0.02/0.09	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.02/0.10	% Command    : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.azZhkTVdHc
0.10/0.30	% Computer   : n016.cluster.edu
0.10/0.30	% Model      : x86_64 x86_64
0.10/0.30	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.30	% Memory     : 8042.1875MB
0.10/0.30	% OS         : Linux 3.10.0-693.el7.x86_64
0.10/0.31	% CPULimit   : 1200
0.10/0.31	% DateTime   : Tue Jul 13 14:06:38 EDT 2021
0.10/0.31	% CPUTime    : 
0.10/0.31	% Running portfolio for 120 s
0.10/0.31	% File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.10/0.31	% Number of cores: 8
0.10/0.31	% Python version: Python 3.6.8
0.10/0.31	% Running in HO mode
0.45/0.58	% Estimated wc time : 1286
0.45/0.58	% Estimated cpu time (7 cpus) : 183.71428571428572
0.45/0.66	% /export/starexec/sandbox2/solver/bin/lams/b.rpo.sh running for 21s
0.45/0.66	% /export/starexec/sandbox2/solver/bin/lams/s6.sh running for 21s
0.45/0.66	% /export/starexec/sandbox2/solver/bin/lams/new_b3.2.norw.sh running for 15s
0.45/0.67	% /export/starexec/sandbox2/solver/bin/lams/s6.ds.sh running for 10s
0.45/0.67	% /export/starexec/sandbox2/solver/bin/lams/c.s.2.sh running for 68s
0.45/0.67	% /export/starexec/sandbox2/solver/bin/lams/old_b3.avatar.sh running for 15s
0.45/0.67	% /export/starexec/sandbox2/solver/bin/lams/c.easy.sh running for 26s
69.41/10.52	% /export/starexec/sandbox2/solver/bin/lams/old_sp2.sh running for 17s
104.32/15.49	% /export/starexec/sandbox2/solver/bin/lams/b.sh running for 31s
105.14/15.68	% /export/starexec/sandbox2/solver/bin/lams/sh1.sh running for 26s
145.86/21.47	% /export/starexec/sandbox2/solver/bin/lams/b.lsimp.sh running for 17s
147.17/21.71	% /export/starexec/sandbox2/solver/bin/lams/b.split.sh running for 31s
182.34/26.73	% /export/starexec/sandbox2/solver/bin/lams/s4.sh running for 15s
186.10/27.39	% /export/starexec/sandbox2/solver/bin/lams/b.rw.sh running for 26s
188.36/27.73	% /export/starexec/sandbox2/solver/bin/lams/c_ic.sh running for 42s
189.73/27.88	% /export/starexec/sandbox2/solver/bin/lams/s1.f.sh running for 15s
227.50/33.32	% Solved by lams/b.rw.sh.
227.50/33.32	% Running : timeout 17 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.azZhkTVdHc/e_inputc43d14 --cpu-limit=15 --auto -s -p.
227.50/33.32	% done 243 iterations in 5.869s
227.50/33.32	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
227.50/33.32	% SZS output start Refutation
227.50/33.32	tff(mvalid, axiom, mvalid() = ^[Phi:(($i > $o))]: (![W]: Phi(W))).
227.50/33.32	tff('0', plain, mvalid = (^[Phi:(($i > $o))]: (![W]: Phi(W))),
227.50/33.32	    inference('simplify_rw_rule', [status(thm)], [mvalid])).
227.50/33.32	tff('1', plain, mvalid = (^[V_1:(($i > $o))]: (![X4]: V_1(X4))),
227.50/33.32	    define([status(thm)])).
227.50/33.32	tff(mdia, axiom, mdia() =
227.50/33.32	  ^[R:(($i * $i) > $o),Phi:(($i > $o))]: mnot(mbox(R,mnot(Phi)))).
227.50/33.32	tff(mbox, axiom, mbox() =
227.50/33.32	  ^[R:(($i * $i) > $o),Phi:(($i > $o)),W]: (![V]: (Phi(V) | (~R(W,V))))).
227.50/33.32	tff('2', plain,
227.50/33.32	    mbox =
227.50/33.32	    (^[R:(($i * $i) > $o),Phi:(($i > $o)),W]: (![V]: (Phi(V) | (~R(W,V))))),
227.50/33.32	    inference('simplify_rw_rule', [status(thm)], [mbox])).
227.50/33.32	tff('3', plain,
227.50/33.32	    mbox =
227.50/33.32	    (^[V_1:(($i * $i) > $o),V_2:(($i > $o)),V_3]:
227.50/33.32	       (![X4]: (V_2(X4) | (~V_1(V_3,X4))))),
227.50/33.32	    define([status(thm)])).
227.50/33.32	tff(mnot, axiom, mnot() = ^[Phi:(($i > $o)),W]: (~Phi(W))).
227.50/33.32	tff('4', plain, mnot = (^[Phi:(($i > $o)),W]: (~Phi(W))),
227.50/33.32	    inference('simplify_rw_rule', [status(thm)], [mnot])).
227.50/33.32	tff('5', plain, mnot = (^[V_1:(($i > $o)),V_2]: (~V_1(V_2))),
227.50/33.32	    define([status(thm)])).
227.50/33.32	tff('6', plain,
227.50/33.32	    mdia = (^[R:(($i * $i) > $o),Phi:(($i > $o))]: mnot(mbox(R,mnot(Phi)))),
227.50/33.32	    inference('simplify_rw_rule', [status(thm)], [mdia, '3', '5'])).
227.50/33.32	tff('7', plain,
227.50/33.32	    mdia =
227.50/33.32	    (^[V_1:(($i * $i) > $o),V_2:(($i > $o))]: mnot(mbox(V_1,mnot(V_2)))),
227.50/33.32	    define([status(thm)])).
227.50/33.32	tff(mforall_prop, axiom, mforall_prop() =
227.50/33.32	  ^[Phi:((($i > $o) * $i) > $o),W]: (![P:(($i > $o))]: Phi(P,W))).
227.50/33.32	tff('8', plain,
227.50/33.32	    mforall_prop =
227.50/33.32	    (^[Phi:((($i > $o) * $i) > $o),W]: (![P:(($i > $o))]: Phi(P,W))),
227.50/33.32	    inference('simplify_rw_rule', [status(thm)], [mforall_prop])).
227.50/33.32	tff('9', plain,
227.50/33.32	    mforall_prop =
227.50/33.32	    (^[V_1:((($i > $o) * $i) > $o),V_2]: (![X4:(($i > $o))]: V_1(X4,V_2))),
227.50/33.32	    define([status(thm)])).
227.50/33.32	tff(mimplies, axiom, mimplies() =
227.50/33.32	  ^[Phi:(($i > $o)),Psi:(($i > $o))]: mor(mnot(Phi),Psi)).
227.50/33.32	tff(mor, axiom, mor() =
227.50/33.32	  ^[Phi:(($i > $o)),Psi:(($i > $o)),W]: (Phi(W) | Psi(W))).
227.50/33.32	tff('10', plain,
227.50/33.32	    mor = (^[Phi:(($i > $o)),Psi:(($i > $o)),W]: (Phi(W) | Psi(W))),
227.50/33.32	    inference('simplify_rw_rule', [status(thm)], [mor])).
227.50/33.32	tff('11', plain,
227.50/33.32	    mor = (^[V_1:(($i > $o)),V_2:(($i > $o)),V_3]: (V_1(V_3) | V_2(V_3))),
227.50/33.32	    define([status(thm)])).
227.50/33.32	tff('12', plain,
227.50/33.32	    mimplies = (^[Phi:(($i > $o)),Psi:(($i > $o))]: mor(mnot(Phi),Psi)),
227.50/33.32	    inference('simplify_rw_rule', [status(thm)], [mimplies, '11', '5'])).
227.50/33.32	tff('13', plain,
227.50/33.32	    mimplies = (^[V_1:(($i > $o)),V_2:(($i > $o))]: mor(mnot(V_1),V_2)),
227.50/33.32	    define([status(thm)])).
