.32 inference('sup-', [status(thm)], ['34', '35'])). 535.87/78.32 tff('135', plain, ~ '$_eq_proxy'($i, sk_B, sk_E), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('136', plain, 535.87/78.32 ![X0]: 535.87/78.32 ( sk_R(sk_E, X0) 535.87/78.32 | sk_R(sk_B, X0) 535.87/78.32 | sk_R(sk_E, sk_B) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0)), 535.87/78.32 inference('sup-', [status(thm)], ['134', '135'])). 535.87/78.32 tff('137', plain, ( sk_R(sk_E, sk_B)) <= (( sk_R(sk_E, sk_B))), 535.87/78.32 inference('split', [status(esa)], ['136'])). 535.87/78.32 tff('138', plain, 535.87/78.32 ![X5, X6, X7]: 535.87/78.32 ( '$_eq_proxy'($i, X5, X6) 535.87/78.32 | ~ sk_R(X5, X6) 535.87/78.32 | ~ sk_R(X6, X7) 535.87/78.32 | ~ sk_R(X5, X7) 535.87/78.32 | '$_eq_proxy'($i, X6, X7) 535.87/78.32 | '$_eq_proxy'($i, X5, X7)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('139', plain, 535.87/78.32 (![X0]: 535.87/78.32 ( '$_eq_proxy'($i, sk_E, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | ~ sk_R(sk_E, X0) 535.87/78.32 | ~ sk_R(sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, sk_B))) 535.87/78.32 <= (( sk_R(sk_E, sk_B))), 535.87/78.32 inference('sup-', [status(thm)], ['137', '138'])). 535.87/78.32 tff('140', plain, 535.87/78.32 ( '$_eq_proxy'($i, sk_E, sk_B)) <= (( '$_eq_proxy'($i, sk_E, sk_B))), 535.87/78.32 inference('split', [status(esa)], ['139'])). 535.87/78.32 tff('141', plain, 535.87/78.32 ![X0 : $tType, X1 : X0, X2 : X0]: 535.87/78.32 (~ '$_eq_proxy'(X0, X1, X2) | '$_eq_proxy'(X0, X2, X1)), 535.87/78.32 trivial([status(thm)])). 535.87/78.32 tff('142', plain, 535.87/78.32 ( '$_eq_proxy'($i, sk_B, sk_E)) <= (( '$_eq_proxy'($i, sk_E, sk_B))), 535.87/78.32 inference('sup-', [status(thm)], ['140', '141'])). 535.87/78.32 tff('143', plain, ~ '$_eq_proxy'($i, sk_B, sk_E), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('144', plain, ~ ( '$_eq_proxy'($i, sk_E, sk_B)), 535.87/78.32 inference('sup-', [status(thm)], ['142', '143'])). 535.87/78.32 tff('145', plain, ( sk_R(sk_B, sk_C)) <= (( sk_R(sk_B, sk_C))), 535.87/78.32 inference('split', [status(esa)], ['122'])). 535.87/78.32 tff('146', plain, ![X3, X4]: ( sk_R(X3, X4) | ~ sk_R(X4, X3)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('147', plain, ( sk_R(sk_C, sk_B)) <= (( sk_R(sk_B, sk_C))), 535.87/78.32 inference('sup-', [status(thm)], ['145', '146'])). 535.87/78.32 tff('148', plain, 535.87/78.32 ![X5, X6, X7]: 535.87/78.32 ( '$_eq_proxy'($i, X5, X6) 535.87/78.32 | sk_R(X5, X7) 535.87/78.32 | sk_R(X6, X7) 535.87/78.32 | sk_R(X5, X6) 535.87/78.32 | '$_eq_proxy'($i, X6, X7) 535.87/78.32 | '$_eq_proxy'($i, X5, X7)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('149', plain, ~ '$_eq_proxy'($i, sk_C, sk_E), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('150', plain, 535.87/78.32 ![X0]: 535.87/78.32 ( '$_eq_proxy'($i, sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0) 535.87/78.32 | sk_R(sk_C, sk_E) 535.87/78.32 | sk_R(sk_E, X0) 535.87/78.32 | sk_R(sk_C, X0)), 535.87/78.32 inference('sup-', [status(thm)], ['148', '149'])). 535.87/78.32 tff('151', plain, ( sk_R(sk_C, sk_E)) <= (( sk_R(sk_C, sk_E))), 535.87/78.32 inference('split', [status(esa)], ['150'])). 535.87/78.32 tff('152', plain, 535.87/78.32 ![X5, X6, X7]: 535.87/78.32 ( '$_eq_proxy'($i, X5, X6) 535.87/78.32 | ~ sk_R(X5, X6) 535.87/78.32 | ~ sk_R(X6, X7) 535.87/78.32 | ~ sk_R(X5, X7) 535.87/78.32 | '$_eq_proxy'($i, X6, X7) 535.87/78.32 | '$_eq_proxy'($i, X5, X7)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('153', plain, 535.87/78.32 (![X0]: 535.87/78.32 ( '$_eq_proxy'($i, sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0) 535.87/78.32 | ~ sk_R(sk_C, X0) 535.87/78.32 | ~ sk_R(sk_E, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_C, sk_E))) 535.87/78.32 <= (( sk_R(sk_C, sk_E))), 535.87/78.32 inference('sup-', [status(thm)], ['151', '152'])). 535.87/78.32 tff('154', plain, 535.87/78.32 (![X0]: 535.87/78.32 (~ sk_R(sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.32 | ~ sk_R(sk_E, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0))) 535.87/78.32 <= ((![X0]: 535.87/78.32 (~ sk_R(sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.32 | ~ sk_R(sk_E, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0)))), 535.87/78.32 inference('split', [status(esa)], ['153'])). 535.87/78.32 tff('155', plain, 535.87/78.32 (( '$_eq_proxy'($i, sk_E, sk_B) 535.87/78.32 | ~ sk_R(sk_E, sk_B) 535.87/78.32 | '$_eq_proxy'($i, sk_C, sk_B))) 535.87/78.32 <= (( sk_R(sk_B, sk_C)) & 535.87/78.32 (![X0]: 535.87/78.32 (~ sk_R(sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.32 | ~ sk_R(sk_E, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0)))), 535.87/78.32 inference('sup-', [status(thm)], ['147', '154'])). 535.87/78.32 tff('156', plain, 535.87/78.32 ( '$_eq_proxy'($i, sk_E, sk_B)) | ( '$_eq_proxy'($i, sk_C, sk_B)) | 535.87/78.32 ~ ( sk_R(sk_B, sk_C)) | ~ ( sk_R(sk_E, sk_B)) | 535.87/78.32 ~ 535.87/78.32 (![X0]: 535.87/78.32 (~ sk_R(sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.32 | ~ sk_R(sk_E, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0))), 535.87/78.32 inference('split', [status(esa)], ['155'])). 535.87/78.32 tff('157', plain, 535.87/78.32 ![X0, X1, X2]: 535.87/78.32 ( '$_eq_proxy'($i, X2, X0) 535.87/78.32 | sk_R(X2, X1) 535.87/78.32 | sk_R(X1, X0) 535.87/78.32 | sk_R(X2, X0) 535.87/78.32 | '$_eq_proxy'($i, X2, X1) 535.87/78.32 | '$_eq_proxy'($i, X0, X1)), 535.87/78.32 inference('sup-', [status(thm)], ['127', '128'])). 535.87/78.32 tff('158', plain, ~ '$_eq_proxy'($i, sk_B, sk_E), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('159', plain, 535.87/78.32 ![X0]: 535.87/78.32 ( '$_eq_proxy'($i, X0, sk_E) 535.87/78.32 | sk_R(X0, sk_B) 535.87/78.32 | sk_R(sk_E, sk_B) 535.87/78.32 | sk_R(X0, sk_E) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_B)), 535.87/78.32 inference('sup-', [status(thm)], ['157', '158'])). 535.87/78.32 tff('160', plain, 535.87/78.32 ( sk_R(sk_E, sk_B)) | 535.87/78.32 (![X0]: 535.87/78.32 ( sk_R(X0, sk_B) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_B) 535.87/78.32 | sk_R(X0, sk_E) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_E))), 535.87/78.32 inference('split', [status(esa)], ['159'])). 535.87/78.32 tff('161', plain, 535.87/78.32 ![X5, X6, X7]: 535.87/78.32 ( '$_eq_proxy'($i, X5, X6) 535.87/78.32 | sk_R(X5, X7) 535.87/78.32 | sk_R(X6, X7) 535.87/78.32 | sk_R(X5, X6) 535.87/78.32 | '$_eq_proxy'($i, X6, X7) 535.87/78.32 | '$_eq_proxy'($i, X5, X7)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('162', plain, ~ '$_eq_proxy'($i, sk_B, sk_E), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('163', plain, 535.87/78.32 ![X0]: 535.87/78.32 ( '$_eq_proxy'($i, X0, sk_E) 535.87/78.32 | sk_R(X0, sk_B) 535.87/78.32 | sk_R(sk_B, sk_E) 535.87/78.32 | sk_R(X0, sk_E) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_B)), 535.87/78.32 inference('sup-', [status(thm)], ['161', '162'])). 535.87/78.32 tff('164', plain, 535.87/78.32 (![X0]: 535.87/78.32 ( sk_R(X0, sk_B) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_B) 535.87/78.32 | sk_R(X0, sk_E) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_E))) 535.87/78.32 <= ((![X0]: 535.87/78.32 ( sk_R(X0, sk_B) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_B) 535.87/78.32 | sk_R(X0, sk_E) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_E)))), 535.87/78.32 inference('split', [status(esa)], ['163'])). 535.87/78.32 tff('165', plain, ~ '$_eq_proxy'($i, sk_A, sk_B), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('166', plain, 535.87/78.32 (( '$_eq_proxy'($i, sk_A, sk_E) | sk_R(sk_A, sk_E) | sk_R(sk_A, sk_B))) 535.87/78.32 <= ((![X0]: 535.87/78.32 ( sk_R(X0, sk_B) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_B) 535.87/78.32 | sk_R(X0, sk_E) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_E)))), 535.87/78.32 inference('sup-', [status(thm)], ['164', '165'])). 535.87/78.32 tff('167', plain, 535.87/78.32 ~ 535.87/78.32 (![X0]: 535.87/78.32 ( sk_R(X0, sk_B) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_B) 535.87/78.32 | sk_R(X0, sk_E) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_E))) | 535.87/78.32 ( sk_R(sk_A, sk_E)) | ( sk_R(sk_A, sk_B)) | 535.87/78.32 ( '$_eq_proxy'($i, sk_A, sk_E)), 535.87/78.32 inference('split', [status(esa)], ['166'])). 535.87/78.32 tff('168', plain, 535.87/78.32 (![X0]: 535.87/78.32 ( sk_R(sk_A, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.32 | sk_R(X0, sk_E) 535.87/78.32 | '$_eq_proxy'($i, X0, sk_E))) | 535.87/78.32 ( sk_R(sk_A, sk_E)), inference('split', [status(esa)], ['79'])). 535.87/78.32 tff('169', plain, ( sk_R(sk_A, sk_E)) <= (( sk_R(sk_A, sk_E))), 535.87/78.32 inference('split', [status(esa)], ['2'])). 535.87/78.32 tff('170', plain, 535.87/78.32 ![X5, X6, X7]: 535.87/78.32 ( '$_eq_proxy'($i, X5, X6) 535.87/78.32 | sk_R(X5, X7) 535.87/78.32 | sk_R(X6, X7) 535.87/78.32 | sk_R(X5, X6) 535.87/78.32 | '$_eq_proxy'($i, X6, X7) 535.87/78.32 | '$_eq_proxy'($i, X5, X7)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('171', plain, ~ '$_eq_proxy'($i, sk_A, sk_C), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('172', plain, 535.87/78.32 ![X0]: 535.87/78.32 ( '$_eq_proxy'($i, sk_A, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.32 | sk_R(sk_A, sk_C) 535.87/78.32 | sk_R(sk_C, X0) 535.87/78.32 | sk_R(sk_A, X0)), 535.87/78.32 inference('sup-', [status(thm)], ['170', '171'])). 535.87/78.32 tff('173', plain, ( sk_R(sk_A, sk_C)) <= (( sk_R(sk_A, sk_C))), 535.87/78.32 inference('split', [status(esa)], ['172'])). 535.87/78.32 tff('174', plain, 535.87/78.32 ![X5, X6, X7]: 535.87/78.32 ( '$_eq_proxy'($i, X5, X6) 535.87/78.32 | ~ sk_R(X5, X6) 535.87/78.32 | ~ sk_R(X6, X7) 535.87/78.32 | ~ sk_R(X5, X7) 535.87/78.32 | '$_eq_proxy'($i, X6, X7) 535.87/78.32 | '$_eq_proxy'($i, X5, X7)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('175', plain, 535.87/78.32 (![X0]: 535.87/78.32 ( '$_eq_proxy'($i, sk_A, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.32 | ~ sk_R(sk_A, X0) 535.87/78.32 | ~ sk_R(sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_A, sk_C))) 535.87/78.32 <= (( sk_R(sk_A, sk_C))), 535.87/78.32 inference('sup-', [status(thm)], ['173', '174'])). 535.87/78.32 tff('176', plain, 535.87/78.32 (![X0]: 535.87/78.32 (~ sk_R(sk_A, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.32 | ~ sk_R(sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_C, X0))) 535.87/78.32 <= ((![X0]: 535.87/78.32 (~ sk_R(sk_A, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.32 | ~ sk_R(sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.32 inference('split', [status(esa)], ['175'])). 535.87/78.32 tff('177', plain, 535.87/78.32 (( '$_eq_proxy'($i, sk_C, sk_E) 535.87/78.32 | ~ sk_R(sk_C, sk_E) 535.87/78.32 | '$_eq_proxy'($i, sk_A, sk_E))) 535.87/78.32 <= (( sk_R(sk_A, sk_E)) & 535.87/78.32 (![X0]: 535.87/78.32 (~ sk_R(sk_A, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.32 | ~ sk_R(sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.32 inference('sup-', [status(thm)], ['169', '176'])). 535.87/78.32 tff('178', plain, 535.87/78.32 ( '$_eq_proxy'($i, sk_C, sk_E)) | ( '$_eq_proxy'($i, sk_A, sk_E)) | 535.87/78.32 ~ ( sk_R(sk_A, sk_E)) | ~ ( sk_R(sk_C, sk_E)) | 535.87/78.32 ~ 535.87/78.32 (![X0]: 535.87/78.32 (~ sk_R(sk_A, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.32 | ~ sk_R(sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_C, X0))), 535.87/78.32 inference('split', [status(esa)], ['177'])). 535.87/78.32 tff('179', plain, 535.87/78.32 ![X5, X6, X7]: 535.87/78.32 ( '$_eq_proxy'($i, X5, X6) 535.87/78.32 | sk_R(X5, X7) 535.87/78.32 | sk_R(X6, X7) 535.87/78.32 | sk_R(X5, X6) 535.87/78.32 | '$_eq_proxy'($i, X6, X7) 535.87/78.32 | '$_eq_proxy'($i, X5, X7)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('180', plain, ~ '$_eq_proxy'($i, sk_A, sk_B), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('181', plain, 535.87/78.32 ![X0]: 535.87/78.32 ( '$_eq_proxy'($i, sk_A, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | sk_R(sk_A, sk_B) 535.87/78.32 | sk_R(sk_B, X0) 535.87/78.32 | sk_R(sk_A, X0)), 535.87/78.32 inference('sup-', [status(thm)], ['179', '180'])). 535.87/78.32 tff('182', plain, 535.87/78.32 (![X0]: 535.87/78.32 ( sk_R(sk_A, X0) 535.87/78.32 | sk_R(sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_A, X0))) 535.87/78.32 <= ((![X0]: 535.87/78.32 ( sk_R(sk_A, X0) 535.87/78.32 | sk_R(sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_A, X0)))), 535.87/78.32 inference('split', [status(esa)], ['181'])). 535.87/78.32 tff('183', plain, ~ '$_eq_proxy'($i, sk_B, sk_C), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('184', plain, 535.87/78.32 (( '$_eq_proxy'($i, sk_A, sk_C) | sk_R(sk_B, sk_C) | sk_R(sk_A, sk_C))) 535.87/78.32 <= ((![X0]: 535.87/78.32 ( sk_R(sk_A, X0) 535.87/78.32 | sk_R(sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_A, X0)))), 535.87/78.32 inference('sup-', [status(thm)], ['182', '183'])). 535.87/78.32 tff('185', plain, 535.87/78.32 ( sk_R(sk_A, sk_C)) | ( sk_R(sk_B, sk_C)) | 535.87/78.32 ~ 535.87/78.32 (![X0]: 535.87/78.32 ( sk_R(sk_A, X0) 535.87/78.32 | sk_R(sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_A, X0))) | 535.87/78.32 ( '$_eq_proxy'($i, sk_A, sk_C)), 535.87/78.32 inference('split', [status(esa)], ['184'])). 535.87/78.32 tff('186', plain, 535.87/78.32 ![X5, X6, X7]: 535.87/78.32 ( '$_eq_proxy'($i, X5, X6) 535.87/78.32 | sk_R(X5, X7) 535.87/78.32 | sk_R(X6, X7) 535.87/78.32 | sk_R(X5, X6) 535.87/78.32 | '$_eq_proxy'($i, X6, X7) 535.87/78.32 | '$_eq_proxy'($i, X5, X7)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('187', plain, ~ '$_eq_proxy'($i, sk_D, sk_E), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('188', plain, 535.87/78.32 ![X0]: 535.87/78.32 ( '$_eq_proxy'($i, sk_D, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0) 535.87/78.32 | sk_R(sk_D, sk_E) 535.87/78.32 | sk_R(sk_E, X0) 535.87/78.32 | sk_R(sk_D, X0)), 535.87/78.32 inference('sup-', [status(thm)], ['186', '187'])). 535.87/78.32 tff('189', plain, 535.87/78.32 (![X0]: 535.87/78.32 ( sk_R(sk_D, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_D, X0) 535.87/78.32 | sk_R(sk_E, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0))) 535.87/78.32 <= ((![X0]: 535.87/78.32 ( sk_R(sk_D, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_D, X0) 535.87/78.32 | sk_R(sk_E, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0)))), 535.87/78.32 inference('split', [status(esa)], ['188'])). 535.87/78.32 tff('190', plain, ~ '$_eq_proxy'($i, sk_D, sk_F), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('191', plain, 535.87/78.32 (( '$_eq_proxy'($i, sk_E, sk_F) | sk_R(sk_E, sk_F) | sk_R(sk_D, sk_F))) 535.87/78.32 <= ((![X0]: 535.87/78.32 ( sk_R(sk_D, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_D, X0) 535.87/78.32 | sk_R(sk_E, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0)))), 535.87/78.32 inference('sup-', [status(thm)], ['189', '190'])). 535.87/78.32 tff('192', plain, 535.87/78.32 ( sk_R(sk_D, sk_F)) | 535.87/78.32 ~ 535.87/78.32 (![X0]: 535.87/78.32 ( sk_R(sk_D, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_D, X0) 535.87/78.32 | sk_R(sk_E, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0))) | 535.87/78.32 ( sk_R(sk_E, sk_F)) | ( '$_eq_proxy'($i, sk_E, sk_F)), 535.87/78.32 inference('split', [status(esa)], ['191'])). 535.87/78.32 tff('193', plain, ( sk_R(sk_C, sk_D)) <= (( sk_R(sk_C, sk_D))), 535.87/78.32 inference('split', [status(esa)], ['70'])). 