0.11/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.12	% Command    : run_portfolio.sh /export/starexec/sandbox/benchmark/theBenchmark.p /export/starexec/sandbox/tmp/tmp.DttC8ylXan
0.12/0.31	% Computer   : n005.cluster.edu
0.12/0.31	% Model      : x86_64 x86_64
0.12/0.31	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.31	% Memory     : 8042.1875MB
0.12/0.31	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.31	% CPULimit   : 960
0.12/0.31	% DateTime   : Thu Jul  2 08:40:21 EDT 2020
0.12/0.31	% CPUTime    : 
0.12/0.31	% Running portfolio for 120 s
0.12/0.31	% File         : /export/starexec/sandbox/benchmark/theBenchmark.p
0.12/0.32	% Number of cores: 8
0.12/0.32	% Python version: Python 3.6.8
0.12/0.32	% Running in HO mode
0.51/0.60	% Estimated wc time : 1286
0.51/0.60	% Estimated cpu time (7 cpus) : 183.71428571428572
0.52/0.67	% /export/starexec/sandbox/solver/bin/lams/s6.sh running for 21s
0.52/0.69	% /export/starexec/sandbox/solver/bin/lams/new_b3.2.norw.sh running for 15s
0.52/0.72	% /export/starexec/sandbox/solver/bin/lams/b.rpo.sh running for 21s
0.52/0.72	% /export/starexec/sandbox/solver/bin/lams/s6.ds.sh running for 10s
0.52/0.72	% /export/starexec/sandbox/solver/bin/lams/c.easy.sh running for 26s
0.52/0.72	% /export/starexec/sandbox/solver/bin/lams/c.s.2.sh running for 68s
0.53/0.73	% /export/starexec/sandbox/solver/bin/lams/old_b3.avatar.sh running for 15s
6.82/1.56	% Solved by lams/s6.ds.sh.
6.82/1.56	% done 134 iterations in 0.808s
6.82/1.56	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
6.82/1.56	% SZS output start Refutation
6.82/1.56	tff(image1Ex, axiom, image1Ex <=>
6.82/1.56	  (![A,Xf:(($i > $i))]:
6.82/1.56	     (?[B]: (![Xx]: (in(Xx,B) <=> (?[Xy]: ((Xx = Xf(Xy)) & in(Xy,A)))))))).
6.82/1.56	tff('0', plain,
6.82/1.56	    image1Ex =
6.82/1.56	    (![X4,X6:(($i > $i))]:
6.82/1.56	       (?[X8]:
6.82/1.56	          (![X10]: (in(X10,X8) <=> (?[X12]: ((X10 = X6(X12)) & in(X12,X4))))))),
6.82/1.56	    define([status(thm)])).
6.82/1.56	tff(setextsub, axiom, setextsub <=>
6.82/1.56	  (![A,B]: (subset(A,B) => (subset(B,A) => (A = B))))).
6.82/1.56	tff('1', plain,
6.82/1.56	    setextsub = (![X4,X6]: (subset(X4,X6) => (subset(X6,X4) => (X4 = X6)))),
6.82/1.56	    define([status(thm)])).
6.82/1.56	tff(subsetI1, axiom, subsetI1 <=>
6.82/1.56	  (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))).
6.82/1.56	tff('2', plain,
6.82/1.56	    subsetI1 =
6.82/1.56	    (![X4,X6]: ((![X8]: (in(X8,X4) => in(X8,X6))) => subset(X4,X6))),
6.82/1.56	    define([status(thm)])).
6.82/1.56	tff(exu, axiom, exu() =
6.82/1.56	  ^[Xphi:(($i > $o))]: (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))).
6.82/1.56	tff('3', plain,
6.82/1.56	    exu =
6.82/1.56	    (^[Xphi:(($i > $o))]:
6.82/1.56	       (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))),
6.82/1.56	    inference('simplify_rw_rule', [status(thm)], [exu])).
6.82/1.56	tff('4', plain,
6.82/1.56	    exu =
6.82/1.56	    (^[V_1:(($i > $o))]: (?[X4]: ((![X6]: (V_1(X6) => (X4 = X6))) & V_1(X4)))),
6.82/1.56	    define([status(thm)])).
6.82/1.56	tff(image1Ex1, conjecture,
6.82/1.56	  (subsetI1 =>
6.82/1.56	   (setextsub =>
6.82/1.56	    (image1Ex =>
6.82/1.56	     (![A,Xf:(($i > $i))]:
6.82/1.56	        exu(^[B]: (![Xx]: (in(Xx,B) <=> (?[Xy]: ((Xx = Xf(Xy)) & in(Xy,A))))))))))).
