0.02/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.02/0.13	% Command    : run_portfolio.sh /export/starexec/sandbox/benchmark/theBenchmark.p /export/starexec/sandbox/tmp/tmp.jv6tkPjpJB
0.12/0.33	% Computer   : n008.cluster.edu
0.12/0.33	% Model      : x86_64 x86_64
0.12/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory     : 8042.1875MB
0.12/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit   : 1200
0.12/0.34	% DateTime   : Tue Jul 13 13:50:44 EDT 2021
0.12/0.34	% CPUTime    : 
0.12/0.34	% Running portfolio for 120 s
0.12/0.34	% File         : /export/starexec/sandbox/benchmark/theBenchmark.p
0.12/0.34	% Number of cores: 8
0.12/0.34	% Python version: Python 3.6.8
0.12/0.34	% Running in HO mode
0.45/0.59	% Estimated wc time : 1286
0.45/0.59	% Estimated cpu time (7 cpus) : 183.71428571428572
0.47/0.67	% /export/starexec/sandbox/solver/bin/lams/s6.sh running for 21s
0.47/0.70	% /export/starexec/sandbox/solver/bin/lams/new_b3.2.norw.sh running for 15s
0.47/0.71	% /export/starexec/sandbox/solver/bin/lams/b.rpo.sh running for 21s
0.47/0.71	% /export/starexec/sandbox/solver/bin/lams/s6.ds.sh running for 10s
0.47/0.71	% /export/starexec/sandbox/solver/bin/lams/c.s.2.sh running for 68s
0.47/0.72	% /export/starexec/sandbox/solver/bin/lams/old_b3.avatar.sh running for 15s
0.47/0.72	% /export/starexec/sandbox/solver/bin/lams/c.easy.sh running for 26s
0.49/0.93	% Solved by lams/new_b3.2.norw.sh.
0.49/0.93	% done 36 iterations in 0.194s
0.49/0.93	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
0.49/0.93	% SZS output start Refutation
0.49/0.93	tff(lam, axiom,
0.49/0.93	  (lam = (^[A,B,Xf:(($i > $i))]: dpsetconstr(A,B,^[Xx,Xy]: (Xf(Xx) = Xy))))).
0.49/0.93	tff('0', plain,
0.49/0.93	    lam
0.49/0.93	     = (^[Y0 : $i,Y1 : $i,Y2 : $i > $i]:
0.49/0.93	          dpsetconstr(Y0, Y1, (^[Y3 : $i,Y4 : $i]: (Y2(Y3) = Y4)))),
0.49/0.93	    inference('cnf', [status(esa)], [lam])).
0.49/0.93	tff('1', plain, lam = ($C(($B(C, ($B(($B(B)), dpsetconstr)))), ($B(=)))),
0.49/0.93	    inference('lams2combs', [status(thm)], ['0'])).
0.49/0.93	tff('2', plain,
0.49/0.93	    ![X1, X2, X3 : $i > $i]:
0.49/0.93	      lam(X1, X2, X3)
0.49/0.93	       = ($C(($B(C, ($B(($B(B)), dpsetconstr)))), ($B(=)), X1, X2, X3)),
0.49/0.93	    inference('ho_complete_eq', [status(thm)], ['1'])).
0.49/0.93	tff('3', plain,
0.49/0.93	    ![X1, X2, X3 : $i > $i]:
0.49/0.93	      lam(X1, X2, X3) = dpsetconstr(X1, X2, ($B(=, X3))),
0.49/0.93	    inference('comb-normalize', [status(thm)], ['2'])).
0.49/0.93	tff(beta1, conjecture,
0.49/0.93	  (dpsetconstrI =>
0.49/0.93	   (lamp =>
0.49/0.93	    (funcGraphProp2 =>
0.49/0.93	     (![A,B,Xf:(($i > $i))]:
0.49/0.93	        ((![Xx]: (in(Xx,A) => in(Xf(Xx),B))) =>
0.49/0.93	         (![Xx]: (in(Xx,A) => (ap(A,B,lam(A,B,^[Xy]: Xf(Xy)),Xx) = Xf(Xx)))))))))).
0.49/0.93	tff(zf_stmt_0, negated_conjecture,
0.49/0.93	  (~
0.49/0.93	    (dpsetconstrI =>
0.49/0.93	     (lamp =>
0.49/0.93	      (funcGraphProp2 =>
0.49/0.93	       (![A,B,Xf:(($i > $i))]:
0.49/0.93	          ((![Xx]: (in(Xx,A) => in(Xf(Xx),B))) =>
0.49/0.93	           (![Xx]: (in(Xx,A) => (ap(A,B,lam(A,B,^[Xy]: Xf(Xy)),Xx) = Xf(Xx))))))))))).