535.87/78.32 tff('194', plain, 535.87/78.32 (![X0]: 535.87/78.32 (~ sk_R(sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.32 | ~ sk_R(sk_E, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0))) 535.87/78.32 <= ((![X0]: 535.87/78.32 (~ sk_R(sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.32 | ~ sk_R(sk_E, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0)))), 535.87/78.32 inference('split', [status(esa)], ['153'])). 535.87/78.32 tff('195', plain, 535.87/78.32 (( '$_eq_proxy'($i, sk_E, sk_D) 535.87/78.32 | ~ sk_R(sk_E, sk_D) 535.87/78.32 | '$_eq_proxy'($i, sk_C, sk_D))) 535.87/78.32 <= (( sk_R(sk_C, sk_D)) & 535.87/78.32 (![X0]: 535.87/78.32 (~ sk_R(sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.32 | ~ sk_R(sk_E, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0)))), 535.87/78.32 inference('sup-', [status(thm)], ['193', '194'])). 535.87/78.32 tff('196', plain, 535.87/78.32 ( '$_eq_proxy'($i, sk_E, sk_D)) | ( '$_eq_proxy'($i, sk_C, sk_D)) | 535.87/78.32 ~ ( sk_R(sk_C, sk_D)) | ~ ( sk_R(sk_E, sk_D)) | 535.87/78.32 ~ 535.87/78.32 (![X0]: 535.87/78.32 (~ sk_R(sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.32 | ~ sk_R(sk_E, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0))), 535.87/78.32 inference('split', [status(esa)], ['195'])). 535.87/78.32 tff('197', plain, 535.87/78.32 ![X0, X1, X2]: 535.87/78.32 ( '$_eq_proxy'($i, X1, X2) 535.87/78.32 | '$_eq_proxy'($i, X0, X2) 535.87/78.32 | sk_R(X1, X0) 535.87/78.32 | sk_R(X0, X2) 535.87/78.32 | sk_R(X1, X2) 535.87/78.32 | '$_eq_proxy'($i, X0, X1)), 535.87/78.32 inference('sup-', [status(thm)], ['34', '35'])). 535.87/78.32 tff('198', plain, ~ '$_eq_proxy'($i, sk_D, sk_E), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('199', plain, 535.87/78.32 ![X0]: 535.87/78.32 ( sk_R(sk_E, X0) 535.87/78.32 | sk_R(sk_D, X0) 535.87/78.32 | sk_R(sk_E, sk_D) 535.87/78.32 | '$_eq_proxy'($i, sk_D, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0)), 535.87/78.32 inference('sup-', [status(thm)], ['197', '198'])). 535.87/78.32 tff('200', plain, 535.87/78.32 (![X0]: 535.87/78.32 ( sk_R(sk_D, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_D, X0) 535.87/78.32 | sk_R(sk_E, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_E, X0))) | 535.87/78.32 ( sk_R(sk_E, sk_D)), inference('split', [status(esa)], ['199'])). 535.87/78.32 tff('201', plain, 535.87/78.32 (![X0]: 535.87/78.32 ( sk_R(sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | sk_R(sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_C, X0))) 535.87/78.32 <= ((![X0]: 535.87/78.32 ( sk_R(sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | sk_R(sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.32 inference('split', [status(esa)], ['122'])). 535.87/78.32 tff('202', plain, ~ '$_eq_proxy'($i, sk_B, sk_F), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('203', plain, 535.87/78.32 (( '$_eq_proxy'($i, sk_C, sk_F) | sk_R(sk_C, sk_F) | sk_R(sk_B, sk_F))) 535.87/78.32 <= ((![X0]: 535.87/78.32 ( sk_R(sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | sk_R(sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.32 inference('sup-', [status(thm)], ['201', '202'])). 535.87/78.32 tff('204', plain, 535.87/78.32 ~ 535.87/78.32 (![X0]: 535.87/78.32 ( sk_R(sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | sk_R(sk_C, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_C, X0))) | 535.87/78.32 ( sk_R(sk_B, sk_F)) | ( sk_R(sk_C, sk_F)) | 535.87/78.32 ( '$_eq_proxy'($i, sk_C, sk_F)), 535.87/78.32 inference('split', [status(esa)], ['203'])). 535.87/78.32 tff('205', plain, ( sk_R(sk_A, sk_E)) <= (( sk_R(sk_A, sk_E))), 535.87/78.32 inference('split', [status(esa)], ['2'])). 535.87/78.32 tff('206', plain, ( sk_R(sk_A, sk_B)) <= (( sk_R(sk_A, sk_B))), 535.87/78.32 inference('split', [status(esa)], ['181'])). 535.87/78.32 tff('207', plain, 535.87/78.32 ![X5, X6, X7]: 535.87/78.32 ( '$_eq_proxy'($i, X5, X6) 535.87/78.32 | ~ sk_R(X5, X6) 535.87/78.32 | ~ sk_R(X6, X7) 535.87/78.32 | ~ sk_R(X5, X7) 535.87/78.32 | '$_eq_proxy'($i, X6, X7) 535.87/78.32 | '$_eq_proxy'($i, X5, X7)), 535.87/78.32 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.32 tff('208', plain, 535.87/78.32 (![X0]: 535.87/78.32 ( '$_eq_proxy'($i, sk_A, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | ~ sk_R(sk_A, X0) 535.87/78.32 | ~ sk_R(sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_A, sk_B))) 535.87/78.32 <= (( sk_R(sk_A, sk_B))), 535.87/78.32 inference('sup-', [status(thm)], ['206', '207'])). 535.87/78.32 tff('209', plain, 535.87/78.32 (![X0]: 535.87/78.32 (~ sk_R(sk_A, X0) 535.87/78.32 | ~ sk_R(sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_A, X0))) 535.87/78.32 <= ((![X0]: 535.87/78.32 (~ sk_R(sk_A, X0) 535.87/78.32 | ~ sk_R(sk_B, X0) 535.87/78.32 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0)))), 535.87/78.33 inference('split', [status(esa)], ['208'])). 535.87/78.33 tff('210', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_A, sk_E) 535.87/78.33 | '$_eq_proxy'($i, sk_B, sk_E) 535.87/78.33 | ~ sk_R(sk_B, sk_E))) 535.87/78.33 <= (( sk_R(sk_A, sk_E)) & 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['205', '209'])). 535.87/78.33 tff('211', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_B, sk_E)) | ( '$_eq_proxy'($i, sk_A, sk_E)) | 535.87/78.33 ~ ( sk_R(sk_A, sk_E)) | ~ ( sk_R(sk_B, sk_E)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0))), 535.87/78.33 inference('split', [status(esa)], ['210'])). 535.87/78.33 tff('212', plain, 535.87/78.33 ![X5, X6, X7]: 535.87/78.33 ( '$_eq_proxy'($i, X5, X6) 535.87/78.33 | sk_R(X5, X7) 535.87/78.33 | sk_R(X6, X7) 535.87/78.33 | sk_R(X5, X6) 535.87/78.33 | '$_eq_proxy'($i, X6, X7) 535.87/78.33 | '$_eq_proxy'($i, X5, X7)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('213', plain, ~ '$_eq_proxy'($i, sk_E, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('214', plain, 535.87/78.33 ![X0]: 535.87/78.33 ( '$_eq_proxy'($i, X0, sk_F) 535.87/78.33 | sk_R(X0, sk_E) 535.87/78.33 | sk_R(sk_E, sk_F) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_E)), 535.87/78.33 inference('sup-', [status(thm)], ['212', '213'])). 535.87/78.33 tff('215', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(X0, sk_E) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_E) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(X0, sk_E) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_E) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.33 inference('split', [status(esa)], ['214'])). 535.87/78.33 tff('216', plain, ~ '$_eq_proxy'($i, sk_C, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('217', plain, 535.87/78.33 (( sk_R(sk_C, sk_F) | '$_eq_proxy'($i, sk_C, sk_E) | sk_R(sk_C, sk_E))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(X0, sk_E) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_E) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.33 inference('sup-', [status(thm)], ['215', '216'])). 535.87/78.33 tff('218', plain, 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(X0, sk_E) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_E) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))) | 535.87/78.33 ( sk_R(sk_C, sk_E)) | ( sk_R(sk_C, sk_F)) | 535.87/78.33 ( '$_eq_proxy'($i, sk_C, sk_E)), 535.87/78.33 inference('split', [status(esa)], ['217'])). 535.87/78.33 tff('219', plain, ( sk_R(sk_C, sk_E)) <= (( sk_R(sk_C, sk_E))), 535.87/78.33 inference('split', [status(esa)], ['150'])). 535.87/78.33 tff('220', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0)))), 535.87/78.33 inference('split', [status(esa)], ['73'])). 535.87/78.33 tff('221', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_D, sk_E) 535.87/78.33 | ~ sk_R(sk_D, sk_E) 535.87/78.33 | '$_eq_proxy'($i, sk_C, sk_E))) 535.87/78.33 <= (( sk_R(sk_C, sk_E)) & 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['219', '220'])). 535.87/78.33 tff('222', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_D, sk_E)) | ( '$_eq_proxy'($i, sk_C, sk_E)) | 535.87/78.33 ~ ( sk_R(sk_C, sk_E)) | ~ ( sk_R(sk_D, sk_E)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0))), 535.87/78.33 inference('split', [status(esa)], ['221'])). 535.87/78.33 tff('223', plain, 535.87/78.33 ![X0, X1, X2]: 535.87/78.33 ( '$_eq_proxy'($i, X1, X2) 535.87/78.33 | '$_eq_proxy'($i, X0, X2) 535.87/78.33 | sk_R(X1, X0) 535.87/78.33 | sk_R(X0, X2) 535.87/78.33 | sk_R(X1, X2) 535.87/78.33 | '$_eq_proxy'($i, X0, X1)), 535.87/78.33 inference('sup-', [status(thm)], ['34', '35'])). 535.87/78.33 tff('224', plain, ~ '$_eq_proxy'($i, sk_B, sk_E), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('225', plain, 535.87/78.33 ![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(X0, sk_E) 535.87/78.33 | sk_R(sk_B, sk_E) 535.87/78.33 | sk_R(X0, sk_B) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_E)), 535.87/78.33 inference('sup-', [status(thm)], ['223', '224'])). 535.87/78.33 tff('226', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(X0, sk_B) 535.87/78.33 | sk_R(X0, sk_E) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_E))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(X0, sk_B) 535.87/78.33 | sk_R(X0, sk_E) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_E)))), 535.87/78.33 inference('split', [status(esa)], ['225'])). 535.87/78.33 tff('227', plain, ~ '$_eq_proxy'($i, sk_B, sk_D), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('228', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_D, sk_E) | sk_R(sk_D, sk_E) | sk_R(sk_D, sk_B))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(X0, sk_B) 535.87/78.33 | sk_R(X0, sk_E) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_E)))), 535.87/78.33 inference('sup-', [status(thm)], ['226', '227'])). 535.87/78.33 tff('229', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_D, sk_E)) | ( sk_R(sk_D, sk_B)) | 535.87/78.33 ( sk_R(sk_D, sk_E)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(X0, sk_B) 535.87/78.33 | sk_R(X0, sk_E) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_E))), 535.87/78.33 inference('split', [status(esa)], ['228'])). 535.87/78.33 tff('230', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(X0, sk_B) 535.87/78.33 | sk_R(X0, sk_E) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_E))) | 535.87/78.33 ( sk_R(sk_B, sk_E)), inference('split', [status(esa)], ['225'])). 535.87/78.33 tff('231', plain, ( sk_R(sk_A, sk_D)) <= (( sk_R(sk_A, sk_D))), 535.87/78.33 inference('split', [status(esa)], ['6'])). 535.87/78.33 tff('232', plain, 535.87/78.33 ![X5, X6, X7]: 535.87/78.33 ( '$_eq_proxy'($i, X5, X6) 535.87/78.33 | sk_R(X5, X7) 535.87/78.33 | sk_R(X6, X7) 535.87/78.33 | sk_R(X5, X6) 535.87/78.33 | '$_eq_proxy'($i, X6, X7) 535.87/78.33 | '$_eq_proxy'($i, X5, X7)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('233', plain, ~ '$_eq_proxy'($i, sk_A, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('234', plain, 535.87/78.33 ![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0) 535.87/78.33 | sk_R(sk_A, sk_F) 535.87/78.33 | sk_R(sk_F, X0) 535.87/78.33 | sk_R(sk_A, X0)), 535.87/78.33 inference('sup-', [status(thm)], ['232', '233'])). 535.87/78.33 tff('235', plain, ( sk_R(sk_A, sk_F)) <= (( sk_R(sk_A, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['234'])). 535.87/78.33 tff('236', plain, 535.87/78.33 ![X5, X6, X7]: 535.87/78.33 ( '$_eq_proxy'($i, X5, X6) 535.87/78.33 | ~ sk_R(X5, X6) 535.87/78.33 | ~ sk_R(X6, X7) 535.87/78.33 | ~ sk_R(X5, X7) 535.87/78.33 | '$_eq_proxy'($i, X6, X7) 535.87/78.33 | '$_eq_proxy'($i, X5, X7)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('237', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0) 535.87/78.33 | ~ sk_R(sk_A, X0) 535.87/78.33 | ~ sk_R(sk_F, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, sk_F))) 535.87/78.33 <= (( sk_R(sk_A, sk_F))), 535.87/78.33 inference('sup-', [status(thm)], ['235', '236'])). 535.87/78.33 tff('238', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_F, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_F, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0)))), 535.87/78.33 inference('split', [status(esa)], ['237'])). 535.87/78.33 tff('239', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_F, sk_D) 535.87/78.33 | ~ sk_R(sk_F, sk_D) 535.87/78.33 | '$_eq_proxy'($i, sk_A, sk_D))) 535.87/78.33 <= (( sk_R(sk_A, sk_D)) & 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_F, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['231', '238'])). 535.87/78.33 tff('240', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_F, sk_D)) | ( '$_eq_proxy'($i, sk_A, sk_D)) | 535.87/78.33 ~ ( sk_R(sk_A, sk_D)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_F, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0))) | 535.87/78.33 ~ ( sk_R(sk_F, sk_D)), inference('split', [status(esa)], ['239'])). 535.87/78.33 tff('241', plain, 535.87/78.33 ![X5, X6, X7]: 535.87/78.33 ( '$_eq_proxy'($i, X5, X6) 535.87/78.33 | sk_R(X5, X7) 535.87/78.33 | sk_R(X6, X7) 535.87/78.33 | sk_R(X5, X6) 535.87/78.33 | '$_eq_proxy'($i, X6, X7) 535.87/78.33 | '$_eq_proxy'($i, X5, X7)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('242', plain, ~ '$_eq_proxy'($i, sk_D, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('243', plain, 535.87/78.33 ![X0]: 535.87/78.33 ( '$_eq_proxy'($i, X0, sk_F) 535.87/78.33 | sk_R(X0, sk_D) 535.87/78.33 | sk_R(sk_D, sk_F) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_D)), 535.87/78.33 inference('sup-', [status(thm)], ['241', '242'])). 535.87/78.33 tff('244', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(X0, sk_D) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_D) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(X0, sk_D) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_D) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.33 inference('split', [status(esa)], ['243'])). 535.87/78.33 tff('245', plain, ~ '$_eq_proxy'($i, sk_C, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('246', plain, 535.87/78.33 (( sk_R(sk_C, sk_F) | '$_eq_proxy'($i, sk_C, sk_D) | sk_R(sk_C, sk_D))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(X0, sk_D) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_D) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.33 inference('sup-', [status(thm)], ['244', '245'])). 535.87/78.33 tff('247', plain, 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(X0, sk_D) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_D) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))) | 535.87/78.33 ( sk_R(sk_C, sk_D)) | ( sk_R(sk_C, sk_F)) | 535.87/78.33 ( '$_eq_proxy'($i, sk_C, sk_D)), 535.87/78.33 inference('split', [status(esa)], ['246'])). 535.87/78.33 tff('248', plain, 535.87/78.33 ![X0, X1, X2]: 535.87/78.33 ( '$_eq_proxy'($i, X2, X0) 535.87/78.33 | sk_R(X2, X1) 535.87/78.33 | sk_R(X1, X0) 535.87/78.33 | sk_R(X2, X0) 535.87/78.33 | '$_eq_proxy'($i, X2, X1) 535.87/78.33 | '$_eq_proxy'($i, X0, X1)), 535.87/78.33 inference('sup-', [status(thm)], ['127', '128'])). 535.87/78.33 tff('249', plain, ~ '$_eq_proxy'($i, sk_D, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('250', plain, 535.87/78.33 ![X0]: 535.87/78.33 ( '$_eq_proxy'($i, X0, sk_F) 535.87/78.33 | sk_R(X0, sk_D) 535.87/78.33 | sk_R(sk_F, sk_D) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_D)), 535.87/78.33 inference('sup-', [status(thm)], ['248', '249'])). 535.87/78.33 tff('251', plain, 535.87/78.33 ( sk_R(sk_F, sk_D)) | 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(X0, sk_D) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_D) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['250'])). 535.87/78.33 tff('252', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.33 inference('split', [status(esa)], ['172'])). 