6.82/1.56	tff(zf_stmt_0, conjecture,
6.82/1.56	  ((![X4,X6]: ((![X8]: (in(X8,X4) => in(X8,X6))) => subset(X4,X6))) =>
6.82/1.56	   ((![X10,X12]: (subset(X10,X12) => (subset(X12,X10) => (X10 = X12)))) =>
6.82/1.56	    ((![X14,X16:(($i > $i))]:
6.82/1.56	        (?[X18]:
6.82/1.56	           (![X20]:
6.82/1.56	              (in(X20,X18) <=> (?[X22]: (in(X22,X14) & (X20 = X16(X22)))))))) =>
6.82/1.56	     (![X24,X26:(($i > $i))]:
6.82/1.56	        (?[X28]:
6.82/1.56	           ((![X36]:
6.82/1.56	               (in(X36,X28) <=> (?[X38]: (in(X38,X24) & (X36 = X26(X38)))))) & 
6.82/1.56	            (![X30]:
6.82/1.56	               ((![X32]:
6.82/1.56	                   (in(X32,X30) <=>
6.82/1.56	                    (?[X34]: (in(X34,X24) & (X32 = X26(X34)))))) =>
6.82/1.56	                (X28 = X30)))))))))).
6.82/1.56	tff(zf_stmt_1, negated_conjecture,
6.82/1.56	  (~
6.82/1.56	    ((![X4,X6]: ((![X8]: (in(X8,X4) => in(X8,X6))) => subset(X4,X6))) =>
6.82/1.56	     ((![X10,X12]: (subset(X10,X12) => (subset(X12,X10) => (X10 = X12)))) =>
6.82/1.56	      ((![X14,X16:(($i > $i))]:
6.82/1.56	          (?[X18]:
6.82/1.56	             (![X20]:
6.82/1.56	                (in(X20,X18) <=> (?[X22]: (in(X22,X14) & (X20 = X16(X22)))))))) =>
6.82/1.56	       (![X24,X26:(($i > $i))]:
6.82/1.56	          (?[X28]:
6.82/1.56	             ((![X36]:
6.82/1.56	                 (in(X36,X28) <=> (?[X38]: (in(X38,X24) & (X36 = X26(X38)))))) & 
6.82/1.56	              (![X30]:
6.82/1.56	                 ((![X32]:
6.82/1.56	                     (in(X32,X30) <=>
6.82/1.56	                      (?[X34]: (in(X34,X24) & (X32 = X26(X34)))))) =>
6.82/1.56	                  (X28 = X30))))))))))).
6.82/1.56	tff('5', plain,
6.82/1.56	    ~ ((!!((^[Y0 : $i]:
6.82/1.56	              (!!((^[Y1 : $i]:
6.82/1.56	                     ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) =>
6.82/1.56	                      subset(Y0, Y1)))))))) =>
6.82/1.56	       ((!!((^[Y0 : $i]:
6.82/1.56	               (!!((^[Y1 : $i]:
6.82/1.56	                      (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1))))))))) =>
6.82/1.56	        ((!!((^[Y0 : $i]:
6.82/1.56	                (!!((^[Y1 : $i > $i]:
6.82/1.56	                       (??((^[Y2 : $i]:
6.82/1.56	                              (!!((^[Y3 : $i]:
6.82/1.56	                                     (in(Y3, Y2) <=>
6.82/1.56	                                      (??((^[Y4 : $i]:
6.82/1.56	                                             (in(Y4, Y0) & (Y3 = Y1(Y4))))))))))))))))))) =>
6.82/1.56	         (!!((^[Y0 : $i]:
6.82/1.56	                (!!((^[Y1 : $i > $i]:
6.82/1.56	                       (??((^[Y2 : $i]:
6.82/1.56	                              ((!!((^[Y3 : $i]:
6.82/1.56	                                      (in(Y3, Y2) <=>
6.82/1.56	                                       (??((^[Y4 : $i]:
6.82/1.56	                                              (in(Y4, Y0) & (Y3 = Y1(Y4)))))))))) &
6.82/1.56	                               (!!((^[Y3 : $i]:
6.82/1.56	                                      ((!!((^[Y4 : $i]:
6.82/1.56	                                              (in(Y4, Y3) <=>
6.82/1.56	                                               (??((^[Y5 : $i]:
6.82/1.56	                                                      (in(Y5, Y0) &
6.82/1.56	                                                       (Y4 = Y1(Y5)))))))))) =>
6.82/1.56	                                       (Y2 = Y3)))))))))))))))))),
6.82/1.56	    inference('cnf', [status(esa)], [zf_stmt_1])).
6.82/1.56	tff('6', plain,
6.82/1.56	     (!!((^[Y0 : $i]:
6.82/1.56	            (!!((^[Y1 : $i]:
6.82/1.56	                   ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) =>
6.82/1.56	                    subset(Y0, Y1)))))))),
6.82/1.56	    inference('lazy_cnf_imply', [status(thm)], ['5'])).
6.82/1.56	tff('7', plain,
6.82/1.56	    ![X1]:
6.82/1.56	       (!!((^[Y0 : $i]:
6.82/1.56	              ((!!((^[Y1 : $i]: (in(Y1, X1) => in(Y1, Y0))))) =>
6.82/1.56	               subset(X1, Y0))))),
6.82/1.56	    inference('lazy_cnf_forall', [status(thm)], ['6'])).
