0.12/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.14 % Command : run_portfolio.sh /export/starexec/sandbox/benchmark/theBenchmark.p /export/starexec/sandbox/tmp/tmp.xHi7hweEiy 0.14/0.35 % Computer : n013.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 1200 0.14/0.35 % DateTime : Tue Jul 13 12:58:48 EDT 2021 0.14/0.35 % CPUTime : 0.14/0.35 % Running portfolio for 120 s 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.14/0.35 % Number of cores: 8 0.14/0.36 % Python version: Python 3.6.8 0.14/0.36 % Running in HO mode 0.59/0.69 % Estimated wc time : 1286 0.59/0.69 % Estimated cpu time (7 cpus) : 183.71428571428572 0.59/0.79 % /export/starexec/sandbox/solver/bin/lams/s6.sh running for 21s 0.59/0.80 % /export/starexec/sandbox/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.59/0.80 % /export/starexec/sandbox/solver/bin/lams/b.rpo.sh running for 21s 0.61/0.80 % /export/starexec/sandbox/solver/bin/lams/s6.ds.sh running for 10s 0.61/0.80 % /export/starexec/sandbox/solver/bin/lams/c.easy.sh running for 26s 0.61/0.80 % /export/starexec/sandbox/solver/bin/lams/c.s.2.sh running for 68s 0.61/0.81 % /export/starexec/sandbox/solver/bin/lams/old_b3.avatar.sh running for 15s 70.87/10.82 % /export/starexec/sandbox/solver/bin/lams/old_sp2.sh running for 17s 105.49/15.83 % /export/starexec/sandbox/solver/bin/lams/b.sh running for 31s 105.49/15.87 % /export/starexec/sandbox/solver/bin/lams/sh1.sh running for 26s 142.14/21.18 % Solved by lams/b.sh. 142.14/21.18 % Running : timeout 14 /export/starexec/sandbox/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox/tmp/tmp.xHi7hweEiy/e_input0cd8f2 --cpu-limit=12 --auto -s -p. 142.14/21.18 % done 58 iterations in 5.323s 142.14/21.18 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 142.14/21.18 % SZS output start Refutation 142.14/21.18 tff(cTHM252_pme, conjecture, 142.14/21.18 (![PROP:(((a * a) > $o > $o)),R:((a * a) > $o),S:((a * a) > $o)]: 142.14/21.18 ((^[Xx:a,Xy:a]: 142.14/21.18 (![Xp:((a * a) > $o)]: 142.14/21.18 ((PROP(Xp) & 142.14/21.18 (![Xx0:a,Xy0:a]: ((S(Xx0,Xy0) | R(Xx0,Xy0)) => Xp(Xx0,Xy0)))) => 142.14/21.18 Xp(Xx,Xy)))) = 142.14/21.18 (^[Xx:a,Xy:a]: 142.14/21.18 (![Xp:((a * a) > $o)]: 142.14/21.18 (((![Xx0:a,Xy0:a]: 142.14/21.18 (((![Xp0:((a * a) > $o)]: 142.14/21.18 ((PROP(Xp0) & 142.14/21.18 (![Xx1:a,Xy1:a]: (R(Xx1,Xy1) => Xp0(Xx1,Xy1)))) => 142.14/21.18 Xp0(Xx0,Xy0))) | 142.14/21.18 (![Xp0:((a * a) > $o)]: 142.14/21.18 (((![Xx1:a,Xy1:a]: (S(Xx1,Xy1) => Xp0(Xx1,Xy1))) & 142.14/21.18 PROP(Xp0)) => 142.14/21.18 Xp0(Xx0,Xy0)))) => 142.14/21.18 Xp(Xx0,Xy0))) & 142.14/21.18 PROP(Xp)) => 142.14/21.18 Xp(Xx,Xy))))))). 142.14/21.18 tff(zf_stmt_0, negated_conjecture, 142.14/21.18 (~ 142.14/21.18 (![PROP:(((a * a) > $o > $o)),R:((a * a) > $o),S:((a * a) > $o)]: 142.14/21.18 ((^[Xx:a,Xy:a]: 142.14/21.18 (![Xp:((a * a) > $o)]: 142.14/21.18 ((PROP(Xp) & 142.14/21.18 (![Xx0:a,Xy0:a]: ((S(Xx0,Xy0) | R(Xx0,Xy0)) => Xp(Xx0,Xy0)))) => 142.14/21.18 Xp(Xx,Xy)))) = 142.14/21.18 (^[Xx:a,Xy:a]: 142.14/21.18 (![Xp:((a * a) > $o)]: 142.14/21.18 (((![Xx0:a,Xy0:a]: 142.14/21.18 (((![Xp0:((a * a) > $o)]: 142.14/21.18 ((PROP(Xp0) & 142.14/21.18 (![Xx1:a,Xy1:a]: (R(Xx1,Xy1) => Xp0(Xx1,Xy1)))) => 142.14/21.18 Xp0(Xx0,Xy0))) | 142.14/21.18 (![Xp0:((a * a) > $o)]: 142.14/21.18 (((![Xx1:a,Xy1:a]: (S(Xx1,Xy1) => Xp0(Xx1,Xy1))) & 142.14/21.18 PROP(Xp0)) => 142.14/21.18 Xp0(Xx0,Xy0)))) => 142.14/21.18 Xp(Xx0,Xy0))) & 142.14/21.18 PROP(Xp)) => 142.14/21.18 Xp(Xx,Xy)))))))). 142.14/21.18 tff('0', plain, 142.14/21.18 ~ (!!((^[Y0 : ((a * a) > $o) > $o]: 142.14/21.18 (!!((^[Y1 : (a * a) > $o]: 142.14/21.18 (!!((^[Y2 : (a * a) > $o]: 142.14/21.18 ((^[Y3 : a,Y4 : a]: 142.14/21.18 (!!((^[Y5 : (a * a) > $o]: 142.14/21.18 ((Y0(Y5) & 142.14/21.18 (!!((^[Y6 : a]: 142.14/21.18 (!!((^[Y7 : a]: 142.14/21.18 ((Y2(Y6, Y7) | 142.14/21.18 Y1(Y6, Y7)) => 142.14/21.18 Y5(Y6, Y7))))))))) => 142.14/21.18 Y5(Y3, Y4)))))) = 142.14/21.18 (^[Y3 : a,Y4 : a]: 142.14/21.18 (!!((^[Y5 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y6 : a]: 142.14/21.18 (!!((^[Y7 : a]: 142.14/21.18 (((!!((^[Y8 : ( 142.14/21.18 a * a) > $o]: 142.14/21.18 ((Y0(Y8) & 142.14/21.18 (!!(( 142.14/21.18 ^[Y9 : a]: 142.14/21.18 ( 142.14/21.18 !!(( 142.14/21.18 ^[Y10 : a]: 142.14/21.18 (Y1(Y9, 142.14/21.18 Y10) => 142.14/21.18 Y8(Y9, 142.14/21.18 Y10))))))))) => 142.14/21.18 Y8(Y6, Y7))))) | 142.14/21.18 (!!((^[Y8 : ( 142.14/21.18 a * a) > $o]: 142.14/21.18 (((!!(( 142.14/21.18 ^[Y9 : a]: 142.14/21.18 ( 142.14/21.18 !!(( 142.14/21.18 ^[Y10 : a]: 142.14/21.18 (Y2(Y9, 142.14/21.18 Y10) => 142.14/21.18 Y8(Y9, 142.14/21.18 Y10)))))))) & 142.14/21.18 Y0(Y8)) => 142.14/21.18 Y8(Y6, Y7)))))) => 142.14/21.18 Y5(Y6, Y7)))))))) & 142.14/21.18 Y0(Y5)) => 142.14/21.18 Y5(Y3, Y4)))))))))))))))), 142.14/21.18 inference('cnf', [status(esa)], [zf_stmt_0])). 142.14/21.18 tff('1', plain, 142.14/21.18 ~ (!!((^[Y0 : (a * a) > $o]: 142.14/21.18 (!!((^[Y1 : (a * a) > $o]: 142.14/21.18 ((^[Y2 : a,Y3 : a]: 142.14/21.18 (!!((^[Y4 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y4) & 142.14/21.18 (!!((^[Y5 : a]: 142.14/21.18 (!!((^[Y6 : a]: 142.14/21.18 ((Y1(Y5, Y6) | Y0(Y5, Y6)) => 142.14/21.18 Y4(Y5, Y6))))))))) => 142.14/21.18 Y4(Y2, Y3)))))) = 142.14/21.18 (^[Y2 : a,Y3 : a]: 142.14/21.18 (!!((^[Y4 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y5 : a]: 142.14/21.18 (!!((^[Y6 : a]: 142.14/21.18 (((!!((^[Y7 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y7) & 142.14/21.18 (!!((^[Y8 : a]: 142.14/21.18 (!!(( 142.14/21.18 ^[Y9 : a]: 142.14/21.18 ( 142.14/21.18 Y0(Y8, 142.14/21.18 Y9) => 142.14/21.18 Y7(Y8, 142.14/21.18 Y9))))))))) => 142.14/21.18 Y7(Y5, Y6))))) | 142.14/21.18 (!!((^[Y7 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y8 : a]: 142.14/21.18 (!!(( 142.14/21.18 ^[Y9 : a]: 142.14/21.18 ( 142.14/21.18 Y1(Y8, 142.14/21.18 Y9) => 142.14/21.18 Y7(Y8, 142.14/21.18 Y9)))))))) & 142.14/21.18 '#sk1'(Y7)) => 142.14/21.18 Y7(Y5, Y6)))))) => 142.14/21.18 Y4(Y5, Y6)))))))) & 142.14/21.18 '#sk1'(Y4)) => 142.14/21.18 Y4(Y2, Y3))))))))))))), 142.14/21.18 inference('lazy_cnf_exists', [status(thm)], ['0'])). 142.14/21.18 tff('2', plain, 142.14/21.18 ~ (!!((^[Y0 : (a * a) > $o]: 142.14/21.18 ((^[Y1 : a,Y2 : a]: 142.14/21.18 (!!((^[Y3 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y3) & 142.14/21.18 (!!((^[Y4 : a]: 142.14/21.18 (!!((^[Y5 : a]: 142.14/21.18 ((Y0(Y4, Y5) | '#sk2'(Y4, Y5)) => 142.14/21.18 Y3(Y4, Y5))))))))) => 142.14/21.18 Y3(Y1, Y2)))))) = 142.14/21.18 (^[Y1 : a,Y2 : a]: 142.14/21.18 (!!((^[Y3 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y4 : a]: 142.14/21.18 (!!((^[Y5 : a]: 142.14/21.18 (((!!((^[Y6 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y6) & 142.14/21.18 (!!((^[Y7 : a]: 142.14/21.18 (!!((^[Y8 : a]: 142.14/21.18 ('#sk2'(Y7, 142.14/21.18 Y8) => 142.14/21.18 Y6(Y7, Y8))))))))) => 142.14/21.18 Y6(Y4, Y5))))) | 142.14/21.18 (!!((^[Y6 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y7 : a]: 142.14/21.18 (!!((^[Y8 : a]: 142.14/21.18 (Y0(Y7, Y8) => 142.14/21.18 Y6(Y7, Y8)))))))) & 142.14/21.18 '#sk1'(Y6)) => 142.14/21.18 Y6(Y4, Y5)))))) => 142.14/21.18 Y3(Y4, Y5)))))))) & 142.14/21.18 '#sk1'(Y3)) => 142.14/21.18 Y3(Y1, Y2)))))))))), 142.14/21.18 inference('lazy_cnf_exists', [status(thm)], ['1'])). 142.14/21.18 tff('3', plain, 142.14/21.18 (^[Y0 : a,Y1 : a]: 142.14/21.18 (!!((^[Y2 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y2) & 142.14/21.18 (!!((^[Y3 : a]: 142.14/21.18 (!!((^[Y4 : a]: 142.14/21.18 (('#sk3'(Y3, Y4) | '#sk2'(Y3, Y4)) => 142.14/21.18 Y2(Y3, Y4))))))))) => 142.14/21.18 Y2(Y0, Y1)))))) 142.14/21.18 != (^[Y0 : a,Y1 : a]: 142.14/21.18 (!!((^[Y2 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y3 : a]: 142.14/21.18 (!!((^[Y4 : a]: 142.14/21.18 (((!!((^[Y5 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y5) & 142.14/21.18 (!!((^[Y6 : a]: 142.14/21.18 (!!((^[Y7 : a]: 142.14/21.18 ('#sk2'(Y6, Y7) => 142.14/21.18 Y5(Y6, Y7))))))))) => 142.14/21.18 Y5(Y3, Y4))))) | 142.14/21.18 (!!((^[Y5 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y6 : a]: 142.14/21.18 (!!((^[Y7 : a]: 142.14/21.18 ('#sk3'(Y6, Y7) => 142.14/21.18 Y5(Y6, Y7)))))))) & 142.14/21.18 '#sk1'(Y5)) => 142.14/21.18 Y5(Y3, Y4)))))) => 142.14/21.18 Y2(Y3, Y4)))))))) & 142.14/21.18 '#sk1'(Y2)) => 142.14/21.18 Y2(Y0, Y1)))))), 142.14/21.18 inference('lazy_cnf_exists', [status(thm)], ['2'])). 142.14/21.18 tff('4', plain, 142.14/21.18 (^[Y0 : a,Y1 : a]: 142.14/21.18 (!!((^[Y2 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y2) & 142.14/21.18 (!!((^[Y3 : a]: 142.14/21.18 (!!((^[Y4 : a]: 142.14/21.18 (('#sk3'(Y3, Y4) | '#sk2'(Y3, Y4)) => 142.14/21.18 Y2(Y3, Y4))))))))) => 142.14/21.18 Y2(Y0, Y1))))))('#_fresh_sk4', '#_fresh_sk5') 142.14/21.18 != (^[Y0 : a,Y1 : a]: 142.14/21.18 (!!((^[Y2 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y3 : a]: 142.14/21.18 (!!((^[Y4 : a]: 142.14/21.18 (((!!((^[Y5 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y5) & 142.14/21.18 (!!((^[Y6 : a]: 142.14/21.18 (!!((^[Y7 : a]: 142.14/21.18 ('#sk2'(Y6, Y7) => 142.14/21.18 Y5(Y6, Y7))))))))) => 142.14/21.18 Y5(Y3, Y4))))) | 142.14/21.18 (!!((^[Y5 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y6 : a]: 142.14/21.18 (!!