535.87/78.33 tff('253', plain, ~ '$_eq_proxy'($i, sk_C, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('254', plain, 535.87/78.33 (( sk_R(sk_C, sk_F) | '$_eq_proxy'($i, sk_A, sk_F) | sk_R(sk_A, sk_F))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['252', '253'])). 535.87/78.33 tff('255', plain, 535.87/78.33 ( sk_R(sk_A, sk_F)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) | 535.87/78.33 ( sk_R(sk_C, sk_F)) | ( '$_eq_proxy'($i, sk_A, sk_F)), 535.87/78.33 inference('split', [status(esa)], ['254'])). 535.87/78.33 tff('256', plain, 535.87/78.33 ![X5, X6, X7]: 535.87/78.33 ( '$_eq_proxy'($i, X5, X6) 535.87/78.33 | sk_R(X5, X7) 535.87/78.33 | sk_R(X6, X7) 535.87/78.33 | sk_R(X5, X6) 535.87/78.33 | '$_eq_proxy'($i, X6, X7) 535.87/78.33 | '$_eq_proxy'($i, X5, X7)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('257', plain, ~ '$_eq_proxy'($i, sk_C, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('258', plain, 535.87/78.33 ![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0) 535.87/78.33 | sk_R(sk_C, sk_F) 535.87/78.33 | sk_R(sk_F, X0) 535.87/78.33 | sk_R(sk_C, X0)), 535.87/78.33 inference('sup-', [status(thm)], ['256', '257'])). 535.87/78.33 tff('259', plain, ( sk_R(sk_C, sk_F)) <= (( sk_R(sk_C, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['258'])). 535.87/78.33 tff('260', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0)))), 535.87/78.33 inference('split', [status(esa)], ['73'])). 535.87/78.33 tff('261', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_D, sk_F) 535.87/78.33 | ~ sk_R(sk_D, sk_F) 535.87/78.33 | '$_eq_proxy'($i, sk_C, sk_F))) 535.87/78.33 <= (( sk_R(sk_C, sk_F)) & 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['259', '260'])). 535.87/78.33 tff('262', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_D, sk_F)) | ( '$_eq_proxy'($i, sk_C, sk_F)) | 535.87/78.33 ~ ( sk_R(sk_C, sk_F)) | ~ ( sk_R(sk_D, sk_F)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0))), 535.87/78.33 inference('split', [status(esa)], ['261'])). 535.87/78.33 tff('263', plain, 535.87/78.33 ![X0, X1, X2]: 535.87/78.33 ( '$_eq_proxy'($i, X1, X2) 535.87/78.33 | '$_eq_proxy'($i, X0, X2) 535.87/78.33 | sk_R(X1, X0) 535.87/78.33 | sk_R(X0, X2) 535.87/78.33 | sk_R(X1, X2) 535.87/78.33 | '$_eq_proxy'($i, X0, X1)), 535.87/78.33 inference('sup-', [status(thm)], ['34', '35'])). 535.87/78.33 tff('264', plain, ~ '$_eq_proxy'($i, sk_B, sk_D), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('265', plain, 535.87/78.33 ![X0]: 535.87/78.33 ( sk_R(sk_D, X0) 535.87/78.33 | sk_R(sk_B, X0) 535.87/78.33 | sk_R(sk_D, sk_B) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0)), 535.87/78.33 inference('sup-', [status(thm)], ['263', '264'])). 535.87/78.33 tff('266', plain, ( sk_R(sk_D, sk_B)) <= (( sk_R(sk_D, sk_B))), 535.87/78.33 inference('split', [status(esa)], ['265'])). 535.87/78.33 tff('267', plain, ![X3, X4]: ( sk_R(X3, X4) | ~ sk_R(X4, X3)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('268', plain, ( sk_R(sk_B, sk_D)) <= (( sk_R(sk_D, sk_B))), 535.87/78.33 inference('sup-', [status(thm)], ['266', '267'])). 535.87/78.33 tff('269', plain, ( sk_R(sk_B, sk_C)) <= (( sk_R(sk_B, sk_C))), 535.87/78.33 inference('split', [status(esa)], ['122'])). 535.87/78.33 tff('270', plain, 535.87/78.33 ![X5, X6, X7]: 535.87/78.33 ( '$_eq_proxy'($i, X5, X6) 535.87/78.33 | ~ sk_R(X5, X6) 535.87/78.33 | ~ sk_R(X6, X7) 535.87/78.33 | ~ sk_R(X5, X7) 535.87/78.33 | '$_eq_proxy'($i, X6, X7) 535.87/78.33 | '$_eq_proxy'($i, X5, X7)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('271', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, sk_C))) 535.87/78.33 <= (( sk_R(sk_B, sk_C))), 535.87/78.33 inference('sup-', [status(thm)], ['269', '270'])). 535.87/78.33 tff('272', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.33 inference('split', [status(esa)], ['271'])). 535.87/78.33 tff('273', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_C, sk_D) 535.87/78.33 | ~ sk_R(sk_C, sk_D) 535.87/78.33 | '$_eq_proxy'($i, sk_B, sk_D))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) & 535.87/78.33 ( sk_R(sk_D, sk_B))), 535.87/78.33 inference('sup-', [status(thm)], ['268', '272'])). 535.87/78.33 tff('274', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_C, sk_D)) | ( '$_eq_proxy'($i, sk_B, sk_D)) | 535.87/78.33 ~ ( sk_R(sk_C, sk_D)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) | 535.87/78.33 ~ ( sk_R(sk_D, sk_B)), inference('split', [status(esa)], ['273'])). 535.87/78.33 tff('275', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0))) | 535.87/78.33 ~ ( sk_R(sk_C, sk_D)) | ( '$_eq_proxy'($i, sk_C, sk_D)), 535.87/78.33 inference('split', [status(esa)], ['73'])). 535.87/78.33 tff('276', plain, ( sk_R(sk_A, sk_D)) <= (( sk_R(sk_A, sk_D))), 535.87/78.33 inference('split', [status(esa)], ['6'])). 535.87/78.33 tff('277', plain, ( sk_R(sk_A, sk_E)) <= (( sk_R(sk_A, sk_E))), 535.87/78.33 inference('split', [status(esa)], ['2'])). 535.87/78.33 tff('278', plain, 535.87/78.33 ![X5, X6, X7]: 535.87/78.33 ( '$_eq_proxy'($i, X5, X6) 535.87/78.33 | ~ sk_R(X5, X6) 535.87/78.33 | ~ sk_R(X6, X7) 535.87/78.33 | ~ sk_R(X5, X7) 535.87/78.33 | '$_eq_proxy'($i, X6, X7) 535.87/78.33 | '$_eq_proxy'($i, X5, X7)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('279', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0) 535.87/78.33 | ~ sk_R(sk_A, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, sk_E))) 535.87/78.33 <= (( sk_R(sk_A, sk_E))), 535.87/78.33 inference('sup-', [status(thm)], ['277', '278'])). 535.87/78.33 tff('280', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0)))), 535.87/78.33 inference('split', [status(esa)], ['279'])). 535.87/78.33 tff('281', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_E, sk_D) 535.87/78.33 | ~ sk_R(sk_E, sk_D) 535.87/78.33 | '$_eq_proxy'($i, sk_A, sk_D))) 535.87/78.33 <= (( sk_R(sk_A, sk_D)) & 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['276', '280'])). 535.87/78.33 tff('282', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_E, sk_D)) | ( '$_eq_proxy'($i, sk_A, sk_D)) | 535.87/78.33 ~ ( sk_R(sk_A, sk_D)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0))) | 535.87/78.33 ~ ( sk_R(sk_E, sk_D)), inference('split', [status(esa)], ['281'])). 535.87/78.33 tff('283', plain, 535.87/78.33 ![X0, X1, X2]: 535.87/78.33 ( '$_eq_proxy'($i, X1, X2) 535.87/78.33 | '$_eq_proxy'($i, X0, X2) 535.87/78.33 | sk_R(X1, X0) 535.87/78.33 | sk_R(X0, X2) 535.87/78.33 | sk_R(X1, X2) 535.87/78.33 | '$_eq_proxy'($i, X0, X1)), 535.87/78.33 inference('sup-', [status(thm)], ['34', '35'])). 535.87/78.33 tff('284', plain, ~ '$_eq_proxy'($i, sk_C, sk_E), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('285', plain, 535.87/78.33 ![X0]: 535.87/78.33 ( '$_eq_proxy'($i, X0, sk_C) 535.87/78.33 | sk_R(sk_C, sk_E) 535.87/78.33 | sk_R(X0, sk_E) 535.87/78.33 | sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_E)), 535.87/78.33 inference('sup-', [status(thm)], ['283', '284'])). 535.87/78.33 tff('286', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_C) 535.87/78.33 | sk_R(X0, sk_E) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_E))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_C) 535.87/78.33 | sk_R(X0, sk_E) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_E)))), 535.87/78.33 inference('split', [status(esa)], ['285'])). 535.87/78.33 tff('287', plain, ~ '$_eq_proxy'($i, sk_D, sk_E), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('288', plain, 535.87/78.33 (( sk_R(sk_D, sk_E) | '$_eq_proxy'($i, sk_D, sk_C) | sk_R(sk_C, sk_D))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_C) 535.87/78.33 | sk_R(X0, sk_E) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_E)))), 535.87/78.33 inference('sup-', [status(thm)], ['286', '287'])). 535.87/78.33 tff('289', plain, 535.87/78.33 ( sk_R(sk_D, sk_E)) | ( sk_R(sk_C, sk_D)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_C) 535.87/78.33 | sk_R(X0, sk_E) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_E))) | 535.87/78.33 ( '$_eq_proxy'($i, sk_D, sk_C)), 535.87/78.33 inference('split', [status(esa)], ['288'])). 535.87/78.33 tff('290', plain, 535.87/78.33 ~ ( sk_R(sk_A, sk_E)) | 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0))) | 535.87/78.33 ( '$_eq_proxy'($i, sk_A, sk_E)), 535.87/78.33 inference('split', [status(esa)], ['279'])). 535.87/78.33 tff('291', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.33 inference('split', [status(esa)], ['172'])). 535.87/78.33 tff('292', plain, ~ '$_eq_proxy'($i, sk_C, sk_E), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('293', plain, 535.87/78.33 (( sk_R(sk_C, sk_E) | '$_eq_proxy'($i, sk_A, sk_E) | sk_R(sk_A, sk_E))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['291', '292'])). 535.87/78.33 tff('294', plain, 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) | 535.87/78.33 ( sk_R(sk_A, sk_E)) | ( sk_R(sk_C, sk_E)) | 535.87/78.33 ( '$_eq_proxy'($i, sk_A, sk_E)), 535.87/78.33 inference('split', [status(esa)], ['293'])). 535.87/78.33 tff('295', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_C) 535.87/78.33 | sk_R(X0, sk_E) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_E))) | 535.87/78.33 ( sk_R(sk_C, sk_E)), inference('split', [status(esa)], ['285'])). 535.87/78.33 tff('296', plain, ( sk_R(sk_F, sk_C)) <= (( sk_R(sk_F, sk_C))), 535.87/78.33 inference('split', [status(esa)], ['111'])). 535.87/78.33 tff('297', plain, ![X3, X4]: ( sk_R(X3, X4) | ~ sk_R(X4, X3)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('298', plain, ( sk_R(sk_C, sk_F)) <= (( sk_R(sk_F, sk_C))), 535.87/78.33 inference('sup-', [status(thm)], ['296', '297'])). 535.87/78.33 tff('299', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0)))), 535.87/78.33 inference('split', [status(esa)], ['153'])). 535.87/78.33 tff('300', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_E, sk_F) 535.87/78.33 | ~ sk_R(sk_E, sk_F) 535.87/78.33 | '$_eq_proxy'($i, sk_C, sk_F))) 535.87/78.33 <= (( sk_R(sk_F, sk_C)) & 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['298', '299'])). 535.87/78.33 tff('301', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_E, sk_F)) | ( '$_eq_proxy'($i, sk_C, sk_F)) | 535.87/78.33 ~ ( sk_R(sk_E, sk_F)) | ~ ( sk_R(sk_F, sk_C)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0))), 535.87/78.33 inference('split', [status(esa)], ['300'])). 535.87/78.33 tff('302', plain, ( sk_R(sk_B, sk_E)) <= (( sk_R(sk_B, sk_E))), 535.87/78.33 inference('split', [status(esa)], ['19'])). 535.87/78.33 tff('303', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.33 inference('split', [status(esa)], ['271'])). 535.87/78.33 tff('304', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_C, sk_E) 535.87/78.33 | ~ sk_R(sk_C, sk_E) 535.87/78.33 | '$_eq_proxy'($i, sk_B, sk_E))) 535.87/78.33 <= (( sk_R(sk_B, sk_E)) & 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['302', '303'])). 535.87/78.33 tff('305', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_C, sk_E)) | ( '$_eq_proxy'($i, sk_B, sk_E)) | 535.87/78.33 ~ ( sk_R(sk_B, sk_E)) | ~ ( sk_R(sk_C, sk_E)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))), 535.87/78.33 inference('split', [status(esa)], ['304'])). 535.87/78.33 tff('306', plain, 535.87/78.33 ![X5, X6, X7]: 535.87/78.33 ( '$_eq_proxy'($i, X5, X6) 535.87/78.33 | sk_R(X5, X7) 535.87/78.33 | sk_R(X6, X7) 535.87/78.33 | sk_R(X5, X6) 535.87/78.33 | '$_eq_proxy'($i, X6, X7) 535.87/78.33 | '$_eq_proxy'($i, X5, X7)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('307', plain, ~ '$_eq_proxy'($i, sk_B, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('308', plain, 535.87/78.33 ![X0]: 535.87/78.33 ( '$_eq_proxy'($i, X0, sk_F) 535.87/78.33 | sk_R(sk_B, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | sk_R(sk_B, sk_F) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0)), 535.87/78.33 inference('sup-', [status(thm)], ['306', '307'])). 535.87/78.33 tff('309', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.33 inference('split', [status(esa)], ['308'])). 535.87/78.33 tff('310', plain, ~ '$_eq_proxy'($i, sk_B, sk_E), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('311', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_E, sk_F) | sk_R(sk_E, sk_F) | sk_R(sk_B, sk_E))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.33 inference('sup-', [status(thm)], ['309', '310'])). 535.87/78.33 tff('312', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_E, sk_F)) | ( sk_R(sk_E, sk_F)) | 535.87/78.33 ( sk_R(sk_B, sk_E)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['311'])). 535.87/78.33 tff('313', plain, 535.87/78.33 ![X0, X1, X2]: 535.87/78.33 ( '$_eq_proxy'($i, X1, X2) 535.87/78.33 | '$_eq_proxy'($i, X0, X2) 535.87/78.33 | sk_R(X1, X0) 535.87/78.33 | sk_R(X0, X2) 535.87/78.33 | sk_R(X1, X2) 535.87/78.33 | '$_eq_proxy'($i, X0, X1)), 535.87/78.33 inference('sup-', [status(thm)], ['34', '35'])). 535.87/78.33 tff('314', plain, ~ '$_eq_proxy'($i, sk_B, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('315', plain, 535.87/78.33 ![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | sk_R(sk_B, sk_F) 535.87/78.33 | sk_R(X0, sk_B) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F)), 535.87/78.33 inference('sup-', [status(thm)], ['313', '314'])). 535.87/78.33 tff('316', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(X0, sk_B) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))) | 535.87/78.33 ( sk_R(sk_B, sk_F)), inference('split', [status(esa)], ['315'])). 535.87/78.33 tff('317', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(X0, sk_B) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(X0, sk_B) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.33 inference('split', [status(esa)], ['315'])). 535.87/78.33 tff('318', plain, ~ '$_eq_proxy'($i, sk_B, sk_D), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('319', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_D, sk_F) | sk_R(sk_D, sk_F) | sk_R(sk_D, sk_B))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(X0, sk_B) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.33 inference('sup-', [status(thm)], ['317', '318'])). 535.87/78.33 tff('320', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_D, sk_F)) | ( sk_R(sk_D, sk_B)) | 535.87/78.33 ( sk_R(sk_D, sk_F)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(X0, sk_B) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['319'])). 535.87/78.33 tff('321', plain, 535.87/78.33 ![X0, X1, X2]: 535.87/78.33 ( '$_eq_proxy'($i, X2, X0) 535.87/78.33 | sk_R(X2, X1) 535.87/78.33 | sk_R(X1, X0) 535.87/78.33 | sk_R(X2, X0) 535.87/78.33 | '$_eq_proxy'($i, X2, X1) 535.87/78.33 | '$_eq_proxy'($i, X0, X1)), 535.87/78.33 inference('sup-', [status(thm)], ['127', '128'])). 535.87/78.33 tff('322', plain, ~ '$_eq_proxy'($i, sk_E, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('323', plain, 535.87/78.33 ![X0]: 535.87/78.33 ( '$_eq_proxy'($i, X0, sk_F) 535.87/78.33 | sk_R(X0, sk_E) 535.87/78.33 | sk_R(sk_F, sk_E) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_E)), 535.87/78.33 inference('sup-', [status(thm)], ['321', '322'])). 535.87/78.33 tff('324', plain, 535.87/78.33 ( sk_R(sk_F, sk_E)) | 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(X0, sk_E) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_E) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['323'])). 535.87/78.33 tff('325', plain, 535.87/78.33 ![X0, X1, X2]: 535.87/78.33 ( '$_eq_proxy'($i, X1, X2) 535.87/78.33 | '$_eq_proxy'($i, X0, X2) 535.87/78.33 | sk_R(X1, X0) 535.87/78.33 | sk_R(X0, X2) 535.87/78.33 | sk_R(X1, X2) 535.87/78.33 | '$_eq_proxy'($i, X0, X1)), 535.87/78.33 inference('sup-', [status(thm)], ['34', '35'])). 