0.49/0.93	tff('4', plain,
0.49/0.93	    ~ (dpsetconstrI =>
0.49/0.93	       (lamp =>
0.49/0.93	        (funcGraphProp2 =>
0.49/0.93	         (!!((^[Y0 : $i]:
0.49/0.93	                (!!((^[Y1 : $i]:
0.49/0.93	                       (!!((^[Y2 : $i > $i]:
0.49/0.93	                              ((!!((^[Y3 : $i]:
0.49/0.93	                                      (in(Y3, Y0) => in(Y2(Y3), Y1))))) =>
0.49/0.93	                               (!!((^[Y3 : $i]:
0.49/0.93	                                      (in(Y3, Y0) =>
0.49/0.93	                                       (ap(Y0, Y1, 
0.49/0.93	                                          lam(Y0, Y1, (^[Y4 : $i]: Y2(Y4))), 
0.49/0.93	                                          Y3) =
0.49/0.93	                                        Y2(Y3))))))))))))))))))),
0.49/0.93	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.49/0.93	tff('5', plain,
0.49/0.93	    ~ (dpsetconstrI =>
0.49/0.93	       (lamp =>
0.49/0.93	        (funcGraphProp2 =>
0.49/0.93	         (!!(($B(!!, 
0.49/0.93	              ($B(($B(!!)), 
0.49/0.93	               ($S(($B(S, 
0.49/0.93	                    ($B(($B(S)), 
0.49/0.93	                     ($B(($B(($B(=>)))), 
0.49/0.93	                      ($B(($B(($B(!!)))), 
0.49/0.93	                       ($C(($B(B, ($B(B, ($B(S, ($B(($B(=>)), ($C(in)))))))))), 
0.49/0.93	                        ($C(($B(C, ($B(in)))))))))))))))), 
0.49/0.93	                ($B(($B(($B(!!)))), 
0.49/0.93	                 ($S(($B(B, ($B(B, ($B(S, ($B(($B(=>)), ($C(in)))))))))), 
0.49/0.93	                  ($C(($B(C, 
0.49/0.93	                       ($B(($B(S)), 
0.49/0.93	                        ($B(($B(($B(S)))), 
0.49/0.93	                         ($B(($B(($B(($B(=)))))), 
0.49/0.93	                          ($S(($B(S, ($B(($B(B)), ap)))), lam)))))))))), 
0.49/0.93	                   I))))))))))))))))),
0.49/0.93	    inference('lams2combs', [status(thm)], ['4'])).
0.49/0.93	tff('6', plain,
0.49/0.93	    ~ (lamp =>
0.49/0.93	       (funcGraphProp2 =>
0.49/0.93	        (!!(($B(!!, 
0.49/0.93	             ($B(($B(!!)), 
0.49/0.93	              ($S(($B(S, 
0.49/0.93	                   ($B(($B(S)), 
0.49/0.93	                    ($B(($B(($B(=>)))), 
0.49/0.93	                     ($B(($B(($B(!!)))), 
0.49/0.93	                      ($C(($B(B, ($B(B, ($B(S, ($B(($B(=>)), ($C(in)))))))))), 
0.49/0.93	                       ($C(($B(C, ($B(in)))))))))))))))), 
0.49/0.93	               ($B(($B(($B(!!)))), 
0.49/0.93	                ($S(($B(B, ($B(B, ($B(S, ($B(($B(=>)), ($C(in)))))))))), 
0.49/0.93	                 ($C(($B(C, 
0.49/0.93	                      ($B(($B(S)), 
0.49/0.93	                       ($B(($B(($B(S)))), 
0.49/0.93	                        ($B(($B(($B(($B(=)))))), 
0.49/0.93	                         ($S(($B(S, ($B(($B(B)), ap)))), lam)))))))))), 
0.49/0.93	                  I)))))))))))))))),
0.49/0.93	    inference('lazy_cnf_imply', [status(thm)], ['5'])).
0.49/0.93	tff('7', plain,
0.49/0.93	    ~ (funcGraphProp2 =>
0.49/0.93	       (!!(($B(!!, 
0.49/0.93	            ($B(($B(!!)), 
0.49/0.93	             ($S(($B(S, 
0.49/0.93	                  ($B(($B(S)), 
0.49/0.93	                   ($B(($B(($B(=>)))), 
0.49/0.93	                    ($B(($B(($B(!!)))), 
0.49/0.93	                     ($C(($B(B, ($B(B, ($B(S, ($B(($B(=>)), ($C(in)))))))))), 
0.49/0.93	                      ($C(($B(C, ($B(in)))))))))))))))), 
0.49/0.93	              ($B(($B(($B(!!)))), 
0.49/0.93	               ($S(($B(B, ($B(B, ($B(S, ($B(($B(=>)), ($C(in)))))))))), 
0.49/0.93	                ($C(($B(C, 
0.49/0.93	                     ($B(($B(S)), 
0.49/0.93	                      ($B(($B(($B(S)))), 
0.49/0.93	                       ($B(($B(($B(($B(=)))))), 
0.49/0.93	                        ($S(($B(S, ($B(($B(B)), ap)))), lam)))))))))), 
0.49/0.93	                 I))))))))))))))),
0.49/0.93	    inference('lazy_cnf_imply', [status(thm)], ['6'])).
0.49/0.93	tff('8', plain,
0.49/0.93	    ~ (!!(($B(!!, 
0.49/0.93	           ($B(($B(!!)), 
0.49/0.93	            ($S(($B(S, 
0.49/0.93	                 ($B(($B(S)), 
0.49/0.93	                  ($B(($B(($B(=>)))), 
0.49/0.93	                   ($B(($B(($B(!!)))), 
0.49/0.93	                    ($C(($B(B, ($B(B, ($B(S, ($B(($B(=>)), ($C(in)))))))))), 
0.49/0.93	                     ($C(($B(C, ($B(in)))))))))))))))), 
0.49/0.93	             ($B(($B(($B(!!)))), 
0.49/0.93	              ($S(($B(B, ($B(B, ($B(S, ($B(($B(=>)), ($C(in)))))))))), 
0.49/0.93	               ($C(($B(C, 
0.49/0.93	                    ($B(($B(S)), 
0.49/0.93	                     ($B(($B(($B(S)))), 
0.49/0.93	                      ($B(($B(($B(($B(=)))))), 
0.49/0.93	                       ($S(($B(S, ($B(($B(B)), ap)))), lam)))))))))), 
0.49/0.93	                I)))))))))))))),
0.49/0.93	    inference('lazy_cnf_imply', [status(thm)], ['7'])).