6.82/1.56	tff('8', plain,
6.82/1.56	    ![X1, X2]:
6.82/1.56	       ((!!((^[Y0 : $i]: (in(Y0, X1) => in(Y0, X2))))) => subset(X1, X2)),
6.82/1.56	    inference('lazy_cnf_forall', [status(thm)], ['7'])).
6.82/1.56	tff('9', plain,
6.82/1.56	    ![X1, X2]:
6.82/1.56	      (~ (!!((^[Y0 : $i]: (in(Y0, X1) => in(Y0, X2))))) |  subset(X1, X2)),
6.82/1.56	    inference('lazy_cnf_imply', [status(thm)], ['8'])).
6.82/1.56	tff('10', plain,
6.82/1.56	    ![X1, X2]:
6.82/1.56	      (~ (in('#sk2'(X1, X2), X1) => in('#sk2'(X1, X2), X2)) |  subset(X1, X2)),
6.82/1.56	    inference('lazy_cnf_exists', [status(thm)], ['9'])).
6.82/1.56	tff('11', plain, ![X1, X2]: ( in('#sk2'(X1, X2), X1) |  subset(X1, X2)),
6.82/1.56	    inference('lazy_cnf_imply', [status(thm)], ['10'])).
6.82/1.56	tff('12', plain,
6.82/1.56	    ~ ((!!((^[Y0 : $i]:
6.82/1.56	              (!!((^[Y1 : $i]:
6.82/1.56	                     (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1))))))))) =>
6.82/1.56	       ((!!((^[Y0 : $i]:
6.82/1.56	               (!!((^[Y1 : $i > $i]:
6.82/1.56	                      (??((^[Y2 : $i]:
6.82/1.56	                             (!!((^[Y3 : $i]:
6.82/1.56	                                    (in(Y3, Y2) <=>
6.82/1.56	                                     (??((^[Y4 : $i]:
6.82/1.56	                                            (in(Y4, Y0) & (Y3 = Y1(Y4))))))))))))))))))) =>
6.82/1.56	        (!!((^[Y0 : $i]:
6.82/1.56	               (!!((^[Y1 : $i > $i]:
6.82/1.56	                      (??((^[Y2 : $i]:
6.82/1.56	                             ((!!((^[Y3 : $i]:
6.82/1.56	                                     (in(Y3, Y2) <=>
6.82/1.56	                                      (??((^[Y4 : $i]:
6.82/1.56	                                             (in(Y4, Y0) & (Y3 = Y1(Y4)))))))))) &
6.82/1.56	                              (!!((^[Y3 : $i]:
6.82/1.56	                                     ((!!((^[Y4 : $i]:
6.82/1.56	                                             (in(Y4, Y3) <=>
6.82/1.56	                                              (??((^[Y5 : $i]:
6.82/1.56	                                                     (in(Y5, Y0) &
6.82/1.56	                                                      (Y4 = Y1(Y5)))))))))) =>
6.82/1.56	                                      (Y2 = Y3))))))))))))))))),
6.82/1.56	    inference('lazy_cnf_imply', [status(thm)], ['5'])).
6.82/1.56	tff('13', plain,
6.82/1.56	    ~ ((!!((^[Y0 : $i]:
6.82/1.56	              (!!((^[Y1 : $i > $i]:
6.82/1.56	                     (??((^[Y2 : $i]:
6.82/1.56	                            (!!((^[Y3 : $i]:
6.82/1.56	                                   (in(Y3, Y2) <=>
6.82/1.56	                                    (??((^[Y4 : $i]:
6.82/1.56	                                           (in(Y4, Y0) & (Y3 = Y1(Y4))))))))))))))))))) =>
6.82/1.56	       (!!((^[Y0 : $i]:
6.82/1.56	              (!!((^[Y1 : $i > $i]:
6.82/1.56	                     (??((^[Y2 : $i]:
6.82/1.56	                            ((!!((^[Y3 : $i]:
6.82/1.56	                                    (in(Y3, Y2) <=>
6.82/1.56	                                     (??((^[Y4 : $i]:
6.82/1.56	                                            (in(Y4, Y0) & (Y3 = Y1(Y4)))))))))) &
6.82/1.56	                             (!!((^[Y3 : $i]:
6.82/1.56	                                    ((!!((^[Y4 : $i]:
6.82/1.56	                                            (in(Y4, Y3) <=>
6.82/1.56	                                             (??((^[Y5 : $i]:
6.82/1.56	                                                    (in(Y5, Y0) &
6.82/1.56	                                                     (Y4 = Y1(Y5)))))))))) =>
6.82/1.56	                                     (Y2 = Y3)))))))))))))))),
6.82/1.56	    inference('lazy_cnf_imply', [status(thm)], ['12'])).