535.87/78.33 tff('326', plain, ~ '$_eq_proxy'($i, sk_C, sk_D), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('327', plain, 535.87/78.33 ![X0]: 535.87/78.33 ( sk_R(sk_D, X0) 535.87/78.33 | sk_R(sk_C, X0) 535.87/78.33 | sk_R(sk_D, sk_C) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0)), 535.87/78.33 inference('sup-', [status(thm)], ['325', '326'])). 535.87/78.33 tff('328', plain, ( sk_R(sk_D, sk_C)) <= (( sk_R(sk_D, sk_C))), 535.87/78.33 inference('split', [status(esa)], ['327'])). 535.87/78.33 tff('329', plain, ![X3, X4]: ( sk_R(X3, X4) | ~ sk_R(X4, X3)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('330', plain, ( sk_R(sk_C, sk_D)) <= (( sk_R(sk_D, sk_C))), 535.87/78.33 inference('sup-', [status(thm)], ['328', '329'])). 535.87/78.33 tff('331', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0)))), 535.87/78.33 inference('split', [status(esa)], ['153'])). 535.87/78.33 tff('332', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_E, sk_D) 535.87/78.33 | ~ sk_R(sk_E, sk_D) 535.87/78.33 | '$_eq_proxy'($i, sk_C, sk_D))) 535.87/78.33 <= (( sk_R(sk_D, sk_C)) & 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['330', '331'])). 535.87/78.33 tff('333', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_E, sk_D)) | ( '$_eq_proxy'($i, sk_C, sk_D)) | 535.87/78.33 ~ ( sk_R(sk_D, sk_C)) | ~ ( sk_R(sk_E, sk_D)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0))), 535.87/78.33 inference('split', [status(esa)], ['332'])). 535.87/78.33 tff('334', plain, 535.87/78.33 ![X0, X1, X2]: 535.87/78.33 ( '$_eq_proxy'($i, X1, X2) 535.87/78.33 | '$_eq_proxy'($i, X0, X2) 535.87/78.33 | sk_R(X1, X0) 535.87/78.33 | sk_R(X0, X2) 535.87/78.33 | sk_R(X1, X2) 535.87/78.33 | '$_eq_proxy'($i, X0, X1)), 535.87/78.33 inference('sup-', [status(thm)], ['34', '35'])). 535.87/78.33 tff('335', plain, ~ '$_eq_proxy'($i, sk_E, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('336', plain, 535.87/78.33 ![X0]: 535.87/78.33 ( sk_R(sk_F, X0) 535.87/78.33 | sk_R(sk_E, X0) 535.87/78.33 | sk_R(sk_F, sk_E) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0)), 535.87/78.33 inference('sup-', [status(thm)], ['334', '335'])). 535.87/78.33 tff('337', plain, ( sk_R(sk_F, sk_E)) <= (( sk_R(sk_F, sk_E))), 535.87/78.33 inference('split', [status(esa)], ['336'])). 535.87/78.33 tff('338', plain, 535.87/78.33 ![X5, X6, X7]: 535.87/78.33 ( '$_eq_proxy'($i, X5, X6) 535.87/78.33 | ~ sk_R(X5, X6) 535.87/78.33 | ~ sk_R(X6, X7) 535.87/78.33 | ~ sk_R(X5, X7) 535.87/78.33 | '$_eq_proxy'($i, X6, X7) 535.87/78.33 | '$_eq_proxy'($i, X5, X7)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('339', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_F, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0) 535.87/78.33 | ~ sk_R(sk_F, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, sk_E))) 535.87/78.33 <= (( sk_R(sk_F, sk_E))), 535.87/78.33 inference('sup-', [status(thm)], ['337', '338'])). 535.87/78.33 tff('340', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_F, sk_E)) <= (( '$_eq_proxy'($i, sk_F, sk_E))), 535.87/78.33 inference('split', [status(esa)], ['339'])). 535.87/78.33 tff('341', plain, 535.87/78.33 ![X0 : $tType, X1 : X0, X2 : X0]: 535.87/78.33 (~ '$_eq_proxy'(X0, X1, X2) | '$_eq_proxy'(X0, X2, X1)), 535.87/78.33 trivial([status(thm)])). 535.87/78.33 tff('342', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_E, sk_F)) <= (( '$_eq_proxy'($i, sk_F, sk_E))), 535.87/78.33 inference('sup-', [status(thm)], ['340', '341'])). 535.87/78.33 tff('343', plain, ~ '$_eq_proxy'($i, sk_E, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('344', plain, ~ ( '$_eq_proxy'($i, sk_F, sk_E)), 535.87/78.33 inference('sup-', [status(thm)], ['342', '343'])). 535.87/78.33 tff('345', plain, ( sk_R(sk_B, sk_E)) <= (( sk_R(sk_B, sk_E))), 535.87/78.33 inference('split', [status(esa)], ['19'])). 535.87/78.33 tff('346', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_F, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_F, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0)))), 535.87/78.33 inference('split', [status(esa)], ['53'])). 535.87/78.33 tff('347', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_F, sk_E) 535.87/78.33 | ~ sk_R(sk_F, sk_E) 535.87/78.33 | '$_eq_proxy'($i, sk_B, sk_E))) 535.87/78.33 <= (( sk_R(sk_B, sk_E)) & 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_F, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['345', '346'])). 535.87/78.33 tff('348', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_F, sk_E)) | ( '$_eq_proxy'($i, sk_B, sk_E)) | 535.87/78.33 ~ ( sk_R(sk_B, sk_E)) | ~ ( sk_R(sk_F, sk_E)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_F, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0))), 535.87/78.33 inference('split', [status(esa)], ['347'])). 535.87/78.33 tff('349', plain, 535.87/78.33 ![X0, X1, X2]: 535.87/78.33 ( '$_eq_proxy'($i, X1, X2) 535.87/78.33 | '$_eq_proxy'($i, X0, X2) 535.87/78.33 | sk_R(X1, X0) 535.87/78.33 | sk_R(X0, X2) 535.87/78.33 | sk_R(X1, X2) 535.87/78.33 | '$_eq_proxy'($i, X0, X1)), 535.87/78.33 inference('sup-', [status(thm)], ['34', '35'])). 535.87/78.33 tff('350', plain, ~ '$_eq_proxy'($i, sk_D, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('351', plain, 535.87/78.33 ![X0]: 535.87/78.33 ( sk_R(sk_F, X0) 535.87/78.33 | sk_R(sk_D, X0) 535.87/78.33 | sk_R(sk_F, sk_D) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0)), 535.87/78.33 inference('sup-', [status(thm)], ['349', '350'])). 535.87/78.33 tff('352', plain, ( sk_R(sk_F, sk_D)) <= (( sk_R(sk_F, sk_D))), 535.87/78.33 inference('split', [status(esa)], ['351'])). 535.87/78.33 tff('353', plain, 535.87/78.33 ![X5, X6, X7]: 535.87/78.33 ( '$_eq_proxy'($i, X5, X6) 535.87/78.33 | ~ sk_R(X5, X6) 535.87/78.33 | ~ sk_R(X6, X7) 535.87/78.33 | ~ sk_R(X5, X7) 535.87/78.33 | '$_eq_proxy'($i, X6, X7) 535.87/78.33 | '$_eq_proxy'($i, X5, X7)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('354', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_F, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0) 535.87/78.33 | ~ sk_R(sk_F, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, sk_D))) 535.87/78.33 <= (( sk_R(sk_F, sk_D))), 535.87/78.33 inference('sup-', [status(thm)], ['352', '353'])). 535.87/78.33 tff('355', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_F, sk_D)) <= (( '$_eq_proxy'($i, sk_F, sk_D))), 535.87/78.33 inference('split', [status(esa)], ['354'])). 535.87/78.33 tff('356', plain, 535.87/78.33 ![X0 : $tType, X1 : X0, X2 : X0]: 535.87/78.33 (~ '$_eq_proxy'(X0, X1, X2) | '$_eq_proxy'(X0, X2, X1)), 535.87/78.33 trivial([status(thm)])). 535.87/78.33 tff('357', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_D, sk_F)) <= (( '$_eq_proxy'($i, sk_F, sk_D))), 535.87/78.33 inference('sup-', [status(thm)], ['355', '356'])). 535.87/78.33 tff('358', plain, ~ '$_eq_proxy'($i, sk_D, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('359', plain, ~ ( '$_eq_proxy'($i, sk_F, sk_D)), 535.87/78.33 inference('sup-', [status(thm)], ['357', '358'])). 535.87/78.33 tff('360', plain, ( sk_R(sk_B, sk_D)) <= (( sk_R(sk_D, sk_B))), 535.87/78.33 inference('sup-', [status(thm)], ['266', '267'])). 535.87/78.33 tff('361', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_F, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_F, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0)))), 535.87/78.33 inference('split', [status(esa)], ['53'])). 535.87/78.33 tff('362', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_F, sk_D) 535.87/78.33 | ~ sk_R(sk_F, sk_D) 535.87/78.33 | '$_eq_proxy'($i, sk_B, sk_D))) 535.87/78.33 <= (( sk_R(sk_D, sk_B)) & 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_F, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['360', '361'])). 535.87/78.33 tff('363', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_F, sk_D)) | ( '$_eq_proxy'($i, sk_B, sk_D)) | 535.87/78.33 ~ ( sk_R(sk_D, sk_B)) | ~ ( sk_R(sk_F, sk_D)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_F, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0))), 535.87/78.33 inference('split', [status(esa)], ['362'])). 535.87/78.33 tff('364', plain, 535.87/78.33 ![X0, X1, X2]: 535.87/78.33 ( '$_eq_proxy'($i, X1, X2) 535.87/78.33 | '$_eq_proxy'($i, X0, X2) 535.87/78.33 | sk_R(X1, X0) 535.87/78.33 | sk_R(X0, X2) 535.87/78.33 | sk_R(X1, X2) 535.87/78.33 | '$_eq_proxy'($i, X0, X1)), 535.87/78.33 inference('sup-', [status(thm)], ['34', '35'])). 535.87/78.33 tff('365', plain, ~ '$_eq_proxy'($i, sk_A, sk_C), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('366', plain, 535.87/78.33 ![X0]: 535.87/78.33 ( sk_R(sk_C, X0) 535.87/78.33 | sk_R(sk_A, X0) 535.87/78.33 | sk_R(sk_C, sk_A) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0)), 535.87/78.33 inference('sup-', [status(thm)], ['364', '365'])). 535.87/78.33 tff('367', plain, ( sk_R(sk_C, sk_A)) <= (( sk_R(sk_C, sk_A))), 535.87/78.33 inference('split', [status(esa)], ['366'])). 535.87/78.33 tff('368', plain, ![X3, X4]: ( sk_R(X3, X4) | ~ sk_R(X4, X3)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('369', plain, ( sk_R(sk_A, sk_C)) <= (( sk_R(sk_C, sk_A))), 535.87/78.33 inference('sup-', [status(thm)], ['367', '368'])). 535.87/78.33 tff('370', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0)))), 535.87/78.33 inference('split', [status(esa)], ['208'])). 535.87/78.33 tff('371', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_A, sk_C) 535.87/78.33 | '$_eq_proxy'($i, sk_B, sk_C) 535.87/78.33 | ~ sk_R(sk_B, sk_C))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0))) & 535.87/78.33 ( sk_R(sk_C, sk_A))), 535.87/78.33 inference('sup-', [status(thm)], ['369', '370'])). 535.87/78.33 tff('372', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_B, sk_C)) | ( '$_eq_proxy'($i, sk_A, sk_C)) | 535.87/78.33 ~ ( sk_R(sk_B, sk_C)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0))) | 535.87/78.33 ~ ( sk_R(sk_C, sk_A)), inference('split', [status(esa)], ['371'])). 535.87/78.33 tff('373', plain, 535.87/78.33 ![X0, X1, X2]: 535.87/78.33 ( '$_eq_proxy'($i, X1, X2) 535.87/78.33 | '$_eq_proxy'($i, X0, X2) 535.87/78.33 | sk_R(X1, X0) 535.87/78.33 | sk_R(X0, X2) 535.87/78.33 | sk_R(X1, X2) 535.87/78.33 | '$_eq_proxy'($i, X0, X1)), 535.87/78.33 inference('sup-', [status(thm)], ['34', '35'])). 535.87/78.33 tff('374', plain, ~ '$_eq_proxy'($i, sk_A, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('375', plain, 535.87/78.33 ![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | sk_R(sk_A, sk_F) 535.87/78.33 | sk_R(X0, sk_A) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F)), 535.87/78.33 inference('sup-', [status(thm)], ['373', '374'])). 535.87/78.33 tff('376', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | sk_R(X0, sk_A) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | sk_R(X0, sk_A) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.33 inference('split', [status(esa)], ['375'])). 535.87/78.33 tff('377', plain, ~ '$_eq_proxy'($i, sk_C, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('378', plain, 535.87/78.33 (( sk_R(sk_C, sk_F) | sk_R(sk_C, sk_A) | '$_eq_proxy'($i, sk_A, sk_C))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | sk_R(X0, sk_A) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.33 inference('sup-', [status(thm)], ['376', '377'])). 535.87/78.33 tff('379', plain, 535.87/78.33 ( sk_R(sk_C, sk_A)) | ( '$_eq_proxy'($i, sk_A, sk_C)) | 535.87/78.33 ( sk_R(sk_C, sk_F)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | sk_R(X0, sk_A) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['378'])). 535.87/78.33 tff('380', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.33 inference('split', [status(esa)], ['104'])). 535.87/78.33 tff('381', plain, ~ '$_eq_proxy'($i, sk_C, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('382', plain, 535.87/78.33 (( sk_R(sk_C, sk_F) | '$_eq_proxy'($i, sk_A, sk_C) | sk_R(sk_A, sk_C))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.33 inference('sup-', [status(thm)], ['380', '381'])). 535.87/78.33 tff('383', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_A, sk_C)) | ( sk_R(sk_C, sk_F)) | 535.87/78.33 ( sk_R(sk_A, sk_C)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['382'])). 535.87/78.33 tff('384', plain, ( sk_R(sk_A, sk_B)) <= (( sk_R(sk_A, sk_B))), 535.87/78.33 inference('split', [status(esa)], ['181'])). 535.87/78.33 tff('385', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.33 inference('split', [status(esa)], ['175'])). 535.87/78.33 tff('386', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_C, sk_B) 535.87/78.33 | ~ sk_R(sk_C, sk_B) 535.87/78.33 | '$_eq_proxy'($i, sk_A, sk_B))) 535.87/78.33 <= (( sk_R(sk_A, sk_B)) & 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['384', '385'])). 535.87/78.33 tff('387', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_C, sk_B)) | ( '$_eq_proxy'($i, sk_A, sk_B)) | 535.87/78.33 ~ ( sk_R(sk_A, sk_B)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) | 535.87/78.33 ~ ( sk_R(sk_C, sk_B)), inference('split', [status(esa)], ['386'])). 535.87/78.33 tff('388', plain, ( sk_R(sk_B, sk_F)) <= (( sk_R(sk_B, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['15'])). 535.87/78.33 tff('389', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.33 inference('split', [status(esa)], ['271'])). 535.87/78.33 tff('390', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_C, sk_F) 535.87/78.33 | ~ sk_R(sk_C, sk_F) 535.87/78.33 | '$_eq_proxy'($i, sk_B, sk_F))) 535.87/78.33 <= (( sk_R(sk_B, sk_F)) & 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['388', '389'])). 535.87/78.33 tff('391', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_C, sk_F)) | ( '$_eq_proxy'($i, sk_B, sk_F)) | 535.87/78.33 ~ ( sk_R(sk_B, sk_F)) | ~ ( sk_R(sk_C, sk_F)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))), 535.87/78.33 inference('split', [status(esa)], ['390'])). 535.87/78.33 tff('392', plain, ( sk_R(sk_C, sk_B)) <= (( sk_R(sk_B, sk_C))), 535.87/78.33 inference('sup-', [status(thm)], ['145', '146'])). 535.87/78.33 tff('393', plain, (~ sk_R(sk_C, sk_B)) <= (~ ( sk_R(sk_C, sk_B))), 535.87/78.33 inference('split', [status(esa)], ['386'])). 535.87/78.33 tff('394', plain, ( sk_R(sk_C, sk_B)) | ~ ( sk_R(sk_B, sk_C)), 535.87/78.33 inference('sup-', [status(thm)], ['392', '393'])). 535.87/78.33 tff('395', plain, ( sk_R(sk_E, sk_D)) <= (( sk_R(sk_E, sk_D))), 535.87/78.33 inference('split', [status(esa)], ['199'])). 535.87/78.33 tff('396', plain, 535.87/78.33 ![X5, X6, X7]: 535.87/78.33 ( '$_eq_proxy'($i, X5, X6) 535.87/78.33 | ~ sk_R(X5, X6) 535.87/78.33 | ~ sk_R(X6, X7) 535.87/78.33 | ~ sk_R(X5, X7) 535.87/78.33 | '$_eq_proxy'($i, X6, X7) 535.87/78.33 | '$_eq_proxy'($i, X5, X7)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('397', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, sk_D))) 535.87/78.33 <= (( sk_R(sk_E, sk_D))), 535.87/78.33 inference('sup-', [status(thm)], ['395', '396'])). 535.87/78.33 tff('398', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_E, sk_D)) <= (( '$_eq_proxy'($i, sk_E, sk_D))), 535.87/78.33 inference('split', [status(esa)], ['397'])). 535.87/78.33 tff('399', plain, 535.87/78.33 ![X0 : $tType, X1 : X0, X2 : X0]: 535.87/78.33 (~ '$_eq_proxy'(X0, X1, X2) | '$_eq_proxy'(X0, X2, X1)), 535.87/78.33 trivial([status(thm)])). 535.87/78.33 tff('400', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_D, sk_E)) <= (( '$_eq_proxy'($i, sk_E, sk_D))), 535.87/78.33 inference('sup-', [status(thm)], ['398', '399'])). 