0.49/0.93	tff('9', plain,
0.49/0.93	    ~ (!!(($B(!!, 
0.49/0.93	           ($S(($B(S, 
0.49/0.93	                ($B(($B(=>)), 
0.49/0.93	                 ($B(($B(!!)), 
0.49/0.93	                  ($B(($B(($S(($B(=>, ($C(in, '#sk1')))))))), 
0.49/0.93	                   ($C(($B(C, ($B(in)))))))))))))), 
0.49/0.93	            ($B(($B(!!)), 
0.49/0.93	             ($B(($B(($S(($B(=>, ($C(in, '#sk1')))))))), 
0.49/0.93	              ($C(($B(S, 
0.49/0.93	                   ($B(($B(S)), 
0.49/0.93	                    ($B(($B(($B(=)))), 
0.49/0.93	                     ($S(($B(B, ap('#sk1'))), lam('#sk1'))))))))), 
0.49/0.93	               I)))))))))))),
0.49/0.93	    inference('lazy_cnf_exists', [status(thm)], ['8'])).
0.49/0.93	tff('10', plain,
0.49/0.93	    ~ (!!(($S(($B(=>, 
0.49/0.93	               ($B(!!, 
0.49/0.93	                ($B(($S(($B(=>, ($C(in, '#sk1')))))), 
0.49/0.93	                 ($C(($B(C, ($B(in)))), '#sk2')))))))), 
0.49/0.93	           ($B(!!, 
0.49/0.93	            ($B(($S(($B(=>, ($C(in, '#sk1')))))), 
0.49/0.93	             ($S(($B(S, 
0.49/0.93	                  ($B(($B(=)), ($B(ap('#sk1', '#sk2'), lam('#sk1', '#sk2'))))))), 
0.49/0.93	              I)))))))))),
0.49/0.93	    inference('lazy_cnf_exists', [status(thm)], ['9'])).
0.49/0.93	tff('11', plain,
0.49/0.93	    ~ ((!!(($S(($B(=>, ($C(in, '#sk1')))), ($C(($B(in, '#sk3')), '#sk2')))))) =>
0.49/0.93	       (!!(($S(($B(=>, ($C(in, '#sk1')))), 
0.49/0.93	            ($S(($B(=, ap('#sk1', '#sk2', lam('#sk1', '#sk2', '#sk3')))), 
0.49/0.93	             '#sk3'))))))),
0.49/0.93	    inference('lazy_cnf_exists', [status(thm)], ['10'])).
0.49/0.93	tff('12', plain,
0.49/0.93	    ~ (!!(($S(($B(=>, ($C(in, '#sk1')))), 
0.49/0.93	           ($S(($B(=, ap('#sk1', '#sk2', lam('#sk1', '#sk2', '#sk3')))), 
0.49/0.93	            '#sk3')))))),
0.49/0.93	    inference('lazy_cnf_imply', [status(thm)], ['11'])).
0.49/0.93	tff('13', plain,
0.49/0.93	    ~ (in('#sk4', '#sk1') =>
0.49/0.93	       (ap('#sk1', '#sk2', lam('#sk1', '#sk2', '#sk3'), '#sk4') =
0.49/0.93	        '#sk3'('#sk4'))),
0.49/0.93	    inference('lazy_cnf_exists', [status(thm)], ['12'])).
0.49/0.93	tff('14', plain,  in('#sk4', '#sk1'),
0.49/0.93	    inference('lazy_cnf_imply', [status(thm)], ['13'])).
0.49/0.93	tff('15', plain,
0.49/0.93	     (!!(($S(($B(=>, ($C(in, '#sk1')))), ($C(($B(in, '#sk3')), '#sk2')))))),
0.49/0.93	    inference('lazy_cnf_imply', [status(thm)], ['11'])).
0.49/0.93	tff('16', plain, ![X1]:  (in(X1, '#sk1') => in('#sk3'(X1), '#sk2')),
0.49/0.93	    inference('lazy_cnf_forall', [status(thm)], ['15'])).
0.49/0.93	tff('17', plain, ![X1]: (~ in(X1, '#sk1') |  in('#sk3'(X1), '#sk2')),
0.49/0.93	    inference('lazy_cnf_imply', [status(thm)], ['16'])).
0.49/0.93	tff('18', plain,  in('#sk3'('#sk4'), '#sk2'),
0.49/0.93	    inference('sup-', [status(thm)], ['14', '17'])).
0.49/0.93	tff('19', plain,  in('#sk4', '#sk1'),
0.49/0.93	    inference('lazy_cnf_imply', [status(thm)], ['13'])).
0.49/0.93	tff(dpsetconstrI, axiom,
0.49/0.93	  (dpsetconstrI <=>
0.49/0.93	   (![A,B,Xphi:(($i * $i) > $o),Xx]:
0.49/0.93	      (in(Xx,A) =>
0.49/0.93	       (![Xy]:
0.49/0.93	          (in(Xy,B) =>
0.49/0.93	           (Xphi(Xx,Xy) =>
0.49/0.93	            in(kpair(Xx,Xy),dpsetconstr(A,B,^[Xz,Xu]: Xphi(Xz,Xu)))))))))).
0.49/0.93	tff('20', plain,
0.49/0.93	    dpsetconstrI
0.49/0.93	     = (!!((^[Y0 : $i]:
0.49/0.93	              (!!((^[Y1 : $i]:
0.49/0.93	                     (!!((^[Y2 : ($i * $i) > $o]:
0.49/0.93	                            (!!((^[Y3 : $i]:
0.49/0.93	                                   (in(Y3, Y0) =>
0.49/0.93	                                    (!!((^[Y4 : $i]:
0.49/0.93	                                           (in(Y4, Y1) =>
0.49/0.93	                                            (Y2(Y3, Y4) =>
0.49/0.93	                                             in(kpair(Y3, Y4), 
0.49/0.93	                                               dpsetconstr(Y0, Y1, 
0.49/0.93	                                                 (^[Y5 : $i,Y6 : $i]:
0.49/0.93	                                                    Y2(Y5, Y6)))))))))))))))))))))),
0.49/0.93	    inference('cnf', [status(esa)], [dpsetconstrI])).