((^[Y7 : a]: 142.14/21.18 ('#sk3'(Y6, Y7) => 142.14/21.18 Y5(Y6, Y7)))))))) & 142.14/21.18 '#sk1'(Y5)) => 142.14/21.18 Y5(Y3, Y4)))))) => 142.14/21.18 Y2(Y3, Y4)))))))) & 142.14/21.18 '#sk1'(Y2)) => 142.14/21.18 Y2(Y0, Y1))))))('#_fresh_sk4', '#_fresh_sk5'), 142.14/21.18 inference('neg_ext', [status(thm)], ['3'])). 142.14/21.18 tff('5', plain, 142.14/21.18 (!!((^[Y0 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y0) & 142.14/21.18 (!!((^[Y1 : a]: 142.14/21.18 (!!((^[Y2 : a]: 142.14/21.18 (('#sk3'(Y1, Y2) | '#sk2'(Y1, Y2)) => Y0(Y1, Y2))))))))) => 142.14/21.18 Y0('#_fresh_sk4', '#_fresh_sk5'))))) 142.14/21.18 != (!!((^[Y0 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y1 : a]: 142.14/21.18 (!!((^[Y2 : a]: 142.14/21.18 (((!!((^[Y3 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y3) & 142.14/21.18 (!!((^[Y4 : a]: 142.14/21.18 (!!((^[Y5 : a]: 142.14/21.18 ('#sk2'(Y4, Y5) => 142.14/21.18 Y3(Y4, Y5))))))))) => 142.14/21.18 Y3(Y1, Y2))))) | 142.14/21.18 (!!((^[Y3 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y4 : a]: 142.14/21.18 (!!((^[Y5 : a]: 142.14/21.18 ('#sk3'(Y4, Y5) => 142.14/21.18 Y3(Y4, Y5)))))))) & 142.14/21.18 '#sk1'(Y3)) => 142.14/21.18 Y3(Y1, Y2)))))) => 142.14/21.18 Y0(Y1, Y2)))))))) & 142.14/21.18 '#sk1'(Y0)) => 142.14/21.18 Y0('#_fresh_sk4', '#_fresh_sk5'))))), 142.14/21.18 inference('ho_norm', [status(thm)], ['4'])). 142.14/21.18 tff('6', plain, 142.14/21.18 (~ (!!((^[Y0 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y0) & 142.14/21.18 (!!((^[Y1 : a]: 142.14/21.18 (!!((^[Y2 : a]: 142.14/21.18 (('#sk3'(Y1, Y2) | '#sk2'(Y1, Y2)) => 142.14/21.18 Y0(Y1, Y2))))))))) => 142.14/21.18 Y0('#_fresh_sk4', '#_fresh_sk5'))))) 142.14/21.18 | ~ (!!((^[Y0 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y1 : a]: 142.14/21.18 (!!((^[Y2 : a]: 142.14/21.18 (((!!((^[Y3 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y3) & 142.14/21.18 (!!((^[Y4 : a]: 142.14/21.18 (!!((^[Y5 : a]: 142.14/21.18 ('#sk2'(Y4, Y5) => 142.14/21.18 Y3(Y4, Y5))))))))) => 142.14/21.18 Y3(Y1, Y2))))) | 142.14/21.18 (!!((^[Y3 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y4 : a]: 142.14/21.18 (!!((^[Y5 : a]: 142.14/21.18 ('#sk3'(Y4, Y5) => 142.14/21.18 Y3(Y4, Y5)))))))) & 142.14/21.18 '#sk1'(Y3)) => 142.14/21.18 Y3(Y1, Y2)))))) => 142.14/21.18 Y0(Y1, Y2)))))))) & 142.14/21.18 '#sk1'(Y0)) => 142.14/21.18 Y0('#_fresh_sk4', '#_fresh_sk5')))))), 142.14/21.18 inference('eq_elim', [status(thm)], ['5'])). 142.14/21.18 tff('7', plain, 142.14/21.18 (~ (('#sk1'('#sk6') & 142.14/21.18 (!!((^[Y0 : a]: 142.14/21.18 (!!((^[Y1 : a]: 142.14/21.18 (('#sk3'(Y0, Y1) | '#sk2'(Y0, Y1)) => '#sk6'(Y0, Y1))))))))) => 142.14/21.18 '#sk6'('#_fresh_sk4', '#_fresh_sk5')) 142.14/21.18 | ~ (!!((^[Y0 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y1 : a]: 142.14/21.18 (!!((^[Y2 : a]: 142.14/21.18 (((!!((^[Y3 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y3) & 142.14/21.18 (!!((^[Y4 : a]: 142.14/21.18 (!!((^[Y5 : a]: 142.14/21.18 ('#sk2'(Y4, Y5) => 142.14/21.18 Y3(Y4, Y5))))))))) => 142.14/21.18 Y3(Y1, Y2))))) | 142.14/21.18 (!!((^[Y3 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y4 : a]: 142.14/21.18 (!!((^[Y5 : a]: 142.14/21.18 ('#sk3'(Y4, Y5) => 142.14/21.18 Y3(Y4, Y5)))))))) & 142.14/21.18 '#sk1'(Y3)) => 142.14/21.18 Y3(Y1, Y2)))))) => 142.14/21.18 Y0(Y1, Y2)))))))) & 142.14/21.18 '#sk1'(Y0)) => 142.14/21.18 Y0('#_fresh_sk4', '#_fresh_sk5')))))), 142.14/21.18 inference('lazy_cnf_exists', [status(thm)], ['6'])). 142.14/21.18 tff('8', plain, 142.14/21.18 (~ '#sk6'('#_fresh_sk4', '#_fresh_sk5') 142.14/21.18 | ~ (!!((^[Y0 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y1 : a]: 142.14/21.18 (!!((^[Y2 : a]: 142.14/21.18 (((!!((^[Y3 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y3) & 142.14/21.18 (!!((^[Y4 : a]: 142.14/21.18 (!!((^[Y5 : a]: 142.14/21.18 ('#sk2'(Y4, Y5) => 142.14/21.18 Y3(Y4, Y5))))))))) => 142.14/21.18 Y3(Y1, Y2))))) | 142.14/21.18 (!!((^[Y3 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y4 : a]: 142.14/21.18 (!!((^[Y5 : a]: 142.14/21.18 ('#sk3'(Y4, Y5) => 142.14/21.18 Y3(Y4, Y5)))))))) & 142.14/21.18 '#sk1'(Y3)) => 142.14/21.18 Y3(Y1, Y2)))))) => 142.14/21.18 Y0(Y1, Y2)))))))) & 142.14/21.18 '#sk1'(Y0)) => 142.14/21.18 Y0('#_fresh_sk4', '#_fresh_sk5')))))), 142.14/21.18 inference('lazy_cnf_imply', [status(thm)], ['7'])). 142.14/21.18 tff('9', plain, 142.14/21.18 (~ (((!!((^[Y0 : a]: 142.14/21.18 (!!((^[Y1 : a]: 142.14/21.18 (((!!((^[Y2 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y2) & 142.14/21.18 (!!((^[Y3 : a]: 142.14/21.18 (!!((^[Y4 : a]: 142.14/21.18 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 142.14/21.18 Y2(Y0, Y1))))) | 142.14/21.18 (!!((^[Y2 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y3 : a]: 142.14/21.18 (!!((^[Y4 : a]: 142.14/21.18 ('#sk3'(Y3, Y4) => Y2(Y3, Y4)))))))) & 142.14/21.18 '#sk1'(Y2)) => 142.14/21.18 Y2(Y0, Y1)))))) => 142.14/21.18 '#sk7'(Y0, Y1)))))))) & 142.14/21.18 '#sk1'('#sk7')) => 142.14/21.18 '#sk7'('#_fresh_sk4', '#_fresh_sk5')) 142.14/21.18 | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5')), 142.14/21.18 inference('lazy_cnf_exists', [status(thm)], ['8'])). 142.14/21.18 tff('10', plain, 142.14/21.18 ( ((!!((^[Y0 : a]: 142.14/21.18 (!!((^[Y1 : a]: 142.14/21.18 (((!!((^[Y2 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y2) & 142.14/21.18 (!!((^[Y3 : a]: 142.14/21.18 (!!((^[Y4 : a]: 142.14/21.18 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 142.14/21.18 Y2(Y0, Y1))))) | 142.14/21.18 (!!((^[Y2 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y3 : a]: 142.14/21.18 (!!((^[Y4 : a]: 142.14/21.18 ('#sk3'(Y3, Y4) => Y2(Y3, Y4)))))))) & 142.14/21.18 '#sk1'(Y2)) => 142.14/21.18 Y2(Y0, Y1)))))) => 142.14/21.18 '#sk7'(Y0, Y1)))))))) & 142.14/21.18 '#sk1'('#sk7')) 142.14/21.18 | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5')), 142.14/21.18 inference('lazy_cnf_imply', [status(thm)], ['9'])). 142.14/21.18 tff('11', plain, 142.14/21.18 ( (!!((^[Y0 : a]: 142.14/21.18 (!!((^[Y1 : a]: 142.14/21.18 (((!!((^[Y2 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y2) & 142.14/21.18 (!!((^[Y3 : a]: 142.14/21.18 (!!((^[Y4 : a]: 142.14/21.18 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 142.14/21.18 Y2(Y0, Y1))))) | 142.14/21.18 (!!((^[Y2 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y3 : a]: 142.14/21.18 (!!((^[Y4 : a]: 142.14/21.18 ('#sk3'(Y3, Y4) => Y2(Y3, Y4)))))))) & 142.14/21.18 '#sk1'(Y2)) => 142.14/21.18 Y2(Y0, Y1)))))) => 142.14/21.18 '#sk7'(Y0, Y1)))))))) 142.14/21.18 | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5')), 142.14/21.18 inference('lazy_cnf_and', [status(thm)], ['10'])). 142.14/21.18 tff('12', plain, 142.14/21.18 ![X1 : a]: 142.14/21.18 ( (!!((^[Y0 : a]: 142.14/21.18 (((!!((^[Y1 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y1) & 142.14/21.18 (!!((^[Y2 : a]: 142.14/21.18 (!!((^[Y3 : a]: 142.14/21.18 ('#sk2'(Y2, Y3) => Y1(Y2, Y3))))))))) => 142.14/21.18 Y1(X1, Y0))))) | 142.14/21.18 (!!((^[Y1 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y2 : a]: 142.14/21.18 (!!((^[Y3 : a]: 142.14/21.18 ('#sk3'(Y2, Y3) => Y1(Y2, Y3)))))))) & 142.14/21.18 '#sk1'(Y1)) => 142.14/21.18 Y1(X1, Y0)))))) => 142.14/21.18 '#sk7'(X1, Y0))))) 142.14/21.18 | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5')), 142.14/21.18 inference('lazy_cnf_forall', [status(thm)], ['11'])). 142.14/21.18 tff('13', plain, 142.14/21.18 ![X1 : a, X2 : a]: 142.14/21.18 ( (((!!((^[Y0 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y0) & 142.14/21.18 (!!((^[Y1 : a]: 142.14/21.18 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 142.14/21.18 Y0(X1, X2))))) | 142.14/21.18 (!!((^[Y0 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y1 : a]: 142.14/21.18 (!!((^[Y2 : a]: ('#sk3'(Y1, Y2) => Y0(Y1, Y2)))))))) & 142.14/21.18 '#sk1'(Y0)) => 142.14/21.18 Y0(X1, X2)))))) => 142.14/21.18 '#sk7'(X1, X2)) 142.14/21.18 | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5')), 142.14/21.18 inference('lazy_cnf_forall', [status(thm)], ['12'])). 142.14/21.18 tff('14', plain, 142.14/21.18 ![X1 : a, X2 : a]: 142.14/21.18 (~ ((!!((^[Y0 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y0) & 142.14/21.18 (!!((^[Y1 : a]: 142.14/21.18 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 142.14/21.18 Y0(X1, X2))))) | 142.14/21.18 (!!((^[Y0 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y1 : a]: 142.14/21.18 (!!((^[Y2 : a]: ('#sk3'(Y1, Y2) => Y0(Y1, Y2)))))))) & 142.14/21.18 '#sk1'(Y0)) => 142.14/21.18 Y0(X1, X2)))))) 142.14/21.18 | '#sk7'(X1, X2) 142.14/21.18 | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5')), 142.14/21.18 inference('lazy_cnf_imply', [status(thm)], ['13'])). 142.14/21.18 tff('15', plain, 142.14/21.18 ![X1 : a, X2 : a]: 142.14/21.18 (~ (!!((^[Y0 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y1 : a]: 142.14/21.18 (!!((^[Y2 : a]: ('#sk3'(Y1, Y2) => Y0(Y1, Y2)))))))) & 142.14/21.18 '#sk1'(Y0)) => 142.14/21.18 Y0(X1, X2))))) 142.14/21.18 | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5') 142.14/21.18 | '#sk7'(X1, X2)), 142.14/21.18 inference('lazy_cnf_or', [status(thm)], ['14'])). 142.14/21.18 tff('16', plain, 142.14/21.18 ![X1 : a, X2 : a]: 142.14/21.18 (~ (((!!((^[Y0 : a]: 142.14/21.18 (!!((^[Y1 : a]: ('#sk3'(Y0, Y1) => '#sk10'(X1, X2, Y0, Y1)))))))) & 142.14/21.18 '#sk1'('#sk10'(X1, X2))) => 142.14/21.18 '#sk10'(X1, X2, X1, X2)) 142.14/21.18 | '#sk7'(X1, X2) 142.14/21.18 | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5')), 142.14/21.18 inference('lazy_cnf_exists', [status(thm)], ['15'])). 