227.50/33.32	tff(conj, conjecture,
227.50/33.32	  (![R:(($i * $i) > $o)]:
227.50/33.32	     (mvalid(mforall_prop(^[Phi:(($i > $o))]:
227.50/33.32	                            mimplies(mdia(R,Phi),mbox(R,mdia(R,Phi))))) <=>
227.50/33.32	      mvalid(mforall_prop(^[Phi:(($i > $o))]:
227.50/33.32	                            mimplies(mnot(mbox(R,Phi)),
227.50/33.32	                                     mbox(R,mnot(mbox(R,Phi))))))))).
227.50/33.32	tff(zf_stmt_0, conjecture,
227.50/33.32	  (![X4:(($i * $i) > $o)]:
227.50/33.32	     ((![X6,X8:(($i > $o))]:
227.50/33.32	         ((![X12]:
227.50/33.32	             ((~X4(X6,X12)) | (~(![X14]: ((~X4(X12,X14)) | (~X8(X14))))))) | 
227.50/33.32	          (![X10]: ((~X4(X6,X10)) | (~X8(X10)))))) <=>
227.50/33.32	      (![X16,X18:(($i > $o))]:
227.50/33.32	         ((![X22]:
227.50/33.32	             ((~X4(X16,X22)) | (~(![X24]: ((~X4(X22,X24)) | X18(X24)))))) | 
227.50/33.32	          (![X20]: ((~X4(X16,X20)) | X18(X20)))))))).
227.50/33.32	tff(zf_stmt_1, negated_conjecture,
227.50/33.32	  (~
227.50/33.32	    (![X4:(($i * $i) > $o)]:
227.50/33.32	       ((![X6,X8:(($i > $o))]:
227.50/33.32	           ((![X12]:
227.50/33.32	               ((~X4(X6,X12)) | (~(![X14]: ((~X4(X12,X14)) | (~X8(X14))))))) | 
227.50/33.32	            (![X10]: ((~X4(X6,X10)) | (~X8(X10)))))) <=>
227.50/33.32	        (![X16,X18:(($i > $o))]:
227.50/33.32	           ((![X22]:
227.50/33.32	               ((~X4(X16,X22)) | (~(![X24]: ((~X4(X22,X24)) | X18(X24)))))) | 
227.50/33.32	            (![X20]: ((~X4(X16,X20)) | X18(X20))))))))).
227.50/33.32	tff('14', plain,
227.50/33.32	    ~ (!!((^[Y0 : ($i * $i) > $o]:
227.50/33.32	             ((!!((^[Y1 : $i]:
227.50/33.32	                     (!!((^[Y2 : $i > $o]:
227.50/33.32	                            ((!!((^[Y3 : $i]:
227.50/33.32	                                    ((~(Y0(Y1, Y3))) |
227.50/33.32	                                     (~((!!((^[Y4 : $i]:
227.50/33.32	                                               ((~(Y0(Y3, Y4))) | (~(Y2(Y4))))))))))))) |
227.50/33.32	                             (!!((^[Y3 : $i]: ((~(Y0(Y1, Y3))) | (~(Y2(Y3)))))))))))))) <=>
227.50/33.32	              (!!((^[Y1 : $i]:
227.50/33.32	                     (!!((^[Y2 : $i > $o]:
227.50/33.32	                            ((!!((^[Y3 : $i]:
227.50/33.32	                                    ((~(Y0(Y1, Y3))) |
227.50/33.32	                                     (~((!!((^[Y4 : $i]:
227.50/33.32	                                               ((~(Y0(Y3, Y4))) | Y2(Y4))))))))))) |
227.50/33.32	                             (!!((^[Y3 : $i]: ((~(Y0(Y1, Y3))) | Y2(Y3)))))))))))))))),
227.50/33.32	    inference('cnf', [status(esa)], [zf_stmt_1])).
227.50/33.32	tff('15', plain,
227.50/33.32	    ~ ((!!((^[Y0 : $i]:
227.50/33.32	              (!!((^[Y1 : $i > $o]:
227.50/33.32	                     ((!!((^[Y2 : $i]:
227.50/33.32	                             ((~('#sk1'(Y0, Y2))) |
227.50/33.32	                              (~((!!((^[Y3 : $i]:
227.50/33.32	                                        ((~('#sk1'(Y2, Y3))) | (~(Y1(Y3))))))))))))) |
227.50/33.32	                      (!!((^[Y2 : $i]: ((~('#sk1'(Y0, Y2))) | (~(Y1(Y2)))))))))))))) <=>
227.50/33.32	       (!!((^[Y0 : $i]:
227.50/33.32	              (!!((^[Y1 : $i > $o]:
227.50/33.32	                     ((!!((^[Y2 : $i]:
227.50/33.32	                             ((~('#sk1'(Y0, Y2))) |
227.50/33.32	                              (~((!!((^[Y3 : $i]:
227.50/33.32	                                        ((~('#sk1'(Y2, Y3))) | Y1(Y3))))))))))) |
227.50/33.32	                      (!!((^[Y2 : $i]: ((~('#sk1'(Y0, Y2))) | Y1(Y2))))))))))))),
227.50/33.32	    inference('lazy_cnf_exists', [status(thm)], ['14'])).
227.50/33.32	tff('16', plain,
227.50/33.32	    (!!((^[Y0 : $i]:
227.50/33.32	           (!!((^[Y1 : $i > $o]:
227.50/33.32	                  ((!!((^[Y2 : $i]:
227.50/33.32	                          ((~('#sk1'(Y0, Y2))) |
227.50/33.32	                           (~((!!((^[Y3 : $i]:
227.50/33.32	                                     ((~('#sk1'(Y2, Y3))) | (~(Y1(Y3))))))))))))) |
227.50/33.32	                   (!!((^[Y2 : $i]: ((~('#sk1'(Y0, Y2))) | (~(Y1(Y2))))))))))))))
227.50/33.32	     != (!!((^[Y0 : $i]:
227.50/33.32	               (!!((^[Y1 : $i > $o]:
227.50/33.32	                      ((!!((^[Y2 : $i]:
227.50/33.32	                              ((~('#sk1'(Y0, Y2))) |
227.50/33.32	                               (~((!!((^[Y3 : $i]:
227.50/33.32	                                         ((~('#sk1'(Y2, Y3))) | Y1(Y3))))))))))) |
227.50/33.32	                       (!!((^[Y2 : $i]: ((~('#sk1'(Y0, Y2))) | Y1(Y2)))))))))))),
227.50/33.32	    inference('simplify nested equalities', [status(thm)], ['15'])).
227.50/33.32	tff('17', plain,
227.50/33.32	    (~ (!!((^[Y0 : $i]:
227.50/33.32	              (!!((^[Y1 : $i > $o]:
227.50/33.32	                     ((!!((^[Y2 : $i]:
227.50/33.32	                             ((~('#sk1'(Y0, Y2))) |
227.50/33.32	                              (~((!!((^[Y3 : $i]:
227.50/33.32	                                        ((~('#sk1'(Y2, Y3))) | (~(Y1(Y3))))))))))))) |
227.50/33.32	                      (!!((^[Y2 : $i]: ((~('#sk1'(Y0, Y2))) | (~(Y1(Y2))))))))))))))
227.50/33.32	     | ~ (!!((^[Y0 : $i]:
227.50/33.32	                (!!((^[Y1 : $i > $o]:
227.50/33.32	                       ((!!((^[Y2 : $i]:
227.50/33.32	                               ((~('#sk1'(Y0, Y2))) |
227.50/33.32	                                (~((!!((^[Y3 : $i]:
227.50/33.32	                                          ((~('#sk1'(Y2, Y3))) | Y1(Y3))))))))))) |
227.50/33.32	                        (!!((^[Y2 : $i]: ((~('#sk1'(Y0, Y2))) | Y1(Y2))))))))))))),
227.50/33.32	    inference('eq_elim', [status(thm)], ['16'])).