0.49/0.93	tff('21', plain,
0.49/0.93	    dpsetconstrI
0.49/0.93	     = (!!(($B(!!, 
0.49/0.93	            ($B(($B(!!)), 
0.49/0.93	             ($B(($B(($B(!!)))), 
0.49/0.93	              ($S(($B(B, ($B(B, ($B(S, ($B(($B(=>)), ($C(in)))))))))), 
0.49/0.93	               ($B(($B(($B(($B(!!)))))), 
0.49/0.93	                ($B(($S(($B(B, ($B(B, ($B(S, ($B(($B(=>)), ($C(in)))))))))))), 
0.49/0.93	                 ($B(($B(($S(($B(S, ($B(($B(S)), ($B(($B(=>)))))))))))), 
0.49/0.93	                  ($B(($B(($B(($C(($B(C, ($B(($B(in)), kpair)))))))))), 
0.49/0.93	                   dpsetconstr)))))))))))))))))),
0.49/0.93	    inference('lams2combs', [status(thm)], ['20'])).
0.49/0.93	tff('22', plain,  dpsetconstrI,
0.49/0.93	    inference('lazy_cnf_imply', [status(thm)], ['5'])).
0.49/0.93	tff('23', plain,
0.49/0.93	     (!!(($B(!!, 
0.49/0.93	          ($B(($B(!!)), 
0.49/0.93	           ($B(($B(($B(!!)))), 
0.49/0.93	            ($S(($B(B, ($B(B, ($B(S, ($B(($B(=>)), ($C(in)))))))))), 
0.49/0.93	             ($B(($B(($B(($B(!!)))))), 
0.49/0.93	              ($B(($S(($B(B, ($B(B, ($B(S, ($B(($B(=>)), ($C(in)))))))))))), 
0.49/0.93	               ($B(($B(($S(($B(S, ($B(($B(S)), ($B(($B(=>)))))))))))), 
0.49/0.93	                ($B(($B(($B(($C(($B(C, ($B(($B(in)), kpair)))))))))), 
0.49/0.93	                 dpsetconstr)))))))))))))))))),
0.49/0.93	    inference('demod', [status(thm)], ['21', '22'])).
0.49/0.93	tff('24', plain,
0.49/0.93	    ![X1]:
0.49/0.93	       (!!(($B(!!, 
0.49/0.93	            ($B(($B(!!)), 
0.49/0.93	             ($B(($B(($S(($B(=>, ($C(in, X1)))))))), 
0.49/0.93	              ($B(($B(($B(!!)))), 
0.49/0.93	               ($S(($B(B, ($B(B, ($B(S, ($B(($B(=>)), ($C(in)))))))))), 
0.49/0.93	                ($B(($S(($B(S, ($B(($B(S)), ($B(($B(=>)))))))))), 
0.49/0.93	                 ($B(($B(($C(($B(C, ($B(($B(in)), kpair)))))))), 
0.49/0.93	                  dpsetconstr(X1))))))))))))))))),
0.49/0.93	    inference('lazy_cnf_forall', [status(thm)], ['23'])).
0.49/0.93	tff('25', plain,
0.49/0.93	    ![X1, X2]:
0.49/0.93	       (!!(($B(!!, 
0.49/0.93	            ($B(($S(($B(=>, ($C(in, X1)))))), 
0.49/0.93	             ($B(($B(!!)), 
0.49/0.93	              ($B(($B(($S(($B(=>, ($C(in, X2)))))))), 
0.49/0.93	               ($S(($B(S, ($B(($B(S)), ($B(($B(=>)))))))), 
0.49/0.93	                ($B(($C(($B(C, ($B(($B(in)), kpair)))))), 
0.49/0.93	                 dpsetconstr(X1, X2))))))))))))))),
0.49/0.93	    inference('lazy_cnf_forall', [status(thm)], ['24'])).
0.49/0.93	tff('26', plain,
0.49/0.93	    ![X1, X2, X3 : ($i * $i) > $o]:
0.49/0.93	       (!!(($S(($B(=>, ($C(in, X1)))), 
0.49/0.93	            ($B(!!, 
0.49/0.93	             ($B(($S(($B(=>, ($C(in, X2)))))), 
0.49/0.93	              ($S(($B(S, ($B(($B(=>)), X3)))), 
0.49/0.93	               ($C(($B(C, ($B(($B(in)), kpair)))), dpsetconstr(X1, X2, X3))))))))))))),
0.49/0.93	    inference('lazy_cnf_forall', [status(thm)], ['25'])).
0.49/0.93	tff('27', plain,
0.49/0.93	    ![X1, X2, X3 : ($i * $i) > $o, X4]:
0.49/0.93	       (in(X4, X1) =>
0.49/0.93	        (!!(($S(($B(=>, ($C(in, X2)))), 
0.49/0.93	             ($S(($B(=>, X3(X4))), 
0.49/0.93	              ($C(($B(in, kpair(X4))), dpsetconstr(X1, X2, X3)))))))))),
0.49/0.93	    inference('lazy_cnf_forall', [status(thm)], ['26'])).
0.49/0.93	tff('28', plain,
0.49/0.93	    ![X1, X2, X3 : ($i * $i) > $o, X4]:
0.49/0.93	      (~ in(X4, X1)
0.49/0.93	       |  (!!(($S(($B(=>, ($C(in, X2)))), 
0.49/0.93	               ($S(($B(=>, X3(X4))), 
0.49/0.93	                ($C(($B(in, kpair(X4))), dpsetconstr(X1, X2, X3)))))))))),
0.49/0.93	    inference('lazy_cnf_imply', [status(thm)], ['27'])).
0.49/0.93	tff('29', plain,
0.49/0.93	    ![X1, X2, X3 : ($i * $i) > $o, X4, X5]:
0.49/0.93	      ( (in(X5, X2) =>
0.49/0.93	         (X3(X4, X5) => in(kpair(X4, X5), dpsetconstr(X1, X2, X3))))
0.49/0.93	       | ~ in(X4, X1)),
0.49/0.93	    inference('lazy_cnf_forall', [status(thm)], ['28'])).