6.82/1.56	tff('14', plain,
6.82/1.56	     (!!((^[Y0 : $i]:
6.82/1.56	            (!!((^[Y1 : $i > $i]:
6.82/1.56	                   (??((^[Y2 : $i]:
6.82/1.56	                          (!!((^[Y3 : $i]:
6.82/1.56	                                 (in(Y3, Y2) <=>
6.82/1.56	                                  (??((^[Y4 : $i]:
6.82/1.56	                                         (in(Y4, Y0) & (Y3 = Y1(Y4))))))))))))))))))),
6.82/1.56	    inference('lazy_cnf_imply', [status(thm)], ['13'])).
6.82/1.56	tff('15', plain,
6.82/1.56	    ![X1]:
6.82/1.56	       (!!((^[Y0 : $i > $i]:
6.82/1.56	              (??((^[Y1 : $i]:
6.82/1.56	                     (!!((^[Y2 : $i]:
6.82/1.56	                            (in(Y2, Y1) <=>
6.82/1.56	                             (??((^[Y3 : $i]: (in(Y3, X1) & (Y2 = Y0(Y3)))))))))))))))),
6.82/1.56	    inference('lazy_cnf_forall', [status(thm)], ['14'])).
6.82/1.56	tff('16', plain,
6.82/1.56	    ![X1, X2 : $i > $i]:
6.82/1.56	       (??((^[Y0 : $i]:
6.82/1.56	              (!!((^[Y1 : $i]:
6.82/1.56	                     (in(Y1, Y0) <=>
6.82/1.56	                      (??((^[Y2 : $i]: (in(Y2, X1) & (Y1 = X2(Y2))))))))))))),
6.82/1.56	    inference('lazy_cnf_forall', [status(thm)], ['15'])).
6.82/1.56	tff('17', plain,
6.82/1.56	    ![X1, X2 : $i > $i]:
6.82/1.56	       (!!((^[Y0 : $i]:
6.82/1.56	              (in(Y0, '#sk5'(X1, X2)) <=>
6.82/1.56	               (??((^[Y1 : $i]: (in(Y1, X1) & (Y0 = X2(Y1)))))))))),
6.82/1.56	    inference('lazy_cnf_exists', [status(thm)], ['16'])).
6.82/1.56	tff('18', plain,
6.82/1.56	    ![X1, X2 : $i > $i, X3]:
6.82/1.56	       (in(X3, '#sk5'(X1, X2)) <=>
6.82/1.56	        (??((^[Y0 : $i]: (in(Y0, X1) & (X3 = X2(Y0))))))),
6.82/1.56	    inference('lazy_cnf_forall', [status(thm)], ['17'])).
6.82/1.56	tff('19', plain,
6.82/1.56	    ![X1, X2 : $i > $i, X3]:
6.82/1.56	      in(X3, '#sk5'(X1, X2))
6.82/1.56	       = (??((^[Y0 : $i]: (in(Y0, X1) & (X3 = X2(Y0)))))),
6.82/1.56	    inference('simplify nested equalities', [status(thm)], ['18'])).
6.82/1.56	tff('20', plain,
6.82/1.56	    ~ (!!((^[Y0 : $i]:
6.82/1.56	             (!!((^[Y1 : $i > $i]:
6.82/1.56	                    (??((^[Y2 : $i]:
6.82/1.56	                           ((!!((^[Y3 : $i]:
6.82/1.56	                                   (in(Y3, Y2) <=>
6.82/1.56	                                    (??((^[Y4 : $i]:
6.82/1.56	                                           (in(Y4, Y0) & (Y3 = Y1(Y4)))))))))) &
6.82/1.56	                            (!!((^[Y3 : $i]:
6.82/1.56	                                   ((!!((^[Y4 : $i]:
6.82/1.56	                                           (in(Y4, Y3) <=>
6.82/1.56	                                            (??((^[Y5 : $i]:
6.82/1.56	                                                   (in(Y5, Y0) &
6.82/1.56	                                                    (Y4 = Y1(Y5)))))))))) =>
6.82/1.56	                                    (Y2 = Y3))))))))))))))),
6.82/1.56	    inference('lazy_cnf_imply', [status(thm)], ['13'])).
6.82/1.56	tff('21', plain,
6.82/1.56	    ~ (!!((^[Y0 : $i > $i]:
6.82/1.56	             (??((^[Y1 : $i]:
6.82/1.56	                    ((!!((^[Y2 : $i]:
6.82/1.56	                            (in(Y2, Y1) <=>
6.82/1.56	                             (??((^[Y3 : $i]:
6.82/1.56	                                    (in(Y3, '#sk1') & (Y2 = Y0(Y3)))))))))) &
6.82/1.56	                     (!!((^[Y2 : $i]:
6.82/1.56	                            ((!!((^[Y3 : $i]:
6.82/1.56	                                    (in(Y3, Y2) <=>
6.82/1.56	                                     (??((^[Y4 : $i]:
6.82/1.56	                                            (in(Y4, '#sk1') & (Y3 = Y0(Y4)))))))))) =>
6.82/1.56	                             (Y1 = Y2)))))))))))),
6.82/1.56	    inference('lazy_cnf_exists', [status(thm)], ['20'])).