535.87/78.33 tff('401', plain, ~ '$_eq_proxy'($i, sk_D, sk_E), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('402', plain, ~ ( '$_eq_proxy'($i, sk_E, sk_D)), 535.87/78.33 inference('sup-', [status(thm)], ['400', '401'])). 535.87/78.33 tff('403', plain, ( sk_R(sk_B, sk_D)) <= (( sk_R(sk_D, sk_B))), 535.87/78.33 inference('sup-', [status(thm)], ['266', '267'])). 535.87/78.33 tff('404', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0)))), 535.87/78.33 inference('split', [status(esa)], ['22'])). 535.87/78.33 tff('405', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_E, sk_D) 535.87/78.33 | ~ sk_R(sk_E, sk_D) 535.87/78.33 | '$_eq_proxy'($i, sk_B, sk_D))) 535.87/78.33 <= (( sk_R(sk_D, sk_B)) & 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['403', '404'])). 535.87/78.33 tff('406', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_E, sk_D)) | ( '$_eq_proxy'($i, sk_B, sk_D)) | 535.87/78.33 ~ ( sk_R(sk_D, sk_B)) | ~ ( sk_R(sk_E, sk_D)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0))), 535.87/78.33 inference('split', [status(esa)], ['405'])). 535.87/78.33 tff('407', plain, 535.87/78.33 ![X0, X1, X2]: 535.87/78.33 ( '$_eq_proxy'($i, X1, X2) 535.87/78.33 | '$_eq_proxy'($i, X0, X2) 535.87/78.33 | sk_R(X1, X0) 535.87/78.33 | sk_R(X0, X2) 535.87/78.33 | sk_R(X1, X2) 535.87/78.33 | '$_eq_proxy'($i, X0, X1)), 535.87/78.33 inference('sup-', [status(thm)], ['34', '35'])). 535.87/78.33 tff('408', plain, ~ '$_eq_proxy'($i, sk_B, sk_C), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('409', plain, 535.87/78.33 ![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(X0, sk_C) 535.87/78.33 | sk_R(sk_B, sk_C) 535.87/78.33 | sk_R(X0, sk_B) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_C)), 535.87/78.33 inference('sup-', [status(thm)], ['407', '408'])). 535.87/78.33 tff('410', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(X0, sk_B) 535.87/78.33 | sk_R(X0, sk_C) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_C))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(X0, sk_B) 535.87/78.33 | sk_R(X0, sk_C) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_C)))), 535.87/78.33 inference('split', [status(esa)], ['409'])). 535.87/78.33 tff('411', plain, ~ '$_eq_proxy'($i, sk_B, sk_D), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('412', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_D, sk_C) | sk_R(sk_D, sk_C) | sk_R(sk_D, sk_B))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(X0, sk_B) 535.87/78.33 | sk_R(X0, sk_C) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_C)))), 535.87/78.33 inference('sup-', [status(thm)], ['410', '411'])). 535.87/78.33 tff('413', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_D, sk_C)) | ( sk_R(sk_D, sk_C)) | 535.87/78.33 ( sk_R(sk_D, sk_B)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(X0, sk_B) 535.87/78.33 | sk_R(X0, sk_C) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_C))), 535.87/78.33 inference('split', [status(esa)], ['412'])). 535.87/78.33 tff('414', plain, ( sk_R(sk_D, sk_E)) <= (( sk_R(sk_D, sk_E))), 535.87/78.33 inference('split', [status(esa)], ['188'])). 535.87/78.33 tff('415', plain, ![X3, X4]: ( sk_R(X3, X4) | ~ sk_R(X4, X3)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('416', plain, ( sk_R(sk_E, sk_D)) <= (( sk_R(sk_D, sk_E))), 535.87/78.33 inference('sup-', [status(thm)], ['414', '415'])). 535.87/78.33 tff('417', plain, (~ sk_R(sk_E, sk_D)) <= (~ ( sk_R(sk_E, sk_D))), 535.87/78.33 inference('split', [status(esa)], ['281'])). 535.87/78.33 tff('418', plain, ( sk_R(sk_E, sk_D)) | ~ ( sk_R(sk_D, sk_E)), 535.87/78.33 inference('sup-', [status(thm)], ['416', '417'])). 535.87/78.33 tff('419', plain, ( sk_R(sk_D, sk_C)) <= (( sk_R(sk_D, sk_C))), 535.87/78.33 inference('split', [status(esa)], ['327'])). 535.87/78.33 tff('420', plain, 535.87/78.33 ![X5, X6, X7]: 535.87/78.33 ( '$_eq_proxy'($i, X5, X6) 535.87/78.33 | ~ sk_R(X5, X6) 535.87/78.33 | ~ sk_R(X6, X7) 535.87/78.33 | ~ sk_R(X5, X7) 535.87/78.33 | '$_eq_proxy'($i, X6, X7) 535.87/78.33 | '$_eq_proxy'($i, X5, X7)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('421', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, sk_C))) 535.87/78.33 <= (( sk_R(sk_D, sk_C))), 535.87/78.33 inference('sup-', [status(thm)], ['419', '420'])). 535.87/78.33 tff('422', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0))) | 535.87/78.33 ~ ( sk_R(sk_D, sk_C)) | ( '$_eq_proxy'($i, sk_D, sk_C)), 535.87/78.33 inference('split', [status(esa)], ['421'])). 535.87/78.33 tff('423', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_D, sk_C)) <= (( '$_eq_proxy'($i, sk_D, sk_C))), 535.87/78.33 inference('split', [status(esa)], ['421'])). 535.87/78.33 tff('424', plain, 535.87/78.33 ![X0 : $tType, X1 : X0, X2 : X0]: 535.87/78.33 (~ '$_eq_proxy'(X0, X1, X2) | '$_eq_proxy'(X0, X2, X1)), 535.87/78.33 trivial([status(thm)])). 535.87/78.33 tff('425', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_C, sk_D)) <= (( '$_eq_proxy'($i, sk_D, sk_C))), 535.87/78.33 inference('sup-', [status(thm)], ['423', '424'])). 535.87/78.33 tff('426', plain, ~ '$_eq_proxy'($i, sk_C, sk_D), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('427', plain, ~ ( '$_eq_proxy'($i, sk_D, sk_C)), 535.87/78.33 inference('sup-', [status(thm)], ['425', '426'])). 535.87/78.33 tff('428', plain, 535.87/78.33 ![X5, X6, X7]: 535.87/78.33 ( '$_eq_proxy'($i, X5, X6) 535.87/78.33 | sk_R(X5, X7) 535.87/78.33 | sk_R(X6, X7) 535.87/78.33 | sk_R(X5, X6) 535.87/78.33 | '$_eq_proxy'($i, X6, X7) 535.87/78.33 | '$_eq_proxy'($i, X5, X7)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('429', plain, ~ '$_eq_proxy'($i, sk_E, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('430', plain, 535.87/78.33 ![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0) 535.87/78.33 | sk_R(sk_E, sk_F) 535.87/78.33 | sk_R(sk_F, X0) 535.87/78.33 | sk_R(sk_E, X0)), 535.87/78.33 inference('sup-', [status(thm)], ['428', '429'])). 535.87/78.33 tff('431', plain, ( sk_R(sk_E, sk_F)) <= (( sk_R(sk_E, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['430'])). 535.87/78.33 tff('432', plain, 535.87/78.33 ![X5, X6, X7]: 535.87/78.33 ( '$_eq_proxy'($i, X5, X6) 535.87/78.33 | ~ sk_R(X5, X6) 535.87/78.33 | ~ sk_R(X6, X7) 535.87/78.33 | ~ sk_R(X5, X7) 535.87/78.33 | '$_eq_proxy'($i, X6, X7) 535.87/78.33 | '$_eq_proxy'($i, X5, X7)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('433', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | ~ sk_R(sk_F, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, sk_F))) 535.87/78.33 <= (( sk_R(sk_E, sk_F))), 535.87/78.33 inference('sup-', [status(thm)], ['431', '432'])). 535.87/78.33 tff('434', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_E, sk_F)) <= (( '$_eq_proxy'($i, sk_E, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['433'])). 535.87/78.33 tff('435', plain, ~ '$_eq_proxy'($i, sk_E, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('436', plain, ~ ( '$_eq_proxy'($i, sk_E, sk_F)), 535.87/78.33 inference('sup-', [status(thm)], ['434', '435'])). 535.87/78.33 tff('437', plain, ( sk_R(sk_C, sk_F)) <= (( sk_R(sk_C, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['258'])). 535.87/78.33 tff('438', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0)))), 535.87/78.33 inference('split', [status(esa)], ['153'])). 535.87/78.33 tff('439', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_E, sk_F) 535.87/78.33 | ~ sk_R(sk_E, sk_F) 535.87/78.33 | '$_eq_proxy'($i, sk_C, sk_F))) 535.87/78.33 <= (( sk_R(sk_C, sk_F)) & 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['437', '438'])). 535.87/78.33 tff('440', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_E, sk_F)) | ( '$_eq_proxy'($i, sk_C, sk_F)) | 535.87/78.33 ~ ( sk_R(sk_C, sk_F)) | ~ ( sk_R(sk_E, sk_F)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0))), 535.87/78.33 inference('split', [status(esa)], ['439'])). 535.87/78.33 tff('441', plain, 535.87/78.33 ![X5, X6, X7]: 535.87/78.33 ( '$_eq_proxy'($i, X5, X6) 535.87/78.33 | sk_R(X5, X7) 535.87/78.33 | sk_R(X6, X7) 535.87/78.33 | sk_R(X5, X6) 535.87/78.33 | '$_eq_proxy'($i, X6, X7) 535.87/78.33 | '$_eq_proxy'($i, X5, X7)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('442', plain, ~ '$_eq_proxy'($i, sk_A, sk_E), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('443', plain, 535.87/78.33 ![X0]: 535.87/78.33 ( '$_eq_proxy'($i, X0, sk_E) 535.87/78.33 | sk_R(X0, sk_A) 535.87/78.33 | sk_R(sk_A, sk_E) 535.87/78.33 | sk_R(X0, sk_E) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_A)), 535.87/78.33 inference('sup-', [status(thm)], ['441', '442'])). 535.87/78.33 tff('444', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, X0, sk_A) 535.87/78.33 | sk_R(X0, sk_A) 535.87/78.33 | sk_R(X0, sk_E) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_E))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( '$_eq_proxy'($i, X0, sk_A) 535.87/78.33 | sk_R(X0, sk_A) 535.87/78.33 | sk_R(X0, sk_E) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_E)))), 535.87/78.33 inference('split', [status(esa)], ['443'])). 535.87/78.33 tff('445', plain, ~ '$_eq_proxy'($i, sk_D, sk_E), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('446', plain, 535.87/78.33 (( sk_R(sk_D, sk_E) | sk_R(sk_D, sk_A) | '$_eq_proxy'($i, sk_D, sk_A))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( '$_eq_proxy'($i, X0, sk_A) 535.87/78.33 | sk_R(X0, sk_A) 535.87/78.33 | sk_R(X0, sk_E) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_E)))), 535.87/78.33 inference('sup-', [status(thm)], ['444', '445'])). 535.87/78.33 tff('447', plain, 535.87/78.33 ( sk_R(sk_D, sk_E)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, X0, sk_A) 535.87/78.33 | sk_R(X0, sk_A) 535.87/78.33 | sk_R(X0, sk_E) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_E))) | 535.87/78.33 ( sk_R(sk_D, sk_A)) | ( '$_eq_proxy'($i, sk_D, sk_A)), 535.87/78.33 inference('split', [status(esa)], ['446'])). 535.87/78.33 tff('448', plain, ( sk_R(sk_C, sk_F)) <= (( sk_R(sk_F, sk_C))), 535.87/78.33 inference('sup-', [status(thm)], ['296', '297'])). 535.87/78.33 tff('449', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0)))), 535.87/78.33 inference('split', [status(esa)], ['73'])). 535.87/78.33 tff('450', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_D, sk_F) 535.87/78.33 | ~ sk_R(sk_D, sk_F) 535.87/78.33 | '$_eq_proxy'($i, sk_C, sk_F))) 535.87/78.33 <= (( sk_R(sk_F, sk_C)) & 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['448', '449'])). 535.87/78.33 tff('451', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_D, sk_F)) | ( '$_eq_proxy'($i, sk_C, sk_F)) | 535.87/78.33 ~ ( sk_R(sk_D, sk_F)) | ~ ( sk_R(sk_F, sk_C)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0))), 535.87/78.33 inference('split', [status(esa)], ['450'])). 535.87/78.33 tff('452', plain, 535.87/78.33 ![X5, X6, X7]: 535.87/78.33 ( '$_eq_proxy'($i, X5, X6) 535.87/78.33 | sk_R(X5, X7) 535.87/78.33 | sk_R(X6, X7) 535.87/78.33 | sk_R(X5, X6) 535.87/78.33 | '$_eq_proxy'($i, X6, X7) 535.87/78.33 | '$_eq_proxy'($i, X5, X7)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('453', plain, ~ '$_eq_proxy'($i, sk_A, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('454', plain, 535.87/78.33 ![X0]: 535.87/78.33 ( '$_eq_proxy'($i, X0, sk_F) 535.87/78.33 | sk_R(X0, sk_A) 535.87/78.33 | sk_R(sk_A, sk_F) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_A)), 535.87/78.33 inference('sup-', [status(thm)], ['452', '453'])). 535.87/78.33 tff('455', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, X0, sk_A) 535.87/78.33 | sk_R(X0, sk_A) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( '$_eq_proxy'($i, X0, sk_A) 535.87/78.33 | sk_R(X0, sk_A) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.33 inference('split', [status(esa)], ['454'])). 535.87/78.33 tff('456', plain, ~ '$_eq_proxy'($i, sk_E, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('457', plain, 535.87/78.33 (( sk_R(sk_E, sk_F) | sk_R(sk_E, sk_A) | '$_eq_proxy'($i, sk_E, sk_A))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( '$_eq_proxy'($i, X0, sk_A) 535.87/78.33 | sk_R(X0, sk_A) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.33 inference('sup-', [status(thm)], ['455', '456'])). 535.87/78.33 tff('458', plain, 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, X0, sk_A) 535.87/78.33 | sk_R(X0, sk_A) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))) | 535.87/78.33 ( sk_R(sk_E, sk_F)) | ( sk_R(sk_E, sk_A)) | 535.87/78.33 ( '$_eq_proxy'($i, sk_E, sk_A)), 535.87/78.33 inference('split', [status(esa)], ['457'])). 535.87/78.33 tff('459', plain, ( sk_R(sk_A, sk_E)) <= (( sk_R(sk_A, sk_E))), 535.87/78.33 inference('split', [status(esa)], ['2'])). 535.87/78.33 tff('460', plain, ![X3, X4]: ( sk_R(X3, X4) | ~ sk_R(X4, X3)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('461', plain, ( sk_R(sk_E, sk_A)) <= (( sk_R(sk_A, sk_E))), 535.87/78.33 inference('sup-', [status(thm)], ['459', '460'])). 535.87/78.33 tff('462', plain, 535.87/78.33 ![X5, X6, X7]: 535.87/78.33 ( '$_eq_proxy'($i, X5, X6) 535.87/78.33 | ~ sk_R(X5, X6) 535.87/78.33 | ~ sk_R(X6, X7) 535.87/78.33 | ~ sk_R(X5, X7) 535.87/78.33 | '$_eq_proxy'($i, X6, X7) 535.87/78.33 | '$_eq_proxy'($i, X5, X7)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('463', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | ~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, sk_A))) 535.87/78.33 <= (( sk_R(sk_A, sk_E))), 535.87/78.33 inference('sup-', [status(thm)], ['461', '462'])). 535.87/78.33 tff('464', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_E, sk_A)) <= (( '$_eq_proxy'($i, sk_E, sk_A))), 535.87/78.33 inference('split', [status(esa)], ['463'])). 535.87/78.33 tff('465', plain, 535.87/78.33 ![X0 : $tType, X1 : X0, X2 : X0]: 535.87/78.33 (~ '$_eq_proxy'(X0, X1, X2) | '$_eq_proxy'(X0, X2, X1)), 535.87/78.33 trivial([status(thm)])). 535.87/78.33 tff('466', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_A, sk_E)) <= (( '$_eq_proxy'($i, sk_E, sk_A))), 535.87/78.33 inference('sup-', [status(thm)], ['464', '465'])). 535.87/78.33 tff('467', plain, ~ '$_eq_proxy'($i, sk_A, sk_E), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('468', plain, ~ ( '$_eq_proxy'($i, sk_E, sk_A)), 535.87/78.33 inference('sup-', [status(thm)], ['466', '467'])). 535.87/78.33 tff('469', plain, 535.87/78.33 ![X0, X1, X2]: 535.87/78.33 ( '$_eq_proxy'($i, X2, X0) 535.87/78.33 | sk_R(X2, X1) 535.87/78.33 | sk_R(X1, X0) 535.87/78.33 | sk_R(X2, X0) 535.87/78.33 | '$_eq_proxy'($i, X2, X1) 535.87/78.33 | '$_eq_proxy'($i, X0, X1)), 535.87/78.33 inference('sup-', [status(thm)], ['127', '128'])). 535.87/78.33 tff('470', plain, ~ '$_eq_proxy'($i, sk_A, sk_E), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('471', plain, 535.87/78.33 ![X0]: 535.87/78.33 ( '$_eq_proxy'($i, X0, sk_E) 535.87/78.33 | sk_R(X0, sk_A) 535.87/78.33 | sk_R(sk_E, sk_A) 535.87/78.33 | sk_R(X0, sk_E) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_A)), 535.87/78.33 inference('sup-', [status(thm)], ['469', '470'])). 535.87/78.33 tff('472', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, X0, sk_A) 535.87/78.33 | sk_R(X0, sk_A) 535.87/78.33 | sk_R(X0, sk_E) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_E))) | 535.87/78.33 ( sk_R(sk_E, sk_A)), inference('split', [status(esa)], ['471'])). 535.87/78.33 tff('473', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, X0, sk_A) 535.87/78.33 | sk_R(X0, sk_A) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( '$_eq_proxy'($i, X0, sk_A) 535.87/78.33 | sk_R(X0, sk_A) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.33 inference('split', [status(esa)], ['454'])). 