0.49/0.93	tff('30', plain,
0.49/0.93	    ![X1, X2, X3 : ($i * $i) > $o, X4, X5]:
0.49/0.93	      (~ in(X5, X2)
0.49/0.93	       |  (X3(X4, X5) => in(kpair(X4, X5), dpsetconstr(X1, X2, X3)))
0.49/0.93	       | ~ in(X4, X1)),
0.49/0.93	    inference('lazy_cnf_imply', [status(thm)], ['29'])).
0.49/0.93	tff('31', plain,
0.49/0.93	    ![X1, X2, X3 : ($i * $i) > $o, X4, X5]:
0.49/0.93	      (~ X3(X4, X5)
0.49/0.93	       |  in(kpair(X4, X5), dpsetconstr(X1, X2, X3))
0.49/0.93	       | ~ in(X4, X1)
0.49/0.93	       | ~ in(X5, X2)),
0.49/0.93	    inference('lazy_cnf_imply', [status(thm)], ['30'])).
0.49/0.93	tff('32', plain,
0.49/0.93	    ![X0, X1, X2 : ($i * $i) > $o]:
0.49/0.93	      (~ in(X1, X0)
0.49/0.93	       |  in(kpair('#sk4', X1), dpsetconstr('#sk1', X0, X2))
0.49/0.93	       | ~ X2('#sk4', X1)),
0.49/0.93	    inference('sup-', [status(thm)], ['19', '31'])).
0.49/0.93	tff('33', plain,
0.49/0.93	    ![X0 : ($i * $i) > $o]:
0.49/0.93	      (~ X0('#sk4', '#sk3'('#sk4'))
0.49/0.93	       |  in(kpair('#sk4', '#sk3'('#sk4')), dpsetconstr('#sk1', '#sk2', X0))),
0.49/0.93	    inference('sup-', [status(thm)], ['18', '32'])).
0.49/0.93	tff('34', plain,
0.49/0.93	    ![X0 : $i > $i]:
0.49/0.93	      ( in(kpair('#sk4', '#sk3'('#sk4')), lam('#sk1', '#sk2', X0))
0.49/0.93	       | ~ ($B(=, X0, '#sk4', '#sk3'('#sk4')))),
0.49/0.93	    inference('sup+', [status(thm)], ['3', '33'])).
0.49/0.93	tff('35', plain,
0.49/0.93	    ![X0 : $i > $i]:
0.49/0.93	      ( in(kpair('#sk4', '#sk3'('#sk4')), lam('#sk1', '#sk2', X0))
0.49/0.93	       | ~ (X0('#sk4') = '#sk3'('#sk4'))),
0.49/0.93	    inference('comb-normalize', [status(thm)], ['34'])).
0.49/0.93	tff('36', plain,
0.49/0.93	    ![X0 : $i > $i]:
0.49/0.93	      ( in(kpair('#sk4', '#sk3'('#sk4')), lam('#sk1', '#sk2', X0))
0.49/0.93	       | X0('#sk4') != '#sk3'('#sk4')),
0.49/0.93	    inference('simplify nested equalities', [status(thm)], ['35'])).
0.49/0.93	tff(lamp, axiom,
0.49/0.93	  (lamp <=>
0.49/0.93	   (![A,B,Xf:(($i > $i))]:
0.49/0.93	      ((![Xx]: (in(Xx,A) => in(Xf(Xx),B))) =>
0.49/0.93	       func(A,B,lam(A,B,^[Xx]: Xf(Xx))))))).
0.49/0.93	tff('37', plain,
0.49/0.93	    lamp
0.49/0.93	     = (!!((^[Y0 : $i]:
0.49/0.93	              (!!((^[Y1 : $i]:
0.49/0.93	                     (!!((^[Y2 : $i > $i]:
0.49/0.93	                            ((!!((^[Y3 : $i]: (in(Y3, Y0) => in(Y2(Y3), Y1))))) =>
0.49/0.93	                             func(Y0, Y1, lam(Y0, Y1, (^[Y3 : $i]: Y2(Y3)))))))))))))),
0.49/0.93	    inference('cnf', [status(esa)], [lamp])).
0.49/0.93	tff('38', plain,
0.49/0.93	    lamp
0.49/0.93	     = (!!(($B(!!, 
0.49/0.93	            ($B(($B(!!)), 
0.49/0.93	             ($S(($B(S, 
0.49/0.93	                  ($B(($B(S)), 
0.49/0.93	                   ($B(($B(($B(=>)))), 
0.49/0.93	                    ($B(($B(($B(!!)))), 
0.49/0.93	                     ($C(($B(B, ($B(B, ($B(S, ($B(($B(=>)), ($C(in)))))))))), 
0.49/0.93	                      ($C(($B(C, ($B(in)))))))))))))))), 
0.49/0.93	              ($S(($B(S, ($B(($B(B)), func)))), lam)))))))))),
0.49/0.93	    inference('lams2combs', [status(thm)], ['37'])).
0.49/0.93	tff('39', plain,  lamp, inference('lazy_cnf_imply', [status(thm)], ['6'])).
0.49/0.93	tff('40', plain,
0.49/0.93	     (!!(($B(!!, 
0.49/0.93	          ($B(($B(!!)), 
0.49/0.93	           ($S(($B(S, 
0.49/0.93	                ($B(($B(S)), 
0.49/0.93	                 ($B(($B(($B(=>)))), 
0.49/0.93	                  ($B(($B(($B(!!)))), 
0.49/0.93	                   ($C(($B(B, ($B(B, ($B(S, ($B(($B(=>)), ($C(in)))))))))), 
0.49/0.93	                    ($C(($B(C, ($B(in)))))))))))))))), 
0.49/0.93	            ($S(($B(S, ($B(($B(B)), func)))), lam)))))))))),
0.49/0.93	    inference('demod', [status(thm)], ['38', '39'])).