227.50/33.32	tff('18', plain,
227.50/33.32	    (~ (!!((^[Y0 : $i > $o]:
227.50/33.32	              ((!!((^[Y1 : $i]:
227.50/33.32	                      ((~('#sk1'('#sk2', Y1))) |
227.50/33.32	                       (~((!!((^[Y2 : $i]:
227.50/33.32	                                 ((~('#sk1'(Y1, Y2))) | (~(Y0(Y2))))))))))))) |
227.50/33.32	               (!!((^[Y1 : $i]: ((~('#sk1'('#sk2', Y1))) | (~(Y0(Y1)))))))))))
227.50/33.32	     | ~ (!!((^[Y0 : $i]:
227.50/33.32	                (!!((^[Y1 : $i > $o]:
227.50/33.32	                       ((!!((^[Y2 : $i]:
227.50/33.32	                               ((~('#sk1'(Y0, Y2))) |
227.50/33.32	                                (~((!!((^[Y3 : $i]:
227.50/33.32	                                          ((~('#sk1'(Y2, Y3))) | Y1(Y3))))))))))) |
227.50/33.32	                        (!!((^[Y2 : $i]: ((~('#sk1'(Y0, Y2))) | Y1(Y2))))))))))))),
227.50/33.32	    inference('lazy_cnf_exists', [status(thm)], ['17'])).
227.50/33.32	tff('19', plain,
227.50/33.32	    (~ ((!!((^[Y0 : $i]:
227.50/33.32	               ((~('#sk1'('#sk2', Y0))) |
227.50/33.32	                (~((!!((^[Y1 : $i]: ((~('#sk1'(Y0, Y1))) | (~('#sk3'(Y1))))))))))))) |
227.50/33.32	        (!!((^[Y0 : $i]: ((~('#sk1'('#sk2', Y0))) | (~('#sk3'(Y0))))))))
227.50/33.32	     | ~ (!!((^[Y0 : $i]:
227.50/33.32	                (!!((^[Y1 : $i > $o]:
227.50/33.32	                       ((!!((^[Y2 : $i]:
227.50/33.32	                               ((~('#sk1'(Y0, Y2))) |
227.50/33.32	                                (~((!!((^[Y3 : $i]:
227.50/33.32	                                          ((~('#sk1'(Y2, Y3))) | Y1(Y3))))))))))) |
227.50/33.32	                        (!!((^[Y2 : $i]: ((~('#sk1'(Y0, Y2))) | Y1(Y2))))))))))))),
227.50/33.32	    inference('lazy_cnf_exists', [status(thm)], ['18'])).
227.50/33.32	tff('20', plain,
227.50/33.32	    (~ (!!((^[Y0 : $i]:
227.50/33.32	              ((~('#sk1'('#sk2', Y0))) |
227.50/33.32	               (~((!!((^[Y1 : $i]: ((~('#sk1'(Y0, Y1))) | (~('#sk3'(Y1)))))))))))))
227.50/33.32	     | ~ (!!((^[Y0 : $i]:
227.50/33.32	                (!!((^[Y1 : $i > $o]:
227.50/33.32	                       ((!!((^[Y2 : $i]:
227.50/33.32	                               ((~('#sk1'(Y0, Y2))) |
227.50/33.32	                                (~((!!((^[Y3 : $i]:
227.50/33.32	                                          ((~('#sk1'(Y2, Y3))) | Y1(Y3))))))))))) |
227.50/33.32	                        (!!((^[Y2 : $i]: ((~('#sk1'(Y0, Y2))) | Y1(Y2))))))))))))),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['19'])).
227.50/33.32	tff('21', plain,
227.50/33.32	    (~ ((~('#sk1'('#sk2', '#sk4'))) |
227.50/33.32	        (~((!!((^[Y0 : $i]: ((~('#sk1'('#sk4', Y0))) | (~('#sk3'(Y0))))))))))
227.50/33.32	     | ~ (!!((^[Y0 : $i]:
227.50/33.32	                (!!((^[Y1 : $i > $o]:
227.50/33.32	                       ((!!((^[Y2 : $i]:
227.50/33.32	                               ((~('#sk1'(Y0, Y2))) |
227.50/33.32	                                (~((!!((^[Y3 : $i]:
227.50/33.32	                                          ((~('#sk1'(Y2, Y3))) | Y1(Y3))))))))))) |
227.50/33.32	                        (!!((^[Y2 : $i]: ((~('#sk1'(Y0, Y2))) | Y1(Y2))))))))))))),
227.50/33.32	    inference('lazy_cnf_exists', [status(thm)], ['20'])).
227.50/33.32	tff('22', plain,
227.50/33.32	    ( (!!((^[Y0 : $i]: ((~('#sk1'('#sk4', Y0))) | (~('#sk3'(Y0)))))))
227.50/33.32	     | ~ (!!((^[Y0 : $i]:
227.50/33.32	                (!!((^[Y1 : $i > $o]:
227.50/33.32	                       ((!!((^[Y2 : $i]:
227.50/33.32	                               ((~('#sk1'(Y0, Y2))) |
227.50/33.32	                                (~((!!((^[Y3 : $i]:
227.50/33.32	                                          ((~('#sk1'(Y2, Y3))) | Y1(Y3))))))))))) |
227.50/33.32	                        (!!((^[Y2 : $i]: ((~('#sk1'(Y0, Y2))) | Y1(Y2))))))))))))),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['21'])).
227.50/33.32	tff('23', plain,
227.50/33.32	    (~ (!!((^[Y0 : $i]: ((~('#sk1'('#sk2', Y0))) | (~('#sk3'(Y0)))))))
227.50/33.32	     | ~ (!!((^[Y0 : $i]:
227.50/33.32	                (!!((^[Y1 : $i > $o]:
227.50/33.32	                       ((!!((^[Y2 : $i]:
227.50/33.32	                               ((~('#sk1'(Y0, Y2))) |
227.50/33.32	                                (~((!!((^[Y3 : $i]:
227.50/33.32	                                          ((~('#sk1'(Y2, Y3))) | Y1(Y3))))))))))) |
227.50/33.32	                        (!!((^[Y2 : $i]: ((~('#sk1'(Y0, Y2))) | Y1(Y2))))))))))))),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['19'])).
227.50/33.32	tff('24', plain,
227.50/33.32	    (~ ((~('#sk1'('#sk2', '#sk5'))) | (~('#sk3'('#sk5'))))
227.50/33.32	     | ~ (!!((^[Y0 : $i]:
227.50/33.32	                (!!((^[Y1 : $i > $o]:
227.50/33.32	                       ((!!((^[Y2 : $i]:
227.50/33.32	                               ((~('#sk1'(Y0, Y2))) |
227.50/33.32	                                (~((!!((^[Y3 : $i]:
227.50/33.32	                                          ((~('#sk1'(Y2, Y3))) | Y1(Y3))))))))))) |
227.50/33.32	                        (!!((^[Y2 : $i]: ((~('#sk1'(Y0, Y2))) | Y1(Y2))))))))))))),
227.50/33.32	    inference('lazy_cnf_exists', [status(thm)], ['23'])).
227.50/33.32	tff('25', plain,
227.50/33.32	    ( '#form6'
227.50/33.32	     | ~ (!!((^[Y0 : $i]:
227.50/33.32	                (!!((^[Y1 : $i > $o]:
227.50/33.32	                       ((!!((^[Y2 : $i]:
227.50/33.32	                               ((~('#sk1'(Y0, Y2))) |
227.50/33.32	                                (~((!!((^[Y3 : $i]:
227.50/33.32	                                          ((~('#sk1'(Y2, Y3))) | Y1(Y3))))))))))) |
227.50/33.32	                        (!!((^[Y2 : $i]: ((~('#sk1'(Y0, Y2))) | Y1(Y2))))))))))))),
227.50/33.32	    define([status(thm)])).
