0.07/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.13	% Command    : run_portfolio.sh /export/starexec/sandbox/benchmark/theBenchmark.p /export/starexec/sandbox/tmp/tmp.pAQijYRFye
0.14/0.34	% Computer   : n027.cluster.edu
0.14/0.34	% Model      : x86_64 x86_64
0.14/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.34	% Memory     : 8042.1875MB
0.14/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.14/0.34	% CPULimit   : 180
0.14/0.34	% DateTime   : Thu Aug 29 16:41:54 EDT 2019
0.14/0.34	% CPUTime    : 
27.06/27.33	% Running portfolio for 180 s
27.06/27.33	% File         : /export/starexec/sandbox/benchmark/theBenchmark.p
27.06/27.33	% TempDir      : /export/starexec/sandbox/tmp/tmp.pAQijYRFye
27.06/27.33	% Recognized as monomorphic HO.
27.06/27.33	% Running /export/starexec/sandbox/solver/bin/competitive.sh for 18
27.06/27.33	% Running /export/starexec/sandbox/solver/bin/competitive.2.sh for 13
27.06/27.33	% Solved by: competitive.2.sh
27.06/27.33	% done 1267 iterations in 8.925s
27.06/27.33	% hashcons stats for terms: size 4096, num 12994, sum length 27541, buckets: small 0, median 7, big 22
27.06/27.33	% proof state stats: {active 598, passive 9897, simpl 0}
27.06/27.33	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
27.06/27.33	% SZS output start Refutation
27.06/27.33	tff(setukpairinjR, axiom, setukpairinjR <=>
27.06/27.33	  (![Xx,Xy,Xz,Xu]: ((kpair(Xx,Xy) = kpair(Xz,Xu)) => (Xy = Xu)))).
27.06/27.33	tff('0', plain,
27.06/27.33	    setukpairinjR =
27.06/27.33	    (![X2,X3,X4,X5]: ((kpair(X2,X3) = kpair(X4,X5)) => (X3 = X5))),
27.06/27.33	    define([status(thm)])).
27.06/27.33	tff(kfstpairEq, axiom, kfstpairEq <=> (![Xx,Xy]: (kfst(kpair(Xx,Xy)) = Xx))).
27.06/27.33	tff('1', plain, kfstpairEq = (![X2,X3]: (kfst(kpair(X2,X3)) = X2)),
27.06/27.33	    define([status(thm)])).
27.06/27.33	tff(ex1I, axiom, ex1I <=>
27.06/27.33	  (![A,Xphi:($i > $o),Xx]:
27.06/27.33	     (in(Xx,A) =>
27.06/27.33	      (Xphi(Xx) =>
27.06/27.33	       ((![Xy]: (in(Xy,A) => (Xphi(Xy) => (Xy = Xx)))) =>
27.06/27.33	        ex1(A,^[Xy]: Xphi(Xy))))))).
27.06/27.33	tff('2', plain,
27.06/27.33	    ex1I =
27.06/27.33	    (![X2,X3:($i > $o),X4]:
27.06/27.33	       (in(X4,X2) =>
27.06/27.33	        (X3(X4) =>
27.06/27.33	         ((![X5]: (in(X5,X2) => (X3(X5) => (X5 = X4)))) =>
27.06/27.33	          ex1(X2,^[V_1]: X3(V_1)))))),
27.06/27.33	    define([status(thm)])).
27.06/27.33	tff(ex1, axiom, ex1() =
27.06/27.33	  ^[A,Xphi:($i > $o)]: singleton(dsetconstr(A,^[Xx]: Xphi(Xx)))).
27.06/27.33	tff('3', plain,
27.06/27.33	    ex1 = (^[V_1,V_2:($i > $o)]: singleton(dsetconstr(V_1,^[V_3]: V_2(V_3)))),
27.06/27.33	    define([status(thm)])).
27.06/27.33	tff(singleton, axiom, singleton() =
27.06/27.33	  ^[A]: (?[Xx]: ((A = setadjoin(Xx,emptyset)) & in(Xx,A)))).
27.06/27.33	tff('4', plain,
27.06/27.33	    singleton =
27.06/27.33	    (^[V_1]: (?[X2]: ((V_1 = setadjoin(X2,emptyset)) & in(X2,V_1)))),
27.06/27.33	    define([status(thm)])).
27.06/27.33	tff(kpair, axiom, kpair() =
27.06/27.33	  ^[Xx,Xy]:
27.06/27.33	    setadjoin(setadjoin(Xx,emptyset),
27.06/27.33	              setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset))).
27.06/27.33	tff('5', plain,
27.06/27.33	    kpair =
27.06/27.33	    (^[V_1,V_2]:
27.06/27.33	       setadjoin(setadjoin(V_1,emptyset),
27.06/27.33	                 setadjoin(setadjoin(V_1,setadjoin(V_2,emptyset)),emptyset))),
27.06/27.33	    define([status(thm)])).
27.06/27.33	tff(iskpair, axiom, iskpair() =
27.06/27.33	  ^[A]:
27.06/27.33	    (?[Xx]:
27.06/27.33	       ((?[Xy]:
27.06/27.33	           ((A =
27.06/27.33	             setadjoin(setadjoin(Xx,emptyset),
27.06/27.33	                       setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),
27.06/27.33	                                 emptyset))) & 
27.06/27.33	            in(Xy,setunion(A)))) & 
27.06/27.33	        in(Xx,setunion(A))))).
27.06/27.33	tff('6', plain,
27.06/27.33	    iskpair =
27.06/27.33	    (^[V_1]:
27.06/27.33	       (?[X2]:
27.06/27.33	          ((?[X3]:
27.06/27.33	              ((V_1 =
27.06/27.33	                setadjoin(setadjoin(X2,emptyset),
27.06/27.33	                          setadjoin(setadjoin(X2,setadjoin(X3,emptyset)),
27.06/27.33	                                    emptyset))) & 
27.06/27.33	               in(X3,setunion(V_1)))) & 
27.06/27.33	           in(X2,setunion(V_1))))),
27.06/27.33	    define([status(thm)])).