6.82/1.56	tff('22', plain,
6.82/1.56	    ~ (??((^[Y0 : $i]:
6.82/1.56	             ((!!((^[Y1 : $i]:
6.82/1.56	                     (in(Y1, Y0) <=>
6.82/1.56	                      (??((^[Y2 : $i]: (in(Y2, '#sk1') & (Y1 = '#sk3'(Y2)))))))))) &
6.82/1.56	              (!!((^[Y1 : $i]:
6.82/1.56	                     ((!!((^[Y2 : $i]:
6.82/1.56	                             (in(Y2, Y1) <=>
6.82/1.56	                              (??((^[Y3 : $i]:
6.82/1.56	                                     (in(Y3, '#sk1') & (Y2 = '#sk3'(Y3)))))))))) =>
6.82/1.56	                      (Y0 = Y1))))))))),
6.82/1.56	    inference('lazy_cnf_exists', [status(thm)], ['21'])).
6.82/1.56	tff('23', plain,
6.82/1.56	    ![X1]:
6.82/1.56	      ~ ((!!((^[Y0 : $i]:
6.82/1.56	                (in(Y0, X1) <=>
6.82/1.56	                 (??((^[Y1 : $i]: (in(Y1, '#sk1') & (Y0 = '#sk3'(Y1)))))))))) &
6.82/1.56	         (!!((^[Y0 : $i]:
6.82/1.56	                ((!!((^[Y1 : $i]:
6.82/1.56	                        (in(Y1, Y0) <=>
6.82/1.56	                         (??((^[Y2 : $i]:
6.82/1.56	                                (in(Y2, '#sk1') & (Y1 = '#sk3'(Y2)))))))))) =>
6.82/1.56	                 (X1 = Y0)))))),
6.82/1.56	    inference('lazy_cnf_forall', [status(thm)], ['22'])).
6.82/1.56	tff('24', plain,
6.82/1.56	    ![X1]:
6.82/1.56	      (~ (!!((^[Y0 : $i]:
6.82/1.56	                (in(Y0, X1) <=>
6.82/1.56	                 (??((^[Y1 : $i]: (in(Y1, '#sk1') & (Y0 = '#sk3'(Y1))))))))))
6.82/1.56	       | ~ (!!((^[Y0 : $i]:
6.82/1.56	                  ((!!((^[Y1 : $i]:
6.82/1.56	                          (in(Y1, Y0) <=>
6.82/1.56	                           (??((^[Y2 : $i]:
6.82/1.56	                                  (in(Y2, '#sk1') & (Y1 = '#sk3'(Y2)))))))))) =>
6.82/1.56	                   (X1 = Y0)))))),
6.82/1.56	    inference('lazy_cnf_and', [status(thm)], ['23'])).
6.82/1.56	tff('25', plain,
6.82/1.56	    ![X1]:
6.82/1.56	      (~ (in('#sk12'(X1), X1) <=>
6.82/1.56	          (??((^[Y0 : $i]: (in(Y0, '#sk1') & ('#sk12'(X1) = '#sk3'(Y0)))))))
6.82/1.56	       | ~ (!!((^[Y0 : $i]:
6.82/1.56	                  ((!!((^[Y1 : $i]:
6.82/1.56	                          (in(Y1, Y0) <=>
6.82/1.56	                           (??((^[Y2 : $i]:
6.82/1.56	                                  (in(Y2, '#sk1') & (Y1 = '#sk3'(Y2)))))))))) =>
6.82/1.56	                   (X1 = Y0)))))),
6.82/1.56	    inference('lazy_cnf_exists', [status(thm)], ['24'])).
6.82/1.56	tff('26', plain,
6.82/1.56	    ![X1]:
6.82/1.56	      (in('#sk12'(X1), X1)
6.82/1.56	        != (??((^[Y0 : $i]: (in(Y0, '#sk1') & ('#sk12'(X1) = '#sk3'(Y0))))))
6.82/1.56	       | ~ (!!((^[Y0 : $i]:
6.82/1.56	                  ((!!((^[Y1 : $i]:
6.82/1.56	                          (in(Y1, Y0) <=>
6.82/1.56	                           (??((^[Y2 : $i]:
6.82/1.56	                                  (in(Y2, '#sk1') & (Y1 = '#sk3'(Y2)))))))))) =>
6.82/1.56	                   (X1 = Y0)))))),
6.82/1.56	    inference('simplify nested equalities', [status(thm)], ['25'])).