227.50/33.32	tff('26', plain,
227.50/33.32	    (~ '#form6'
227.50/33.32	     |  (!!((^[Y0 : $i]: ((~('#sk1'('#sk4', Y0))) | (~('#sk3'(Y0)))))))),
227.50/33.32	    inference('renaming', [status(thm)], ['22', '25'])).
227.50/33.32	tff('27', plain,
227.50/33.32	    ![X1]: ( ((~('#sk1'('#sk4', X1))) | (~('#sk3'(X1)))) | ~ '#form6'),
227.50/33.32	    inference('lazy_cnf_forall', [status(thm)], ['26'])).
227.50/33.32	tff('28', plain, ![X1]: (~ '#sk1'('#sk4', X1) | ~ '#sk3'(X1) | ~ '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['27'])).
227.50/33.32	tff('29', plain,
227.50/33.32	    ( '#sk1'('#sk2', '#sk4')
227.50/33.32	     | ~ (!!((^[Y0 : $i]:
227.50/33.32	                (!!((^[Y1 : $i > $o]:
227.50/33.32	                       ((!!((^[Y2 : $i]:
227.50/33.32	                               ((~('#sk1'(Y0, Y2))) |
227.50/33.32	                                (~((!!((^[Y3 : $i]:
227.50/33.32	                                          ((~('#sk1'(Y2, Y3))) | Y1(Y3))))))))))) |
227.50/33.32	                        (!!((^[Y2 : $i]: ((~('#sk1'(Y0, Y2))) | Y1(Y2))))))))))))),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['21'])).
227.50/33.32	tff('30', plain,
227.50/33.32	    ( '#form6'
227.50/33.32	     | ~ (!!((^[Y0 : $i]:
227.50/33.32	                (!!((^[Y1 : $i > $o]:
227.50/33.32	                       ((!!((^[Y2 : $i]:
227.50/33.32	                               ((~('#sk1'(Y0, Y2))) |
227.50/33.32	                                (~((!!((^[Y3 : $i]:
227.50/33.32	                                          ((~('#sk1'(Y2, Y3))) | Y1(Y3))))))))))) |
227.50/33.32	                        (!!((^[Y2 : $i]: ((~('#sk1'(Y0, Y2))) | Y1(Y2))))))))))))),
227.50/33.32	    define([status(thm)])).
227.50/33.32	tff('31', plain, (~ '#form6' |  '#sk1'('#sk2', '#sk4')),
227.50/33.32	    inference('renaming', [status(thm)], ['29', '30'])).
227.50/33.32	tff('32', plain,
227.50/33.32	    (~ ((~('#sk1'('#sk2', '#sk5'))) | (~('#sk3'('#sk5'))))
227.50/33.32	     | ~ (!!((^[Y0 : $i]:
227.50/33.32	                (!!((^[Y1 : $i > $o]:
227.50/33.32	                       ((!!((^[Y2 : $i]:
227.50/33.32	                               ((~('#sk1'(Y0, Y2))) |
227.50/33.32	                                (~((!!((^[Y3 : $i]:
227.50/33.32	                                          ((~('#sk1'(Y2, Y3))) | Y1(Y3))))))))))) |
227.50/33.32	                        (!!((^[Y2 : $i]: ((~('#sk1'(Y0, Y2))) | Y1(Y2))))))))))))),
227.50/33.32	    inference('lazy_cnf_exists', [status(thm)], ['23'])).
227.50/33.32	tff('33', plain,
227.50/33.32	    ( '#form6'
227.50/33.32	     | ~ (!!((^[Y0 : $i]:
227.50/33.32	                (!!((^[Y1 : $i > $o]:
227.50/33.32	                       ((!!((^[Y2 : $i]:
227.50/33.32	                               ((~('#sk1'(Y0, Y2))) |
227.50/33.32	                                (~((!!((^[Y3 : $i]:
227.50/33.32	                                          ((~('#sk1'(Y2, Y3))) | Y1(Y3))))))))))) |
227.50/33.32	                        (!!((^[Y2 : $i]: ((~('#sk1'(Y0, Y2))) | Y1(Y2))))))))))))),
227.50/33.32	    define([status(thm)])).
227.50/33.32	tff('34', plain,
227.50/33.32	    (~ '#form6' | ~ ((~('#sk1'('#sk2', '#sk5'))) | (~('#sk3'('#sk5'))))),
227.50/33.32	    inference('renaming', [status(thm)], ['32', '33'])).
227.50/33.32	tff('35', plain, ( '#sk1'('#sk2', '#sk5') | ~ '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['34'])).
227.50/33.32	tff('36', plain,
227.50/33.32	    (!!((^[Y0 : $i]:
227.50/33.32	           (!!((^[Y1 : $i > $o]:
227.50/33.32	                  ((!!((^[Y2 : $i]:
227.50/33.32	                          ((~('#sk1'(Y0, Y2))) |
227.50/33.32	                           (~((!!((^[Y3 : $i]:
227.50/33.32	                                     ((~('#sk1'(Y2, Y3))) | (~(Y1(Y3))))))))))))) |
227.50/33.32	                   (!!((^[Y2 : $i]: ((~('#sk1'(Y0, Y2))) | (~(Y1(Y2))))))))))))))
227.50/33.32	     != (!!((^[Y0 : $i]:
227.50/33.32	               (!!((^[Y1 : $i > $o]:
227.50/33.32	                      ((!!((^[Y2 : $i]:
227.50/33.32	                              ((~('#sk1'(Y0, Y2))) |
227.50/33.32	                               (~((!!((^[Y3 : $i]:
227.50/33.32	                                         ((~('#sk1'(Y2, Y3))) | Y1(Y3))))))))))) |
227.50/33.32	                       (!!((^[Y2 : $i]: ((~('#sk1'(Y0, Y2))) | Y1(Y2)))))))))))),
227.50/33.32	    inference('simplify nested equalities', [status(thm)], ['15'])).
227.50/33.32	tff('37', plain,
227.50/33.32	    ( (!!((^[Y0 : $i]:
227.50/33.32	             (!!((^[Y1 : $i > $o]:
227.50/33.32	                    ((!!((^[Y2 : $i]:
227.50/33.32	                            ((~('#sk1'(Y0, Y2))) |
227.50/33.32	                             (~((!!((^[Y3 : $i]:
227.50/33.32	                                       ((~('#sk1'(Y2, Y3))) | (~(Y1(Y3))))))))))))) |
227.50/33.32	                     (!!((^[Y2 : $i]: ((~('#sk1'(Y0, Y2))) | (~(Y1(Y2))))))))))))))
227.50/33.32	     |  (!!((^[Y0 : $i]:
227.50/33.32	               (!!((^[Y1 : $i > $o]:
227.50/33.32	                      ((!!((^[Y2 : $i]:
227.50/33.32	                              ((~('#sk1'(Y0, Y2))) |
227.50/33.32	                               (~((!!((^[Y3 : $i]:
227.50/33.32	                                         ((~('#sk1'(Y2, Y3))) | Y1(Y3))))))))))) |
227.50/33.32	                       (!!((^[Y2 : $i]: ((~('#sk1'(Y0, Y2))) | Y1(Y2))))))))))))),
227.50/33.32	    inference('eq_elim', [status(thm)], ['36'])).
227.50/33.32	tff('38', plain,
227.50/33.32	    ( (!!((^[Y0 : $i]:
227.50/33.32	             (!!((^[Y1 : $i > $o]:
227.50/33.32	                    ((!!((^[Y2 : $i]:
227.50/33.32	                            ((~('#sk1'(Y0, Y2))) |
227.50/33.32	                             (~((!!((^[Y3 : $i]:
227.50/33.32	                                       ((~('#sk1'(Y2, Y3))) | (~(Y1(Y3))))))))))))) |
227.50/33.32	                     (!!((^[Y2 : $i]: ((~('#sk1'(Y0, Y2))) | (~(Y1(Y2))))))))))))))
227.50/33.32	     |  (!!((^[Y0 : $i]:
227.50/33.32	               (!!((^[Y1 : $i > $o]:
227.50/33.32	                      ((!!((^[Y2 : $i]:
227.50/33.32	                              ((~('#sk1'(Y0, Y2))) |
227.50/33.32	                               (~((!!((^[Y3 : $i]:
227.50/33.32	                                         ((~('#sk1'(Y2, Y3))) | Y1(Y3))))))))))) |
227.50/33.32	                       (!!((^[Y2 : $i]: ((~('#sk1'(Y0, Y2))) | Y1(Y2))))))))))))),
227.50/33.32	    inference('eq_elim', [status(thm)], ['36'])).