27.06/27.33	tff(ksndsingleton, conjecture,
27.06/27.33	  (ex1I =>
27.06/27.33	   (kfstpairEq =>
27.06/27.33	    (setukpairinjR =>
27.06/27.33	     (![Xu]:
27.06/27.33	        (iskpair(Xu) =>
27.06/27.33	         singleton(dsetconstr(setunion(Xu),^[Xx]: (Xu = kpair(kfst(Xu),Xx)))))))))).
27.06/27.33	tff(zf_stmt_0, conjecture,
27.06/27.33	  ((![X2,X3:($i > $o),X4]:
27.06/27.33	      (in(X4,X2) =>
27.06/27.33	       (X3(X4) =>
27.06/27.33	        ((![X5]: (in(X5,X2) => (X3(X5) => (X5 = X4)))) =>
27.06/27.33	         (?[X6]:
27.06/27.33	            ((dsetconstr(X2,^[V_1]: X3(V_1)) = setadjoin(X6,emptyset)) & 
27.06/27.33	             in(X6,dsetconstr(X2,^[V_2]: X3(V_2))))))))) =>
27.06/27.33	   ((![X7,X8]:
27.06/27.33	       (kfst(setadjoin(setadjoin(X7,emptyset),
27.06/27.33	                       setadjoin(setadjoin(X7,setadjoin(X8,emptyset)),
27.06/27.33	                                 emptyset))) =
27.06/27.33	        X7)) =>
27.06/27.33	    ((![X9,X10,X11,X12]:
27.06/27.33	        ((setadjoin(setadjoin(X9,emptyset),
27.06/27.33	                    setadjoin(setadjoin(X9,setadjoin(X10,emptyset)),emptyset)) =
27.06/27.33	          setadjoin(setadjoin(X11,emptyset),
27.06/27.33	                    setadjoin(setadjoin(X11,setadjoin(X12,emptyset)),emptyset))) =>
27.06/27.33	         (X10 = X12))) =>
27.06/27.33	     (![X13]:
27.06/27.33	        ((?[X14]:
27.06/27.33	            ((?[X15]:
27.06/27.33	                ((X13 =
27.06/27.33	                  setadjoin(setadjoin(X14,emptyset),
27.06/27.33	                            setadjoin(setadjoin(X14,setadjoin(X15,emptyset)),
27.06/27.33	                                      emptyset))) & 
27.06/27.33	                 in(X15,setunion(X13)))) & 
27.06/27.33	             in(X14,setunion(X13)))) =>
27.06/27.33	         (?[X16]:
27.06/27.33	            ((dsetconstr(setunion(X13),
27.06/27.33	                         ^[V_3]:
27.06/27.33	                           (X13 =
27.06/27.33	                            setadjoin(setadjoin(kfst(X13),emptyset),
27.06/27.33	                                      setadjoin(setadjoin(kfst(X13),
27.06/27.33	                                                          setadjoin(V_3,
27.06/27.33	                                                                    emptyset)),
27.06/27.33	                                                emptyset)))) =
27.06/27.33	              setadjoin(X16,emptyset)) & 
27.06/27.33	             in(X16,
27.06/27.33	                dsetconstr(setunion(X13),
27.06/27.33	                           ^[V_4]:
27.06/27.33	                             (X13 =
27.06/27.33	                              setadjoin(setadjoin(kfst(X13),emptyset),
27.06/27.33	                                        setadjoin(setadjoin(kfst(X13),
27.06/27.33	                                                            setadjoin(
27.06/27.33	                                                            V_4,emptyset)),
27.06/27.33	                                                  emptyset))))))))))))).
27.06/27.33	tff(zf_stmt_1, negated_conjecture,
27.06/27.33	  (~
27.06/27.33	    ((![X2,X3:($i > $o),X4]:
27.06/27.33	        (in(X4,X2) =>
27.06/27.33	         (X3(X4) =>
27.06/27.33	          ((![X5]: (in(X5,X2) => (X3(X5) => (X5 = X4)))) =>
27.06/27.33	           (?[X6]:
27.06/27.33	              ((dsetconstr(X2,^[V_1]: X3(V_1)) = setadjoin(X6,emptyset)) & 
27.06/27.33	               in(X6,dsetconstr(X2,^[V_2]: X3(V_2))))))))) =>
27.06/27.33	     ((![X7,X8]:
27.06/27.33	         (kfst(setadjoin(setadjoin(X7,emptyset),
27.06/27.33	                         setadjoin(setadjoin(X7,setadjoin(X8,emptyset)),
27.06/27.33	                                   emptyset))) =
27.06/27.33	          X7)) =>
27.06/27.33	      ((![X9,X10,X11,X12]:
27.06/27.33	          ((setadjoin(setadjoin(X9,emptyset),
27.06/27.33	                      setadjoin(setadjoin(X9,setadjoin(X10,emptyset)),
27.06/27.33	                                emptyset)) =
27.06/27.33	            setadjoin(setadjoin(X11,emptyset),
27.06/27.33	                      setadjoin(setadjoin(X11,setadjoin(X12,emptyset)),
27.06/27.33	                                emptyset))) =>
27.06/27.33	           (X10 = X12))) =>
27.06/27.33	       (![X13]:
27.06/27.33	          ((?[X14]:
27.06/27.33	              ((?[X15]:
27.06/27.33	                  ((X13 =
27.06/27.33	                    setadjoin(setadjoin(X14,emptyset),
27.06/27.33	                              setadjoin(setadjoin(X14,setadjoin(X15,emptyset)),
27.06/27.33	                                        emptyset))) & 
27.06/27.33	                   in(X15,setunion(X13)))) & 
27.06/27.33	               in(X14,setunion(X13)))) =>
27.06/27.33	           (?[X16]:
27.06/27.33	              ((dsetconstr(setunion(X13),
27.06/27.33	                           ^[V_3]:
27.06/27.33	                             (X13 =
27.06/27.33	                              setadjoin(setadjoin(kfst(X13),emptyset),
27.06/27.33	                                        setadjoin(setadjoin(kfst(X13),
27.06/27.33	                                                            setadjoin(
27.06/27.33	                                                            V_3,emptyset)),
27.06/27.33	                                                  emptyset)))) =
27.06/27.33	                setadjoin(X16,emptyset)) & 
27.06/27.33	               in(X16,
27.06/27.33	                  dsetconstr(setunion(X13),
27.06/27.33	                             ^[V_4]:
27.06/27.33	                               (X13 =
27.06/27.33	                                setadjoin(setadjoin(kfst(X13),emptyset),
27.06/27.33	                                          setadjoin(setadjoin(kfst(X13),
27.06/27.33	                                                              setadjoin(
27.06/27.33	                                                              V_4,emptyset)),
27.06/27.33	                                                    emptyset)))))))))))))).