142.14/21.18 tff('17', plain, 142.14/21.18 ![X1 : a, X2 : a]: 142.14/21.18 ( ((!!((^[Y0 : a]: 142.14/21.18 (!!((^[Y1 : a]: ('#sk3'(Y0, Y1) => '#sk10'(X1, X2, Y0, Y1)))))))) & 142.14/21.18 '#sk1'('#sk10'(X1, X2))) 142.14/21.18 | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5') 142.14/21.18 | '#sk7'(X1, X2)), 142.14/21.18 inference('lazy_cnf_imply', [status(thm)], ['16'])). 142.14/21.18 tff('18', plain, 142.14/21.18 ![X1 : a, X2 : a]: 142.14/21.18 ( (!!((^[Y0 : a]: 142.14/21.18 (!!((^[Y1 : a]: ('#sk3'(Y0, Y1) => '#sk10'(X1, X2, Y0, Y1)))))))) 142.14/21.18 | '#sk7'(X1, X2) 142.14/21.18 | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5')), 142.14/21.18 inference('lazy_cnf_and', [status(thm)], ['17'])). 142.14/21.18 tff('19', plain, 142.14/21.18 ![X1 : a, X2 : a, X3 : a]: 142.14/21.18 ( (!!((^[Y0 : a]: ('#sk3'(X3, Y0) => '#sk10'(X1, X2, X3, Y0))))) 142.14/21.18 | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5') 142.14/21.18 | '#sk7'(X1, X2)), 142.14/21.18 inference('lazy_cnf_forall', [status(thm)], ['18'])). 142.14/21.18 tff('20', plain, 142.14/21.18 ![X1 : a, X2 : a, X3 : a, X4 : a]: 142.14/21.18 ( ('#sk3'(X3, X4) => '#sk10'(X1, X2, X3, X4)) 142.14/21.18 | '#sk7'(X1, X2) 142.14/21.18 | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5')), 142.14/21.18 inference('lazy_cnf_forall', [status(thm)], ['19'])). 142.14/21.18 tff('21', plain, 142.14/21.18 ![X1 : a, X2 : a, X3 : a, X4 : a]: 142.14/21.18 (~ '#sk3'(X3, X4) 142.14/21.18 | '#sk10'(X1, X2, X3, X4) 142.14/21.18 | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5') 142.14/21.18 | '#sk7'(X1, X2)), 142.14/21.18 inference('lazy_cnf_imply', [status(thm)], ['20'])). 142.14/21.18 tff('22', plain, 142.14/21.18 ![X1 : a, X2 : a]: 142.14/21.18 (~ '#sk10'(X1, X2, X1, X2) 142.14/21.18 | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5') 142.14/21.18 | '#sk7'(X1, X2)), 142.14/21.18 inference('lazy_cnf_imply', [status(thm)], ['16'])). 142.14/21.18 tff('23', plain, 142.14/21.18 ![X0 : a, X1 : a]: 142.14/21.18 ( '#sk7'(X1, X0) 142.14/21.18 | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5') 142.14/21.18 | ~ '#sk3'(X1, X0) 142.14/21.18 | '#sk7'(X1, X0) 142.14/21.18 | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5')), 142.14/21.18 inference('sup-', [status(thm)], ['21', '22'])). 142.14/21.18 tff('24', plain, 142.14/21.18 ![X0 : a, X1 : a]: 142.14/21.18 (~ '#sk3'(X1, X0) 142.14/21.18 | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5') 142.14/21.18 | '#sk7'(X1, X0)), 142.14/21.18 inference('simplify', [status(thm)], ['23'])). 142.14/21.18 tff('25', plain, 142.14/21.18 (~ '#sk7'('#_fresh_sk4', '#_fresh_sk5') 142.14/21.18 | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5')), 142.14/21.18 inference('lazy_cnf_imply', [status(thm)], ['9'])). 142.14/21.18 tff('26', plain, 142.14/21.18 ![X1 : a, X2 : a]: 142.14/21.18 (~ (!!((^[Y0 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y0) & 142.14/21.18 (!!((^[Y1 : a]: 142.14/21.18 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 142.14/21.18 Y0(X1, X2))))) 142.14/21.18 | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5') 142.14/21.18 | '#sk7'(X1, X2)), 142.14/21.18 inference('lazy_cnf_or', [status(thm)], ['14'])). 142.14/21.18 tff('27', plain, 142.14/21.18 ![X1 : a, X2 : a]: 142.14/21.18 (~ (('#sk1'('#sk9'(X1, X2)) & 142.14/21.18 (!!((^[Y0 : a]: 142.14/21.18 (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => '#sk9'(X1, X2, Y0, Y1))))))))) => 142.14/21.18 '#sk9'(X1, X2, X1, X2)) 142.14/21.18 | '#sk7'(X1, X2) 142.14/21.18 | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5')), 142.14/21.18 inference('lazy_cnf_exists', [status(thm)], ['26'])). 142.14/21.18 tff('28', plain, 142.14/21.18 ![X1 : a, X2 : a]: 142.14/21.18 ( ('#sk1'('#sk9'(X1, X2)) & 142.14/21.18 (!!((^[Y0 : a]: 142.14/21.18 (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => '#sk9'(X1, X2, Y0, Y1))))))))) 142.14/21.18 | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5') 142.14/21.18 | '#sk7'(X1, X2)), 142.14/21.18 inference('lazy_cnf_imply', [status(thm)], ['27'])). 142.14/21.18 tff('29', plain, 142.14/21.18 ![X1 : a, X2 : a]: 142.14/21.18 ( (!!((^[Y0 : a]: 142.14/21.18 (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => '#sk9'(X1, X2, Y0, Y1)))))))) 142.14/21.18 | '#sk7'(X1, X2) 142.14/21.18 | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5')), 142.14/21.18 inference('lazy_cnf_and', [status(thm)], ['28'])). 142.14/21.18 tff('30', plain, 142.14/21.18 ![X1 : a, X2 : a, X3 : a]: 142.14/21.18 ( (!!((^[Y0 : a]: ('#sk2'(X3, Y0) => '#sk9'(X1, X2, X3, Y0))))) 142.14/21.18 | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5') 142.14/21.18 | '#sk7'(X1, X2)), 142.14/21.18 inference('lazy_cnf_forall', [status(thm)], ['29'])). 142.14/21.18 tff('31', plain, 142.14/21.18 ![X1 : a, X2 : a, X3 : a, X4 : a]: 142.14/21.18 ( ('#sk2'(X3, X4) => '#sk9'(X1, X2, X3, X4)) 142.14/21.18 | '#sk7'(X1, X2) 142.14/21.18 | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5')), 142.14/21.18 inference('lazy_cnf_forall', [status(thm)], ['30'])). 142.14/21.18 tff('32', plain, 142.14/21.18 ![X1 : a, X2 : a, X3 : a, X4 : a]: 142.14/21.18 (~ '#sk2'(X3, X4) 142.14/21.18 | '#sk9'(X1, X2, X3, X4) 142.14/21.18 | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5') 142.14/21.18 | '#sk7'(X1, X2)), 142.14/21.18 inference('lazy_cnf_imply', [status(thm)], ['31'])). 142.14/21.18 tff('33', plain, 142.14/21.18 ![X1 : a, X2 : a]: 142.14/21.18 (~ '#sk9'(X1, X2, X1, X2) 142.14/21.18 | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5') 142.14/21.18 | '#sk7'(X1, X2)), 142.14/21.18 inference('lazy_cnf_imply', [status(thm)], ['27'])). 142.14/21.18 tff('34', plain, 142.14/21.18 ![X0 : a, X1 : a]: 142.14/21.18 ( '#sk7'(X1, X0) 142.14/21.18 | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5') 142.14/21.18 | ~ '#sk2'(X1, X0) 142.14/21.18 | '#sk7'(X1, X0) 142.14/21.18 | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5')), 142.14/21.18 inference('sup-', [status(thm)], ['32', '33'])). 142.14/21.18 tff('35', plain, 142.14/21.18 ![X0 : a, X1 : a]: 142.14/21.18 (~ '#sk2'(X1, X0) 142.14/21.18 | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5') 142.14/21.18 | '#sk7'(X1, X0)), 142.14/21.18 inference('simplify', [status(thm)], ['34'])). 142.14/21.18 tff('36', plain, 142.14/21.18 ( ('#sk1'('#sk6') & 142.14/21.18 (!!((^[Y0 : a]: 142.14/21.18 (!!((^[Y1 : a]: 142.14/21.18 (('#sk3'(Y0, Y1) | '#sk2'(Y0, Y1)) => '#sk6'(Y0, Y1))))))))) 142.14/21.18 | ~ (!!((^[Y0 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y1 : a]: 142.14/21.18 (!!((^[Y2 : a]: 142.14/21.18 (((!!((^[Y3 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y3) & 142.14/21.18 (!!((^[Y4 : a]: 142.14/21.18 (!!((^[Y5 : a]: 142.14/21.18 ('#sk2'(Y4, Y5) => 142.14/21.18 Y3(Y4, Y5))))))))) => 142.14/21.18 Y3(Y1, Y2))))) | 142.14/21.18 (!!((^[Y3 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y4 : a]: 142.14/21.18 (!!((^[Y5 : a]: 142.14/21.18 ('#sk3'(Y4, Y5) => 142.14/21.18 Y3(Y4, Y5)))))))) & 142.14/21.18 '#sk1'(Y3)) => 142.14/21.18 Y3(Y1, Y2)))))) => 142.14/21.18 Y0(Y1, Y2)))))))) & 142.14/21.18 '#sk1'(Y0)) => 142.14/21.18 Y0('#_fresh_sk4', '#_fresh_sk5')))))), 142.14/21.18 inference('lazy_cnf_imply', [status(thm)], ['7'])). 142.14/21.18 tff('37', plain, 142.14/21.18 ( '#sk1'('#sk6') 142.14/21.18 | ~ (!!((^[Y0 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y1 : a]: 142.14/21.18 (!!((^[Y2 : a]: 142.14/21.18 (((!!((^[Y3 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y3) & 142.14/21.18 (!!((^[Y4 : a]: 142.14/21.18 (!!((^[Y5 : a]: 142.14/21.18 ('#sk2'(Y4, Y5) => 142.14/21.18 Y3(Y4, Y5))))))))) => 142.14/21.18 Y3(Y1, Y2))))) | 142.14/21.18 (!!((^[Y3 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y4 : a]: 142.14/21.18 (!!((^[Y5 : a]: 142.14/21.18 ('#sk3'(Y4, Y5) => 142.14/21.18 Y3(Y4, Y5)))))))) & 142.14/21.18 '#sk1'(Y3)) => 142.14/21.18 Y3(Y1, Y2)))))) => 142.14/21.18 Y0(Y1, Y2)))))))) & 142.14/21.18 '#sk1'(Y0)) => 142.14/21.18 Y0('#_fresh_sk4', '#_fresh_sk5')))))), 142.14/21.18 inference('lazy_cnf_and', [status(thm)], ['36'])). 142.14/21.18 tff('38', plain, 142.14/21.18 (~ (((!!((^[Y0 : a]: 142.14/21.18 (!!((^[Y1 : a]: 142.14/21.18 (((!!((^[Y2 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y2) & 142.14/21.18 (!!((^[Y3 : a]: 142.14/21.18 (!!((^[Y4 : a]: 142.14/21.18 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 142.14/21.18 Y2(Y0, Y1))))) | 142.14/21.18 (!!((^[Y2 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y3 : a]: 142.14/21.18 (!!((^[Y4 : a]: 142.14/21.18 ('#sk3'(Y3, Y4) => Y2(Y3, Y4)))))))) & 142.14/21.18 '#sk1'(Y2)) => 142.14/21.18 Y2(Y0, Y1)))))) => 142.14/21.18 '#sk7'(Y0, Y1)))))))) & 142.14/21.18 '#sk1'('#sk7')) => 142.14/21.18 '#sk7'('#_fresh_sk4', '#_fresh_sk5')) 142.14/21.18 | '#sk1'('#sk6')), 142.14/21.18 inference('lazy_cnf_exists', [status(thm)], ['37'])). 142.14/21.18 tff('39', plain, 142.14/21.18 ( ((!!((^[Y0 : a]: 142.14/21.18 (!!((^[Y1 : a]: 142.14/21.18 (((!!((^[Y2 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y2) & 142.14/21.18 (!!((^[Y3 : a]: 142.14/21.18 (!!((^[Y4 : a]: 142.14/21.18 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 142.14/21.18 Y2(Y0, Y1))))) | 142.14/21.18 (!!