0.49/0.93	tff('41', plain,
0.49/0.93	    ![X1]:
0.49/0.93	       (!!(($B(!!, 
0.49/0.93	            ($S(($B(S, 
0.49/0.93	                 ($B(($B(=>)), 
0.49/0.93	                  ($B(($B(!!)), 
0.49/0.93	                   ($B(($B(($S(($B(=>, ($C(in, X1)))))))), 
0.49/0.93	                    ($C(($B(C, ($B(in)))))))))))))), 
0.49/0.93	             ($S(($B(B, func(X1))), lam(X1))))))))),
0.49/0.93	    inference('lazy_cnf_forall', [status(thm)], ['40'])).
0.49/0.93	tff('42', plain,
0.49/0.93	    ![X1, X2]:
0.49/0.93	       (!!(($S(($B(=>, 
0.49/0.93	                ($B(!!, 
0.49/0.93	                 ($B(($S(($B(=>, ($C(in, X1)))))), 
0.49/0.93	                  ($C(($B(C, ($B(in)))), X2)))))))), 
0.49/0.93	            ($B(func(X1, X2), lam(X1, X2))))))),
0.49/0.93	    inference('lazy_cnf_forall', [status(thm)], ['41'])).
0.49/0.93	tff('43', plain,
0.49/0.93	    ![X1, X2, X3 : $i > $i]:
0.49/0.93	       ((!!(($S(($B(=>, ($C(in, X1)))), ($C(($B(in, X3)), X2)))))) =>
0.49/0.93	        func(X1, X2, lam(X1, X2, X3))),
0.49/0.93	    inference('lazy_cnf_forall', [status(thm)], ['42'])).
0.49/0.93	tff('44', plain,
0.49/0.93	    ![X1, X2, X3 : $i > $i]:
0.49/0.93	      (~ (!!(($S(($B(=>, ($C(in, X1)))), ($C(($B(in, X3)), X2))))))
0.49/0.93	       |  func(X1, X2, lam(X1, X2, X3))),
0.49/0.93	    inference('lazy_cnf_imply', [status(thm)], ['43'])).
0.49/0.93	tff('45', plain,
0.49/0.93	    ![X1, X2, X3 : $i > $i]:
0.49/0.93	      (~ (in('#sk5'(X1, X2, X3), X1) => in(X3('#sk5'(X1, X2, X3)), X2))
0.49/0.93	       |  func(X1, X2, lam(X1, X2, X3))),
0.49/0.93	    inference('lazy_cnf_exists', [status(thm)], ['44'])).
0.49/0.93	tff('46', plain,
0.49/0.93	    ![X1, X2, X3 : $i > $i]:
0.49/0.93	      ( in('#sk5'(X1, X2, X3), X1) |  func(X1, X2, lam(X1, X2, X3))),
0.49/0.93	    inference('lazy_cnf_imply', [status(thm)], ['45'])).
0.49/0.93	tff('47', plain, ![X1]: (~ in(X1, '#sk1') |  in('#sk3'(X1), '#sk2')),
0.49/0.93	    inference('lazy_cnf_imply', [status(thm)], ['16'])).
0.49/0.93	tff('48', plain,
0.49/0.93	    ![X0 : $i > $i, X1]:
0.49/0.93	      ( func('#sk1', X1, lam('#sk1', X1, X0))
0.49/0.93	       |  in('#sk3'('#sk5'('#sk1', X1, X0)), '#sk2')),
0.49/0.93	    inference('sup-', [status(thm)], ['46', '47'])).
0.49/0.93	tff('49', plain,
0.49/0.93	    ![X1, X2, X3 : $i > $i]:
0.49/0.93	      (~ in(X3('#sk5'(X1, X2, X3)), X2) |  func(X1, X2, lam(X1, X2, X3))),
0.49/0.93	    inference('lazy_cnf_imply', [status(thm)], ['45'])).
0.49/0.93	tff('50', plain,
0.49/0.93	    ( func('#sk1', '#sk2', lam('#sk1', '#sk2', '#sk3'))
0.49/0.93	     |  func('#sk1', '#sk2', lam('#sk1', '#sk2', '#sk3'))),
0.49/0.93	    inference('sup-', [status(thm)], ['48', '49'])).
0.49/0.93	tff('51', plain,  func('#sk1', '#sk2', lam('#sk1', '#sk2', '#sk3')),
0.49/0.93	    inference('simplify', [status(thm)], ['50'])).
0.49/0.93	tff(funcGraphProp2, axiom,
0.49/0.93	  (funcGraphProp2 <=>
0.49/0.93	   (![A,B,Xf]:
0.49/0.93	      (func(A,B,Xf) =>
0.49/0.93	       (![Xx]:
0.49/0.93	          (in(Xx,A) =>
0.49/0.93	           (![Xy]:
0.49/0.93	              (in(Xy,B) => (in(kpair(Xx,Xy),Xf) => (ap(A,B,Xf,Xx) = Xy)))))))))).
0.49/0.93	tff('52', plain,
0.49/0.93	    funcGraphProp2
0.49/0.93	     = (!!((^[Y0 : $i]:
0.49/0.93	              (!!((^[Y1 : $i]:
0.49/0.93	                     (!!((^[Y2 : $i]:
0.49/0.93	                            (func(Y0, Y1, Y2) =>
0.49/0.93	                             (!!((^[Y3 : $i]:
0.49/0.93	                                    (in(Y3, Y0) =>
0.49/0.93	                                     (!!((^[Y4 : $i]:
0.49/0.93	                                            (in(Y4, Y1) =>
0.49/0.93	                                             (in(kpair(Y3, Y4), Y2) =>
0.49/0.93	                                              (ap(Y0, Y1, Y2, Y3) = Y4)))))))))))))))))))),
0.49/0.93	    inference('cnf', [status(esa)], [funcGraphProp2])).