27.06/27.33	tff('7', plain,
27.06/27.33	    sk_X13_
27.06/27.33	     = setadjoin(setadjoin(sk_X14_, emptyset), 
27.06/27.33	         setadjoin(setadjoin(sk_X14_, setadjoin(sk_X15_, emptyset)), 
27.06/27.33	           emptyset)),
27.06/27.33	    inference('cnf', [status(esa)], [zf_stmt_1])).
27.06/27.33	tff('8', plain,
27.06/27.33	    ![X27, X28]:
27.06/27.33	      kfst(
27.06/27.33	        setadjoin(setadjoin(X27, emptyset), 
27.06/27.33	          setadjoin(setadjoin(X27, setadjoin(X28, emptyset)), emptyset)))
27.06/27.33	       = X27,
27.06/27.33	    inference('cnf', [status(esa)], [zf_stmt_1])).
27.06/27.33	tff('9', plain, kfst(sk_X13_) = sk_X14_,
27.06/27.33	    inference('sup+', [status(thm)], ['7', '8'])).
27.06/27.33	tff('10', plain, in(sk_X15_, setunion(sk_X13_)),
27.06/27.33	    inference('cnf', [status(esa)], [zf_stmt_1])).
27.06/27.33	tff('11', plain,
27.06/27.33	    ![X19 : $i > $o, X20, X21]:
27.06/27.33	      (in(sk_X6_(X19, X20), dsetconstr(X20, (^[Y0 : $i]: X19(Y0))))
27.06/27.33	       | ~ in(X21, X20)
27.06/27.33	       | X19(sk_X5_(X21, X19, X20))
27.06/27.33	       | ~ X19(X21)),
27.06/27.33	    inference('cnf', [status(esa)], [zf_stmt_1])).
27.06/27.33	tff('12', plain,
27.06/27.33	    ![X19 : $i > $o, X20, X21]:
27.06/27.33	      (in(sk_X6_(X19, X20), dsetconstr(X20, X19))
27.06/27.33	       | ~ in(X21, X20)
27.06/27.33	       | X19(sk_X5_(X21, X19, X20))
27.06/27.33	       | ~ X19(X21)),
27.06/27.33	    inference('lambda-normalize', [status(thm)], ['11'])).
27.06/27.33	tff('13', plain,
27.06/27.33	    ![X0 : $i > $o]:
27.06/27.33	      (~ X0(sk_X15_)
27.06/27.33	       | X0(sk_X5_(sk_X15_, X0, setunion(sk_X13_)))
27.06/27.33	       | in(sk_X6_(X0, setunion(sk_X13_)), dsetconstr(setunion(sk_X13_), X0))),
27.06/27.33	    inference('sup-', [status(thm)], ['10', '12'])).
27.06/27.33	tff('14', plain,
27.06/27.33	    ![X19 : $i > $o, X20, X21]:
27.06/27.33	      (dsetconstr(X20, (^[Y0 : $i]: X19(Y0)))
27.06/27.33	        = setadjoin(sk_X6_(X19, X20), emptyset)
27.06/27.33	       | ~ in(X21, X20)
27.06/27.33	       | X19(sk_X5_(X21, X19, X20))
27.06/27.33	       | ~ X19(X21)),
27.06/27.33	    inference('cnf', [status(esa)], [zf_stmt_1])).
27.06/27.33	tff('15', plain,
27.06/27.33	    ![X19 : $i > $o, X20, X21]:
27.06/27.33	      (dsetconstr(X20, X19) = setadjoin(sk_X6_(X19, X20), emptyset)
27.06/27.33	       | ~ in(X21, X20)
27.06/27.33	       | X19(sk_X5_(X21, X19, X20))
27.06/27.33	       | ~ X19(X21)),
27.06/27.33	    inference('lambda-normalize', [status(thm)], ['14'])).
27.06/27.33	tff('16', plain,
27.06/27.33	    ![X0 : $i > $o]:
27.06/27.33	      (~ X0(sk_X15_)
27.06/27.33	       | X0(sk_X5_(sk_X15_, X0, setunion(sk_X13_)))
27.06/27.33	       | dsetconstr(setunion(sk_X13_), X0)
27.06/27.33	          = setadjoin(sk_X6_(X0, setunion(sk_X13_)), emptyset)),
27.06/27.33	    inference('sup-', [status(thm)], ['10', '15'])).