((^[Y2 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y3 : a]: 142.14/21.18 (!!((^[Y4 : a]: 142.14/21.18 ('#sk3'(Y3, Y4) => Y2(Y3, Y4)))))))) & 142.14/21.18 '#sk1'(Y2)) => 142.14/21.18 Y2(Y0, Y1)))))) => 142.14/21.18 '#sk7'(Y0, Y1)))))))) & 142.14/21.18 '#sk1'('#sk7')) 142.14/21.18 | '#sk1'('#sk6')), 142.14/21.18 inference('lazy_cnf_imply', [status(thm)], ['38'])). 142.14/21.18 tff('40', plain, 142.14/21.18 ( (!!((^[Y0 : a]: 142.14/21.18 (!!((^[Y1 : a]: 142.14/21.18 (((!!((^[Y2 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y2) & 142.14/21.18 (!!((^[Y3 : a]: 142.14/21.18 (!!((^[Y4 : a]: 142.14/21.18 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 142.14/21.18 Y2(Y0, Y1))))) | 142.14/21.18 (!!((^[Y2 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y3 : a]: 142.14/21.18 (!!((^[Y4 : a]: 142.14/21.18 ('#sk3'(Y3, Y4) => Y2(Y3, Y4)))))))) & 142.14/21.18 '#sk1'(Y2)) => 142.14/21.18 Y2(Y0, Y1)))))) => 142.14/21.18 '#sk7'(Y0, Y1)))))))) 142.14/21.18 | '#sk1'('#sk6')), 142.14/21.18 inference('lazy_cnf_and', [status(thm)], ['39'])). 142.14/21.18 tff('41', plain, 142.14/21.18 ![X1 : a]: 142.14/21.18 ( (!!((^[Y0 : a]: 142.14/21.18 (((!!((^[Y1 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y1) & 142.14/21.18 (!!((^[Y2 : a]: 142.14/21.18 (!!((^[Y3 : a]: 142.14/21.18 ('#sk2'(Y2, Y3) => Y1(Y2, Y3))))))))) => 142.14/21.18 Y1(X1, Y0))))) | 142.14/21.18 (!!((^[Y1 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y2 : a]: 142.14/21.18 (!!((^[Y3 : a]: 142.14/21.18 ('#sk3'(Y2, Y3) => Y1(Y2, Y3)))))))) & 142.14/21.18 '#sk1'(Y1)) => 142.14/21.18 Y1(X1, Y0)))))) => 142.14/21.18 '#sk7'(X1, Y0))))) 142.14/21.18 | '#sk1'('#sk6')), 142.14/21.18 inference('lazy_cnf_forall', [status(thm)], ['40'])). 142.14/21.18 tff('42', plain, 142.14/21.18 ![X1 : a, X2 : a]: 142.14/21.18 ( (((!!((^[Y0 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y0) & 142.14/21.18 (!!((^[Y1 : a]: 142.14/21.18 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 142.14/21.18 Y0(X1, X2))))) | 142.14/21.18 (!!((^[Y0 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y1 : a]: 142.14/21.18 (!!((^[Y2 : a]: ('#sk3'(Y1, Y2) => Y0(Y1, Y2)))))))) & 142.14/21.18 '#sk1'(Y0)) => 142.14/21.18 Y0(X1, X2)))))) => 142.14/21.18 '#sk7'(X1, X2)) 142.14/21.18 | '#sk1'('#sk6')), 142.14/21.18 inference('lazy_cnf_forall', [status(thm)], ['41'])). 142.14/21.18 tff('43', plain, 142.14/21.18 ![X1 : a, X2 : a]: 142.14/21.18 (~ ((!!((^[Y0 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y0) & 142.14/21.18 (!!((^[Y1 : a]: 142.14/21.18 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 142.14/21.18 Y0(X1, X2))))) | 142.14/21.18 (!!((^[Y0 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y1 : a]: 142.14/21.18 (!!((^[Y2 : a]: ('#sk3'(Y1, Y2) => Y0(Y1, Y2)))))))) & 142.14/21.18 '#sk1'(Y0)) => 142.14/21.18 Y0(X1, X2)))))) 142.14/21.18 | '#sk7'(X1, X2) 142.14/21.18 | '#sk1'('#sk6')), 142.14/21.18 inference('lazy_cnf_imply', [status(thm)], ['42'])). 142.14/21.18 tff('44', plain, 142.14/21.18 ![X1 : a, X2 : a]: 142.14/21.18 (~ (!!((^[Y0 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y1 : a]: 142.14/21.18 (!!((^[Y2 : a]: ('#sk3'(Y1, Y2) => Y0(Y1, Y2)))))))) & 142.14/21.18 '#sk1'(Y0)) => 142.14/21.18 Y0(X1, X2))))) 142.14/21.18 | '#sk1'('#sk6') 142.14/21.18 | '#sk7'(X1, X2)), 142.14/21.18 inference('lazy_cnf_or', [status(thm)], ['43'])). 142.14/21.18 tff('45', plain, 142.14/21.18 ![X1 : a, X2 : a]: 142.14/21.18 (~ (((!!((^[Y0 : a]: 142.14/21.18 (!!((^[Y1 : a]: ('#sk3'(Y0, Y1) => '#sk10'(X1, X2, Y0, Y1)))))))) & 142.14/21.18 '#sk1'('#sk10'(X1, X2))) => 142.14/21.18 '#sk10'(X1, X2, X1, X2)) 142.14/21.18 | '#sk7'(X1, X2) 142.14/21.18 | '#sk1'('#sk6')), 142.14/21.18 inference('lazy_cnf_exists', [status(thm)], ['44'])). 142.14/21.18 tff('46', plain, 142.14/21.18 ![X1 : a, X2 : a]: 142.14/21.18 (~ '#sk10'(X1, X2, X1, X2) | '#sk1'('#sk6') | '#sk7'(X1, X2)), 142.14/21.18 inference('lazy_cnf_imply', [status(thm)], ['45'])). 142.14/21.18 tff('47', plain, 142.14/21.18 ![X1 : a, X2 : a]: 142.14/21.18 ( ((!!((^[Y0 : a]: 142.14/21.18 (!!((^[Y1 : a]: ('#sk3'(Y0, Y1) => '#sk10'(X1, X2, Y0, Y1)))))))) & 142.14/21.18 '#sk1'('#sk10'(X1, X2))) 142.14/21.18 | '#sk1'('#sk6') 142.14/21.18 | '#sk7'(X1, X2)), 142.14/21.18 inference('lazy_cnf_imply', [status(thm)], ['45'])). 142.14/21.18 tff('48', plain, 142.14/21.18 ![X1 : a, X2 : a]: 142.14/21.18 ( (!!((^[Y0 : a]: 142.14/21.18 (!!((^[Y1 : a]: ('#sk3'(Y0, Y1) => '#sk10'(X1, X2, Y0, Y1)))))))) 142.14/21.18 | '#sk7'(X1, X2) 142.14/21.18 | '#sk1'('#sk6')), 142.14/21.18 inference('lazy_cnf_and', [status(thm)], ['47'])). 142.14/21.18 tff('49', plain, 142.14/21.18 ![X1 : a, X2 : a, X3 : a]: 142.14/21.18 ( (!!((^[Y0 : a]: ('#sk3'(X3, Y0) => '#sk10'(X1, X2, X3, Y0))))) 142.14/21.18 | '#sk1'('#sk6') 142.14/21.18 | '#sk7'(X1, X2)), 142.14/21.18 inference('lazy_cnf_forall', [status(thm)], ['48'])). 142.14/21.18 tff('50', plain, 142.14/21.18 ![X1 : a, X2 : a, X3 : a, X4 : a]: 142.14/21.18 ( ('#sk3'(X3, X4) => '#sk10'(X1, X2, X3, X4)) 142.14/21.18 | '#sk7'(X1, X2) 142.14/21.18 | '#sk1'('#sk6')), 142.14/21.18 inference('lazy_cnf_forall', [status(thm)], ['49'])). 142.14/21.18 tff('51', plain, 142.14/21.18 ![X1 : a, X2 : a, X3 : a, X4 : a]: 142.14/21.18 (~ '#sk3'(X3, X4) 142.14/21.18 | '#sk10'(X1, X2, X3, X4) 142.14/21.18 | '#sk1'('#sk6') 142.14/21.18 | '#sk7'(X1, X2)), 142.14/21.18 inference('lazy_cnf_imply', [status(thm)], ['50'])). 142.14/21.18 tff('52', plain, (~ '#sk7'('#_fresh_sk4', '#_fresh_sk5') | '#sk1'('#sk6')), 142.14/21.18 inference('lazy_cnf_imply', [status(thm)], ['38'])). 142.14/21.18 tff('53', plain, 142.14/21.18 ![X1 : a, X2 : a]: 142.14/21.18 (~ (!!((^[Y0 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y0) & 142.14/21.18 (!!((^[Y1 : a]: 142.14/21.18 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 142.14/21.18 Y0(X1, X2))))) 142.14/21.18 | '#sk1'('#sk6') 142.14/21.18 | '#sk7'(X1, X2)), 142.14/21.18 inference('lazy_cnf_or', [status(thm)], ['43'])). 142.14/21.18 tff('54', plain, 142.14/21.18 ![X1 : a, X2 : a]: 142.14/21.18 (~ (('#sk1'('#sk9'(X1, X2)) & 142.14/21.18 (!!((^[Y0 : a]: 142.14/21.18 (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => '#sk9'(X1, X2, Y0, Y1))))))))) => 142.14/21.18 '#sk9'(X1, X2, X1, X2)) 142.14/21.18 | '#sk7'(X1, X2) 142.14/21.18 | '#sk1'('#sk6')), 142.14/21.18 inference('lazy_cnf_exists', [status(thm)], ['53'])). 142.14/21.18 tff('55', plain, 142.14/21.18 ![X1 : a, X2 : a]: 142.14/21.18 ( ('#sk1'('#sk9'(X1, X2)) & 142.14/21.18 (!!((^[Y0 : a]: 142.14/21.18 (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => '#sk9'(X1, X2, Y0, Y1))))))))) 142.14/21.18 | '#sk1'('#sk6') 142.14/21.18 | '#sk7'(X1, X2)), 142.14/21.18 inference('lazy_cnf_imply', [status(thm)], ['54'])). 142.14/21.18 tff('56', plain, 142.14/21.18 ![X1 : a, X2 : a]: 142.14/21.18 ( (!!((^[Y0 : a]: 142.14/21.18 (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => '#sk9'(X1, X2, Y0, Y1)))))))) 142.14/21.18 | '#sk7'(X1, X2) 142.14/21.18 | '#sk1'('#sk6')), 142.14/21.18 inference('lazy_cnf_and', [status(thm)], ['55'])). 142.14/21.18 tff('57', plain, 142.14/21.18 ![X1 : a, X2 : a, X3 : a]: 142.14/21.18 ( (!!((^[Y0 : a]: ('#sk2'(X3, Y0) => '#sk9'(X1, X2, X3, Y0))))) 142.14/21.18 | '#sk1'('#sk6') 142.14/21.18 | '#sk7'(X1, X2)), 142.14/21.18 inference('lazy_cnf_forall', [status(thm)], ['56'])). 142.14/21.18 tff('58', plain, 142.14/21.18 ![X1 : a, X2 : a, X3 : a, X4 : a]: 142.14/21.18 ( ('#sk2'(X3, X4) => '#sk9'(X1, X2, X3, X4)) 142.14/21.18 | '#sk7'(X1, X2) 142.14/21.18 | '#sk1'('#sk6')), 142.14/21.18 inference('lazy_cnf_forall', [status(thm)], ['57'])). 142.14/21.18 tff('59', plain, 142.14/21.18 ![X1 : a, X2 : a, X3 : a, X4 : a]: 142.14/21.18 (~ '#sk2'(X3, X4) 142.14/21.18 | '#sk9'(X1, X2, X3, X4) 142.14/21.18 | '#sk1'('#sk6') 142.14/21.18 | '#sk7'(X1, X2)), 142.14/21.18 inference('lazy_cnf_imply', [status(thm)], ['58'])). 142.14/21.18 tff('60', plain, 142.14/21.18 ![X1 : a, X2 : a]: 142.14/21.18 (~ '#sk9'(X1, X2, X1, X2) | '#sk1'('#sk6') | '#sk7'(X1, X2)), 142.14/21.18 inference('lazy_cnf_imply', [status(thm)], ['54'])). 142.14/21.18 tff('61', plain, 142.14/21.18 (!!((^[Y0 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y0) & 142.14/21.18 (!!((^[Y1 : a]: 142.14/21.18 (!!((^[Y2 : a]: 142.14/21.18 (('#sk3'(Y1, Y2) | '#sk2'(Y1, Y2)) => Y0(Y1, Y2))))))))) => 142.14/21.18 Y0('#_fresh_sk4', '#_fresh_sk5'))))) 142.14/21.18 != (!!((^[Y0 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y1 : a]: 142.14/21.18 (!!((^[Y2 : a]: 142.14/21.18 (((!!((^[Y3 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y3) & 142.14/21.18 (!!((^[Y4 : a]: 142.14/21.18 (!!((^[Y5 : a]: 142.14/21.18 ('#sk2'(Y4, Y5) => 142.14/21.18 Y3(Y4, Y5))))))))) => 142.14/21.18 Y3(Y1, Y2))))) | 142.14/21.18 (!!((^[Y3 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y4 : a]: 142.14/21.18 (!!((^[Y5 : a]: 142.14/21.18 ('#sk3'(Y4, Y5) => 142.14/21.18 Y3(Y4, Y5)))))))) & 142.14/21.18 '#sk1'(Y3)) => 142.14/21.18 Y3(Y1, Y2)))))) => 142.14/21.18 Y0(Y1, Y2)))))))) & 142.14/21.18 '#sk1'(Y0)) => 142.14/21.18 Y0('#_fresh_sk4', '#_fresh_sk5'))))), 142.14/21.18 inference('ho_norm', [status(thm)], ['4'])). 142.14/21.18 tff('62', plain, 142.14/21.18 ( (!!((^[Y0 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y0) & 142.14/21.18 (!!((^[Y1 : a]: 142.14/21.18 (!!