0.49/0.93	tff('53', plain,
0.49/0.93	    funcGraphProp2
0.49/0.93	     = (!!(($B(!!, 
0.49/0.93	            ($B(($B(!!)), 
0.49/0.93	             ($S(($B(S, ($B(($B(S)), ($B(($B(($B(=>)))), func)))))), 
0.49/0.93	              ($B(($B(($B(!!)))), 
0.49/0.93	               ($S(($B(B, ($B(B, ($B(S, ($B(($B(=>)), ($C(in)))))))))), 
0.49/0.93	                ($B(($B(($B(($B(!!)))))), 
0.49/0.93	                 ($B(($S(($B(B, ($B(B, ($B(S, ($B(($B(=>)), ($C(in)))))))))))), 
0.49/0.93	                  ($B(($B(($S(($B(S, 
0.49/0.93	                               ($B(($B(S)), 
0.49/0.93	                                ($B(($B(($B(=>)))), 
0.49/0.93	                                 ($C(($B(C, ($B(($B(in)), kpair)))))))))))))))), 
0.49/0.93	                   ($B(($B(($B(($B(=)))))), ap)))))))))))))))))))),
0.49/0.93	    inference('lams2combs', [status(thm)], ['52'])).
0.49/0.93	tff('54', plain,  funcGraphProp2,
0.49/0.93	    inference('lazy_cnf_imply', [status(thm)], ['7'])).
0.49/0.93	tff('55', plain,
0.49/0.93	     (!!(($B(!!, 
0.49/0.93	          ($B(($B(!!)), 
0.49/0.93	           ($S(($B(S, ($B(($B(S)), ($B(($B(($B(=>)))), func)))))), 
0.49/0.93	            ($B(($B(($B(!!)))), 
0.49/0.93	             ($S(($B(B, ($B(B, ($B(S, ($B(($B(=>)), ($C(in)))))))))), 
0.49/0.93	              ($B(($B(($B(($B(!!)))))), 
0.49/0.93	               ($B(($S(($B(B, ($B(B, ($B(S, ($B(($B(=>)), ($C(in)))))))))))), 
0.49/0.93	                ($B(($B(($S(($B(S, 
0.49/0.93	                             ($B(($B(S)), 
0.49/0.93	                              ($B(($B(($B(=>)))), 
0.49/0.93	                               ($C(($B(C, ($B(($B(in)), kpair)))))))))))))))), 
0.49/0.93	                 ($B(($B(($B(($B(=)))))), ap)))))))))))))))))))),
0.49/0.93	    inference('demod', [status(thm)], ['53', '54'])).
0.49/0.93	tff('56', plain,
0.49/0.93	    ![X1]:
0.49/0.93	       (!!(($B(!!, 
0.49/0.93	            ($S(($B(S, ($B(($B(=>)), func(X1))))), 
0.49/0.93	             ($B(($B(!!)), 
0.49/0.93	              ($B(($B(($S(($B(=>, ($C(in, X1)))))))), 
0.49/0.93	               ($B(($B(($B(!!)))), 
0.49/0.93	                ($S(($B(B, ($B(B, ($B(S, ($B(($B(=>)), ($C(in)))))))))), 
0.49/0.93	                 ($B(($S(($B(S, 
0.49/0.93	                          ($B(($B(S)), 
0.49/0.93	                           ($B(($B(($B(=>)))), 
0.49/0.93	                            ($C(($B(C, ($B(($B(in)), kpair)))))))))))))), 
0.49/0.93	                  ($B(($B(($B(=)))), ap(X1))))))))))))))))))),
0.49/0.93	    inference('lazy_cnf_forall', [status(thm)], ['55'])).
0.49/0.93	tff('57', plain,
0.49/0.93	    ![X1, X2]:
0.49/0.93	       (!!(($S(($B(=>, func(X1, X2))), 
0.49/0.93	            ($B(!!, 
0.49/0.93	             ($B(($S(($B(=>, ($C(in, X1)))))), 
0.49/0.93	              ($B(($B(!!)), 
0.49/0.93	               ($B(($B(($S(($B(=>, ($C(in, X2)))))))), 
0.49/0.93	                ($S(($B(S, 
0.49/0.93	                     ($B(($B(S)), 
0.49/0.93	                      ($B(($B(($B(=>)))), 
0.49/0.93	                       ($C(($B(C, ($B(($B(in)), kpair)))))))))))), 
0.49/0.93	                 ($B(($B(=)), ap(X1, X2))))))))))))))))),
0.49/0.93	    inference('lazy_cnf_forall', [status(thm)], ['56'])).
0.49/0.93	tff('58', plain,
0.49/0.93	    ![X1, X2, X3]:
0.49/0.93	       (func(X1, X2, X3) =>
0.49/0.93	        (!!(($S(($B(=>, ($C(in, X1)))), 
0.49/0.93	             ($B(!!, 
0.49/0.93	              ($B(($S(($B(=>, ($C(in, X2)))))), 
0.49/0.93	               ($S(($B(S, 
0.49/0.93	                    ($B(($B(=>)), ($C(($B(C, ($B(($B(in)), kpair)))), X3)))))), 
0.49/0.93	                ($B(=, ap(X1, X2, X3)))))))))))))),
0.49/0.93	    inference('lazy_cnf_forall', [status(thm)], ['57'])).
0.49/0.93	tff('59', plain,
0.49/0.93	    ![X1, X2, X3]:
0.49/0.93	      (~ func(X1, X2, X3)
0.49/0.93	       |  (!!(($S(($B(=>, ($C(in, X1)))), 
0.49/0.93	               ($B(!!, 
0.49/0.93	                ($B(($S(($B(=>, ($C(in, X2)))))), 
0.49/0.93	                 ($S(($B(S, 
0.49/0.93	                      ($B(($B(=>)), ($C(($B(C, ($B(($B(in)), kpair)))), X3)))))), 
0.49/0.93	                  ($B(=, ap(X1, X2, X3)))))))))))))),
0.49/0.93	    inference('lazy_cnf_imply', [status(thm)], ['58'])).