227.50/33.32	tff('39', plain,
227.50/33.32	    (~ '#form6'
227.50/33.32	     |  (!!((^[Y0 : $i]:
227.50/33.32	               (!!((^[Y1 : $i > $o]:
227.50/33.32	                      ((!!((^[Y2 : $i]:
227.50/33.32	                              ((~('#sk1'(Y0, Y2))) |
227.50/33.32	                               (~((!!((^[Y3 : $i]:
227.50/33.32	                                         ((~('#sk1'(Y2, Y3))) | Y1(Y3))))))))))) |
227.50/33.32	                       (!!((^[Y2 : $i]: ((~('#sk1'(Y0, Y2))) | Y1(Y2))))))))))))),
227.50/33.32	    define([status(thm)])).
227.50/33.32	tff('40', plain,
227.50/33.32	    ( '#form6'
227.50/33.32	     |  (!!((^[Y0 : $i]:
227.50/33.32	               (!!((^[Y1 : $i > $o]:
227.50/33.32	                      ((!!((^[Y2 : $i]:
227.50/33.32	                              ((~('#sk1'(Y0, Y2))) |
227.50/33.32	                               (~((!!((^[Y3 : $i]:
227.50/33.32	                                         ((~('#sk1'(Y2, Y3))) | (~(Y1(Y3))))))))))))) |
227.50/33.32	                       (!!((^[Y2 : $i]: ((~('#sk1'(Y0, Y2))) | (~(Y1(Y2))))))))))))))),
227.50/33.32	    inference('renaming', [status(thm)], ['37', '39'])).
227.50/33.32	tff('41', plain,
227.50/33.32	    ![X1]:
227.50/33.32	      ( (!!((^[Y0 : $i > $o]:
227.50/33.32	               ((!!((^[Y1 : $i]:
227.50/33.32	                       ((~('#sk1'(X1, Y1))) |
227.50/33.32	                        (~((!!((^[Y2 : $i]:
227.50/33.32	                                  ((~('#sk1'(Y1, Y2))) | (~(Y0(Y2))))))))))))) |
227.50/33.32	                (!!((^[Y1 : $i]: ((~('#sk1'(X1, Y1))) | (~(Y0(Y1)))))))))))
227.50/33.32	       |  '#form6'),
227.50/33.32	    inference('lazy_cnf_forall', [status(thm)], ['40'])).
227.50/33.32	tff('42', plain,
227.50/33.32	    ![X1, X2 : $i > $o]:
227.50/33.32	      ( ((!!((^[Y0 : $i]:
227.50/33.32	                ((~('#sk1'(X1, Y0))) |
227.50/33.32	                 (~((!!((^[Y1 : $i]: ((~('#sk1'(Y0, Y1))) | (~(X2(Y1))))))))))))) |
227.50/33.32	         (!!((^[Y0 : $i]: ((~('#sk1'(X1, Y0))) | (~(X2(Y0))))))))
227.50/33.32	       |  '#form6'),
227.50/33.32	    inference('lazy_cnf_forall', [status(thm)], ['41'])).
227.50/33.32	tff('43', plain,
227.50/33.32	    ![X1, X2 : $i > $o]:
227.50/33.32	      ( (!!((^[Y0 : $i]:
227.50/33.32	               ((~('#sk1'(X1, Y0))) |
227.50/33.32	                (~((!!((^[Y1 : $i]: ((~('#sk1'(Y0, Y1))) | (~(X2(Y1)))))))))))))
227.50/33.32	       |  (!!((^[Y0 : $i]: ((~('#sk1'(X1, Y0))) | (~(X2(Y0)))))))
227.50/33.32	       |  '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['42'])).
227.50/33.32	tff('44', plain,
227.50/33.32	    ![X1, X2 : $i > $o, X3]:
227.50/33.32	      ( ((~('#sk1'(X1, X3))) |
227.50/33.32	         (~((!!((^[Y0 : $i]: ((~('#sk1'(X3, Y0))) | (~(X2(Y0))))))))))
227.50/33.32	       |  '#form6'
227.50/33.32	       |  (!!((^[Y0 : $i]: ((~('#sk1'(X1, Y0))) | (~(X2(Y0)))))))),
227.50/33.32	    inference('lazy_cnf_forall', [status(thm)], ['43'])).
227.50/33.32	tff('45', plain,
227.50/33.32	    ![X1, X2 : $i > $o, X3]:
227.50/33.32	      (~ '#sk1'(X1, X3)
227.50/33.32	       | ~ (!!((^[Y0 : $i]: ((~('#sk1'(X3, Y0))) | (~(X2(Y0)))))))
227.50/33.32	       |  (!!((^[Y0 : $i]: ((~('#sk1'(X1, Y0))) | (~(X2(Y0)))))))
227.50/33.32	       |  '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['44'])).
227.50/33.32	tff('46', plain,
227.50/33.32	    ![X1, X2 : $i > $o, X3]:
227.50/33.32	      (~ ((~('#sk1'(X3, '#sk25'(X2, X3)))) | (~(X2('#sk25'(X2, X3)))))
227.50/33.32	       |  '#form6'
227.50/33.32	       |  (!!((^[Y0 : $i]: ((~('#sk1'(X1, Y0))) | (~(X2(Y0)))))))
227.50/33.32	       | ~ '#sk1'(X1, X3)),
227.50/33.32	    inference('lazy_cnf_exists', [status(thm)], ['45'])).
227.50/33.32	tff('47', plain,
227.50/33.32	    ![X1, X2 : $i > $o, X3]:
227.50/33.32	      ( X2('#sk25'(X2, X3))
227.50/33.32	       | ~ '#sk1'(X1, X3)
227.50/33.32	       |  (!!((^[Y0 : $i]: ((~('#sk1'(X1, Y0))) | (~(X2(Y0)))))))
227.50/33.32	       |  '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['46'])).
227.50/33.32	tff('48', plain,
227.50/33.32	    ![X1, X2 : $i > $o, X3, X4]:
227.50/33.32	      ( ((~('#sk1'(X1, X4))) | (~(X2(X4))))
227.50/33.32	       |  '#form6'
227.50/33.32	       | ~ '#sk1'(X1, X3)
227.50/33.32	       |  X2('#sk25'(X2, X3))),
227.50/33.32	    inference('lazy_cnf_forall', [status(thm)], ['47'])).
227.50/33.32	tff('49', plain,
227.50/33.32	    ![X1, X2 : $i > $o, X3, X4]:
227.50/33.32	      (~ '#sk1'(X1, X4)
227.50/33.32	       | ~ X2(X4)
227.50/33.32	       |  X2('#sk25'(X2, X3))
227.50/33.32	       | ~ '#sk1'(X1, X3)
227.50/33.32	       |  '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['48'])).
227.50/33.32	tff('50', plain,
227.50/33.32	    (~ '#form6'
227.50/33.32	     |  (!!((^[Y0 : $i]:
227.50/33.32	               (!!((^[Y1 : $i > $o]:
227.50/33.32	                      ((!!((^[Y2 : $i]:
227.50/33.32	                              ((~('#sk1'(Y0, Y2))) |
227.50/33.32	                               (~((!!((^[Y3 : $i]:
227.50/33.32	                                         ((~('#sk1'(Y2, Y3))) | Y1(Y3))))))))))) |
227.50/33.32	                       (!!((^[Y2 : $i]: ((~('#sk1'(Y0, Y2))) | Y1(Y2))))))))))))),
227.50/33.32	    define([status(thm)])).