535.87/78.33 tff('474', plain, ~ '$_eq_proxy'($i, sk_D, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('475', plain, 535.87/78.33 (( sk_R(sk_D, sk_F) | sk_R(sk_D, sk_A) | '$_eq_proxy'($i, sk_D, sk_A))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( '$_eq_proxy'($i, X0, sk_A) 535.87/78.33 | sk_R(X0, sk_A) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.33 inference('sup-', [status(thm)], ['473', '474'])). 535.87/78.33 tff('476', plain, 535.87/78.33 ( sk_R(sk_D, sk_F)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, X0, sk_A) 535.87/78.33 | sk_R(X0, sk_A) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))) | 535.87/78.33 ( sk_R(sk_D, sk_A)) | ( '$_eq_proxy'($i, sk_D, sk_A)), 535.87/78.33 inference('split', [status(esa)], ['475'])). 535.87/78.33 tff('477', plain, ( sk_R(sk_A, sk_D)) <= (( sk_R(sk_A, sk_D))), 535.87/78.33 inference('split', [status(esa)], ['6'])). 535.87/78.33 tff('478', plain, ![X3, X4]: ( sk_R(X3, X4) | ~ sk_R(X4, X3)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('479', plain, ( sk_R(sk_D, sk_A)) <= (( sk_R(sk_A, sk_D))), 535.87/78.33 inference('sup-', [status(thm)], ['477', '478'])). 535.87/78.33 tff('480', plain, 535.87/78.33 ![X5, X6, X7]: 535.87/78.33 ( '$_eq_proxy'($i, X5, X6) 535.87/78.33 | ~ sk_R(X5, X6) 535.87/78.33 | ~ sk_R(X6, X7) 535.87/78.33 | ~ sk_R(X5, X7) 535.87/78.33 | '$_eq_proxy'($i, X6, X7) 535.87/78.33 | '$_eq_proxy'($i, X5, X7)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('481', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | ~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, sk_A))) 535.87/78.33 <= (( sk_R(sk_A, sk_D))), 535.87/78.33 inference('sup-', [status(thm)], ['479', '480'])). 535.87/78.33 tff('482', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_D, sk_A)) <= (( '$_eq_proxy'($i, sk_D, sk_A))), 535.87/78.33 inference('split', [status(esa)], ['481'])). 535.87/78.33 tff('483', plain, 535.87/78.33 ![X0 : $tType, X1 : X0, X2 : X0]: 535.87/78.33 (~ '$_eq_proxy'(X0, X1, X2) | '$_eq_proxy'(X0, X2, X1)), 535.87/78.33 trivial([status(thm)])). 535.87/78.33 tff('484', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_A, sk_D)) <= (( '$_eq_proxy'($i, sk_D, sk_A))), 535.87/78.33 inference('sup-', [status(thm)], ['482', '483'])). 535.87/78.33 tff('485', plain, ~ '$_eq_proxy'($i, sk_A, sk_D), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('486', plain, ~ ( '$_eq_proxy'($i, sk_D, sk_A)), 535.87/78.33 inference('sup-', [status(thm)], ['484', '485'])). 535.87/78.33 tff('487', plain, 535.87/78.33 ![X0, X1, X2]: 535.87/78.33 ( '$_eq_proxy'($i, X1, X2) 535.87/78.33 | '$_eq_proxy'($i, X0, X2) 535.87/78.33 | sk_R(X1, X0) 535.87/78.33 | sk_R(X0, X2) 535.87/78.33 | sk_R(X1, X2) 535.87/78.33 | '$_eq_proxy'($i, X0, X1)), 535.87/78.33 inference('sup-', [status(thm)], ['34', '35'])). 535.87/78.33 tff('488', plain, ~ '$_eq_proxy'($i, sk_A, sk_E), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('489', plain, 535.87/78.33 ![X0]: 535.87/78.33 ( sk_R(sk_E, X0) 535.87/78.33 | sk_R(sk_A, X0) 535.87/78.33 | sk_R(sk_E, sk_A) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0)), 535.87/78.33 inference('sup-', [status(thm)], ['487', '488'])). 535.87/78.33 tff('490', plain, ( sk_R(sk_E, sk_A)) <= (( sk_R(sk_E, sk_A))), 535.87/78.33 inference('split', [status(esa)], ['489'])). 535.87/78.33 tff('491', plain, ![X3, X4]: ( sk_R(X3, X4) | ~ sk_R(X4, X3)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('492', plain, ( sk_R(sk_A, sk_E)) <= (( sk_R(sk_E, sk_A))), 535.87/78.33 inference('sup-', [status(thm)], ['490', '491'])). 535.87/78.33 tff('493', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.33 inference('split', [status(esa)], ['175'])). 535.87/78.33 tff('494', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_C, sk_E) 535.87/78.33 | ~ sk_R(sk_C, sk_E) 535.87/78.33 | '$_eq_proxy'($i, sk_A, sk_E))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) & 535.87/78.33 ( sk_R(sk_E, sk_A))), 535.87/78.33 inference('sup-', [status(thm)], ['492', '493'])). 535.87/78.33 tff('495', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_C, sk_E)) | ( '$_eq_proxy'($i, sk_A, sk_E)) | 535.87/78.33 ~ ( sk_R(sk_C, sk_E)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) | 535.87/78.33 ~ ( sk_R(sk_E, sk_A)), inference('split', [status(esa)], ['494'])). 535.87/78.33 tff('496', plain, ( sk_R(sk_A, sk_E)) <= (( sk_R(sk_E, sk_A))), 535.87/78.33 inference('sup-', [status(thm)], ['490', '491'])). 535.87/78.33 tff('497', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0)))), 535.87/78.33 inference('split', [status(esa)], ['208'])). 535.87/78.33 tff('498', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_A, sk_E) 535.87/78.33 | '$_eq_proxy'($i, sk_B, sk_E) 535.87/78.33 | ~ sk_R(sk_B, sk_E))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0))) & 535.87/78.33 ( sk_R(sk_E, sk_A))), 535.87/78.33 inference('sup-', [status(thm)], ['496', '497'])). 535.87/78.33 tff('499', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_B, sk_E)) | ( '$_eq_proxy'($i, sk_A, sk_E)) | 535.87/78.33 ~ ( sk_R(sk_B, sk_E)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0))) | 535.87/78.33 ~ ( sk_R(sk_E, sk_A)), inference('split', [status(esa)], ['498'])). 535.87/78.33 tff('500', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.33 inference('split', [status(esa)], ['122'])). 535.87/78.33 tff('501', plain, ~ '$_eq_proxy'($i, sk_B, sk_E), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('502', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_C, sk_E) | sk_R(sk_C, sk_E) | sk_R(sk_B, sk_E))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['500', '501'])). 535.87/78.33 tff('503', plain, 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) | 535.87/78.33 ( sk_R(sk_B, sk_E)) | ( sk_R(sk_C, sk_E)) | 535.87/78.33 ( '$_eq_proxy'($i, sk_C, sk_E)), 535.87/78.33 inference('split', [status(esa)], ['502'])). 535.87/78.33 tff('504', plain, 535.87/78.33 ![X0, X1, X2]: 535.87/78.33 ( '$_eq_proxy'($i, X1, X2) 535.87/78.33 | '$_eq_proxy'($i, X0, X2) 535.87/78.33 | sk_R(X1, X0) 535.87/78.33 | sk_R(X0, X2) 535.87/78.33 | sk_R(X1, X2) 535.87/78.33 | '$_eq_proxy'($i, X0, X1)), 535.87/78.33 inference('sup-', [status(thm)], ['34', '35'])). 535.87/78.33 tff('505', plain, ~ '$_eq_proxy'($i, sk_A, sk_D), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('506', plain, 535.87/78.33 ![X0]: 535.87/78.33 ( sk_R(sk_D, X0) 535.87/78.33 | sk_R(sk_A, X0) 535.87/78.33 | sk_R(sk_D, sk_A) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0)), 535.87/78.33 inference('sup-', [status(thm)], ['504', '505'])). 535.87/78.33 tff('507', plain, ( sk_R(sk_D, sk_A)) <= (( sk_R(sk_D, sk_A))), 535.87/78.33 inference('split', [status(esa)], ['506'])). 535.87/78.33 tff('508', plain, ![X3, X4]: ( sk_R(X3, X4) | ~ sk_R(X4, X3)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('509', plain, ( sk_R(sk_A, sk_D)) <= (( sk_R(sk_D, sk_A))), 535.87/78.33 inference('sup-', [status(thm)], ['507', '508'])). 535.87/78.33 tff('510', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.33 inference('split', [status(esa)], ['175'])). 535.87/78.33 tff('511', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_C, sk_D) 535.87/78.33 | ~ sk_R(sk_C, sk_D) 535.87/78.33 | '$_eq_proxy'($i, sk_A, sk_D))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) & 535.87/78.33 ( sk_R(sk_D, sk_A))), 535.87/78.33 inference('sup-', [status(thm)], ['509', '510'])). 535.87/78.33 tff('512', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_C, sk_D)) | ( '$_eq_proxy'($i, sk_A, sk_D)) | 535.87/78.33 ~ ( sk_R(sk_C, sk_D)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) | 535.87/78.33 ~ ( sk_R(sk_D, sk_A)), inference('split', [status(esa)], ['511'])). 535.87/78.33 tff('513', plain, ( sk_R(sk_A, sk_D)) <= (( sk_R(sk_D, sk_A))), 535.87/78.33 inference('sup-', [status(thm)], ['507', '508'])). 535.87/78.33 tff('514', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0)))), 535.87/78.33 inference('split', [status(esa)], ['208'])). 535.87/78.33 tff('515', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_A, sk_D) 535.87/78.33 | '$_eq_proxy'($i, sk_B, sk_D) 535.87/78.33 | ~ sk_R(sk_B, sk_D))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0))) & 535.87/78.33 ( sk_R(sk_D, sk_A))), 535.87/78.33 inference('sup-', [status(thm)], ['513', '514'])). 535.87/78.33 tff('516', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_B, sk_D)) | ( '$_eq_proxy'($i, sk_A, sk_D)) | 535.87/78.33 ~ ( sk_R(sk_B, sk_D)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0))) | 535.87/78.33 ~ ( sk_R(sk_D, sk_A)), inference('split', [status(esa)], ['515'])). 535.87/78.33 tff('517', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.33 inference('split', [status(esa)], ['122'])). 535.87/78.33 tff('518', plain, ~ '$_eq_proxy'($i, sk_B, sk_D), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('519', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_C, sk_D) | sk_R(sk_C, sk_D) | sk_R(sk_B, sk_D))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['517', '518'])). 535.87/78.33 tff('520', plain, 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) | 535.87/78.33 ( sk_R(sk_B, sk_D)) | ( sk_R(sk_C, sk_D)) | 535.87/78.33 ( '$_eq_proxy'($i, sk_C, sk_D)), 535.87/78.33 inference('split', [status(esa)], ['519'])). 535.87/78.33 tff('521', plain, 535.87/78.33 ( sk_R(sk_B, sk_C)) | 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(X0, sk_B) 535.87/78.33 | sk_R(X0, sk_C) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_C))), 535.87/78.33 inference('split', [status(esa)], ['409'])). 535.87/78.33 tff('522', plain, 535.87/78.33 ( sk_R(sk_B, sk_C)) | 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))), 535.87/78.33 inference('split', [status(esa)], ['122'])). 535.87/78.33 tff('523', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0))) | 535.87/78.33 ~ ( sk_R(sk_B, sk_E)) | ( '$_eq_proxy'($i, sk_B, sk_E)), 535.87/78.33 inference('split', [status(esa)], ['22'])). 535.87/78.33 tff('524', plain, ( sk_R(sk_C, sk_F)) <= (( sk_R(sk_C, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['258'])). 535.87/78.33 tff('525', plain, ![X3, X4]: ( sk_R(X3, X4) | ~ sk_R(X4, X3)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('526', plain, ( sk_R(sk_F, sk_C)) <= (( sk_R(sk_C, sk_F))), 535.87/78.33 inference('sup-', [status(thm)], ['524', '525'])). 535.87/78.33 tff('527', plain, ( sk_R(sk_A, sk_C)) <= (( sk_R(sk_A, sk_C))), 535.87/78.33 inference('split', [status(esa)], ['172'])). 535.87/78.33 tff('528', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_F, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_F, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0)))), 535.87/78.33 inference('split', [status(esa)], ['237'])). 535.87/78.33 tff('529', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_F, sk_C) 535.87/78.33 | ~ sk_R(sk_F, sk_C) 535.87/78.33 | '$_eq_proxy'($i, sk_A, sk_C))) 535.87/78.33 <= (( sk_R(sk_A, sk_C)) & 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_F, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['527', '528'])). 535.87/78.33 tff('530', plain, (~ sk_R(sk_F, sk_C)) <= (~ ( sk_R(sk_F, sk_C))), 535.87/78.33 inference('split', [status(esa)], ['529'])). 535.87/78.33 tff('531', plain, ~ ( sk_R(sk_C, sk_F)) | ( sk_R(sk_F, sk_C)), 535.87/78.33 inference('sup-', [status(thm)], ['526', '530'])). 535.87/78.33 tff('532', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.33 inference('split', [status(esa)], ['104'])). 535.87/78.33 tff('533', plain, ~ '$_eq_proxy'($i, sk_B, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('534', plain, 535.87/78.33 (( sk_R(sk_B, sk_F) | '$_eq_proxy'($i, sk_A, sk_B) | sk_R(sk_A, sk_B))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.33 inference('sup-', [status(thm)], ['532', '533'])). 535.87/78.33 tff('535', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_A, sk_B)) | ( sk_R(sk_B, sk_F)) | 535.87/78.33 ( sk_R(sk_A, sk_B)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['534'])). 535.87/78.33 tff('536', plain, 535.87/78.33 ( sk_R(sk_A, sk_F)) | 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | sk_R(X0, sk_A) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['375'])). 535.87/78.33 tff('537', plain, 535.87/78.33 ( sk_R(sk_A, sk_F)) | 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, X0, sk_A) 535.87/78.33 | sk_R(X0, sk_A) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['454'])). 535.87/78.33 tff('538', plain, 535.87/78.33 ( sk_R(sk_A, sk_F)) | 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['104'])). 535.87/78.33 tff('539', plain, 535.87/78.33 ![X5, X6, X7]: 535.87/78.33 ( '$_eq_proxy'($i, X5, X6) 535.87/78.33 | sk_R(X5, X7) 535.87/78.33 | sk_R(X6, X7) 535.87/78.33 | sk_R(X5, X6) 535.87/78.33 | '$_eq_proxy'($i, X6, X7) 535.87/78.33 | '$_eq_proxy'($i, X5, X7)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('540', plain, ~ '$_eq_proxy'($i, sk_C, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('541', plain, 535.87/78.33 ![X0]: 535.87/78.33 ( '$_eq_proxy'($i, X0, sk_F) 535.87/78.33 | sk_R(sk_C, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | sk_R(sk_C, sk_F) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0)), 535.87/78.33 inference('sup-', [status(thm)], ['539', '540'])). 535.87/78.33 tff('542', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.33 inference('split', [status(esa)], ['541'])). 535.87/78.33 tff('543', plain, ~ '$_eq_proxy'($i, sk_D, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('544', plain, 535.87/78.33 (( sk_R(sk_D, sk_F) | '$_eq_proxy'($i, sk_C, sk_D) | sk_R(sk_C, sk_D))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.33 inference('sup-', [status(thm)], ['542', '543'])). 535.87/78.33 tff('545', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_C, sk_D)) | ( sk_R(sk_D, sk_F)) | 535.87/78.33 ( sk_R(sk_C, sk_D)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['544'])). 535.87/78.33 tff('546', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.33 inference('split', [status(esa)], ['172'])). 535.87/78.33 tff('547', plain, ~ '$_eq_proxy'($i, sk_C, sk_D), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('548', plain, 535.87/78.33 (( sk_R(sk_C, sk_D) | '$_eq_proxy'($i, sk_A, sk_D) | sk_R(sk_A, sk_D))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['546', '547'])). 535.87/78.33 tff('549', plain, 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) | 535.87/78.33 ( sk_R(sk_C, sk_D)) | ( sk_R(sk_A, sk_D)) | 535.87/78.33 ( '$_eq_proxy'($i, sk_A, sk_D)), 535.87/78.33 inference('split', [status(esa)], ['548'])). 535.87/78.33 tff('550', plain, ( sk_R(sk_B, sk_D)) <= (( sk_R(sk_B, sk_D))), 535.87/78.33 inference('split', [status(esa)], ['49'])). 535.87/78.33 tff('551', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.33 inference('split', [status(esa)], ['271'])). 535.87/78.33 tff('552', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_C, sk_D) 535.87/78.33 | ~ sk_R(sk_C, sk_D) 535.87/78.33 | '$_eq_proxy'($i, sk_B, sk_D))) 535.87/78.33 <= (( sk_R(sk_B, sk_D)) & 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['550', '551'])). 535.87/78.33 tff('553', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_C, sk_D)) | ( '$_eq_proxy'($i, sk_B, sk_D)) | 535.87/78.33 ~ ( sk_R(sk_B, sk_D)) | ~ ( sk_R(sk_C, sk_D)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))), 535.87/78.33 inference('split', [status(esa)], ['552'])). 535.87/78.33 tff('554', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_C, sk_D)) <= (( '$_eq_proxy'($i, sk_C, sk_D))), 535.87/78.33 inference('split', [status(esa)], ['73'])). 