27.06/27.33	tff('17', plain,
27.06/27.33	    ![X26]:
27.06/27.33	      (dsetconstr(setunion(sk_X13_), 
27.06/27.33	         (^[Y0 : $i]:
27.06/27.33	            (sk_X13_ =
27.06/27.33	             setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	               setadjoin(setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                 emptyset)))))
27.06/27.33	        != setadjoin(X26, emptyset)
27.06/27.33	       | ~ in(X26, 
27.06/27.33	             dsetconstr(setunion(sk_X13_), 
27.06/27.33	               (^[Y0 : $i]:
27.06/27.33	                  (sk_X13_ =
27.06/27.33	                   setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	                     setadjoin(
27.06/27.33	                       setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                       emptyset))))))),
27.06/27.33	    inference('cnf', [status(esa)], [zf_stmt_1])).
27.06/27.33	tff('18', plain,
27.06/27.33	    ![X0 : $i > $o]:
27.06/27.33	      (dsetconstr(setunion(sk_X13_), 
27.06/27.33	         (^[Y0 : $i]:
27.06/27.33	            (sk_X13_ =
27.06/27.33	             setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	               setadjoin(setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                 emptyset)))))
27.06/27.33	        != dsetconstr(setunion(sk_X13_), X0)
27.06/27.33	       | X0(sk_X5_(sk_X15_, X0, setunion(sk_X13_)))
27.06/27.33	       | ~ X0(sk_X15_)
27.06/27.33	       | ~ in(sk_X6_(X0, setunion(sk_X13_)), 
27.06/27.33	             dsetconstr(setunion(sk_X13_), 
27.06/27.33	               (^[Y0 : $i]:
27.06/27.33	                  (sk_X13_ =
27.06/27.33	                   setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	                     setadjoin(
27.06/27.33	                       setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                       emptyset))))))),
27.06/27.33	    inference('sup-', [status(thm)], ['16', '17'])).
27.06/27.33	tff('19', plain,
27.06/27.33	    ((^[Y0 : $i]:
27.06/27.33	        (sk_X13_ =
27.06/27.33	         setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	           setadjoin(setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	             emptyset))))(
27.06/27.33	       sk_X5_(sk_X15_, 
27.06/27.33	         (^[Y0 : $i]:
27.06/27.33	            (sk_X13_ =
27.06/27.33	             setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	               setadjoin(setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                 emptyset)))), setunion(sk_X13_)))
27.06/27.33	     | ~ (^[Y0 : $i]:
27.06/27.33	            (sk_X13_ =
27.06/27.33	             setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	               setadjoin(setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                 emptyset))))(sk_X15_)
27.06/27.33	     | ~ (^[Y0 : $i]:
27.06/27.33	            (sk_X13_ =
27.06/27.33	             setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	               setadjoin(setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                 emptyset))))(sk_X15_)
27.06/27.33	     | (^[Y0 : $i]:
27.06/27.33	          (sk_X13_ =
27.06/27.33	           setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	             setadjoin(setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	               emptyset))))(
27.06/27.33	         sk_X5_(sk_X15_, 
27.06/27.33	           (^[Y0 : $i]:
27.06/27.33	              (sk_X13_ =
27.06/27.33	               setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	                 setadjoin(
27.06/27.33	                   setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                   emptyset)))), setunion(sk_X13_)))
27.06/27.33	     | dsetconstr(setunion(sk_X13_), 
27.06/27.33	         (^[Y0 : $i]:
27.06/27.33	            (sk_X13_ =
27.06/27.33	             setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	               setadjoin(setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                 emptyset)))))
27.06/27.33	        != dsetconstr(setunion(sk_X13_), 
27.06/27.33	             (^[Y0 : $i]:
27.06/27.33	                (sk_X13_ =
27.06/27.33	                 setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	                   setadjoin(
27.06/27.33	                     setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                     emptyset)))))),
27.06/27.33	    inference('sup-', [status(thm)], ['13', '18'])).
27.06/27.33	tff('20', plain,
27.06/27.33	    ((sk_X13_ =
27.06/27.33	      setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	        setadjoin(
27.06/27.33	          setadjoin(kfst(sk_X13_), 
27.06/27.33	            setadjoin(
27.06/27.33	              sk_X5_(sk_X15_, 
27.06/27.33	                (^[Y0 : $i]:
27.06/27.33	                   (sk_X13_ =
27.06/27.33	                    setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	                      setadjoin(
27.06/27.33	                        setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                        emptyset)))), setunion(sk_X13_)), emptyset)), 
27.06/27.33	          emptyset)))
27.06/27.33	     | ~ (sk_X13_ =
27.06/27.33	          setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	            setadjoin(
27.06/27.33	              setadjoin(kfst(sk_X13_), setadjoin(sk_X15_, emptyset)), 
27.06/27.33	              emptyset)))
27.06/27.33	     | ~ (sk_X13_ =
27.06/27.33	          setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	            setadjoin(
27.06/27.33	              setadjoin(kfst(sk_X13_), setadjoin(sk_X15_, emptyset)), 
27.06/27.33	              emptyset)))
27.06/27.33	     | (sk_X13_ =
27.06/27.33	        setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	          setadjoin(
27.06/27.33	            setadjoin(kfst(sk_X13_), 
27.06/27.33	              setadjoin(
27.06/27.33	                sk_X5_(sk_X15_, 
27.06/27.33	                  (^[Y0 : $i]:
27.06/27.33	                     (sk_X13_ =
27.06/27.33	                      setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	                        setadjoin(
27.06/27.33	                          setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                          emptyset)))), setunion(sk_X13_)), emptyset)), 
27.06/27.33	            emptyset)))
27.06/27.33	     | dsetconstr(setunion(sk_X13_), 
27.06/27.33	         (^[Y0 : $i]:
27.06/27.33	            (sk_X13_ =
27.06/27.33	             setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	               setadjoin(setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                 emptyset)))))
27.06/27.33	        != dsetconstr(setunion(sk_X13_), 
27.06/27.33	             (^[Y0 : $i]:
27.06/27.33	                (sk_X13_ =
27.06/27.33	                 setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	                   setadjoin(
27.06/27.33	                     setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                     emptyset)))))),
27.06/27.33	    inference('lambda-normalize', [status(thm)], ['19'])).