227.50/33.32	tff('51', plain,
227.50/33.32	    ![X1]:
227.50/33.32	      ( (!!((^[Y0 : $i > $o]:
227.50/33.32	               ((!!((^[Y1 : $i]:
227.50/33.32	                       ((~('#sk1'(X1, Y1))) |
227.50/33.32	                        (~((!!((^[Y2 : $i]: ((~('#sk1'(Y1, Y2))) | Y0(Y2))))))))))) |
227.50/33.32	                (!!((^[Y1 : $i]: ((~('#sk1'(X1, Y1))) | Y0(Y1)))))))))
227.50/33.32	       | ~ '#form6'),
227.50/33.32	    inference('lazy_cnf_forall', [status(thm)], ['50'])).
227.50/33.32	tff('52', plain,
227.50/33.32	    ![X1, X2 : $i > $o]:
227.50/33.32	      ( ((!!((^[Y0 : $i]:
227.50/33.32	                ((~('#sk1'(X1, Y0))) |
227.50/33.32	                 (~((!!((^[Y1 : $i]: ((~('#sk1'(Y0, Y1))) | X2(Y1))))))))))) |
227.50/33.32	         (!!((^[Y0 : $i]: ((~('#sk1'(X1, Y0))) | X2(Y0))))))
227.50/33.32	       | ~ '#form6'),
227.50/33.32	    inference('lazy_cnf_forall', [status(thm)], ['51'])).
227.50/33.32	tff('53', plain,
227.50/33.32	    ![X0 : $i > $o, X1]:
227.50/33.32	      ( ((!!((^[Y0 : $i]:
227.50/33.32	                ((~('#sk1'(X1, Y0))) |
227.50/33.32	                 (~((!!((^[Y1 : $i]: ((~('#sk1'(Y0, Y1))) | (~(X0(Y1))))))))))))) |
227.50/33.32	         (!!((^[Y0 : $i]: ((~('#sk1'(X1, Y0))) | (~(X0(Y0))))))))
227.50/33.32	       | ~ '#form6'),
227.50/33.32	    inference('ho.refine.early.bird', [status(thm)], ['52'])).
227.50/33.32	tff('54', plain,
227.50/33.32	    ![X0 : $i > $o, X1]:
227.50/33.32	      ( (!!((^[Y0 : $i]:
227.50/33.32	               ((~('#sk1'(X1, Y0))) |
227.50/33.32	                (~((!!((^[Y1 : $i]: ((~('#sk1'(Y0, Y1))) | (~(X0(Y1)))))))))))))
227.50/33.32	       |  (!!((^[Y0 : $i]: ((~('#sk1'(X1, Y0))) | (~(X0(Y0)))))))
227.50/33.32	       | ~ '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['53'])).
227.50/33.32	tff('55', plain,
227.50/33.32	    ![X0 : $i > $o, X1, X2]:
227.50/33.32	      ( ((~('#sk1'(X1, X2))) |
227.50/33.32	         (~((!!((^[Y0 : $i]: ((~('#sk1'(X2, Y0))) | (~(X0(Y0))))))))))
227.50/33.32	       | ~ '#form6'
227.50/33.32	       |  (!!((^[Y0 : $i]: ((~('#sk1'(X1, Y0))) | (~(X0(Y0)))))))),
227.50/33.32	    inference('lazy_cnf_forall', [status(thm)], ['54'])).
227.50/33.32	tff('56', plain,
227.50/33.32	    ![X0 : $i > $o, X1, X2]:
227.50/33.32	      (~ '#sk1'(X1, X2)
227.50/33.32	       | ~ (!!((^[Y0 : $i]: ((~('#sk1'(X2, Y0))) | (~(X0(Y0)))))))
227.50/33.32	       |  (!!((^[Y0 : $i]: ((~('#sk1'(X1, Y0))) | (~(X0(Y0)))))))
227.50/33.32	       | ~ '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['55'])).
227.50/33.32	tff('57', plain,
227.50/33.32	    ![X0 : $i > $o, X1, X2]:
227.50/33.32	      (~ ((~('#sk1'(X2, '#sk25'(X0, X2)))) | (~(X0('#sk25'(X0, X2)))))
227.50/33.32	       | ~ '#form6'
227.50/33.32	       |  (!!((^[Y0 : $i]: ((~('#sk1'(X1, Y0))) | (~(X0(Y0)))))))
227.50/33.32	       | ~ '#sk1'(X1, X2)),
227.50/33.32	    inference('lazy_cnf_exists', [status(thm)], ['56'])).
227.50/33.32	tff('58', plain,
227.50/33.32	    ![X0 : $i > $o, X1, X2]:
227.50/33.32	      ( X0('#sk25'(X0, X2))
227.50/33.32	       | ~ '#sk1'(X1, X2)
227.50/33.32	       |  (!!((^[Y0 : $i]: ((~('#sk1'(X1, Y0))) | (~(X0(Y0)))))))
227.50/33.32	       | ~ '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['57'])).
227.50/33.32	tff('59', plain,
227.50/33.32	    ![X0 : $i > $o, X1, X2, X3]:
227.50/33.32	      ( ((~('#sk1'(X1, X3))) | (~(X0(X3))))
227.50/33.32	       | ~ '#form6'
227.50/33.32	       | ~ '#sk1'(X1, X2)
227.50/33.32	       |  X0('#sk25'(X0, X2))),
227.50/33.32	    inference('lazy_cnf_forall', [status(thm)], ['58'])).
227.50/33.32	tff('60', plain,
227.50/33.32	    ![X0 : $i > $o, X1, X2, X3]:
227.50/33.32	      (~ '#sk1'(X1, X3)
227.50/33.32	       | ~ X0(X3)
227.50/33.32	       |  X0('#sk25'(X0, X2))
227.50/33.32	       | ~ '#sk1'(X1, X2)
227.50/33.32	       | ~ '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['59'])).
227.50/33.32	tff('61', plain, ( '#sk3'('#sk5') | ~ '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['34'])).
227.50/33.32	tff('62', plain,
227.50/33.32	    ![X1, X2 : $i > $o, X3]:
227.50/33.32	      ( '#sk1'(X3, '#sk25'(X2, X3))
227.50/33.32	       | ~ '#sk1'(X1, X3)
227.50/33.32	       |  (!!((^[Y0 : $i]: ((~('#sk1'(X1, Y0))) | (~(X2(Y0)))))))
227.50/33.32	       |  '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['46'])).
227.50/33.32	tff('63', plain,
227.50/33.32	    ![X1, X2 : $i > $o, X3, X4]:
227.50/33.32	      ( ((~('#sk1'(X1, X4))) | (~(X2(X4))))
227.50/33.32	       |  '#form6'
227.50/33.32	       | ~ '#sk1'(X1, X3)
227.50/33.32	       |  '#sk1'(X3, '#sk25'(X2, X3))),
227.50/33.32	    inference('lazy_cnf_forall', [status(thm)], ['62'])).
227.50/33.32	tff('64', plain,
227.50/33.32	    ![X1, X2 : $i > $o, X3, X4]:
227.50/33.32	      (~ '#sk1'(X1, X4)
227.50/33.32	       | ~ X2(X4)
227.50/33.32	       |  '#sk1'(X3, '#sk25'(X2, X3))
227.50/33.32	       | ~ '#sk1'(X1, X3)
227.50/33.32	       |  '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['63'])).
227.50/33.32	tff('65', plain,
227.50/33.32	    ![X0 : $i > $o, X1, X2]:
227.50/33.32	      ( '#sk1'(X2, '#sk25'(X0, X2))
227.50/33.32	       | ~ '#sk1'(X1, X2)
227.50/33.32	       |  (!!((^[Y0 : $i]: ((~('#sk1'(X1, Y0))) | (~(X0(Y0)))))))
227.50/33.32	       | ~ '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['57'])).