6.82/1.56	tff('27', plain,
6.82/1.56	    ![X1]:
6.82/1.56	      (~ ((!!((^[Y0 : $i]:
6.82/1.56	                 (in(Y0, '#sk13'(X1)) <=>
6.82/1.56	                  (??((^[Y1 : $i]: (in(Y1, '#sk1') & (Y0 = '#sk3'(Y1)))))))))) =>
6.82/1.56	          (X1 = '#sk13'(X1)))
6.82/1.56	       | in('#sk12'(X1), X1)
6.82/1.56	          != (??((^[Y0 : $i]: (in(Y0, '#sk1') & ('#sk12'(X1) = '#sk3'(Y0))))))),
6.82/1.56	    inference('lazy_cnf_exists', [status(thm)], ['26'])).
6.82/1.56	tff('28', plain,
6.82/1.56	    ![X1]:
6.82/1.56	      ( (!!((^[Y0 : $i]:
6.82/1.56	               (in(Y0, '#sk13'(X1)) <=>
6.82/1.56	                (??((^[Y1 : $i]: (in(Y1, '#sk1') & (Y0 = '#sk3'(Y1))))))))))
6.82/1.56	       | in('#sk12'(X1), X1)
6.82/1.56	          != (??((^[Y0 : $i]: (in(Y0, '#sk1') & ('#sk12'(X1) = '#sk3'(Y0))))))),
6.82/1.56	    inference('lazy_cnf_imply', [status(thm)], ['27'])).
6.82/1.56	tff('29', plain,
6.82/1.56	    ![X1, X2]:
6.82/1.56	      ( (in(X2, '#sk13'(X1)) <=>
6.82/1.56	         (??((^[Y0 : $i]: (in(Y0, '#sk1') & (X2 = '#sk3'(Y0)))))))
6.82/1.56	       | in('#sk12'(X1), X1)
6.82/1.56	          != (??((^[Y0 : $i]: (in(Y0, '#sk1') & ('#sk12'(X1) = '#sk3'(Y0))))))),
6.82/1.56	    inference('lazy_cnf_forall', [status(thm)], ['28'])).
6.82/1.56	tff('30', plain,
6.82/1.56	    ![X1, X2]:
6.82/1.56	      (in(X2, '#sk13'(X1))
6.82/1.56	        = (??((^[Y0 : $i]: (in(Y0, '#sk1') & (X2 = '#sk3'(Y0))))))
6.82/1.56	       | in('#sk12'(X1), X1)
6.82/1.56	          != (??((^[Y0 : $i]: (in(Y0, '#sk1') & ('#sk12'(X1) = '#sk3'(Y0))))))),
6.82/1.56	    inference('simplify nested equalities', [status(thm)], ['29'])).
6.82/1.56	tff('31', plain,
6.82/1.56	    ![X1]:
6.82/1.56	      ( '#form18'(X1)
6.82/1.56	       | ~ (in('#sk12'(X1), X1) <=>
6.82/1.56	            (??((^[Y0 : $i]: (in(Y0, '#sk1') & ('#sk12'(X1) = '#sk3'(Y0)))))))),
6.82/1.56	    define([status(thm)])).
6.82/1.56	tff('32', plain,
6.82/1.56	    ![X1]:
6.82/1.56	      ( '#form18'(X1)
6.82/1.56	       | in('#sk12'(X1), X1)
6.82/1.56	          != (??((^[Y0 : $i]: (in(Y0, '#sk1') & ('#sk12'(X1) = '#sk3'(Y0))))))),
6.82/1.56	    inference('simplify nested equalities', [status(thm)], ['31'])).
6.82/1.56	tff('33', plain,
6.82/1.56	    ![X0]:
6.82/1.56	      (in('#sk12'(X0), X0)
6.82/1.56	        != in('#sk12'(X0), '#sk5'('#sk1', (^[Y0 : $i]: '#sk3'(Y0))))
6.82/1.56	       |  '#form18'(X0)),
6.82/1.56	    inference('sup-', [status(thm)], ['19', '32'])).
6.82/1.56	tff('34', plain,
6.82/1.56	    ![X0]:
6.82/1.56	      (in('#sk12'(X0), X0) != in('#sk12'(X0), '#sk5'('#sk1', '#sk3'))
6.82/1.56	       |  '#form18'(X0)),
6.82/1.56	    inference('ho_norm', [status(thm)], ['33'])).
6.82/1.56	tff('35', plain,  '#form18'('#sk5'('#sk1', '#sk3')),
6.82/1.56	    inference('eq_res', [status(thm)], ['34'])).
6.82/1.56	tff('36', plain,
6.82/1.56	    ![X1, X2]:
6.82/1.56	      (in(X2, '#sk13'(X1))
6.82/1.56	        = (??((^[Y0 : $i]: (in(Y0, '#sk1') & (X2 = '#sk3'(Y0))))))
6.82/1.56	       | in('#sk12'(X1), X1)
6.82/1.56	          != (??((^[Y0 : $i]: (in(Y0, '#sk1') & ('#sk12'(X1) = '#sk3'(Y0))))))),
6.82/1.56	    inference('simplify nested equalities', [status(thm)], ['29'])).