27.06/27.33	tff('21', plain,
27.06/27.33	    (~ (sk_X13_ =
27.06/27.33	        setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	          setadjoin(setadjoin(kfst(sk_X13_), setadjoin(sk_X15_, emptyset)), 
27.06/27.33	            emptyset)))
27.06/27.33	     | (sk_X13_ =
27.06/27.33	        setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	          setadjoin(
27.06/27.33	            setadjoin(kfst(sk_X13_), 
27.06/27.33	              setadjoin(
27.06/27.33	                sk_X5_(sk_X15_, 
27.06/27.33	                  (^[Y0 : $i]:
27.06/27.33	                     (sk_X13_ =
27.06/27.33	                      setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	                        setadjoin(
27.06/27.33	                          setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                          emptyset)))), setunion(sk_X13_)), emptyset)), 
27.06/27.33	            emptyset)))),
27.06/27.33	    inference('simplify', [status(thm)], ['20'])).
27.06/27.33	tff('22', plain,
27.06/27.33	    (sk_X13_
27.06/27.33	      != setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	           setadjoin(setadjoin(kfst(sk_X13_), setadjoin(sk_X15_, emptyset)), 
27.06/27.33	             emptyset))
27.06/27.33	     | sk_X13_
27.06/27.33	        = setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	            setadjoin(
27.06/27.33	              setadjoin(kfst(sk_X13_), 
27.06/27.33	                setadjoin(
27.06/27.33	                  sk_X5_(sk_X15_, 
27.06/27.33	                    (^[Y0 : $i]:
27.06/27.33	                       (sk_X13_ =
27.06/27.33	                        setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	                          setadjoin(
27.06/27.33	                            setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                            emptyset)))), setunion(sk_X13_)), emptyset)), 
27.06/27.33	              emptyset))),
27.06/27.33	    inference('simplify nested equalities', [status(thm)], ['21'])).
27.06/27.33	tff('23', plain,
27.06/27.33	    (sk_X13_
27.06/27.33	      != setadjoin(setadjoin(sk_X14_, emptyset), 
27.06/27.33	           setadjoin(setadjoin(kfst(sk_X13_), setadjoin(sk_X15_, emptyset)), 
27.06/27.33	             emptyset))
27.06/27.33	     | sk_X13_
27.06/27.33	        = setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	            setadjoin(
27.06/27.33	              setadjoin(kfst(sk_X13_), 
27.06/27.33	                setadjoin(
27.06/27.33	                  sk_X5_(sk_X15_, 
27.06/27.33	                    (^[Y0 : $i]:
27.06/27.33	                       (sk_X13_ =
27.06/27.33	                        setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	                          setadjoin(
27.06/27.33	                            setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                            emptyset)))), setunion(sk_X13_)), emptyset)), 
27.06/27.33	              emptyset))),
27.06/27.33	    inference('sup-', [status(thm)], ['9', '22'])).
27.06/27.33	tff('24', plain,
27.06/27.33	    (sk_X13_
27.06/27.33	      != setadjoin(setadjoin(sk_X14_, emptyset), 
27.06/27.33	           setadjoin(setadjoin(sk_X14_, setadjoin(sk_X15_, emptyset)), 
27.06/27.33	             emptyset))
27.06/27.33	     | sk_X13_
27.06/27.33	        = setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	            setadjoin(
27.06/27.33	              setadjoin(kfst(sk_X13_), 
27.06/27.33	                setadjoin(
27.06/27.33	                  sk_X5_(sk_X15_, 
27.06/27.33	                    (^[Y0 : $i]:
27.06/27.33	                       (sk_X13_ =
27.06/27.33	                        setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	                          setadjoin(
27.06/27.33	                            setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                            emptyset)))), setunion(sk_X13_)), emptyset)), 
27.06/27.33	              emptyset))),
27.06/27.33	    inference('sup-', [status(thm)], ['9', '23'])).
27.06/27.33	tff('25', plain,
27.06/27.33	    sk_X13_
27.06/27.33	     = setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	         setadjoin(
27.06/27.33	           setadjoin(kfst(sk_X13_), 
27.06/27.33	             setadjoin(
27.06/27.33	               sk_X5_(sk_X15_, 
27.06/27.33	                 (^[Y0 : $i]:
27.06/27.33	                    (sk_X13_ =
27.06/27.33	                     setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	                       setadjoin(
27.06/27.33	                         setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                         emptyset)))), setunion(sk_X13_)), emptyset)), 
27.06/27.33	           emptyset)),
27.06/27.33	    inference('clc', [status(thm)], ['24', '7'])).
27.06/27.33	tff('26', plain,
27.06/27.33	    ![X22, X23, X24, X25]:
27.06/27.33	      (X23 = X22
27.06/27.33	       | setadjoin(setadjoin(X25, emptyset), 
27.06/27.33	           setadjoin(setadjoin(X25, setadjoin(X23, emptyset)), emptyset))
27.06/27.33	          != setadjoin(setadjoin(X24, emptyset), 
27.06/27.33	               setadjoin(setadjoin(X24, setadjoin(X22, emptyset)), emptyset))),
27.06/27.33	    inference('cnf', [status(esa)], [zf_stmt_1])).
27.06/27.33	tff('27', plain,
27.06/27.33	    ![X0, X1]:
27.06/27.33	      (sk_X13_
27.06/27.33	        != setadjoin(setadjoin(X1, emptyset), 
27.06/27.33	             setadjoin(setadjoin(X1, setadjoin(X0, emptyset)), emptyset))
27.06/27.33	       | sk_X15_ = X0),
27.06/27.33	    inference('sup-', [status(thm)], ['7', '26'])).