535.87/78.33 tff('555', plain, ~ '$_eq_proxy'($i, sk_C, sk_D), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('556', plain, ~ ( '$_eq_proxy'($i, sk_C, sk_D)), 535.87/78.33 inference('sup-', [status(thm)], ['554', '555'])). 535.87/78.33 tff('557', plain, ( sk_R(sk_A, sk_D)) <= (( sk_R(sk_A, sk_D))), 535.87/78.33 inference('split', [status(esa)], ['6'])). 535.87/78.33 tff('558', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.33 inference('split', [status(esa)], ['175'])). 535.87/78.33 tff('559', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_C, sk_D) 535.87/78.33 | ~ sk_R(sk_C, sk_D) 535.87/78.33 | '$_eq_proxy'($i, sk_A, sk_D))) 535.87/78.33 <= (( sk_R(sk_A, sk_D)) & 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['557', '558'])). 535.87/78.33 tff('560', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_C, sk_D)) | ( '$_eq_proxy'($i, sk_A, sk_D)) | 535.87/78.33 ~ ( sk_R(sk_A, sk_D)) | ~ ( sk_R(sk_C, sk_D)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))), 535.87/78.33 inference('split', [status(esa)], ['559'])). 535.87/78.33 tff('561', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0)))), 535.87/78.33 inference('split', [status(esa)], ['181'])). 535.87/78.33 tff('562', plain, ~ '$_eq_proxy'($i, sk_B, sk_D), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('563', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_A, sk_D) | sk_R(sk_B, sk_D) | sk_R(sk_A, sk_D))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['561', '562'])). 535.87/78.33 tff('564', plain, 535.87/78.33 ( sk_R(sk_B, sk_D)) | ( sk_R(sk_A, sk_D)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0))) | 535.87/78.33 ( '$_eq_proxy'($i, sk_A, sk_D)), 535.87/78.33 inference('split', [status(esa)], ['563'])). 535.87/78.33 tff('565', plain, 535.87/78.33 ![X0, X1, X2]: 535.87/78.33 ( '$_eq_proxy'($i, X1, X2) 535.87/78.33 | '$_eq_proxy'($i, X0, X2) 535.87/78.33 | sk_R(X1, X0) 535.87/78.33 | sk_R(X0, X2) 535.87/78.33 | sk_R(X1, X2) 535.87/78.33 | '$_eq_proxy'($i, X0, X1)), 535.87/78.33 inference('sup-', [status(thm)], ['34', '35'])). 535.87/78.33 tff('566', plain, ~ '$_eq_proxy'($i, sk_A, sk_B), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('567', plain, 535.87/78.33 ![X0]: 535.87/78.33 ( sk_R(sk_B, X0) 535.87/78.33 | sk_R(sk_A, X0) 535.87/78.33 | sk_R(sk_B, sk_A) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0)), 535.87/78.33 inference('sup-', [status(thm)], ['565', '566'])). 535.87/78.33 tff('568', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0))) | 535.87/78.33 ( sk_R(sk_B, sk_A)), inference('split', [status(esa)], ['567'])). 535.87/78.33 tff('569', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_A, sk_B)) <= (( '$_eq_proxy'($i, sk_A, sk_B))), 535.87/78.33 inference('split', [status(esa)], ['208'])). 535.87/78.33 tff('570', plain, ~ '$_eq_proxy'($i, sk_A, sk_B), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('571', plain, ~ ( '$_eq_proxy'($i, sk_A, sk_B)), 535.87/78.33 inference('sup-', [status(thm)], ['569', '570'])). 535.87/78.33 tff('572', plain, ( sk_R(sk_B, sk_A)) <= (( sk_R(sk_B, sk_A))), 535.87/78.33 inference('split', [status(esa)], ['567'])). 535.87/78.33 tff('573', plain, ![X3, X4]: ( sk_R(X3, X4) | ~ sk_R(X4, X3)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('574', plain, ( sk_R(sk_A, sk_B)) <= (( sk_R(sk_B, sk_A))), 535.87/78.33 inference('sup-', [status(thm)], ['572', '573'])). 535.87/78.33 tff('575', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.33 inference('split', [status(esa)], ['175'])). 535.87/78.33 tff('576', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_C, sk_B) 535.87/78.33 | ~ sk_R(sk_C, sk_B) 535.87/78.33 | '$_eq_proxy'($i, sk_A, sk_B))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) & 535.87/78.33 ( sk_R(sk_B, sk_A))), 535.87/78.33 inference('sup-', [status(thm)], ['574', '575'])). 535.87/78.33 tff('577', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_C, sk_B)) | ( '$_eq_proxy'($i, sk_A, sk_B)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) | 535.87/78.33 ~ ( sk_R(sk_B, sk_A)) | ~ ( sk_R(sk_C, sk_B)), 535.87/78.33 inference('split', [status(esa)], ['576'])). 535.87/78.33 tff('578', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.33 inference('split', [status(esa)], ['541'])). 535.87/78.33 tff('579', plain, ~ '$_eq_proxy'($i, sk_B, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('580', plain, 535.87/78.33 (( sk_R(sk_B, sk_F) | '$_eq_proxy'($i, sk_C, sk_B) | sk_R(sk_C, sk_B))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.33 inference('sup-', [status(thm)], ['578', '579'])). 535.87/78.33 tff('581', plain, 535.87/78.33 ( sk_R(sk_C, sk_B)) | ( sk_R(sk_B, sk_F)) | 535.87/78.33 ( '$_eq_proxy'($i, sk_C, sk_B)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['580'])). 535.87/78.33 tff('582', plain, ( sk_R(sk_C, sk_B)) <= (( sk_R(sk_B, sk_C))), 535.87/78.33 inference('sup-', [status(thm)], ['145', '146'])). 535.87/78.33 tff('583', plain, 535.87/78.33 ![X5, X6, X7]: 535.87/78.33 ( '$_eq_proxy'($i, X5, X6) 535.87/78.33 | ~ sk_R(X5, X6) 535.87/78.33 | ~ sk_R(X6, X7) 535.87/78.33 | ~ sk_R(X5, X7) 535.87/78.33 | '$_eq_proxy'($i, X6, X7) 535.87/78.33 | '$_eq_proxy'($i, X5, X7)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('584', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, sk_B))) 535.87/78.33 <= (( sk_R(sk_B, sk_C))), 535.87/78.33 inference('sup-', [status(thm)], ['582', '583'])). 535.87/78.33 tff('585', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_C, sk_B)) <= (( '$_eq_proxy'($i, sk_C, sk_B))), 535.87/78.33 inference('split', [status(esa)], ['584'])). 535.87/78.33 tff('586', plain, 535.87/78.33 ![X0 : $tType, X1 : X0, X2 : X0]: 535.87/78.33 (~ '$_eq_proxy'(X0, X1, X2) | '$_eq_proxy'(X0, X2, X1)), 535.87/78.33 trivial([status(thm)])). 535.87/78.33 tff('587', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_B, sk_C)) <= (( '$_eq_proxy'($i, sk_C, sk_B))), 535.87/78.33 inference('sup-', [status(thm)], ['585', '586'])). 535.87/78.33 tff('588', plain, ~ '$_eq_proxy'($i, sk_B, sk_C), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('589', plain, ~ ( '$_eq_proxy'($i, sk_C, sk_B)), 535.87/78.33 inference('sup-', [status(thm)], ['587', '588'])). 535.87/78.33 tff('590', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))) | 535.87/78.33 ( sk_R(sk_C, sk_F)), inference('split', [status(esa)], ['541'])). 535.87/78.33 tff('591', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_B, sk_C)) <= (( '$_eq_proxy'($i, sk_B, sk_C))), 535.87/78.33 inference('split', [status(esa)], ['271'])). 535.87/78.33 tff('592', plain, ~ '$_eq_proxy'($i, sk_B, sk_C), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('593', plain, ~ ( '$_eq_proxy'($i, sk_B, sk_C)), 535.87/78.33 inference('sup-', [status(thm)], ['591', '592'])). 535.87/78.33 tff('594', plain, ( sk_R(sk_A, sk_C)) <= (( sk_R(sk_A, sk_C))), 535.87/78.33 inference('split', [status(esa)], ['172'])). 535.87/78.33 tff('595', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0)))), 535.87/78.33 inference('split', [status(esa)], ['208'])). 535.87/78.33 tff('596', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_A, sk_C) 535.87/78.33 | '$_eq_proxy'($i, sk_B, sk_C) 535.87/78.33 | ~ sk_R(sk_B, sk_C))) 535.87/78.33 <= (( sk_R(sk_A, sk_C)) & 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['594', '595'])). 535.87/78.33 tff('597', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_B, sk_C)) | ( '$_eq_proxy'($i, sk_A, sk_C)) | 535.87/78.33 ~ ( sk_R(sk_A, sk_C)) | ~ ( sk_R(sk_B, sk_C)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0))), 535.87/78.33 inference('split', [status(esa)], ['596'])). 535.87/78.33 tff('598', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.33 inference('split', [status(esa)], ['308'])). 535.87/78.33 tff('599', plain, ~ '$_eq_proxy'($i, sk_B, sk_C), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('600', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_C, sk_F) | sk_R(sk_C, sk_F) | sk_R(sk_B, sk_C))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.33 inference('sup-', [status(thm)], ['598', '599'])). 535.87/78.33 tff('601', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_C, sk_F)) | ( sk_R(sk_C, sk_F)) | 535.87/78.33 ( sk_R(sk_B, sk_C)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['600'])). 535.87/78.33 tff('602', plain, ( sk_R(sk_C, sk_F)) <= (( sk_R(sk_C, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['258'])). 535.87/78.33 tff('603', plain, 535.87/78.33 ![X5, X6, X7]: 535.87/78.33 ( '$_eq_proxy'($i, X5, X6) 535.87/78.33 | ~ sk_R(X5, X6) 535.87/78.33 | ~ sk_R(X6, X7) 535.87/78.33 | ~ sk_R(X5, X7) 535.87/78.33 | '$_eq_proxy'($i, X6, X7) 535.87/78.33 | '$_eq_proxy'($i, X5, X7)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('604', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | ~ sk_R(sk_F, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, sk_F))) 535.87/78.33 <= (( sk_R(sk_C, sk_F))), 535.87/78.33 inference('sup-', [status(thm)], ['602', '603'])). 535.87/78.33 tff('605', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_C, sk_F)) <= (( '$_eq_proxy'($i, sk_C, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['604'])). 535.87/78.33 tff('606', plain, ~ '$_eq_proxy'($i, sk_C, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('607', plain, ~ ( '$_eq_proxy'($i, sk_C, sk_F)), 535.87/78.33 inference('sup-', [status(thm)], ['605', '606'])). 535.87/78.33 tff('608', plain, ( sk_R(sk_A, sk_F)) <= (( sk_R(sk_A, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['234'])). 535.87/78.33 tff('609', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.33 inference('split', [status(esa)], ['175'])). 535.87/78.33 tff('610', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_C, sk_F) 535.87/78.33 | ~ sk_R(sk_C, sk_F) 535.87/78.33 | '$_eq_proxy'($i, sk_A, sk_F))) 535.87/78.33 <= (( sk_R(sk_A, sk_F)) & 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['608', '609'])). 535.87/78.33 tff('611', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_C, sk_F)) | ( '$_eq_proxy'($i, sk_A, sk_F)) | 535.87/78.33 ~ ( sk_R(sk_A, sk_F)) | ~ ( sk_R(sk_C, sk_F)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))), 535.87/78.33 inference('split', [status(esa)], ['610'])). 535.87/78.33 tff('612', plain, 535.87/78.33 ![X5, X6, X7]: 535.87/78.33 ( '$_eq_proxy'($i, X5, X6) 535.87/78.33 | sk_R(X5, X7) 535.87/78.33 | sk_R(X6, X7) 535.87/78.33 | sk_R(X5, X6) 535.87/78.33 | '$_eq_proxy'($i, X6, X7) 535.87/78.33 | '$_eq_proxy'($i, X5, X7)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('613', plain, ~ '$_eq_proxy'($i, sk_D, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('614', plain, 535.87/78.33 ![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0) 535.87/78.33 | sk_R(sk_D, sk_F) 535.87/78.33 | sk_R(sk_F, X0) 535.87/78.33 | sk_R(sk_D, X0)), 535.87/78.33 inference('sup-', [status(thm)], ['612', '613'])). 535.87/78.33 tff('615', plain, ( sk_R(sk_D, sk_F)) <= (( sk_R(sk_D, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['614'])). 535.87/78.33 tff('616', plain, 535.87/78.33 ![X5, X6, X7]: 535.87/78.33 ( '$_eq_proxy'($i, X5, X6) 535.87/78.33 | ~ sk_R(X5, X6) 535.87/78.33 | ~ sk_R(X6, X7) 535.87/78.33 | ~ sk_R(X5, X7) 535.87/78.33 | '$_eq_proxy'($i, X6, X7) 535.87/78.33 | '$_eq_proxy'($i, X5, X7)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('617', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | ~ sk_R(sk_F, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, sk_F))) 535.87/78.33 <= (( sk_R(sk_D, sk_F))), 535.87/78.33 inference('sup-', [status(thm)], ['615', '616'])). 535.87/78.33 tff('618', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_D, sk_F)) <= (( '$_eq_proxy'($i, sk_D, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['617'])). 535.87/78.33 tff('619', plain, ~ '$_eq_proxy'($i, sk_D, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('620', plain, ~ ( '$_eq_proxy'($i, sk_D, sk_F)), 535.87/78.33 inference('sup-', [status(thm)], ['618', '619'])). 535.87/78.33 tff('621', plain, ( sk_R(sk_A, sk_F)) <= (( sk_R(sk_A, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['234'])). 535.87/78.33 tff('622', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0)))), 535.87/78.33 inference('split', [status(esa)], ['9'])). 535.87/78.33 tff('623', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_D, sk_F) 535.87/78.33 | ~ sk_R(sk_D, sk_F) 535.87/78.33 | '$_eq_proxy'($i, sk_A, sk_F))) 535.87/78.33 <= (( sk_R(sk_A, sk_F)) & 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['621', '622'])). 535.87/78.33 tff('624', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_D, sk_F)) | ( '$_eq_proxy'($i, sk_A, sk_F)) | 535.87/78.33 ~ ( sk_R(sk_A, sk_F)) | ~ ( sk_R(sk_D, sk_F)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0))), 535.87/78.33 inference('split', [status(esa)], ['623'])). 535.87/78.33 tff('625', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_A, sk_F)) <= (( '$_eq_proxy'($i, sk_A, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['237'])). 535.87/78.33 tff('626', plain, ~ '$_eq_proxy'($i, sk_A, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('627', plain, ~ ( '$_eq_proxy'($i, sk_A, sk_F)), 535.87/78.33 inference('sup-', [status(thm)], ['625', '626'])). 535.87/78.33 tff('628', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_B, sk_F)) <= (( '$_eq_proxy'($i, sk_B, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['53'])). 535.87/78.33 tff('629', plain, ~ '$_eq_proxy'($i, sk_B, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('630', plain, ~ ( '$_eq_proxy'($i, sk_B, sk_F)), 535.87/78.33 inference('sup-', [status(thm)], ['628', '629'])). 535.87/78.33 tff('631', plain, ( sk_R(sk_A, sk_F)) <= (( sk_R(sk_A, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['234'])). 535.87/78.33 tff('632', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0)))), 535.87/78.33 inference('split', [status(esa)], ['208'])). 535.87/78.33 tff('633', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_A, sk_F) 535.87/78.33 | '$_eq_proxy'($i, sk_B, sk_F) 535.87/78.33 | ~ sk_R(sk_B, sk_F))) 535.87/78.33 <= (( sk_R(sk_A, sk_F)) & 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['631', '632'])). 535.87/78.33 tff('634', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_B, sk_F)) | ( '$_eq_proxy'($i, sk_A, sk_F)) | 535.87/78.33 ~ ( sk_R(sk_A, sk_F)) | ~ ( sk_R(sk_B, sk_F)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0))), 535.87/78.33 inference('split', [status(esa)], ['633'])). 535.87/78.33 tff('635', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))) | 535.87/78.33 ( sk_R(sk_B, sk_F)), inference('split', [status(esa)], ['308'])). 535.87/78.33 tff('636', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_A, sk_D)) <= (( '$_eq_proxy'($i, sk_A, sk_D))), 535.87/78.33 inference('split', [status(esa)], ['9'])). 535.87/78.33 tff('637', plain, ~ '$_eq_proxy'($i, sk_A, sk_D), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('638', plain, ~ ( '$_eq_proxy'($i, sk_A, sk_D)), 535.87/78.33 inference('sup-', [status(thm)], ['636', '637'])). 535.87/78.33 tff('639', plain, ( sk_R(sk_B, sk_D)) <= (( sk_R(sk_B, sk_D))), 535.87/78.33 inference('split', [status(esa)], ['49'])). 535.87/78.33 tff('640', plain, 535.87/78.33 ![X5, X6, X7]: 535.87/78.33 ( '$_eq_proxy'($i, X5, X6) 535.87/78.33 | ~ sk_R(X5, X6) 535.87/78.33 | ~ sk_R(X6, X7) 535.87/78.33 | ~ sk_R(X5, X7) 535.87/78.33 | '$_eq_proxy'($i, X6, X7) 535.87/78.33 | '$_eq_proxy'($i, X5, X7)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('641', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, sk_D))) 535.87/78.33 <= (( sk_R(sk_B, sk_D))), 535.87/78.33 inference('sup-', [status(thm)], ['639', '640'])). 