((^[Y2 : a]: 142.14/21.18 (('#sk3'(Y1, Y2) | '#sk2'(Y1, Y2)) => Y0(Y1, Y2))))))))) => 142.14/21.18 Y0('#_fresh_sk4', '#_fresh_sk5'))))) 142.14/21.18 | (!!((^[Y0 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y1 : a]: 142.14/21.18 (!!((^[Y2 : a]: 142.14/21.18 (((!!((^[Y3 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y3) & 142.14/21.18 (!!((^[Y4 : a]: 142.14/21.18 (!!((^[Y5 : a]: 142.14/21.18 ('#sk2'(Y4, Y5) => 142.14/21.18 Y3(Y4, Y5))))))))) => 142.14/21.18 Y3(Y1, Y2))))) | 142.14/21.18 (!!((^[Y3 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y4 : a]: 142.14/21.18 (!!((^[Y5 : a]: 142.14/21.18 ('#sk3'(Y4, Y5) => 142.14/21.18 Y3(Y4, Y5)))))))) & 142.14/21.18 '#sk1'(Y3)) => 142.14/21.18 Y3(Y1, Y2)))))) => 142.14/21.18 Y0(Y1, Y2)))))))) & 142.14/21.18 '#sk1'(Y0)) => 142.14/21.18 Y0('#_fresh_sk4', '#_fresh_sk5')))))), 142.14/21.18 inference('eq_elim', [status(thm)], ['61'])). 142.14/21.18 tff('63', plain, 142.14/21.18 (~ '#form8' 142.14/21.18 | (!!((^[Y0 : (a * a) > $o]: 142.14/21.18 (((!!((^[Y1 : a]: 142.14/21.18 (!!((^[Y2 : a]: 142.14/21.18 (((!!((^[Y3 : (a * a) > $o]: 142.14/21.18 (('#sk1'(Y3) & 142.14/21.18 (!!((^[Y4 : a]: 142.14/21.19 (!!((^[Y5 : a]: 142.14/21.19 ('#sk2'(Y4, Y5) => 142.14/21.19 Y3(Y4, Y5))))))))) => 142.14/21.19 Y3(Y1, Y2))))) | 142.14/21.19 (!!((^[Y3 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y4 : a]: 142.14/21.19 (!!((^[Y5 : a]: 142.14/21.19 ('#sk3'(Y4, Y5) => 142.14/21.19 Y3(Y4, Y5)))))))) & 142.14/21.19 '#sk1'(Y3)) => 142.14/21.19 Y3(Y1, Y2)))))) => 142.14/21.19 Y0(Y1, Y2)))))))) & 142.14/21.19 '#sk1'(Y0)) => 142.14/21.19 Y0('#_fresh_sk4', '#_fresh_sk5')))))), 142.14/21.19 define([status(thm)])). 142.14/21.19 tff('64', plain, 142.14/21.19 ![X1 : (a * a) > $o]: 142.14/21.19 ( (((!!((^[Y0 : a]: 142.14/21.19 (!!((^[Y1 : a]: 142.14/21.19 (((!!((^[Y2 : (a * a) > $o]: 142.14/21.19 (('#sk1'(Y2) & 142.14/21.19 (!!((^[Y3 : a]: 142.14/21.19 (!!((^[Y4 : a]: 142.14/21.19 ('#sk2'(Y3, Y4) => 142.14/21.19 Y2(Y3, Y4))))))))) => 142.14/21.19 Y2(Y0, Y1))))) | 142.14/21.19 (!!((^[Y2 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y3 : a]: 142.14/21.19 (!!((^[Y4 : a]: 142.14/21.19 ('#sk3'(Y3, Y4) => 142.14/21.19 Y2(Y3, Y4)))))))) & 142.14/21.19 '#sk1'(Y2)) => 142.14/21.19 Y2(Y0, Y1)))))) => 142.14/21.19 X1(Y0, Y1)))))))) & 142.14/21.19 '#sk1'(X1)) => 142.14/21.19 X1('#_fresh_sk4', '#_fresh_sk5')) 142.14/21.19 | ~ '#form8'), 142.14/21.19 inference('lazy_cnf_forall', [status(thm)], ['63'])). 142.14/21.19 tff('65', plain, 142.14/21.19 ![X1 : (a * a) > $o]: 142.14/21.19 (~ ((!!((^[Y0 : a]: 142.14/21.19 (!!((^[Y1 : a]: 142.14/21.19 (((!!((^[Y2 : (a * a) > $o]: 142.14/21.19 (('#sk1'(Y2) & 142.14/21.19 (!!((^[Y3 : a]: 142.14/21.19 (!!((^[Y4 : a]: 142.14/21.19 ('#sk2'(Y3, Y4) => 142.14/21.19 Y2(Y3, Y4))))))))) => 142.14/21.19 Y2(Y0, Y1))))) | 142.14/21.19 (!!((^[Y2 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y3 : a]: 142.14/21.19 (!!((^[Y4 : a]: 142.14/21.19 ('#sk3'(Y3, Y4) => 142.14/21.19 Y2(Y3, Y4)))))))) & 142.14/21.19 '#sk1'(Y2)) => 142.14/21.19 Y2(Y0, Y1)))))) => 142.14/21.19 X1(Y0, Y1)))))))) & 142.14/21.19 '#sk1'(X1)) 142.14/21.19 | X1('#_fresh_sk4', '#_fresh_sk5') 142.14/21.19 | ~ '#form8'), 142.14/21.19 inference('lazy_cnf_imply', [status(thm)], ['64'])). 142.14/21.19 tff('66', plain, 142.14/21.19 ![X1 : (a * a) > $o]: 142.14/21.19 (~ (!!((^[Y0 : a]: 142.14/21.19 (!!((^[Y1 : a]: 142.14/21.19 (((!!((^[Y2 : (a * a) > $o]: 142.14/21.19 (('#sk1'(Y2) & 142.14/21.19 (!!((^[Y3 : a]: 142.14/21.19 (!!((^[Y4 : a]: 142.14/21.19 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 142.14/21.19 Y2(Y0, Y1))))) | 142.14/21.19 (!!((^[Y2 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y3 : a]: 142.14/21.19 (!!((^[Y4 : a]: 142.14/21.19 ('#sk3'(Y3, Y4) => Y2(Y3, Y4)))))))) & 142.14/21.19 '#sk1'(Y2)) => 142.14/21.19 Y2(Y0, Y1)))))) => 142.14/21.19 X1(Y0, Y1)))))))) 142.14/21.19 | ~ '#sk1'(X1) 142.14/21.19 | ~ '#form8' 142.14/21.19 | X1('#_fresh_sk4', '#_fresh_sk5')), 142.14/21.19 inference('lazy_cnf_and', [status(thm)], ['65'])). 142.14/21.19 tff('67', plain, 142.14/21.19 ![X1 : (a * a) > $o]: 142.14/21.19 (~ (!!((^[Y0 : a]: 142.14/21.19 (((!!((^[Y1 : (a * a) > $o]: 142.14/21.19 (('#sk1'(Y1) & 142.14/21.19 (!!((^[Y2 : a]: 142.14/21.19 (!!((^[Y3 : a]: 142.14/21.19 ('#sk2'(Y2, Y3) => Y1(Y2, Y3))))))))) => 142.14/21.19 Y1('#sk36'(X1), Y0))))) | 142.14/21.19 (!!((^[Y1 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y2 : a]: 142.14/21.19 (!!((^[Y3 : a]: 142.14/21.19 ('#sk3'(Y2, Y3) => Y1(Y2, Y3)))))))) & 142.14/21.19 '#sk1'(Y1)) => 142.14/21.19 Y1('#sk36'(X1), Y0)))))) => 142.14/21.19 X1('#sk36'(X1), Y0))))) 142.14/21.19 | X1('#_fresh_sk4', '#_fresh_sk5') 142.14/21.19 | ~ '#form8' 142.14/21.19 | ~ '#sk1'(X1)), 142.14/21.19 inference('lazy_cnf_exists', [status(thm)], ['66'])). 142.14/21.19 tff('68', plain, 142.14/21.19 ![X1 : (a * a) > $o]: 142.14/21.19 (~ (((!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (('#sk1'(Y0) & 142.14/21.19 (!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 142.14/21.19 Y0('#sk36'(X1), '#sk56'(X1)))))) | 142.14/21.19 (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: ('#sk3'(Y1, Y2) => Y0(Y1, Y2)))))))) & 142.14/21.19 '#sk1'(Y0)) => 142.14/21.19 Y0('#sk36'(X1), '#sk56'(X1))))))) => 142.14/21.19 X1('#sk36'(X1), '#sk56'(X1))) 142.14/21.19 | ~ '#sk1'(X1) 142.14/21.19 | ~ '#form8' 142.14/21.19 | X1('#_fresh_sk4', '#_fresh_sk5')), 142.14/21.19 inference('lazy_cnf_exists', [status(thm)], ['67'])). 142.14/21.19 tff('69', plain, 142.14/21.19 ![X1 : (a * a) > $o]: 142.14/21.19 ( ((!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (('#sk1'(Y0) & 142.14/21.19 (!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 142.14/21.19 Y0('#sk36'(X1), '#sk56'(X1)))))) | 142.14/21.19 (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: ('#sk3'(Y1, Y2) => Y0(Y1, Y2)))))))) & 142.14/21.19 '#sk1'(Y0)) => 142.14/21.19 Y0('#sk36'(X1), '#sk56'(X1))))))) 142.14/21.19 | X1('#_fresh_sk4', '#_fresh_sk5') 142.14/21.19 | ~ '#form8' 142.14/21.19 | ~ '#sk1'(X1)), 142.14/21.19 inference('lazy_cnf_imply', [status(thm)], ['68'])). 142.14/21.19 tff('70', plain, 142.14/21.19 ![X1 : (a * a) > $o]: 142.14/21.19 ( (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (('#sk1'(Y0) & 142.14/21.19 (!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 142.14/21.19 Y0('#sk36'(X1), '#sk56'(X1)))))) 142.14/21.19 | (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: ('#sk3'(Y1, Y2) => Y0(Y1, Y2)))))))) & 142.14/21.19 '#sk1'(Y0)) => 142.14/21.19 Y0('#sk36'(X1), '#sk56'(X1)))))) 142.14/21.19 | ~ '#sk1'(X1) 142.14/21.19 | ~ '#form8' 142.14/21.19 | X1('#_fresh_sk4', '#_fresh_sk5')), 142.14/21.19 inference('lazy_cnf_or', [status(thm)], ['69'])). 142.14/21.19 tff('71', plain, 142.14/21.19 ![X1 : (a * a) > $o, X2 : (a * a) > $o]: 142.14/21.19 ( (('#sk1'(X2) & 142.14/21.19 (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X2(Y0, Y1))))))))) => 142.14/21.19 X2('#sk36'(X1), '#sk56'(X1))) 142.14/21.19 | X1('#_fresh_sk4', '#_fresh_sk5') 142.14/21.19 | ~ '#form8' 142.14/21.19 | ~ '#sk1'(X1) 142.14/21.19 | (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: ('#sk3'(Y1, Y2) => Y0(Y1, Y2)))))))) & 142.14/21.19 '#sk1'(Y0)) => 142.14/21.19 Y0('#sk36'(X1), '#sk56'(X1))))))), 142.14/21.19 inference('lazy_cnf_forall', [status(thm)], ['70'])). 142.14/21.19 tff('72', plain, 142.14/21.19 ![X1 : (a * a) > $o, X2 : (a * a) > $o]: 142.14/21.19 (~ ('#sk1'(X2) & 142.14/21.19 (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X2(Y0, Y1))))))))) 142.14/21.19 | X2('#sk36'(X1), '#sk56'(X1)) 142.14/21.19 | (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: ('#sk3'(Y1, Y2) => Y0(Y1, Y2)))))))) & 142.14/21.19 '#sk1'(Y0)) => 142.14/21.19 Y0('#sk36'(X1), '#sk56'(X1)))))) 142.14/21.19 | ~ '#sk1'(X1) 142.14/21.19 | ~ '#form8' 142.14/21.19 | X1('#_fresh_sk4', '#_fresh_sk5')), 142.14/21.19 inference('lazy_cnf_imply', [status(thm)], ['71'])). 142.14/21.19 tff('73', plain, 142.14/21.19 ![X1 : (a * a) > $o, X2 : (a * a) > $o]: 142.14/21.19 (~ '#sk1'(X2) 142.14/21.19 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X2(Y0, Y1)))))))) 142.14/21.19 | X1('#_fresh_sk4', '#_fresh_sk5') 142.14/21.19 | ~ '#form8' 142.14/21.19 | ~ '#sk1'(X1) 142.14/21.19 | (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: ('#sk3'(Y1, Y2) => Y0(Y1, Y2)))))))) & 142.14/21.19 '#sk1'(Y0)) => 142.14/21.19 Y0('#sk36'(X1), '#sk56'(X1)))))) 142.14/21.19 | X2('#sk36'(X1), '#sk56'(X1))), 142.14/21.19 inference('lazy_cnf_and', [status(thm)], ['72'])). 142.14/21.19 tff('74', plain, 142.14/21.19 ![X1 : (a * a) > $o, X2 : (a * a) > $o]: 142.14/21.19 (~ (!!((^[Y0 : a]: ('#sk2'('#sk179'(X2), Y0) => X2('#sk179'(X2), Y0))))) 142.14/21.19 | X2('#sk36'(X1), '#sk56'(X1)) 142.14/21.19 | (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: ('#sk3'(Y1, Y2) => Y0(Y1, Y2)))))))) & 142.14/21.19 '#sk1'(Y0)) => 142.14/21.19 Y0('#sk36'(X1), '#sk56'(X1)))))) 142.14/21.19 | ~ '#sk1'(X1) 142.14/21.19 | ~ '#form8' 142.14/21.19 | X1('#_fresh_sk4', '#_fresh_sk5') 142.14/21.19 | ~ '#sk1'(X2)), 142.14/21.19 inference('lazy_cnf_exists', [status(thm)], ['73'])). 