27.06/27.33	tff('28', plain,
27.06/27.33	    (sk_X13_ != sk_X13_
27.06/27.33	     | sk_X15_
27.06/27.33	        = sk_X5_(sk_X15_, 
27.06/27.33	            (^[Y0 : $i]:
27.06/27.33	               (sk_X13_ =
27.06/27.33	                setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	                  setadjoin(
27.06/27.33	                    setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                    emptyset)))), setunion(sk_X13_))),
27.06/27.33	    inference('sup-', [status(thm)], ['25', '27'])).
27.06/27.33	tff('29', plain,
27.06/27.33	    sk_X15_
27.06/27.33	     = sk_X5_(sk_X15_, 
27.06/27.33	         (^[Y0 : $i]:
27.06/27.33	            (sk_X13_ =
27.06/27.33	             setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	               setadjoin(setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                 emptyset)))), setunion(sk_X13_)),
27.06/27.33	    inference('simplify', [status(thm)], ['28'])).
27.06/27.33	tff('30', plain,
27.06/27.33	    ![X19 : $i > $o, X20, X21]:
27.06/27.33	      (in(sk_X6_(X19, X20), dsetconstr(X20, (^[Y0 : $i]: X19(Y0))))
27.06/27.33	       | ~ in(X21, X20)
27.06/27.33	       | sk_X5_(X21, X19, X20) != X21
27.06/27.33	       | ~ X19(X21)),
27.06/27.33	    inference('cnf', [status(esa)], [zf_stmt_1])).
27.06/27.33	tff('31', plain,
27.06/27.33	    ![X19 : $i > $o, X20, X21]:
27.06/27.33	      (in(sk_X6_(X19, X20), dsetconstr(X20, X19))
27.06/27.33	       | ~ in(X21, X20)
27.06/27.33	       | sk_X5_(X21, X19, X20) != X21
27.06/27.33	       | ~ X19(X21)),
27.06/27.33	    inference('lambda-normalize', [status(thm)], ['30'])).
27.06/27.33	tff('32', plain,
27.06/27.33	    (sk_X15_ != sk_X15_
27.06/27.33	     | ~ (^[Y0 : $i]:
27.06/27.33	            (sk_X13_ =
27.06/27.33	             setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	               setadjoin(setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                 emptyset))))(sk_X15_)
27.06/27.33	     | ~ in(sk_X15_, setunion(sk_X13_))
27.06/27.33	     | in(
27.06/27.33	         sk_X6_(
27.06/27.33	           (^[Y0 : $i]:
27.06/27.33	              (sk_X13_ =
27.06/27.33	               setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	                 setadjoin(
27.06/27.33	                   setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                   emptyset)))), setunion(sk_X13_)), 
27.06/27.33	         dsetconstr(setunion(sk_X13_), 
27.06/27.33	           (^[Y0 : $i]:
27.06/27.33	              (sk_X13_ =
27.06/27.33	               setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	                 setadjoin(
27.06/27.33	                   setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                   emptyset))))))),
27.06/27.33	    inference('sup-', [status(thm)], ['29', '31'])).
27.06/27.33	tff('33', plain,
27.06/27.33	    (sk_X15_ != sk_X15_
27.06/27.33	     | ~ (sk_X13_ =
27.06/27.33	          setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	            setadjoin(
27.06/27.33	              setadjoin(kfst(sk_X13_), setadjoin(sk_X15_, emptyset)), 
27.06/27.33	              emptyset)))
27.06/27.33	     | ~ in(sk_X15_, setunion(sk_X13_))
27.06/27.33	     | in(
27.06/27.33	         sk_X6_(
27.06/27.33	           (^[Y0 : $i]:
27.06/27.33	              (sk_X13_ =
27.06/27.33	               setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	                 setadjoin(
27.06/27.33	                   setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                   emptyset)))), setunion(sk_X13_)), 
27.06/27.33	         dsetconstr(setunion(sk_X13_), 
27.06/27.33	           (^[Y0 : $i]:
27.06/27.33	              (sk_X13_ =
27.06/27.33	               setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	                 setadjoin(
27.06/27.33	                   setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                   emptyset))))))),
27.06/27.33	    inference('lambda-normalize', [status(thm)], ['32'])).
27.06/27.33	tff('34', plain,
27.06/27.33	    (in(
27.06/27.33	       sk_X6_(
27.06/27.33	         (^[Y0 : $i]:
27.06/27.33	            (sk_X13_ =
27.06/27.33	             setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	               setadjoin(setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                 emptyset)))), setunion(sk_X13_)), 
27.06/27.33	       dsetconstr(setunion(sk_X13_), 
27.06/27.33	         (^[Y0 : $i]:
27.06/27.33	            (sk_X13_ =
27.06/27.33	             setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	               setadjoin(setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                 emptyset))))))
27.06/27.33	     | ~ in(sk_X15_, setunion(sk_X13_))
27.06/27.33	     | ~ (sk_X13_ =
27.06/27.33	          setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	            setadjoin(
27.06/27.33	              setadjoin(kfst(sk_X13_), setadjoin(sk_X15_, emptyset)), 
27.06/27.33	              emptyset)))),
27.06/27.33	    inference('simplify', [status(thm)], ['33'])).
27.06/27.33	tff('35', plain,
27.06/27.33	    (in(
27.06/27.33	       sk_X6_(
27.06/27.33	         (^[Y0 : $i]:
27.06/27.33	            (sk_X13_ =
27.06/27.33	             setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	               setadjoin(setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                 emptyset)))), setunion(sk_X13_)), 
27.06/27.33	       dsetconstr(setunion(sk_X13_), 
27.06/27.33	         (^[Y0 : $i]:
27.06/27.33	            (sk_X13_ =
27.06/27.33	             setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	               setadjoin(setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                 emptyset))))))
27.06/27.33	     | ~ in(sk_X15_, setunion(sk_X13_))
27.06/27.33	     | sk_X13_
27.06/27.33	        != setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	             setadjoin(
27.06/27.33	               setadjoin(kfst(sk_X13_), setadjoin(sk_X15_, emptyset)), 
27.06/27.33	               emptyset))),
27.06/27.33	    inference('simplify nested equalities', [status(thm)], ['34'])).