535.87/78.33 tff('642', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_B, sk_D)) <= (( '$_eq_proxy'($i, sk_B, sk_D))), 535.87/78.33 inference('split', [status(esa)], ['641'])). 535.87/78.33 tff('643', plain, ~ '$_eq_proxy'($i, sk_B, sk_D), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('644', plain, ~ ( '$_eq_proxy'($i, sk_B, sk_D)), 535.87/78.33 inference('sup-', [status(thm)], ['642', '643'])). 535.87/78.33 tff('645', plain, ( sk_R(sk_A, sk_D)) <= (( sk_R(sk_A, sk_D))), 535.87/78.33 inference('split', [status(esa)], ['6'])). 535.87/78.33 tff('646', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0)))), 535.87/78.33 inference('split', [status(esa)], ['208'])). 535.87/78.33 tff('647', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_A, sk_D) 535.87/78.33 | '$_eq_proxy'($i, sk_B, sk_D) 535.87/78.33 | ~ sk_R(sk_B, sk_D))) 535.87/78.33 <= (( sk_R(sk_A, sk_D)) & 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['645', '646'])). 535.87/78.33 tff('648', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_B, sk_D)) | ( '$_eq_proxy'($i, sk_A, sk_D)) | 535.87/78.33 ~ ( sk_R(sk_A, sk_D)) | ~ ( sk_R(sk_B, sk_D)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0))), 535.87/78.33 inference('split', [status(esa)], ['647'])). 535.87/78.33 tff('649', plain, 535.87/78.33 ~ ( sk_R(sk_A, sk_B)) | 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | ~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0))) | 535.87/78.33 ( '$_eq_proxy'($i, sk_A, sk_B)), 535.87/78.33 inference('split', [status(esa)], ['208'])). 535.87/78.33 tff('650', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0))) | 535.87/78.33 ( sk_R(sk_A, sk_B)), inference('split', [status(esa)], ['181'])). 535.87/78.33 tff('651', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_A, sk_C)) <= (( '$_eq_proxy'($i, sk_A, sk_C))), 535.87/78.33 inference('split', [status(esa)], ['175'])). 535.87/78.33 tff('652', plain, ~ '$_eq_proxy'($i, sk_A, sk_C), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('653', plain, ~ ( '$_eq_proxy'($i, sk_A, sk_C)), 535.87/78.33 inference('sup-', [status(thm)], ['651', '652'])). 535.87/78.33 tff('654', plain, 535.87/78.33 ( sk_R(sk_A, sk_C)) | 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))), 535.87/78.33 inference('split', [status(esa)], ['172'])). 535.87/78.33 tff('655', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) | 535.87/78.33 ~ ( sk_R(sk_B, sk_C)) | ( '$_eq_proxy'($i, sk_B, sk_C)), 535.87/78.33 inference('split', [status(esa)], ['271'])). 535.87/78.33 tff('656', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0))) | 535.87/78.33 ~ ( sk_R(sk_A, sk_C)) | ( '$_eq_proxy'($i, sk_A, sk_C)), 535.87/78.33 inference('split', [status(esa)], ['175'])). 535.87/78.33 tff('657', plain, ( sk_R(sk_C, sk_E)) <= (( sk_R(sk_C, sk_E))), 535.87/78.33 inference('split', [status(esa)], ['150'])). 535.87/78.33 tff('658', plain, ![X3, X4]: ( sk_R(X3, X4) | ~ sk_R(X4, X3)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('659', plain, ( sk_R(sk_E, sk_C)) <= (( sk_R(sk_C, sk_E))), 535.87/78.33 inference('sup-', [status(thm)], ['657', '658'])). 535.87/78.33 tff('660', plain, ( sk_R(sk_A, sk_C)) <= (( sk_R(sk_A, sk_C))), 535.87/78.33 inference('split', [status(esa)], ['172'])). 535.87/78.33 tff('661', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0)))), 535.87/78.33 inference('split', [status(esa)], ['279'])). 535.87/78.33 tff('662', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_E, sk_C) 535.87/78.33 | ~ sk_R(sk_E, sk_C) 535.87/78.33 | '$_eq_proxy'($i, sk_A, sk_C))) 535.87/78.33 <= (( sk_R(sk_A, sk_C)) & 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['660', '661'])). 535.87/78.33 tff('663', plain, (~ sk_R(sk_E, sk_C)) <= (~ ( sk_R(sk_E, sk_C))), 535.87/78.33 inference('split', [status(esa)], ['662'])). 535.87/78.33 tff('664', plain, ~ ( sk_R(sk_C, sk_E)) | ( sk_R(sk_E, sk_C)), 535.87/78.33 inference('sup-', [status(thm)], ['659', '663'])). 535.87/78.33 tff('665', plain, 535.87/78.33 ~ ( sk_R(sk_C, sk_E)) | 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_C, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0))) | 535.87/78.33 ( '$_eq_proxy'($i, sk_C, sk_E)), 535.87/78.33 inference('split', [status(esa)], ['153'])). 535.87/78.33 tff('666', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_C, sk_E)) <= (( '$_eq_proxy'($i, sk_C, sk_E))), 535.87/78.33 inference('split', [status(esa)], ['153'])). 535.87/78.33 tff('667', plain, ~ '$_eq_proxy'($i, sk_C, sk_E), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('668', plain, ~ ( '$_eq_proxy'($i, sk_C, sk_E)), 535.87/78.33 inference('sup-', [status(thm)], ['666', '667'])). 535.87/78.33 tff('669', plain, ( sk_R(sk_D, sk_F)) <= (( sk_R(sk_D, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['614'])). 535.87/78.33 tff('670', plain, ![X3, X4]: ( sk_R(X3, X4) | ~ sk_R(X4, X3)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('671', plain, ( sk_R(sk_F, sk_D)) <= (( sk_R(sk_D, sk_F))), 535.87/78.33 inference('sup-', [status(thm)], ['669', '670'])). 535.87/78.33 tff('672', plain, (~ sk_R(sk_F, sk_D)) <= (~ ( sk_R(sk_F, sk_D))), 535.87/78.33 inference('split', [status(esa)], ['239'])). 535.87/78.33 tff('673', plain, ( sk_R(sk_F, sk_D)) | ~ ( sk_R(sk_D, sk_F)), 535.87/78.33 inference('sup-', [status(thm)], ['671', '672'])). 535.87/78.33 tff('674', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_C) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_C) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.33 inference('split', [status(esa)], ['59'])). 535.87/78.33 tff('675', plain, ~ '$_eq_proxy'($i, sk_E, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('676', plain, 535.87/78.33 (( sk_R(sk_E, sk_F) | '$_eq_proxy'($i, sk_E, sk_C) | sk_R(sk_C, sk_E))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_C) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F)))), 535.87/78.33 inference('sup-', [status(thm)], ['674', '675'])). 535.87/78.33 tff('677', plain, 535.87/78.33 ( sk_R(sk_E, sk_F)) | ( sk_R(sk_C, sk_E)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_C, X0) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_C) 535.87/78.33 | sk_R(X0, sk_F) 535.87/78.33 | '$_eq_proxy'($i, X0, sk_F))) | 535.87/78.33 ( '$_eq_proxy'($i, sk_E, sk_C)), 535.87/78.33 inference('split', [status(esa)], ['676'])). 535.87/78.33 tff('678', plain, ( sk_R(sk_E, sk_F)) <= (( sk_R(sk_E, sk_F))), 535.87/78.33 inference('split', [status(esa)], ['430'])). 535.87/78.33 tff('679', plain, ![X3, X4]: ( sk_R(X3, X4) | ~ sk_R(X4, X3)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('680', plain, ( sk_R(sk_F, sk_E)) <= (( sk_R(sk_E, sk_F))), 535.87/78.33 inference('sup-', [status(thm)], ['678', '679'])). 535.87/78.33 tff('681', plain, ( sk_R(sk_A, sk_E)) <= (( sk_R(sk_A, sk_E))), 535.87/78.33 inference('split', [status(esa)], ['2'])). 535.87/78.33 tff('682', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_F, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_F, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0)))), 535.87/78.33 inference('split', [status(esa)], ['237'])). 535.87/78.33 tff('683', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_F, sk_E) 535.87/78.33 | ~ sk_R(sk_F, sk_E) 535.87/78.33 | '$_eq_proxy'($i, sk_A, sk_E))) 535.87/78.33 <= (( sk_R(sk_A, sk_E)) & 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_F, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['681', '682'])). 535.87/78.33 tff('684', plain, (~ sk_R(sk_F, sk_E)) <= (~ ( sk_R(sk_F, sk_E))), 535.87/78.33 inference('split', [status(esa)], ['683'])). 535.87/78.33 tff('685', plain, ( sk_R(sk_F, sk_E)) | ~ ( sk_R(sk_E, sk_F)), 535.87/78.33 inference('sup-', [status(thm)], ['680', '684'])). 535.87/78.33 tff('686', plain, 535.87/78.33 ~ ( sk_R(sk_A, sk_D)) | 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0))) | 535.87/78.33 ( '$_eq_proxy'($i, sk_A, sk_D)), inference('split', [status(esa)], ['9'])). 535.87/78.33 tff('687', plain, 535.87/78.33 ~ ( sk_R(sk_B, sk_F)) | 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_F, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0))) | 535.87/78.33 ( '$_eq_proxy'($i, sk_B, sk_F)), 535.87/78.33 inference('split', [status(esa)], ['53'])). 535.87/78.33 tff('688', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0)))), 535.87/78.33 inference('split', [status(esa)], ['181'])). 535.87/78.33 tff('689', plain, ~ '$_eq_proxy'($i, sk_B, sk_F), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('690', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_A, sk_F) | sk_R(sk_B, sk_F) | sk_R(sk_A, sk_F))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['688', '689'])). 535.87/78.33 tff('691', plain, 535.87/78.33 ( sk_R(sk_A, sk_F)) | ( sk_R(sk_B, sk_F)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0))) | 535.87/78.33 ( '$_eq_proxy'($i, sk_A, sk_F)), 535.87/78.33 inference('split', [status(esa)], ['690'])). 535.87/78.33 tff('692', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_F, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0))) | 535.87/78.33 ~ ( sk_R(sk_A, sk_F)) | ( '$_eq_proxy'($i, sk_A, sk_F)), 535.87/78.33 inference('split', [status(esa)], ['237'])). 535.87/78.33 tff('693', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_A, sk_E)) <= (( '$_eq_proxy'($i, sk_A, sk_E))), 535.87/78.33 inference('split', [status(esa)], ['279'])). 535.87/78.33 tff('694', plain, ~ '$_eq_proxy'($i, sk_A, sk_E), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('695', plain, ~ ( '$_eq_proxy'($i, sk_A, sk_E)), 535.87/78.33 inference('sup-', [status(thm)], ['693', '694'])). 535.87/78.33 tff('696', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_F, sk_E)) | ( '$_eq_proxy'($i, sk_A, sk_E)) | 535.87/78.33 ~ ( sk_R(sk_A, sk_E)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_A, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0) 535.87/78.33 | ~ sk_R(sk_F, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_F, X0))) | 535.87/78.33 ~ ( sk_R(sk_F, sk_E)), inference('split', [status(esa)], ['683'])). 535.87/78.33 tff('697', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0)))), 535.87/78.33 inference('split', [status(esa)], ['181'])). 535.87/78.33 tff('698', plain, ~ '$_eq_proxy'($i, sk_B, sk_E), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('699', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_A, sk_E) | sk_R(sk_B, sk_E) | sk_R(sk_A, sk_E))) 535.87/78.33 <= ((![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['697', '698'])). 535.87/78.33 tff('700', plain, 535.87/78.33 ( sk_R(sk_B, sk_E)) | ( sk_R(sk_A, sk_E)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 ( sk_R(sk_A, X0) 535.87/78.33 | sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_A, X0))) | 535.87/78.33 ( '$_eq_proxy'($i, sk_A, sk_E)), 535.87/78.33 inference('split', [status(esa)], ['699'])). 535.87/78.33 tff('701', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_B, sk_E)) <= (( '$_eq_proxy'($i, sk_B, sk_E))), 535.87/78.33 inference('split', [status(esa)], ['22'])). 535.87/78.33 tff('702', plain, ~ '$_eq_proxy'($i, sk_B, sk_E), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('703', plain, ~ ( '$_eq_proxy'($i, sk_B, sk_E)), 535.87/78.33 inference('sup-', [status(thm)], ['701', '702'])). 535.87/78.33 tff('704', plain, ( sk_R(sk_D, sk_E)) <= (( sk_R(sk_D, sk_E))), 535.87/78.33 inference('split', [status(esa)], ['188'])). 535.87/78.33 tff('705', plain, 535.87/78.33 ![X5, X6, X7]: 535.87/78.33 ( '$_eq_proxy'($i, X5, X6) 535.87/78.33 | ~ sk_R(X5, X6) 535.87/78.33 | ~ sk_R(X6, X7) 535.87/78.33 | ~ sk_R(X5, X7) 535.87/78.33 | '$_eq_proxy'($i, X6, X7) 535.87/78.33 | '$_eq_proxy'($i, X5, X7)), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('706', plain, 535.87/78.33 (![X0]: 535.87/78.33 ( '$_eq_proxy'($i, sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_E, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | ~ sk_R(sk_E, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, sk_E))) 535.87/78.33 <= (( sk_R(sk_D, sk_E))), 535.87/78.33 inference('sup-', [status(thm)], ['704', '705'])). 535.87/78.33 tff('707', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_D, sk_E)) <= (( '$_eq_proxy'($i, sk_D, sk_E))), 535.87/78.33 inference('split', [status(esa)], ['706'])). 535.87/78.33 tff('708', plain, ~ '$_eq_proxy'($i, sk_D, sk_E), 535.87/78.33 inference('eq_encode', [status(esa)], [zf_stmt_1])). 535.87/78.33 tff('709', plain, ~ ( '$_eq_proxy'($i, sk_D, sk_E)), 535.87/78.33 inference('sup-', [status(thm)], ['707', '708'])). 535.87/78.33 tff('710', plain, ( sk_R(sk_B, sk_E)) <= (( sk_R(sk_B, sk_E))), 535.87/78.33 inference('split', [status(esa)], ['19'])). 535.87/78.33 tff('711', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0))) 535.87/78.33 <= ((![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0)))), 535.87/78.33 inference('split', [status(esa)], ['641'])). 535.87/78.33 tff('712', plain, 535.87/78.33 (( '$_eq_proxy'($i, sk_D, sk_E) 535.87/78.33 | ~ sk_R(sk_D, sk_E) 535.87/78.33 | '$_eq_proxy'($i, sk_B, sk_E))) 535.87/78.33 <= (( sk_R(sk_B, sk_E)) & 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0)))), 535.87/78.33 inference('sup-', [status(thm)], ['710', '711'])). 535.87/78.33 tff('713', plain, 535.87/78.33 ( '$_eq_proxy'($i, sk_D, sk_E)) | ( '$_eq_proxy'($i, sk_B, sk_E)) | 535.87/78.33 ~ ( sk_R(sk_B, sk_E)) | ~ ( sk_R(sk_D, sk_E)) | 535.87/78.33 ~ 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0))), 535.87/78.33 inference('split', [status(esa)], ['712'])). 535.87/78.33 tff('714', plain, 535.87/78.33 (![X0]: 535.87/78.33 (~ sk_R(sk_B, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_B, X0) 535.87/78.33 | ~ sk_R(sk_D, X0) 535.87/78.33 | '$_eq_proxy'($i, sk_D, X0))) | 535.87/78.33 ~ ( sk_R(sk_B, sk_D)) | ( '$_eq_proxy'($i, sk_B, sk_D)), 535.87/78.33 inference('split', [status(esa)], ['641'])). 535.87/78.33 tff('715', plain, $false, 535.87/78.33 inference('sat_resolution*', [status(thm)], 535.87/78.33 ['12', '25', '32', '33', '46', '56', '63', '64', '76', '83', 535.87/78.33 '90', '94', '101', '108', '119', '126', '132', '133', '144', 535.87/78.33 '156', '160', '167', '168', '178', '185', '192', '196', 535.87/78.33 '200', '204', '211', '218', '222', '229', '230', '240', 535.87/78.33 '247', '251', '255', '262', '274', '275', '282', '289', 535.87/78.33 '290', '294', '295', '301', '305', '312', '316', '320', 535.87/78.33 '324', '333', '344', '348', '359', '363', '372', '379', 535.87/78.33 '383', '387', '391', '394', '402', '406', '413', '418', 535.87/78.33 '422', '427', '436', '440', '447', '451', '458', '468', 535.87/78.33 '472', '476', '486', '495', '499', '503', '512', '516', 535.87/78.33 '520', '521', '522', '523', '531', '535', '536', '537', 535.87/78.33 '538', '545', '549', '553', '556', '560', '564', '568', 535.87/78.33 '571', '577', '581', '589', '590', '593', '597', '601', 535.87/78.33 '607', '611', '620', '624', '627', '630', '634', '635', 535.87/78.33 '638', '644', '648', '649', '650', '653', '654', '655', 535.87/78.33 '656', '664', '665', '668', '673', '677', '685', '686', 535.87/78.33 '687', '691', '692', '695', '696', '700', '703', '709', 535.87/78.33 '713', '714'])). 535.87/78.33 535.87/78.33 % SZS output end Refutation 535.87/78.33 535.87/78.33 535.87/78.33 % Terminating... 535.87/78.33 % /export/starexec/sandbox2/solver/bin/lams/p.ll.e2.sh running for 17s 535.95/78.43 % Runner terminated. 535.95/78.45 % Zipperpin 1.5 exiting 535.95/78.45 EOF