142.14/21.19 tff('75', plain, 142.14/21.19 ![X1 : (a * a) > $o, X2 : (a * a) > $o]: 142.14/21.19 (~ ('#sk2'('#sk179'(X2), '#sk197'(X2)) => 142.14/21.19 X2('#sk179'(X2), '#sk197'(X2))) 142.14/21.19 | ~ '#sk1'(X2) 142.14/21.19 | X1('#_fresh_sk4', '#_fresh_sk5') 142.14/21.19 | ~ '#form8' 142.14/21.19 | ~ '#sk1'(X1) 142.14/21.19 | (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: ('#sk3'(Y1, Y2) => Y0(Y1, Y2)))))))) & 142.14/21.19 '#sk1'(Y0)) => 142.14/21.19 Y0('#sk36'(X1), '#sk56'(X1)))))) 142.14/21.19 | X2('#sk36'(X1), '#sk56'(X1))), 142.14/21.19 inference('lazy_cnf_exists', [status(thm)], ['74'])). 142.14/21.19 tff('76', plain, 142.14/21.19 ![X1 : (a * a) > $o, X2 : (a * a) > $o]: 142.14/21.19 ( '#sk2'('#sk179'(X2), '#sk197'(X2)) 142.14/21.19 | X2('#sk36'(X1), '#sk56'(X1)) 142.14/21.19 | (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: ('#sk3'(Y1, Y2) => Y0(Y1, Y2)))))))) & 142.14/21.19 '#sk1'(Y0)) => 142.14/21.19 Y0('#sk36'(X1), '#sk56'(X1)))))) 142.14/21.19 | ~ '#sk1'(X1) 142.14/21.19 | ~ '#form8' 142.14/21.19 | X1('#_fresh_sk4', '#_fresh_sk5') 142.14/21.19 | ~ '#sk1'(X2)), 142.14/21.19 inference('lazy_cnf_imply', [status(thm)], ['75'])). 142.14/21.19 tff('77', plain, 142.14/21.19 ![X1 : (a * a) > $o]: 142.14/21.19 (~ '#form234'(X1) 142.14/21.19 | (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: ('#sk3'(Y1, Y2) => Y0(Y1, Y2)))))))) & 142.14/21.19 '#sk1'(Y0)) => 142.14/21.19 Y0('#sk36'(X1), '#sk56'(X1))))))), 142.14/21.19 define([status(thm)])). 142.14/21.19 tff('78', plain, 142.14/21.19 ![X1 : (a * a) > $o, X2 : (a * a) > $o]: 142.14/21.19 ( (((!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk3'(Y0, Y1) => X2(Y0, Y1)))))))) & 142.14/21.19 '#sk1'(X2)) => 142.14/21.19 X2('#sk36'(X1), '#sk56'(X1))) 142.14/21.19 | ~ '#form234'(X1)), 142.14/21.19 inference('lazy_cnf_forall', [status(thm)], ['77'])). 142.14/21.19 tff('79', plain, 142.14/21.19 ![X1 : (a * a) > $o, X2 : (a * a) > $o]: 142.14/21.19 (~ ((!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk3'(Y0, Y1) => X2(Y0, Y1)))))))) & 142.14/21.19 '#sk1'(X2)) 142.14/21.19 | X2('#sk36'(X1), '#sk56'(X1)) 142.14/21.19 | ~ '#form234'(X1)), 142.14/21.19 inference('lazy_cnf_imply', [status(thm)], ['78'])). 142.14/21.19 tff('80', plain, 142.14/21.19 ![X1 : (a * a) > $o, X2 : (a * a) > $o]: 142.14/21.19 (~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk3'(Y0, Y1) => X2(Y0, Y1)))))))) 142.14/21.19 | ~ '#sk1'(X2) 142.14/21.19 | ~ '#form234'(X1) 142.14/21.19 | X2('#sk36'(X1), '#sk56'(X1))), 142.14/21.19 inference('lazy_cnf_and', [status(thm)], ['79'])). 142.14/21.19 tff('81', plain, 142.14/21.19 ![X1 : (a * a) > $o, X2 : (a * a) > $o]: 142.14/21.19 (~ (!!((^[Y0 : a]: ('#sk3'('#sk315'(X2), Y0) => X2('#sk315'(X2), Y0))))) 142.14/21.19 | X2('#sk36'(X1), '#sk56'(X1)) 142.14/21.19 | ~ '#form234'(X1) 142.14/21.19 | ~ '#sk1'(X2)), 142.14/21.19 inference('lazy_cnf_exists', [status(thm)], ['80'])). 142.14/21.19 tff('82', plain, 142.14/21.19 ![X1 : (a * a) > $o, X2 : (a * a) > $o]: 142.14/21.19 (~ ('#sk3'('#sk315'(X2), '#sk329'(X2)) => 142.14/21.19 X2('#sk315'(X2), '#sk329'(X2))) 142.14/21.19 | ~ '#sk1'(X2) 142.14/21.19 | ~ '#form234'(X1) 142.14/21.19 | X2('#sk36'(X1), '#sk56'(X1))), 142.14/21.19 inference('lazy_cnf_exists', [status(thm)], ['81'])). 142.14/21.19 tff('83', plain, 142.14/21.19 ![X1 : (a * a) > $o, X2 : (a * a) > $o]: 142.14/21.19 (~ X2('#sk315'(X2), '#sk329'(X2)) 142.14/21.19 | X2('#sk36'(X1), '#sk56'(X1)) 142.14/21.19 | ~ '#form234'(X1) 142.14/21.19 | ~ '#sk1'(X2)), 142.14/21.19 inference('lazy_cnf_imply', [status(thm)], ['82'])). 142.14/21.19 tff('84', plain, 142.14/21.19 ![X1 : (a * a) > $o, X2 : (a * a) > $o]: 142.14/21.19 ( '#sk3'('#sk315'(X2), '#sk329'(X2)) 142.14/21.19 | X2('#sk36'(X1), '#sk56'(X1)) 142.14/21.19 | ~ '#form234'(X1) 142.14/21.19 | ~ '#sk1'(X2)), 142.14/21.19 inference('lazy_cnf_imply', [status(thm)], ['82'])). 142.14/21.19 tff('85', plain, 142.14/21.19 ( (!!((^[Y0 : a]: 142.14/21.19 (!!((^[Y1 : a]: 142.14/21.19 (('#sk3'(Y0, Y1) | '#sk2'(Y0, Y1)) => '#sk6'(Y0, Y1)))))))) 142.14/21.19 | ~ (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: 142.14/21.19 (((!!((^[Y3 : (a * a) > $o]: 142.14/21.19 (('#sk1'(Y3) & 142.14/21.19 (!!((^[Y4 : a]: 142.14/21.19 (!!((^[Y5 : a]: 142.14/21.19 ('#sk2'(Y4, Y5) => 142.14/21.19 Y3(Y4, Y5))))))))) => 142.14/21.19 Y3(Y1, Y2))))) | 142.14/21.19 (!!((^[Y3 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y4 : a]: 142.14/21.19 (!!((^[Y5 : a]: 142.14/21.19 ('#sk3'(Y4, Y5) => 142.14/21.19 Y3(Y4, Y5)))))))) & 142.14/21.19 '#sk1'(Y3)) => 142.14/21.19 Y3(Y1, Y2)))))) => 142.14/21.19 Y0(Y1, Y2)))))))) & 142.14/21.19 '#sk1'(Y0)) => 142.14/21.19 Y0('#_fresh_sk4', '#_fresh_sk5')))))), 142.14/21.19 inference('lazy_cnf_and', [status(thm)], ['36'])). 142.14/21.19 tff('86', plain, 142.14/21.19 ![X1 : a]: 142.14/21.19 ( (!!((^[Y0 : a]: (('#sk3'(X1, Y0) | '#sk2'(X1, Y0)) => '#sk6'(X1, Y0))))) 142.14/21.19 | ~ (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: 142.14/21.19 (((!!((^[Y3 : (a * a) > $o]: 142.14/21.19 (('#sk1'(Y3) & 142.14/21.19 (!!((^[Y4 : a]: 142.14/21.19 (!!((^[Y5 : a]: 142.14/21.19 ('#sk2'(Y4, Y5) => 142.14/21.19 Y3(Y4, Y5))))))))) => 142.14/21.19 Y3(Y1, Y2))))) | 142.14/21.19 (!!((^[Y3 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y4 : a]: 142.14/21.19 (!!((^[Y5 : a]: 142.14/21.19 ('#sk3'(Y4, Y5) => 142.14/21.19 Y3(Y4, Y5)))))))) & 142.14/21.19 '#sk1'(Y3)) => 142.14/21.19 Y3(Y1, Y2)))))) => 142.14/21.19 Y0(Y1, Y2)))))))) & 142.14/21.19 '#sk1'(Y0)) => 142.14/21.19 Y0('#_fresh_sk4', '#_fresh_sk5')))))), 142.14/21.19 inference('lazy_cnf_forall', [status(thm)], ['85'])). 142.14/21.19 tff('87', plain, 142.14/21.19 ![X1 : a, X2 : a]: 142.14/21.19 ( (('#sk3'(X1, X2) | '#sk2'(X1, X2)) => '#sk6'(X1, X2)) 142.14/21.19 | ~ (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: 142.14/21.19 (((!!((^[Y3 : (a * a) > $o]: 142.14/21.19 (('#sk1'(Y3) & 142.14/21.19 (!!((^[Y4 : a]: 142.14/21.19 (!!((^[Y5 : a]: 142.14/21.19 ('#sk2'(Y4, Y5) => 142.14/21.19 Y3(Y4, Y5))))))))) => 142.14/21.19 Y3(Y1, Y2))))) | 142.14/21.19 (!!((^[Y3 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y4 : a]: 142.14/21.19 (!!((^[Y5 : a]: 142.14/21.19 ('#sk3'(Y4, Y5) => 142.14/21.19 Y3(Y4, Y5)))))))) & 142.14/21.19 '#sk1'(Y3)) => 142.14/21.19 Y3(Y1, Y2)))))) => 142.14/21.19 Y0(Y1, Y2)))))))) & 142.14/21.19 '#sk1'(Y0)) => 142.14/21.19 Y0('#_fresh_sk4', '#_fresh_sk5')))))), 142.14/21.19 inference('lazy_cnf_forall', [status(thm)], ['86'])). 142.14/21.19 tff('88', plain, 142.14/21.19 ![X1 : a, X2 : a]: 142.14/21.19 (~ ('#sk3'(X1, X2) | '#sk2'(X1, X2)) 142.14/21.19 | '#sk6'(X1, X2) 142.14/21.19 | ~ (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: 142.14/21.19 (((!!((^[Y3 : (a * a) > $o]: 142.14/21.19 (('#sk1'(Y3) & 142.14/21.19 (!!((^[Y4 : a]: 142.14/21.19 (!!((^[Y5 : a]: 142.14/21.19 ('#sk2'(Y4, Y5) => 142.14/21.19 Y3(Y4, Y5))))))))) => 142.14/21.19 Y3(Y1, Y2))))) | 142.14/21.19 (!!((^[Y3 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y4 : a]: 142.14/21.19 (!!((^[Y5 : a]: 142.14/21.19 ('#sk3'(Y4, Y5) => 142.14/21.19 Y3(Y4, Y5)))))))) & 142.14/21.19 '#sk1'(Y3)) => 142.14/21.19 Y3(Y1, Y2)))))) => 142.14/21.19 Y0(Y1, Y2)))))))) & 142.14/21.19 '#sk1'(Y0)) => 142.14/21.19 Y0('#_fresh_sk4', '#_fresh_sk5')))))), 142.14/21.19 inference('lazy_cnf_imply', [status(thm)], ['87'])). 142.14/21.19 tff('89', plain, 142.14/21.19 ![X1 : a, X2 : a]: 142.14/21.19 (~ ('#sk3'(X1, X2) | '#sk2'(X1, X2)) 142.14/21.19 | '#sk6'(X1, X2) 142.14/21.19 | ~ (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: 142.14/21.19 (((!!((^[Y3 : (a * a) > $o]: 142.14/21.19 (('#sk1'(Y3) & 142.14/21.19 (!!((^[Y4 : a]: 142.14/21.19 (!!((^[Y5 : a]: 142.14/21.19 ('#sk2'(Y4, Y5) => 142.14/21.19 Y3(Y4, Y5))))))))) => 142.14/21.19 Y3(Y1, Y2))))) | 142.14/21.19 (!!((^[Y3 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y4 : a]: 142.14/21.19 (!!((^[Y5 : a]: 142.14/21.19 ('#sk3'(Y4, Y5) => 142.14/21.19 Y3(Y4, Y5)))))))) & 142.14/21.19 '#sk1'(Y3)) => 142.14/21.19 Y3(Y1, Y2)))))) => 142.14/21.19 Y0(Y1, Y2)))))))) & 142.14/21.19 '#sk1'(Y0)) => 142.14/21.19 Y0('#_fresh_sk4', '#_fresh_sk5')))))), 142.14/21.19 inference('lazy_cnf_imply', [status(thm)], ['87'])). 142.14/21.19 tff('90', plain, 142.14/21.19 ( '#form8' 142.14/21.19 | ~ (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: 142.14/21.19 (((!!((^[Y3 : (a * a) > $o]: 142.14/21.19 (('#sk1'(Y3) & 142.14/21.19 (!!((^[Y4 : a]: 142.14/21.19 (!!((^[Y5 : a]: 142.14/21.19 ('#sk2'(Y4, Y5) => 142.14/21.19 Y3(Y4, Y5))))))))) => 142.14/21.19 Y3(Y1, Y2))))) | 142.14/21.19 (!!((^[Y3 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y4 : a]: 142.14/21.19 (!!((^[Y5 : a]: 142.14/21.19 ('#sk3'(Y4, Y5) => 142.14/21.19 Y3(Y4, Y5)))))))) & 142.14/21.19 '#sk1'(Y3)) => 142.14/21.19 Y3(Y1, Y2)))))) => 142.14/21.19 Y0(Y1, Y2)))))))) & 142.14/21.19 '#sk1'(Y0)) => 142.14/21.19 Y0('#_fresh_sk4', '#_fresh_sk5')))))), 142.14/21.19 define([status(thm)])). 142.14/21.19 tff('91', plain, 142.14/21.19 ![X1 : a, X2 : a]: 142.14/21.19 (~ '#form8' | '#sk6'(X1, X2) | ~ ('#sk3'(X1, X2) | '#sk2'(X1, X2))), 142.14/21.19 inference('renaming', [status(thm)], ['88', '90'])). 142.14/21.19 tff('92', plain, 142.14/21.19 ![X1 : a, X2 : a]: (~ '#sk3'(X1, X2) | '#sk6'(X1, X2) | ~ '#form8'), 142.14/21.19 inference('lazy_cnf_or', [status(thm)], ['91'])). 142.14/21.19 tff('93', plain, 142.14/21.19 ![X1 : (a * a) > $o]: 142.14/21.19 (~ X1('#sk36'(X1), '#sk56'(X1)) 142.14/21.19 | X1('#_fresh_sk4', '#_fresh_sk5') 142.14/21.19 | ~ '#form8' 142.14/21.19 | ~ '#sk1'(X1)), 142.14/21.19 inference('lazy_cnf_imply', [status(thm)], ['68'])). 