27.06/27.33	tff('36', plain,
27.06/27.33	    (sk_X13_
27.06/27.33	      != setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	           setadjoin(setadjoin(kfst(sk_X13_), setadjoin(sk_X15_, emptyset)), 
27.06/27.33	             emptyset))
27.06/27.33	     | in(
27.06/27.33	         sk_X6_(
27.06/27.33	           (^[Y0 : $i]:
27.06/27.33	              (sk_X13_ =
27.06/27.33	               setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	                 setadjoin(
27.06/27.33	                   setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                   emptyset)))), setunion(sk_X13_)), 
27.06/27.33	         dsetconstr(setunion(sk_X13_), 
27.06/27.33	           (^[Y0 : $i]:
27.06/27.33	              (sk_X13_ =
27.06/27.33	               setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	                 setadjoin(
27.06/27.33	                   setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                   emptyset))))))),
27.06/27.33	    inference('clc', [status(thm)], ['35', '10'])).
27.06/27.33	tff('37', plain,
27.06/27.33	    sk_X13_
27.06/27.33	     = setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	         setadjoin(setadjoin(kfst(sk_X13_), setadjoin(sk_X15_, emptyset)), 
27.06/27.33	           emptyset)),
27.06/27.33	    inference('sup+', [status(thm)], ['29', '25'])).
27.06/27.33	tff('38', plain,
27.06/27.33	    in(
27.06/27.33	      sk_X6_(
27.06/27.33	        (^[Y0 : $i]:
27.06/27.33	           (sk_X13_ =
27.06/27.33	            setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	              setadjoin(setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                emptyset)))), setunion(sk_X13_)), 
27.06/27.33	      dsetconstr(setunion(sk_X13_), 
27.06/27.33	        (^[Y0 : $i]:
27.06/27.33	           (sk_X13_ =
27.06/27.33	            setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	              setadjoin(setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                emptyset)))))),
27.06/27.33	    inference('clc', [status(thm)], ['36', '37'])).
27.06/27.33	tff('39', plain,
27.06/27.33	    ![X19 : $i > $o, X20, X21]:
27.06/27.33	      (dsetconstr(X20, (^[Y0 : $i]: X19(Y0)))
27.06/27.33	        = setadjoin(sk_X6_(X19, X20), emptyset)
27.06/27.33	       | ~ in(X21, X20)
27.06/27.33	       | sk_X5_(X21, X19, X20) != X21
27.06/27.33	       | ~ X19(X21)),
27.06/27.33	    inference('cnf', [status(esa)], [zf_stmt_1])).
27.06/27.33	tff('40', plain,
27.06/27.33	    ![X19 : $i > $o, X20, X21]:
27.06/27.33	      (dsetconstr(X20, X19) = setadjoin(sk_X6_(X19, X20), emptyset)
27.06/27.33	       | ~ in(X21, X20)
27.06/27.33	       | sk_X5_(X21, X19, X20) != X21
27.06/27.33	       | ~ X19(X21)),
27.06/27.33	    inference('lambda-normalize', [status(thm)], ['39'])).
27.06/27.33	tff('41', plain,
27.06/27.33	    (sk_X15_ != sk_X15_
27.06/27.33	     | ~ (^[Y0 : $i]:
27.06/27.33	            (sk_X13_ =
27.06/27.33	             setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	               setadjoin(setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                 emptyset))))(sk_X15_)
27.06/27.33	     | ~ in(sk_X15_, setunion(sk_X13_))
27.06/27.33	     | dsetconstr(setunion(sk_X13_), 
27.06/27.33	         (^[Y0 : $i]:
27.06/27.33	            (sk_X13_ =
27.06/27.33	             setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	               setadjoin(setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                 emptyset)))))
27.06/27.33	        = setadjoin(
27.06/27.33	            sk_X6_(
27.06/27.33	              (^[Y0 : $i]:
27.06/27.33	                 (sk_X13_ =
27.06/27.33	                  setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.33	                    setadjoin(
27.06/27.33	                      setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.33	                      emptyset)))), setunion(sk_X13_)), emptyset)),
27.06/27.33	    inference('sup-', [status(thm)], ['29', '40'])).
27.06/27.33	tff('42', plain,
27.06/27.33	    (sk_X15_ != sk_X15_
27.06/27.33	     | ~ (sk_X13_ =
27.06/27.34	          setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.34	            setadjoin(
27.06/27.34	              setadjoin(kfst(sk_X13_), setadjoin(sk_X15_, emptyset)), 
27.06/27.34	              emptyset)))
27.06/27.34	     | ~ in(sk_X15_, setunion(sk_X13_))
27.06/27.34	     | dsetconstr(setunion(sk_X13_), 
27.06/27.34	         (^[Y0 : $i]:
27.06/27.34	            (sk_X13_ =
27.06/27.34	             setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.34	               setadjoin(setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.34	                 emptyset)))))
27.06/27.34	        = setadjoin(
27.06/27.34	            sk_X6_(
27.06/27.34	              (^[Y0 : $i]:
27.06/27.34	                 (sk_X13_ =
27.06/27.34	                  setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.34	                    setadjoin(
27.06/27.34	                      setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.34	                      emptyset)))), setunion(sk_X13_)), emptyset)),
27.06/27.34	    inference('lambda-normalize', [status(thm)], ['41'])).