6.82/1.56	tff('37', plain,
6.82/1.56	    ![X1]:
6.82/1.56	      ( '#form18'(X1)
6.82/1.56	       | ~ (in('#sk12'(X1), X1) <=>
6.82/1.56	            (??((^[Y0 : $i]: (in(Y0, '#sk1') & ('#sk12'(X1) = '#sk3'(Y0)))))))),
6.82/1.56	    define([status(thm)])).
6.82/1.56	tff('38', plain,
6.82/1.56	    ![X1, X2]:
6.82/1.56	      (~ '#form18'(X1)
6.82/1.56	       | in(X2, '#sk13'(X1))
6.82/1.56	          = (??((^[Y0 : $i]: (in(Y0, '#sk1') & (X2 = '#sk3'(Y0))))))),
6.82/1.56	    inference('renaming', [status(thm)], ['36', '37'])).
6.82/1.56	tff('39', plain,
6.82/1.56	    ![X0]:
6.82/1.56	      in(X0, '#sk13'('#sk5'('#sk1', '#sk3')))
6.82/1.56	       = (??((^[Y0 : $i]: (in(Y0, '#sk1') & (X0 = '#sk3'(Y0)))))),
6.82/1.56	    inference('sup-', [status(thm)], ['35', '38'])).
6.82/1.56	tff('40', plain,
6.82/1.56	    ![X1, X2 : $i > $i, X3]:
6.82/1.56	      in(X3, '#sk5'(X1, X2))
6.82/1.56	       = (??((^[Y0 : $i]: (in(Y0, X1) & (X3 = X2(Y0)))))),
6.82/1.56	    inference('simplify nested equalities', [status(thm)], ['18'])).
6.82/1.56	tff('41', plain,
6.82/1.56	    ![X0]:
6.82/1.56	      in(X0, '#sk5'('#sk1', (^[Y0 : $i]: '#sk3'(Y0))))
6.82/1.56	       = in(X0, '#sk13'('#sk5'('#sk1', '#sk3'))),
6.82/1.56	    inference('sup+', [status(thm)], ['39', '40'])).
6.82/1.56	tff('42', plain,
6.82/1.56	    ![X0]:
6.82/1.56	      in(X0, '#sk5'('#sk1', '#sk3'))
6.82/1.56	       = in(X0, '#sk13'('#sk5'('#sk1', '#sk3'))),
6.82/1.56	    inference('ho_norm', [status(thm)], ['41'])).
6.82/1.56	tff('43', plain, ![X1, X2]: (~ in('#sk2'(X1, X2), X2) |  subset(X1, X2)),
6.82/1.56	    inference('lazy_cnf_imply', [status(thm)], ['10'])).
6.82/1.56	tff('44', plain,
6.82/1.56	    ![X0]:
6.82/1.56	      (~ in('#sk2'(X0, '#sk13'('#sk5'('#sk1', '#sk3'))), 
6.82/1.56	           '#sk5'('#sk1', '#sk3'))
6.82/1.56	       |  subset(X0, '#sk13'('#sk5'('#sk1', '#sk3')))),
6.82/1.56	    inference('sup-', [status(thm)], ['42', '43'])).
6.82/1.56	tff('45', plain,
6.82/1.56	    ( subset('#sk5'('#sk1', '#sk3'), '#sk13'('#sk5'('#sk1', '#sk3')))
6.82/1.56	     |  subset('#sk5'('#sk1', '#sk3'), '#sk13'('#sk5'('#sk1', '#sk3')))),
6.82/1.56	    inference('sup-', [status(thm)], ['11', '44'])).
6.82/1.56	tff('46', plain,
6.82/1.56	     subset('#sk5'('#sk1', '#sk3'), '#sk13'('#sk5'('#sk1', '#sk3'))),
6.82/1.56	    inference('simplify', [status(thm)], ['45'])).
6.82/1.56	tff('47', plain,
6.82/1.56	     (!!((^[Y0 : $i]:
6.82/1.56	            (!!((^[Y1 : $i]:
6.82/1.56	                   (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1))))))))),
6.82/1.56	    inference('lazy_cnf_imply', [status(thm)], ['12'])).
6.82/1.56	tff('48', plain,
6.82/1.56	    ![X1]:
6.82/1.56	       (!!((^[Y0 : $i]: (subset(X1, Y0) => (subset(Y0, X1) => (X1 = Y0)))))),
6.82/1.56	    inference('lazy_cnf_forall', [status(thm)], ['47'])).
6.82/1.56	tff('49', plain,
6.82/1.56	    ![X1, X2]:  (subset(X1, X2) => (subset(X2, X1) => (X1 = X2))),
6.82/1.56	    inference('lazy_cnf_forall', [status(thm)], ['48'])).
6.82/1.56	tff('50', plain,
6.82/1.56	    ![X1, X2]: (~ subset(X1, X2) |  (subset(X2, X1) => (X1 = X2))),
6.82/1.56	    inference('lazy_cnf_imply', [status(thm)], ['49'])).