142.14/21.19 tff('94', plain, 142.14/21.19 ![X1 : (a * a) > $o, X2 : (a * a) > $o]: 142.14/21.19 (~ X2('#sk179'(X2), '#sk197'(X2)) 142.14/21.19 | X2('#sk36'(X1), '#sk56'(X1)) 142.14/21.19 | (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: ('#sk3'(Y1, Y2) => Y0(Y1, Y2)))))))) & 142.14/21.19 '#sk1'(Y0)) => 142.14/21.19 Y0('#sk36'(X1), '#sk56'(X1)))))) 142.14/21.19 | ~ '#sk1'(X1) 142.14/21.19 | ~ '#form8' 142.14/21.19 | X1('#_fresh_sk4', '#_fresh_sk5') 142.14/21.19 | ~ '#sk1'(X2)), 142.14/21.19 inference('lazy_cnf_imply', [status(thm)], ['75'])). 142.14/21.19 tff('95', plain, 142.14/21.19 ![X1 : (a * a) > $o]: 142.14/21.19 (~ '#form234'(X1) 142.14/21.19 | (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: ('#sk3'(Y1, Y2) => Y0(Y1, Y2)))))))) & 142.14/21.19 '#sk1'(Y0)) => 142.14/21.19 Y0('#sk36'(X1), '#sk56'(X1))))))), 142.14/21.19 define([status(thm)])). 142.14/21.19 tff('96', plain, 142.14/21.19 ![X1 : (a * a) > $o, X2 : (a * a) > $o]: 142.14/21.19 ( '#form234'(X1) 142.14/21.19 | ~ '#sk1'(X2) 142.14/21.19 | X1('#_fresh_sk4', '#_fresh_sk5') 142.14/21.19 | ~ '#form8' 142.14/21.19 | ~ '#sk1'(X1) 142.14/21.19 | X2('#sk36'(X1), '#sk56'(X1)) 142.14/21.19 | ~ X2('#sk179'(X2), '#sk197'(X2))), 142.14/21.19 inference('renaming', [status(thm)], ['94', '95'])). 142.14/21.19 tff('97', plain, ( '#sk1'('#sk7') | ~ '#sk6'('#_fresh_sk4', '#_fresh_sk5')), 142.14/21.19 inference('lazy_cnf_and', [status(thm)], ['10'])). 142.14/21.19 tff('98', plain, ( '#sk1'('#sk7') | '#sk1'('#sk6')), 142.14/21.19 inference('lazy_cnf_and', [status(thm)], ['39'])). 142.14/21.19 tff('99', plain, 142.14/21.19 ![X1 : a, X2 : a]: (~ '#sk2'(X1, X2) | '#sk6'(X1, X2) | ~ '#form8'), 142.14/21.19 inference('lazy_cnf_or', [status(thm)], ['91'])). 142.14/21.19 tff('100', plain, 142.14/21.19 ( '#form8' 142.14/21.19 | ~ (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: 142.14/21.19 (((!!((^[Y3 : (a * a) > $o]: 142.14/21.19 (('#sk1'(Y3) & 142.14/21.19 (!!((^[Y4 : a]: 142.14/21.19 (!!((^[Y5 : a]: 142.14/21.19 ('#sk2'(Y4, Y5) => 142.14/21.19 Y3(Y4, Y5))))))))) => 142.14/21.19 Y3(Y1, Y2))))) | 142.14/21.19 (!!((^[Y3 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y4 : a]: 142.14/21.19 (!!((^[Y5 : a]: 142.14/21.19 ('#sk3'(Y4, Y5) => 142.14/21.19 Y3(Y4, Y5)))))))) & 142.14/21.19 '#sk1'(Y3)) => 142.14/21.19 Y3(Y1, Y2)))))) => 142.14/21.19 Y0(Y1, Y2)))))))) & 142.14/21.19 '#sk1'(Y0)) => 142.14/21.19 Y0('#_fresh_sk4', '#_fresh_sk5')))))), 142.14/21.19 define([status(thm)])). 142.14/21.19 tff('101', plain, 142.14/21.19 (~ (((!!((^[Y0 : a]: 142.14/21.19 (!!((^[Y1 : a]: 142.14/21.19 (((!!((^[Y2 : (a * a) > $o]: 142.14/21.19 (('#sk1'(Y2) & 142.14/21.19 (!!((^[Y3 : a]: 142.14/21.19 (!!((^[Y4 : a]: 142.14/21.19 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 142.14/21.19 Y2(Y0, Y1))))) | 142.14/21.19 (!!((^[Y2 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y3 : a]: 142.14/21.19 (!!((^[Y4 : a]: 142.14/21.19 ('#sk3'(Y3, Y4) => Y2(Y3, Y4)))))))) & 142.14/21.19 '#sk1'(Y2)) => 142.14/21.19 Y2(Y0, Y1)))))) => 142.14/21.19 '#sk7'(Y0, Y1)))))))) & 142.14/21.19 '#sk1'('#sk7')) => 142.14/21.19 '#sk7'('#_fresh_sk4', '#_fresh_sk5')) 142.14/21.19 | '#form8'), 142.14/21.19 inference('lazy_cnf_exists', [status(thm)], ['100'])). 142.14/21.19 tff('102', plain, 142.14/21.19 ( ((!!((^[Y0 : a]: 142.14/21.19 (!!((^[Y1 : a]: 142.14/21.19 (((!!((^[Y2 : (a * a) > $o]: 142.14/21.19 (('#sk1'(Y2) & 142.14/21.19 (!!((^[Y3 : a]: 142.14/21.19 (!!((^[Y4 : a]: 142.14/21.19 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 142.14/21.19 Y2(Y0, Y1))))) | 142.14/21.19 (!!((^[Y2 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y3 : a]: 142.14/21.19 (!!((^[Y4 : a]: 142.14/21.19 ('#sk3'(Y3, Y4) => Y2(Y3, Y4)))))))) & 142.14/21.19 '#sk1'(Y2)) => 142.14/21.19 Y2(Y0, Y1)))))) => 142.14/21.19 '#sk7'(Y0, Y1)))))))) & 142.14/21.19 '#sk1'('#sk7')) 142.14/21.19 | '#form8'), 142.14/21.19 inference('lazy_cnf_imply', [status(thm)], ['101'])). 142.14/21.19 tff('103', plain, ( '#sk1'('#sk7') | '#form8'), 142.14/21.19 inference('lazy_cnf_and', [status(thm)], ['102'])). 142.14/21.19 tff('104', plain, 142.14/21.19 ![X1 : (a * a) > $o, X2 : (a * a) > $o]: 142.14/21.19 ( '#sk2'('#sk179'(X2), '#sk197'(X2)) 142.14/21.19 | X2('#sk36'(X1), '#sk56'(X1)) 142.14/21.19 | (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: ('#sk3'(Y1, Y2) => Y0(Y1, Y2)))))))) & 142.14/21.19 '#sk1'(Y0)) => 142.14/21.19 Y0('#sk36'(X1), '#sk56'(X1)))))) 142.14/21.19 | ~ '#sk1'(X1) 142.14/21.19 | ~ '#form8' 142.14/21.19 | X1('#_fresh_sk4', '#_fresh_sk5') 142.14/21.19 | ~ '#sk1'(X2)), 142.14/21.19 inference('lazy_cnf_imply', [status(thm)], ['75'])). 142.14/21.19 tff('105', plain, 142.14/21.19 ![X1 : (a * a) > $o]: 142.14/21.19 (~ '#form234'(X1) 142.14/21.19 | (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: ('#sk3'(Y1, Y2) => Y0(Y1, Y2)))))))) & 142.14/21.19 '#sk1'(Y0)) => 142.14/21.19 Y0('#sk36'(X1), '#sk56'(X1))))))), 142.14/21.19 define([status(thm)])). 142.14/21.19 tff('106', plain, 142.14/21.19 ![X1 : (a * a) > $o, X2 : (a * a) > $o]: 142.14/21.19 ( '#form234'(X1) 142.14/21.19 | ~ '#sk1'(X2) 142.14/21.19 | X1('#_fresh_sk4', '#_fresh_sk5') 142.14/21.19 | ~ '#form8' 142.14/21.19 | ~ '#sk1'(X1) 142.14/21.19 | X2('#sk36'(X1), '#sk56'(X1)) 142.14/21.19 | '#sk2'('#sk179'(X2), '#sk197'(X2))), 142.14/21.19 inference('renaming', [status(thm)], ['104', '105'])). 142.14/21.19 tff('107', plain, (~ '#sk7'('#_fresh_sk4', '#_fresh_sk5') | '#form8'), 142.14/21.19 inference('lazy_cnf_imply', [status(thm)], ['101'])). 142.14/21.19 tff('108', plain, 142.14/21.19 ( (!!((^[Y0 : a]: 142.14/21.19 (!!((^[Y1 : a]: 142.14/21.19 (((!!((^[Y2 : (a * a) > $o]: 142.14/21.19 (('#sk1'(Y2) & 142.14/21.19 (!!((^[Y3 : a]: 142.14/21.19 (!!((^[Y4 : a]: 142.14/21.19 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 142.14/21.19 Y2(Y0, Y1))))) | 142.14/21.19 (!!((^[Y2 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y3 : a]: 142.14/21.19 (!!((^[Y4 : a]: 142.14/21.19 ('#sk3'(Y3, Y4) => Y2(Y3, Y4)))))))) & 142.14/21.19 '#sk1'(Y2)) => 142.14/21.19 Y2(Y0, Y1)))))) => 142.14/21.19 '#sk7'(Y0, Y1)))))))) 142.14/21.19 | '#form8'), 142.14/21.19 inference('lazy_cnf_and', [status(thm)], ['102'])). 142.14/21.19 tff('109', plain, 142.14/21.19 ![X1 : a]: 142.14/21.19 ( (!!((^[Y0 : a]: 142.14/21.19 (((!!((^[Y1 : (a * a) > $o]: 142.14/21.19 (('#sk1'(Y1) & 142.14/21.19 (!!((^[Y2 : a]: 142.14/21.19 (!!((^[Y3 : a]: 142.14/21.19 ('#sk2'(Y2, Y3) => Y1(Y2, Y3))))))))) => 142.14/21.19 Y1(X1, Y0))))) | 142.14/21.19 (!!((^[Y1 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y2 : a]: 142.14/21.19 (!!((^[Y3 : a]: 142.14/21.19 ('#sk3'(Y2, Y3) => Y1(Y2, Y3)))))))) & 142.14/21.19 '#sk1'(Y1)) => 142.14/21.19 Y1(X1, Y0)))))) => 142.14/21.19 '#sk7'(X1, Y0))))) 142.14/21.19 | '#form8'), 142.14/21.19 inference('lazy_cnf_forall', [status(thm)], ['108'])). 142.14/21.19 tff('110', plain, 142.14/21.19 ![X1 : a, X2 : a]: 142.14/21.19 ( (((!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (('#sk1'(Y0) & 142.14/21.19 (!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 142.14/21.19 Y0(X1, X2))))) | 142.14/21.19 (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: ('#sk3'(Y1, Y2) => Y0(Y1, Y2)))))))) & 142.14/21.19 '#sk1'(Y0)) => 142.14/21.19 Y0(X1, X2)))))) => 142.14/21.19 '#sk7'(X1, X2)) 142.14/21.19 | '#form8'), 142.14/21.19 inference('lazy_cnf_forall', [status(thm)], ['109'])). 142.14/21.19 tff('111', plain, 142.14/21.19 ![X1 : a, X2 : a]: 142.14/21.19 (~ ((!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (('#sk1'(Y0) & 142.14/21.19 (!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 142.14/21.19 Y0(X1, X2))))) | 142.14/21.19 (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: ('#sk3'(Y1, Y2) => Y0(Y1, Y2)))))))) & 142.14/21.19 '#sk1'(Y0)) => 142.14/21.19 Y0(X1, X2)))))) 142.14/21.19 | '#sk7'(X1, X2) 142.14/21.19 | '#form8'), 142.14/21.19 inference('lazy_cnf_imply', [status(thm)], ['110'])). 142.14/21.19 tff('112', plain, 142.14/21.19 ![X1 : a, X2 : a]: 142.14/21.19 (~ (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: ('#sk3'(Y1, Y2) => Y0(Y1, Y2)))))))) & 142.14/21.19 '#sk1'(Y0)) => 142.14/21.19 Y0(X1, X2))))) 142.14/21.19 | '#form8' 142.14/21.19 | '#sk7'(X1, X2)), 142.14/21.19 inference('lazy_cnf_or', [status(thm)], ['111'])). 142.14/21.19 tff('113', plain, 142.14/21.19 ![X1 : a, X2 : a]: 142.14/21.19 (~ (((!!((^[Y0 : a]: 142.14/21.19 (!!((^[Y1 : a]: ('#sk3'(Y0, Y1) => '#sk10'(X1, X2, Y0, Y1)))))))) & 142.14/21.19 '#sk1'('#sk10'(X1, X2))) => 142.14/21.19 '#sk10'(X1, X2, X1, X2)) 142.14/21.19 | '#sk7'(X1, X2) 142.14/21.19 | '#form8'), 142.14/21.19 inference('lazy_cnf_exists', [status(thm)], ['112'])). 142.14/21.19 tff('114', plain, 142.14/21.19 ![X1 : a, X2 : a]: 142.14/21.19 (~ '#sk10'(X1, X2, X1, X2) | '#form8' | '#sk7'(X1, X2)), 142.14/21.19 inference('lazy_cnf_imply', [status(thm)], ['113'])). 142.14/21.19 tff('115', plain, 142.14/21.19 ( (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (('#sk1'(Y0) & 142.14/21.19 (!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: 142.14/21.19 (('#sk3'(Y1, Y2) | '#sk2'(Y1, Y2)) => Y0(Y1, Y2))))))))) => 142.14/21.19 Y0('#_fresh_sk4', '#_fresh_sk5'))))) 142.14/21.19 | (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: 142.14/21.19 (((!!