227.50/33.32	tff('66', plain,
227.50/33.32	    ![X0 : $i > $o, X1, X2, X3]:
227.50/33.32	      ( ((~('#sk1'(X1, X3))) | (~(X0(X3))))
227.50/33.32	       | ~ '#form6'
227.50/33.32	       | ~ '#sk1'(X1, X2)
227.50/33.32	       |  '#sk1'(X2, '#sk25'(X0, X2))),
227.50/33.32	    inference('lazy_cnf_forall', [status(thm)], ['65'])).
227.50/33.32	tff('67', plain,
227.50/33.32	    ![X0 : $i > $o, X1, X2, X3]:
227.50/33.32	      (~ '#sk1'(X1, X3)
227.50/33.32	       | ~ X0(X3)
227.50/33.32	       |  '#sk1'(X2, '#sk25'(X0, X2))
227.50/33.32	       | ~ '#sk1'(X1, X2)
227.50/33.32	       | ~ '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['66'])).
227.50/33.32	tff('68', plain,
227.50/33.32	    ( '#form6'
227.50/33.32	     | ~ (!!((^[Y0 : $i]:
227.50/33.32	                (!!((^[Y1 : $i > $o]:
227.50/33.32	                       ((!!((^[Y2 : $i]:
227.50/33.32	                               ((~('#sk1'(Y0, Y2))) |
227.50/33.32	                                (~((!!((^[Y3 : $i]:
227.50/33.32	                                          ((~('#sk1'(Y2, Y3))) | Y1(Y3))))))))))) |
227.50/33.32	                        (!!((^[Y2 : $i]: ((~('#sk1'(Y0, Y2))) | Y1(Y2))))))))))))),
227.50/33.32	    define([status(thm)])).
227.50/33.32	tff('69', plain,
227.50/33.32	    (~ (!!((^[Y0 : $i > $o]:
227.50/33.32	              ((!!((^[Y1 : $i]:
227.50/33.32	                      ((~('#sk1'('#sk7', Y1))) |
227.50/33.32	                       (~((!!((^[Y2 : $i]: ((~('#sk1'(Y1, Y2))) | Y0(Y2))))))))))) |
227.50/33.32	               (!!((^[Y1 : $i]: ((~('#sk1'('#sk7', Y1))) | Y0(Y1)))))))))
227.50/33.32	     |  '#form6'),
227.50/33.32	    inference('lazy_cnf_exists', [status(thm)], ['68'])).
227.50/33.32	tff('70', plain,
227.50/33.32	    (~ ((!!((^[Y0 : $i]:
227.50/33.32	               ((~('#sk1'('#sk7', Y0))) |
227.50/33.32	                (~((!!((^[Y1 : $i]: ((~('#sk1'(Y0, Y1))) | '#sk8'(Y1))))))))))) |
227.50/33.32	        (!!((^[Y0 : $i]: ((~('#sk1'('#sk7', Y0))) | '#sk8'(Y0))))))
227.50/33.32	     |  '#form6'),
227.50/33.32	    inference('lazy_cnf_exists', [status(thm)], ['69'])).
227.50/33.32	tff('71', plain,
227.50/33.32	    (~ (!!((^[Y0 : $i]: ((~('#sk1'('#sk7', Y0))) | '#sk8'(Y0))))) |  '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['70'])).
227.50/33.32	tff('72', plain,
227.50/33.32	    (~ ((~('#sk1'('#sk7', '#sk10'))) | '#sk8'('#sk10')) |  '#form6'),
227.50/33.32	    inference('lazy_cnf_exists', [status(thm)], ['71'])).
227.50/33.32	tff('73', plain, (~ '#sk8'('#sk10') |  '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['72'])).
227.50/33.32	tff('74', plain,
227.50/33.32	    (~ (!!((^[Y0 : $i]:
227.50/33.32	              ((~('#sk1'('#sk7', Y0))) |
227.50/33.32	               (~((!!((^[Y1 : $i]: ((~('#sk1'(Y0, Y1))) | '#sk8'(Y1)))))))))))
227.50/33.32	     |  '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['70'])).
227.50/33.32	tff('75', plain,
227.50/33.32	    (~ ((~('#sk1'('#sk7', '#sk9'))) |
227.50/33.32	        (~((!!((^[Y0 : $i]: ((~('#sk1'('#sk9', Y0))) | '#sk8'(Y0))))))))
227.50/33.32	     |  '#form6'),
227.50/33.32	    inference('lazy_cnf_exists', [status(thm)], ['74'])).
227.50/33.32	tff('76', plain,
227.50/33.32	    ( (!!((^[Y0 : $i]: ((~('#sk1'('#sk9', Y0))) | '#sk8'(Y0))))) |  '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['75'])).
227.50/33.32	tff('77', plain,
227.50/33.32	    ![X1]: ( ((~('#sk1'('#sk9', X1))) | '#sk8'(X1)) |  '#form6'),
227.50/33.32	    inference('lazy_cnf_forall', [status(thm)], ['76'])).
227.50/33.32	tff('78', plain, ![X1]: (~ '#sk1'('#sk9', X1) |  '#sk8'(X1) |  '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['77'])).
227.50/33.32	tff('79', plain, ( '#sk1'('#sk7', '#sk9') |  '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['75'])).
227.50/33.32	tff('80', plain, ( '#sk1'('#sk7', '#sk10') |  '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['72'])).
227.50/33.32	tff('81', plain,
227.50/33.32	    ![X1, X2 : $i > $o]:
227.50/33.32	      ( ((!!((^[Y0 : $i]:
227.50/33.32	                ((~('#sk1'(X1, Y0))) |
227.50/33.32	                 (~((!!((^[Y1 : $i]: ((~('#sk1'(Y0, Y1))) | (~(X2(Y1))))))))))))) |
227.50/33.32	         (!!((^[Y0 : $i]: ((~('#sk1'(X1, Y0))) | (~(X2(Y0))))))))
227.50/33.32	       |  '#form6'),
227.50/33.32	    inference('lazy_cnf_forall', [status(thm)], ['41'])).
227.50/33.32	tff('82', plain,
227.50/33.32	    ![X0 : $i > $o, X1]:
227.50/33.32	      ( ((!!((^[Y0 : $i]:
227.50/33.32	                ((~('#sk1'(X1, Y0))) |
227.50/33.32	                 (~((!!((^[Y1 : $i]: ((~('#sk1'(Y0, Y1))) | (~((~(X0(Y1))))))))))))))) |
227.50/33.32	         (!!((^[Y0 : $i]: ((~('#sk1'(X1, Y0))) | (~((~(X0(Y0))))))))))
227.50/33.32	       |  '#form6'),
227.50/33.32	    inference('ho.refine.early.bird', [status(thm)], ['81'])).
227.50/33.32	tff('83', plain,
227.50/33.32	    ![X0 : $i > $o, X1]:
227.50/33.32	      ( ((!!((^[Y0 : $i]:
227.50/33.32	                ((~('#sk1'(X1, Y0))) |
227.50/33.32	                 (~((!!((^[Y1 : $i]: ((~('#sk1'(Y0, Y1))) | X0(Y1))))))))))) |
227.50/33.32	         (!!((^[Y0 : $i]: ((~('#sk1'(X1, Y0))) | X0(Y0))))))
227.50/33.32	       |  '#form6'),
227.50/33.32	    inference('simplify boolean subterms', [status(thm)], ['82'])).
227.50/33.32	tff('84', plain,
227.50/33.32	    ![X0 : $i > $o, X1]:
227.50/33.32	      ( (!!((^[Y0 : $i]:
227.50/33.32	               ((~('#sk1'(X1, Y0))) |
227.50/33.32	                (~((!!((^[Y1 : $i]: ((~('#sk1'(Y0, Y1))) | X0(Y1)))))))))))
227.50/33.32	       |  (!!((^[Y0 : $i]: ((~('#sk1'(X1, Y0))) | X0(Y0)))))
227.50/33.32	       |  '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['83'])).