6.82/1.56	tff('51', plain, ![X1, X2]: (~ subset(X2, X1) | X1 = X2 | ~ subset(X1, X2)),
6.82/1.56	    inference('lazy_cnf_imply', [status(thm)], ['50'])).
6.82/1.56	tff('52', plain,
6.82/1.56	    (~ subset('#sk13'('#sk5'('#sk1', '#sk3')), '#sk5'('#sk1', '#sk3'))
6.82/1.56	     | '#sk13'('#sk5'('#sk1', '#sk3')) = '#sk5'('#sk1', '#sk3')),
6.82/1.56	    inference('sup-', [status(thm)], ['46', '51'])).
6.82/1.56	tff('53', plain,  '#form18'('#sk5'('#sk1', '#sk3')),
6.82/1.56	    inference('eq_res', [status(thm)], ['34'])).
6.82/1.56	tff('54', plain,
6.82/1.56	    ![X1]:
6.82/1.56	      (X1 != '#sk13'(X1)
6.82/1.56	       | in('#sk12'(X1), X1)
6.82/1.56	          != (??((^[Y0 : $i]: (in(Y0, '#sk1') & ('#sk12'(X1) = '#sk3'(Y0))))))),
6.82/1.56	    inference('lazy_cnf_imply', [status(thm)], ['27'])).
6.82/1.56	tff('55', plain,
6.82/1.56	    ![X1]:
6.82/1.56	      ( '#form18'(X1)
6.82/1.56	       | ~ (in('#sk12'(X1), X1) <=>
6.82/1.56	            (??((^[Y0 : $i]: (in(Y0, '#sk1') & ('#sk12'(X1) = '#sk3'(Y0)))))))),
6.82/1.56	    define([status(thm)])).
6.82/1.56	tff('56', plain, ![X1]: (~ '#form18'(X1) | X1 != '#sk13'(X1)),
6.82/1.56	    inference('renaming', [status(thm)], ['54', '55'])).
6.82/1.56	tff('57', plain, '#sk5'('#sk1', '#sk3') != '#sk13'('#sk5'('#sk1', '#sk3')),
6.82/1.56	    inference('sup-', [status(thm)], ['53', '56'])).
6.82/1.56	tff('58', plain,
6.82/1.56	    ~ subset('#sk13'('#sk5'('#sk1', '#sk3')), '#sk5'('#sk1', '#sk3')),
6.82/1.56	    inference('simplify_reflect-', [status(thm)], ['52', '57'])).
6.82/1.56	tff('59', plain,
6.82/1.56	    ![X0]:
6.82/1.56	      in(X0, '#sk5'('#sk1', '#sk3'))
6.82/1.56	       = in(X0, '#sk13'('#sk5'('#sk1', '#sk3'))),
6.82/1.56	    inference('ho_norm', [status(thm)], ['41'])).
6.82/1.56	tff('60', plain, ![X1, X2]: ( in('#sk2'(X1, X2), X1) |  subset(X1, X2)),
6.82/1.56	    inference('lazy_cnf_imply', [status(thm)], ['10'])).
6.82/1.56	tff('61', plain,
6.82/1.56	    ![X0]:
6.82/1.56	      ( in('#sk2'('#sk13'('#sk5'('#sk1', '#sk3')), X0), 
6.82/1.56	          '#sk5'('#sk1', '#sk3'))
6.82/1.56	       |  subset('#sk13'('#sk5'('#sk1', '#sk3')), X0)),
6.82/1.56	    inference('sup+', [status(thm)], ['59', '60'])).
6.82/1.56	tff('62', plain, ![X1, X2]: (~ in('#sk2'(X1, X2), X2) |  subset(X1, X2)),
6.82/1.56	    inference('lazy_cnf_imply', [status(thm)], ['10'])).
6.82/1.56	tff('63', plain,
6.82/1.56	    ( subset('#sk13'('#sk5'('#sk1', '#sk3')), '#sk5'('#sk1', '#sk3'))
6.82/1.56	     |  subset('#sk13'('#sk5'('#sk1', '#sk3')), '#sk5'('#sk1', '#sk3'))),
6.82/1.56	    inference('sup-', [status(thm)], ['61', '62'])).
6.82/1.56	tff('64', plain,
6.82/1.56	     subset('#sk13'('#sk5'('#sk1', '#sk3')), '#sk5'('#sk1', '#sk3')),
6.82/1.56	    inference('simplify', [status(thm)], ['63'])).
6.82/1.56	tff('65', plain, $false, inference('demod', [status(thm)], ['58', '64'])).
6.82/1.56	
6.82/1.56	% SZS output end Refutation
6.82/1.56	
6.82/1.56	
6.82/1.56	% Terminating...
7.30/1.63	% Runner terminated.
7.30/1.63	% Zipperpin 1.5 exiting
7.30/1.64	EOF