((^[Y3 : (a * a) > $o]: 142.14/21.19 (('#sk1'(Y3) & 142.14/21.19 (!!((^[Y4 : a]: 142.14/21.19 (!!((^[Y5 : a]: 142.14/21.19 ('#sk2'(Y4, Y5) => 142.14/21.19 Y3(Y4, Y5))))))))) => 142.14/21.19 Y3(Y1, Y2))))) | 142.14/21.19 (!!((^[Y3 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y4 : a]: 142.14/21.19 (!!((^[Y5 : a]: 142.14/21.19 ('#sk3'(Y4, Y5) => 142.14/21.19 Y3(Y4, Y5)))))))) & 142.14/21.19 '#sk1'(Y3)) => 142.14/21.19 Y3(Y1, Y2)))))) => 142.14/21.19 Y0(Y1, Y2)))))))) & 142.14/21.19 '#sk1'(Y0)) => 142.14/21.19 Y0('#_fresh_sk4', '#_fresh_sk5')))))), 142.14/21.19 inference('eq_elim', [status(thm)], ['61'])). 142.14/21.19 tff('116', plain, 142.14/21.19 (~ '#form8' 142.14/21.19 | (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: 142.14/21.19 (((!!((^[Y3 : (a * a) > $o]: 142.14/21.19 (('#sk1'(Y3) & 142.14/21.19 (!!((^[Y4 : a]: 142.14/21.19 (!!((^[Y5 : a]: 142.14/21.19 ('#sk2'(Y4, Y5) => 142.14/21.19 Y3(Y4, Y5))))))))) => 142.14/21.19 Y3(Y1, Y2))))) | 142.14/21.19 (!!((^[Y3 : (a * a) > $o]: 142.14/21.19 (((!!((^[Y4 : a]: 142.14/21.19 (!!((^[Y5 : a]: 142.14/21.19 ('#sk3'(Y4, Y5) => 142.14/21.19 Y3(Y4, Y5)))))))) & 142.14/21.19 '#sk1'(Y3)) => 142.14/21.19 Y3(Y1, Y2)))))) => 142.14/21.19 Y0(Y1, Y2)))))))) & 142.14/21.19 '#sk1'(Y0)) => 142.14/21.19 Y0('#_fresh_sk4', '#_fresh_sk5')))))), 142.14/21.19 define([status(thm)])). 142.14/21.19 tff('117', plain, 142.14/21.19 ( '#form8' 142.14/21.19 | (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (('#sk1'(Y0) & 142.14/21.19 (!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: 142.14/21.19 (('#sk3'(Y1, Y2) | '#sk2'(Y1, Y2)) => 142.14/21.19 Y0(Y1, Y2))))))))) => 142.14/21.19 Y0('#_fresh_sk4', '#_fresh_sk5')))))), 142.14/21.19 inference('renaming', [status(thm)], ['115', '116'])). 142.14/21.19 tff('118', plain, 142.14/21.19 ![X1 : (a * a) > $o]: 142.14/21.19 ( (('#sk1'(X1) & 142.14/21.19 (!!((^[Y0 : a]: 142.14/21.19 (!!((^[Y1 : a]: 142.14/21.19 (('#sk3'(Y0, Y1) | '#sk2'(Y0, Y1)) => X1(Y0, Y1))))))))) => 142.14/21.19 X1('#_fresh_sk4', '#_fresh_sk5')) 142.14/21.19 | '#form8'), 142.14/21.19 inference('lazy_cnf_forall', [status(thm)], ['117'])). 142.14/21.19 tff('119', plain, 142.14/21.19 ![X1 : (a * a) > $o]: 142.14/21.19 (~ ('#sk1'(X1) & 142.14/21.19 (!!((^[Y0 : a]: 142.14/21.19 (!!((^[Y1 : a]: 142.14/21.19 (('#sk3'(Y0, Y1) | '#sk2'(Y0, Y1)) => X1(Y0, Y1))))))))) 142.14/21.19 | X1('#_fresh_sk4', '#_fresh_sk5') 142.14/21.19 | '#form8'), 142.14/21.19 inference('lazy_cnf_imply', [status(thm)], ['118'])). 142.14/21.19 tff('120', plain, 142.14/21.19 ![X1 : (a * a) > $o]: 142.14/21.19 (~ '#sk1'(X1) 142.14/21.19 | ~ (!!((^[Y0 : a]: 142.14/21.19 (!!((^[Y1 : a]: 142.14/21.19 (('#sk3'(Y0, Y1) | '#sk2'(Y0, Y1)) => X1(Y0, Y1)))))))) 142.14/21.19 | '#form8' 142.14/21.19 | X1('#_fresh_sk4', '#_fresh_sk5')), 142.14/21.19 inference('lazy_cnf_and', [status(thm)], ['119'])). 142.14/21.19 tff('121', plain, 142.14/21.19 ![X1 : (a * a) > $o]: 142.14/21.19 (~ (!!((^[Y0 : a]: 142.14/21.19 (('#sk3'('#sk31'(X1), Y0) | '#sk2'('#sk31'(X1), Y0)) => 142.14/21.19 X1('#sk31'(X1), Y0))))) 142.14/21.19 | X1('#_fresh_sk4', '#_fresh_sk5') 142.14/21.19 | '#form8' 142.14/21.19 | ~ '#sk1'(X1)), 142.14/21.19 inference('lazy_cnf_exists', [status(thm)], ['120'])). 142.14/21.19 tff('122', plain, 142.14/21.19 ![X1 : (a * a) > $o]: 142.14/21.19 (~ (('#sk3'('#sk31'(X1), '#sk46'(X1)) | 142.14/21.19 '#sk2'('#sk31'(X1), '#sk46'(X1))) => 142.14/21.19 X1('#sk31'(X1), '#sk46'(X1))) 142.14/21.19 | ~ '#sk1'(X1) 142.14/21.19 | '#form8' 142.14/21.19 | X1('#_fresh_sk4', '#_fresh_sk5')), 142.14/21.19 inference('lazy_cnf_exists', [status(thm)], ['121'])). 142.14/21.19 tff('123', plain, 142.14/21.19 ![X1 : (a * a) > $o]: 142.14/21.19 (~ X1('#sk31'(X1), '#sk46'(X1)) 142.14/21.19 | X1('#_fresh_sk4', '#_fresh_sk5') 142.14/21.19 | '#form8' 142.14/21.19 | ~ '#sk1'(X1)), 142.14/21.19 inference('lazy_cnf_imply', [status(thm)], ['122'])). 142.14/21.19 tff('124', plain, 142.14/21.19 ![X0 : (a * a) > $o]: 142.14/21.19 (X0('#_fresh_sk4', '#_fresh_sk5') != '#form8' 142.14/21.19 | ~ '#sk1'(X0) 142.14/21.19 | '#form8' 142.14/21.19 | ~ X0('#sk31'(X0), '#sk46'(X0))), 142.14/21.19 inference('eq_fact', [status(thm)], ['123'])). 142.14/21.19 tff('125', plain, 142.14/21.19 ![X1 : a, X2 : a]: 142.14/21.19 (~ (!!((^[Y0 : (a * a) > $o]: 142.14/21.19 (('#sk1'(Y0) & 142.14/21.19 (!!((^[Y1 : a]: 142.14/21.19 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 142.14/21.19 Y0(X1, X2))))) 142.14/21.19 | '#form8' 142.14/21.19 | '#sk7'(X1, X2)), 142.14/21.19 inference('lazy_cnf_or', [status(thm)], ['111'])). 142.14/21.19 tff('126', plain, 142.14/21.19 ![X1 : a, X2 : a]: 142.14/21.19 (~ (('#sk1'('#sk9'(X1, X2)) & 142.14/21.19 (!!((^[Y0 : a]: 142.14/21.19 (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => '#sk9'(X1, X2, Y0, Y1))))))))) => 142.14/21.19 '#sk9'(X1, X2, X1, X2)) 142.14/21.19 | '#sk7'(X1, X2) 142.14/21.19 | '#form8'), 142.14/21.19 inference('lazy_cnf_exists', [status(thm)], ['125'])). 142.14/21.19 tff('127', plain, 142.14/21.19 ![X1 : a, X2 : a]: 142.14/21.19 ( ('#sk1'('#sk9'(X1, X2)) & 142.14/21.19 (!!((^[Y0 : a]: 142.14/21.19 (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => '#sk9'(X1, X2, Y0, Y1))))))))) 142.14/21.19 | '#form8' 142.14/21.19 | '#sk7'(X1, X2)), 142.14/21.19 inference('lazy_cnf_imply', [status(thm)], ['126'])). 142.14/21.19 tff('128', plain, 142.14/21.19 ![X1 : a, X2 : a]: 142.14/21.19 ( (!!((^[Y0 : a]: 142.14/21.19 (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => '#sk9'(X1, X2, Y0, Y1)))))))) 142.14/21.19 | '#sk7'(X1, X2) 142.14/21.19 | '#form8'), 142.14/21.19 inference('lazy_cnf_and', [status(thm)], ['127'])). 142.14/21.19 tff('129', plain, 142.14/21.19 ![X1 : a, X2 : a, X3 : a]: 142.14/21.19 ( (!!((^[Y0 : a]: ('#sk2'(X3, Y0) => '#sk9'(X1, X2, X3, Y0))))) 142.14/21.19 | '#form8' 142.14/21.19 | '#sk7'(X1, X2)), 142.14/21.19 inference('lazy_cnf_forall', [status(thm)], ['128'])). 142.14/21.19 tff('130', plain, 142.14/21.19 ![X1 : a, X2 : a, X3 : a, X4 : a]: 142.14/21.19 ( ('#sk2'(X3, X4) => '#sk9'(X1, X2, X3, X4)) 142.14/21.19 | '#sk7'(X1, X2) 142.14/21.19 | '#form8'), 142.14/21.19 inference('lazy_cnf_forall', [status(thm)], ['129'])). 142.14/21.19 tff('131', plain, 142.14/21.19 ![X1 : a, X2 : a, X3 : a, X4 : a]: 142.14/21.19 (~ '#sk2'(X3, X4) 142.14/21.19 | '#sk9'(X1, X2, X3, X4) 142.14/21.19 | '#form8' 142.14/21.19 | '#sk7'(X1, X2)), 142.14/21.19 inference('lazy_cnf_imply', [status(thm)], ['130'])). 142.14/21.19 tff('132', plain, 142.14/21.19 ![X1 : a, X2 : a]: 142.14/21.19 (~ '#sk9'(X1, X2, X1, X2) | '#form8' | '#sk7'(X1, X2)), 142.14/21.19 inference('lazy_cnf_imply', [status(thm)], ['126'])). 142.14/21.19 tff('133', plain, 142.14/21.19 ![X1 : (a * a) > $o]: 142.14/21.19 ( ('#sk3'('#sk31'(X1), '#sk46'(X1)) | '#sk2'('#sk31'(X1), '#sk46'(X1))) 142.14/21.19 | X1('#_fresh_sk4', '#_fresh_sk5') 142.14/21.19 | '#form8' 142.14/21.19 | ~ '#sk1'(X1)), 142.14/21.19 inference('lazy_cnf_imply', [status(thm)], ['122'])). 142.14/21.19 tff('134', plain, 142.14/21.19 ![X1 : (a * a) > $o]: 142.14/21.19 ( '#sk3'('#sk31'(X1), '#sk46'(X1)) 142.14/21.19 | '#sk2'('#sk31'(X1), '#sk46'(X1)) 142.14/21.19 | ~ '#sk1'(X1) 142.14/21.19 | '#form8' 142.14/21.19 | X1('#_fresh_sk4', '#_fresh_sk5')), 142.14/21.19 inference('lazy_cnf_or', [status(thm)], ['133'])). 142.14/21.19 tff('135', plain, 142.14/21.19 ![X1 : a, X2 : a]: 142.14/21.19 ( ((!!((^[Y0 : a]: 142.14/21.19 (!!((^[Y1 : a]: ('#sk3'(Y0, Y1) => '#sk10'(X1, X2, Y0, Y1)))))))) & 142.14/21.19 '#sk1'('#sk10'(X1, X2))) 142.14/21.19 | '#form8' 142.14/21.19 | '#sk7'(X1, X2)), 142.14/21.19 inference('lazy_cnf_imply', [status(thm)], ['113'])). 142.14/21.19 tff('136', plain, 142.14/21.19 ![X1 : a, X2 : a]: 142.14/21.19 ( (!!((^[Y0 : a]: 142.14/21.19 (!!((^[Y1 : a]: ('#sk3'(Y0, Y1) => '#sk10'(X1, X2, Y0, Y1)))))))) 142.14/21.19 | '#sk7'(X1, X2) 142.14/21.19 | '#form8'), 142.14/21.19 inference('lazy_cnf_and', [status(thm)], ['135'])). 142.14/21.19 tff('137', plain, 142.14/21.19 ![X1 : a, X2 : a, X3 : a]: 142.14/21.19 ( (!!((^[Y0 : a]: ('#sk3'(X3, Y0) => '#sk10'(X1, X2, X3, Y0))))) 142.14/21.19 | '#form8' 142.14/21.19 | '#sk7'(X1, X2)), 142.14/21.19 inference('lazy_cnf_forall', [status(thm)], ['136'])). 142.14/21.19 tff('138', plain, 142.14/21.19 ![X1 : a, X2 : a, X3 : a, X4 : a]: 142.14/21.19 ( ('#sk3'(X3, X4) => '#sk10'(X1, X2, X3, X4)) 142.14/21.19 | '#sk7'(X1, X2) 142.14/21.19 | '#form8'), 142.14/21.19 inference('lazy_cnf_forall', [status(thm)], ['137'])). 142.14/21.19 tff('139', plain, 142.14/21.19 ![X1 : a, X2 : a, X3 : a, X4 : a]: 142.14/21.19 (~ '#sk3'(X3, X4) 142.14/21.19 | '#sk10'(X1, X2, X3, X4) 142.14/21.19 | '#form8' 142.14/21.19 | '#sk7'(X1, X2)), 142.14/21.19 inference('lazy_cnf_imply', [status(thm)], ['138'])). 142.14/21.19 tff('140', plain, $false, 142.14/21.19 inference('eprover', [status(thm)], 142.14/21.19 ['24', '25', '35', '46', '51', '52', '59', '60', '83', '84', 142.14/21.19 '92', '93', '96', '97', '98', '99', '103', '106', '107', 142.14/21.19 '114', '124', '131', '132', '134', '139'])). 142.14/21.19 142.14/21.19 % SZS output end Refutation 142.14/21.19 142.14/21.19 142.14/21.19 % Terminating... 142.50/21.25 % Runner terminated. 142.50/21.26 % Zipperpin 1.5 exiting 142.50/21.27 EOF