27.06/27.34	tff('43', plain,
27.06/27.34	    (dsetconstr(setunion(sk_X13_), 
27.06/27.34	       (^[Y0 : $i]:
27.06/27.34	          (sk_X13_ =
27.06/27.34	           setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.34	             setadjoin(setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.34	               emptyset)))))
27.06/27.34	      = setadjoin(
27.06/27.34	          sk_X6_(
27.06/27.34	            (^[Y0 : $i]:
27.06/27.34	               (sk_X13_ =
27.06/27.34	                setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.34	                  setadjoin(
27.06/27.34	                    setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.34	                    emptyset)))), setunion(sk_X13_)), emptyset)
27.06/27.34	     | ~ in(sk_X15_, setunion(sk_X13_))
27.06/27.34	     | ~ (sk_X13_ =
27.06/27.34	          setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.34	            setadjoin(
27.06/27.34	              setadjoin(kfst(sk_X13_), setadjoin(sk_X15_, emptyset)), 
27.06/27.34	              emptyset)))),
27.06/27.34	    inference('simplify', [status(thm)], ['42'])).
27.06/27.34	tff('44', plain,
27.06/27.34	    (dsetconstr(setunion(sk_X13_), 
27.06/27.34	       (^[Y0 : $i]:
27.06/27.34	          (sk_X13_ =
27.06/27.34	           setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.34	             setadjoin(setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.34	               emptyset)))))
27.06/27.34	      = setadjoin(
27.06/27.34	          sk_X6_(
27.06/27.34	            (^[Y0 : $i]:
27.06/27.34	               (sk_X13_ =
27.06/27.34	                setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.34	                  setadjoin(
27.06/27.34	                    setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.34	                    emptyset)))), setunion(sk_X13_)), emptyset)
27.06/27.34	     | ~ in(sk_X15_, setunion(sk_X13_))
27.06/27.34	     | sk_X13_
27.06/27.34	        != setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.34	             setadjoin(
27.06/27.34	               setadjoin(kfst(sk_X13_), setadjoin(sk_X15_, emptyset)), 
27.06/27.34	               emptyset))),
27.06/27.34	    inference('simplify nested equalities', [status(thm)], ['43'])).
27.06/27.34	tff('45', plain,
27.06/27.34	    (sk_X13_
27.06/27.34	      != setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.34	           setadjoin(setadjoin(kfst(sk_X13_), setadjoin(sk_X15_, emptyset)), 
27.06/27.34	             emptyset))
27.06/27.34	     | dsetconstr(setunion(sk_X13_), 
27.06/27.34	         (^[Y0 : $i]:
27.06/27.34	            (sk_X13_ =
27.06/27.34	             setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.34	               setadjoin(setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.34	                 emptyset)))))
27.06/27.34	        = setadjoin(
27.06/27.34	            sk_X6_(
27.06/27.34	              (^[Y0 : $i]:
27.06/27.34	                 (sk_X13_ =
27.06/27.34	                  setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.34	                    setadjoin(
27.06/27.34	                      setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.34	                      emptyset)))), setunion(sk_X13_)), emptyset)),
27.06/27.34	    inference('clc', [status(thm)], ['44', '10'])).
27.06/27.34	tff('46', plain,
27.06/27.34	    dsetconstr(setunion(sk_X13_), 
27.06/27.34	      (^[Y0 : $i]:
27.06/27.34	         (sk_X13_ =
27.06/27.34	          setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.34	            setadjoin(setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.34	              emptyset)))))
27.06/27.34	     = setadjoin(
27.06/27.34	         sk_X6_(
27.06/27.34	           (^[Y0 : $i]:
27.06/27.34	              (sk_X13_ =
27.06/27.34	               setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.34	                 setadjoin(
27.06/27.34	                   setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.34	                   emptyset)))), setunion(sk_X13_)), emptyset),
27.06/27.34	    inference('clc', [status(thm)], ['45', '37'])).
27.06/27.34	tff('47', plain,
27.06/27.34	    (dsetconstr(setunion(sk_X13_), 
27.06/27.34	       (^[Y0 : $i]:
27.06/27.34	          (sk_X13_ =
27.06/27.34	           setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.34	             setadjoin(setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.34	               emptyset)))))
27.06/27.34	      != dsetconstr(setunion(sk_X13_), 
27.06/27.34	           (^[Y0 : $i]:
27.06/27.34	              (sk_X13_ =
27.06/27.34	               setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.34	                 setadjoin(
27.06/27.34	                   setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.34	                   emptyset)))))
27.06/27.34	     | ~ in(
27.06/27.34	           sk_X6_(
27.06/27.34	             (^[Y0 : $i]:
27.06/27.34	                (sk_X13_ =
27.06/27.34	                 setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.34	                   setadjoin(
27.06/27.34	                     setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.34	                     emptyset)))), setunion(sk_X13_)), 
27.06/27.34	           dsetconstr(setunion(sk_X13_), 
27.06/27.34	             (^[Y0 : $i]:
27.06/27.34	                (sk_X13_ =
27.06/27.34	                 setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.34	                   setadjoin(
27.06/27.34	                     setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.34	                     emptyset))))))),
27.06/27.34	    inference('sup-', [status(thm)], ['46', '17'])).
27.06/27.34	tff('48', plain,
27.06/27.34	    ~ in(
27.06/27.34	        sk_X6_(
27.06/27.34	          (^[Y0 : $i]:
27.06/27.34	             (sk_X13_ =
27.06/27.34	              setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.34	                setadjoin(setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.34	                  emptyset)))), setunion(sk_X13_)), 
27.06/27.34	        dsetconstr(setunion(sk_X13_), 
27.06/27.34	          (^[Y0 : $i]:
27.06/27.34	             (sk_X13_ =
27.06/27.34	              setadjoin(setadjoin(kfst(sk_X13_), emptyset), 
27.06/27.34	                setadjoin(setadjoin(kfst(sk_X13_), setadjoin(Y0, emptyset)), 
27.06/27.34	                  emptyset)))))),
27.06/27.34	    inference('simplify', [status(thm)], ['47'])).
27.06/27.34	tff('49', plain, $false, inference('sup-', [status(thm)], ['38', '48'])).
27.06/27.34	
27.06/27.34	% SZS output end Refutation
27.06/27.34	% Zipperpin 1.5 exiting
27.06/27.34	EOF