227.50/33.32	tff('85', plain,
227.50/33.32	    ![X0 : $i > $o, X1, X2]:
227.50/33.32	      ( ((~('#sk1'(X1, X2))) |
227.50/33.32	         (~((!!((^[Y0 : $i]: ((~('#sk1'(X2, Y0))) | X0(Y0))))))))
227.50/33.32	       |  '#form6'
227.50/33.32	       |  (!!((^[Y0 : $i]: ((~('#sk1'(X1, Y0))) | X0(Y0)))))),
227.50/33.32	    inference('lazy_cnf_forall', [status(thm)], ['84'])).
227.50/33.32	tff('86', plain,
227.50/33.32	    ![X0 : $i > $o, X1, X2]:
227.50/33.32	      (~ '#sk1'(X1, X2)
227.50/33.32	       | ~ (!!((^[Y0 : $i]: ((~('#sk1'(X2, Y0))) | X0(Y0)))))
227.50/33.32	       |  (!!((^[Y0 : $i]: ((~('#sk1'(X1, Y0))) | X0(Y0)))))
227.50/33.32	       |  '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['85'])).
227.50/33.32	tff('87', plain,
227.50/33.32	    ![X0 : $i > $o, X1, X2]:
227.50/33.32	      (~ ((~('#sk1'(X2, '#sk28'(X0, X2)))) | X0('#sk28'(X0, X2)))
227.50/33.32	       |  '#form6'
227.50/33.32	       |  (!!((^[Y0 : $i]: ((~('#sk1'(X1, Y0))) | X0(Y0)))))
227.50/33.32	       | ~ '#sk1'(X1, X2)),
227.50/33.32	    inference('lazy_cnf_exists', [status(thm)], ['86'])).
227.50/33.32	tff('88', plain,
227.50/33.32	    ![X0 : $i > $o, X1, X2]:
227.50/33.32	      ( '#sk1'(X2, '#sk28'(X0, X2))
227.50/33.32	       | ~ '#sk1'(X1, X2)
227.50/33.32	       |  (!!((^[Y0 : $i]: ((~('#sk1'(X1, Y0))) | X0(Y0)))))
227.50/33.32	       |  '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['87'])).
227.50/33.32	tff('89', plain,
227.50/33.32	    ![X0 : $i > $o, X1, X2, X3]:
227.50/33.32	      ( ((~('#sk1'(X1, X3))) | X0(X3))
227.50/33.32	       |  '#form6'
227.50/33.32	       | ~ '#sk1'(X1, X2)
227.50/33.32	       |  '#sk1'(X2, '#sk28'(X0, X2))),
227.50/33.32	    inference('lazy_cnf_forall', [status(thm)], ['88'])).
227.50/33.32	tff('90', plain,
227.50/33.32	    ![X0 : $i > $o, X1, X2, X3]:
227.50/33.32	      (~ '#sk1'(X1, X3)
227.50/33.32	       |  X0(X3)
227.50/33.32	       |  '#sk1'(X2, '#sk28'(X0, X2))
227.50/33.32	       | ~ '#sk1'(X1, X2)
227.50/33.32	       |  '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['89'])).
227.50/33.32	tff('91', plain,
227.50/33.32	    ![X0, X1 : $i > $o]:
227.50/33.32	      ( '#form6'
227.50/33.32	       |  '#form6'
227.50/33.32	       | ~ '#sk1'('#sk7', X0)
227.50/33.32	       |  '#sk1'(X0, '#sk28'(X1, X0))
227.50/33.32	       |  X1('#sk10')),
227.50/33.32	    inference('sup-', [status(thm)], ['80', '90'])).
227.50/33.32	tff('92', plain,
227.50/33.32	    ![X0, X1 : $i > $o]:
227.50/33.32	      ( X1('#sk10')
227.50/33.32	       |  '#sk1'(X0, '#sk28'(X1, X0))
227.50/33.32	       | ~ '#sk1'('#sk7', X0)
227.50/33.32	       |  '#form6'),
227.50/33.32	    inference('simplify', [status(thm)], ['91'])).
227.50/33.32	tff('93', plain, ( '#sk1'('#sk7', '#sk10') |  '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['72'])).
227.50/33.32	tff('94', plain, ( '#sk1'('#sk7', '#sk9') |  '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['75'])).
227.50/33.32	tff('95', plain,
227.50/33.32	    ![X0 : $i > $o, X1, X2]:
227.50/33.32	      (~ X0('#sk28'(X0, X2))
227.50/33.32	       | ~ '#sk1'(X1, X2)
227.50/33.32	       |  (!!((^[Y0 : $i]: ((~('#sk1'(X1, Y0))) | X0(Y0)))))
227.50/33.32	       |  '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['87'])).
227.50/33.32	tff('96', plain,
227.50/33.32	    ![X0 : $i > $o, X1, X2, X3]:
227.50/33.32	      ( ((~('#sk1'(X1, X3))) | X0(X3))
227.50/33.32	       |  '#form6'
227.50/33.32	       | ~ '#sk1'(X1, X2)
227.50/33.32	       | ~ X0('#sk28'(X0, X2))),
227.50/33.32	    inference('lazy_cnf_forall', [status(thm)], ['95'])).
227.50/33.32	tff('97', plain,
227.50/33.32	    ![X0 : $i > $o, X1, X2, X3]:
227.50/33.32	      (~ '#sk1'(X1, X3)
227.50/33.32	       |  X0(X3)
227.50/33.32	       | ~ X0('#sk28'(X0, X2))
227.50/33.32	       | ~ '#sk1'(X1, X2)
227.50/33.32	       |  '#form6'),
227.50/33.32	    inference('lazy_cnf_or', [status(thm)], ['96'])).
227.50/33.32	tff('98', plain,
227.50/33.32	    ![X0 : $i > $o, X1]:
227.50/33.32	      ( '#form6'
227.50/33.32	       |  '#form6'
227.50/33.32	       | ~ X0('#sk28'(X0, '#sk9'))
227.50/33.32	       |  X0(X1)
227.50/33.32	       | ~ '#sk1'('#sk7', X1)),
227.50/33.32	    inference('sup-', [status(thm)], ['94', '97'])).
227.50/33.32	tff('99', plain,
227.50/33.32	    ![X0 : $i > $o, X1]:
227.50/33.32	      (~ '#sk1'('#sk7', X1) |  X0(X1) | ~ X0('#sk28'(X0, '#sk9')) |  '#form6'),
227.50/33.32	    inference('simplify', [status(thm)], ['98'])).
227.50/33.32	tff('100', plain,
227.50/33.32	    ![X0 : $i > $o]:
227.50/33.32	      ( '#form6' |  '#form6' | ~ X0('#sk28'(X0, '#sk9')) |  X0('#sk10')),
227.50/33.32	    inference('sup-', [status(thm)], ['93', '99'])).
227.50/33.32	tff('101', plain,
227.50/33.32	    ![X0 : $i > $o]: ( X0('#sk10') | ~ X0('#sk28'(X0, '#sk9')) |  '#form6'),
227.50/33.32	    inference('simplify', [status(thm)], ['100'])).
227.50/33.32	tff('102', plain,
227.50/33.32	    ![X0 : $i > $o]:
227.50/33.32	      (X0('#sk10') != '#form6' |  '#form6' | ~ X0('#sk28'(X0, '#sk9'))),
227.50/33.32	    inference('eq_fact', [status(thm)], ['101'])).
227.50/33.32	tff('103', plain, $false,
227.50/33.32	    inference('eprover', [status(thm)],
227.50/33.32	              ['28', '31', '35', '49', '60', '61', '64', '67', '73', '78', 
227.50/33.32	               '79', '92', '102'])).
227.50/33.32	
227.50/33.32	% SZS output end Refutation
227.50/33.32	
227.50/33.32	
227.50/33.32	% Terminating...
242.56/33.39	% Runner terminated.
242.56/33.39	% Zipperpin 1.5 exiting
242.56/33.39	EOF