0.49/0.93	tff('60', plain,
0.49/0.93	    ![X1, X2, X3, X4]:
0.49/0.93	      ( (in(X4, X1) =>
0.49/0.93	         (!!(($S(($B(=>, ($C(in, X2)))), 
0.49/0.93	              ($S(($B(=>, ($C(($B(in, kpair(X4))), X3)))), 
0.49/0.93	               (=(ap(X1, X2, X3, X4))))))))))
0.49/0.93	       | ~ func(X1, X2, X3)),
0.49/0.93	    inference('lazy_cnf_forall', [status(thm)], ['59'])).
0.49/0.93	tff('61', plain,
0.49/0.93	    ![X1, X2, X3, X4]:
0.49/0.93	      (~ in(X4, X1)
0.49/0.93	       |  (!!(($S(($B(=>, ($C(in, X2)))), 
0.49/0.93	               ($S(($B(=>, ($C(($B(in, kpair(X4))), X3)))), 
0.49/0.93	                (=(ap(X1, X2, X3, X4)))))))))
0.49/0.93	       | ~ func(X1, X2, X3)),
0.49/0.93	    inference('lazy_cnf_imply', [status(thm)], ['60'])).
0.49/0.93	tff('62', plain,
0.49/0.93	    ![X1, X2, X3, X4, X5]:
0.49/0.93	      ( (in(X5, X2) => (in(kpair(X4, X5), X3) => (ap(X1, X2, X3, X4) = X5)))
0.49/0.93	       | ~ func(X1, X2, X3)
0.49/0.93	       | ~ in(X4, X1)),
0.49/0.93	    inference('lazy_cnf_forall', [status(thm)], ['61'])).
0.49/0.93	tff('63', plain,
0.49/0.93	    ![X1, X2, X3, X4, X5]:
0.49/0.93	      (~ in(X5, X2)
0.49/0.93	       |  (in(kpair(X4, X5), X3) => (ap(X1, X2, X3, X4) = X5))
0.49/0.93	       | ~ in(X4, X1)
0.49/0.93	       | ~ func(X1, X2, X3)),
0.49/0.93	    inference('lazy_cnf_imply', [status(thm)], ['62'])).
0.49/0.93	tff('64', plain,
0.49/0.93	    ![X1, X2, X3, X4, X5]:
0.49/0.93	      (~ in(kpair(X4, X5), X3)
0.49/0.93	       | ap(X1, X2, X3, X4) = X5
0.49/0.93	       | ~ func(X1, X2, X3)
0.49/0.93	       | ~ in(X4, X1)
0.49/0.93	       | ~ in(X5, X2)),
0.49/0.93	    inference('lazy_cnf_imply', [status(thm)], ['63'])).
0.49/0.93	tff('65', plain,
0.49/0.93	    ![X0, X1]:
0.49/0.93	      (~ in(X0, '#sk2')
0.49/0.93	       | ~ in(X1, '#sk1')
0.49/0.93	       | ap('#sk1', '#sk2', lam('#sk1', '#sk2', '#sk3'), X1) = X0
0.49/0.93	       | ~ in(kpair(X1, X0), lam('#sk1', '#sk2', '#sk3'))),
0.49/0.93	    inference('sup-', [status(thm)], ['51', '64'])).
0.49/0.93	tff('66', plain,
0.49/0.93	    ('#sk3'('#sk4') != '#sk3'('#sk4')
0.49/0.93	     | ap('#sk1', '#sk2', lam('#sk1', '#sk2', '#sk3'), '#sk4')
0.49/0.93	        = '#sk3'('#sk4')
0.49/0.93	     | ~ in('#sk4', '#sk1')
0.49/0.93	     | ~ in('#sk3'('#sk4'), '#sk2')),
0.49/0.93	    inference('sup-', [status(thm)], ['36', '65'])).
0.49/0.93	tff('67', plain,  in('#sk4', '#sk1'),
0.49/0.93	    inference('lazy_cnf_imply', [status(thm)], ['13'])).
0.49/0.93	tff('68', plain,  in('#sk3'('#sk4'), '#sk2'),
0.49/0.93	    inference('sup-', [status(thm)], ['14', '17'])).
0.49/0.93	tff('69', plain,
0.49/0.93	    ('#sk3'('#sk4') != '#sk3'('#sk4')
0.49/0.93	     | ap('#sk1', '#sk2', lam('#sk1', '#sk2', '#sk3'), '#sk4')
0.49/0.93	        = '#sk3'('#sk4')),
0.49/0.93	    inference('demod', [status(thm)], ['66', '67', '68'])).
0.49/0.93	tff('70', plain,
0.49/0.93	    ap('#sk1', '#sk2', lam('#sk1', '#sk2', '#sk3'), '#sk4') = '#sk3'('#sk4'),
0.49/0.93	    inference('simplify', [status(thm)], ['69'])).
0.49/0.93	tff('71', plain,
0.49/0.93	    ap('#sk1', '#sk2', lam('#sk1', '#sk2', '#sk3'), '#sk4') != '#sk3'('#sk4'),
0.49/0.93	    inference('lazy_cnf_imply', [status(thm)], ['13'])).
0.49/0.93	tff('72', plain, $false,
0.49/0.93	    inference('simplify_reflect-', [status(thm)], ['70', '71'])).
0.49/0.93	
0.49/0.93	% SZS output end Refutation
0.49/0.93	
0.49/0.93	
0.49/0.93	% Terminating...
0.53/1.03	% Runner terminated.
1.62/1.05	% Zipperpin 1.5 exiting
1.62/1.06	EOF