0.11/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.13	% Command    : run_portfolio.sh /export/starexec/sandbox/benchmark/theBenchmark.p /export/starexec/sandbox/tmp/tmp.Rlg2irSLbl
0.13/0.34	% Computer   : n020.cluster.edu
0.13/0.34	% Model      : x86_64 x86_64
0.13/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory     : 8042.1875MB
0.13/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit   : 180
0.13/0.34	% DateTime   : Thu Aug 29 16:12:55 EDT 2019
0.13/0.34	% CPUTime    : 
34.37/34.62	% Running portfolio for 180 s
34.37/34.62	% File         : /export/starexec/sandbox/benchmark/theBenchmark.p
34.37/34.62	% TempDir      : /export/starexec/sandbox/tmp/tmp.Rlg2irSLbl
34.37/34.62	% Recognized as monomorphic HO.
34.37/34.62	% Running /export/starexec/sandbox/solver/bin/competitive.sh for 18
34.37/34.62	% Running /export/starexec/sandbox/solver/bin/competitive.2.sh for 13
34.37/34.62	% Running /export/starexec/sandbox/solver/bin/competitive.3.sh for 3
34.37/34.62	% Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.sh for 28
34.37/34.62	% Solved by: pragmatic.rudimentary.sh
34.37/34.62	% done 375 iterations in 0.658s
34.37/34.62	% hashcons stats for terms: size 4096, num 1747, sum length 8854, buckets: small 0, median 3, big 7
34.37/34.62	% proof state stats: {active 57, passive 1162, simpl 0}
34.37/34.62	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
34.37/34.62	% SZS output start Refutation
34.37/34.62	tff(caseood, axiom, case() =
34.37/34.62	  ^[B:($o > $o),X,Y,U,V]:
34.37/34.62	    eps(^[Z]:
34.37/34.62	          (((Z = V) & (B = (^[A:$o]: $true))) | 
34.37/34.62	           ((Z = U) & (B = (^[A:$o]: A))) | ((Z = Y) & (B = ~)) | 
34.37/34.62	           ((Z = X) & (B = (^[A:$o]: $false)))))).
34.37/34.62	tff('0', plain,
34.37/34.62	    case =
34.37/34.62	    (^[V_1:($o > $o),V_2,V_3,V_4,V_5]:
34.37/34.62	       eps(^[V_6]:
34.37/34.62	             (((V_6 = V_5) & (V_1 = (^[V_7:$o]: $true))) | 
34.37/34.62	              ((V_6 = V_4) & (V_1 = (^[V_8:$o]: V_8))) | 
34.37/34.62	              ((V_6 = V_3) & (V_1 = ~)) | 
34.37/34.62	              ((V_6 = V_2) & (V_1 = (^[V_9:$o]: $false)))))),
34.37/34.62	    define([status(thm)])).
34.37/34.62	tff(conj, conjecture,
34.37/34.62	  (![X,Y,U,V]:
34.37/34.62	     ((case(f,X,Y,U,V) = X) | (case(f,X,Y,U,V) = Y) | 
34.37/34.62	      (case(f,X,Y,U,V) = U) | (case(f,X,Y,U,V) = V)))).
34.37/34.62	tff(zf_stmt_0, conjecture,
34.37/34.62	  (![X2,X3,X4,X5]:
34.37/34.62	     ((eps(^[V_1]:
34.37/34.62	             (((f = (^[V_4:$o]: $false)) & (V_1 = X2)) | 
34.37/34.62	              ((f = ~) & (V_1 = X3)) | 
34.37/34.62	              ((f = (^[V_3:$o]: V_3)) & (V_1 = X4)) | 
34.37/34.62	              ((f = (^[V_2:$o]: $true)) & (V_1 = X5)))) =
34.37/34.62	       X2) | 
34.37/34.62	      (eps(^[V_5]:
34.37/34.62	             (((f = (^[V_8:$o]: $false)) & (V_5 = X2)) | 
34.37/34.62	              ((f = ~) & (V_5 = X3)) | 
34.37/34.62	              ((f = (^[V_7:$o]: V_7)) & (V_5 = X4)) | 
34.37/34.62	              ((f = (^[V_6:$o]: $true)) & (V_5 = X5)))) =
34.37/34.62	       X3) | 
34.37/34.62	      (eps(^[V_9]:
34.37/34.62	             (((f = (^[V_12:$o]: $false)) & (V_9 = X2)) | 
34.37/34.62	              ((f = ~) & (V_9 = X3)) | 
34.37/34.62	              ((f = (^[V_11:$o]: V_11)) & (V_9 = X4)) | 
34.37/34.62	              ((f = (^[V_10:$o]: $true)) & (V_9 = X5)))) =
34.37/34.62	       X4) | 
34.37/34.62	      (eps(^[V_13]:
34.37/34.62	             (((f = (^[V_16:$o]: $false)) & (V_13 = X2)) | 
34.37/34.62	              ((f = ~) & (V_13 = X3)) | 
34.37/34.62	              ((f = (^[V_15:$o]: V_15)) & (V_13 = X4)) | 
34.37/34.62	              ((f = (^[V_14:$o]: $true)) & (V_13 = X5)))) =
34.37/34.62	       X5)))).
34.37/34.62	tff(zf_stmt_1, negated_conjecture,
34.37/34.62	  (~
34.37/34.62	    (![X2,X3,X4,X5]:
34.37/34.62	       ((eps(^[V_1]:
34.37/34.62	               (((f = (^[V_4:$o]: $false)) & (V_1 = X2)) | 
34.37/34.62	                ((f = ~) & (V_1 = X3)) | 
34.37/34.62	                ((f = (^[V_3:$o]: V_3)) & (V_1 = X4)) | 
34.37/34.62	                ((f = (^[V_2:$o]: $true)) & (V_1 = X5)))) =
34.37/34.62	         X2) | 
34.37/34.62	        (eps(^[V_5]:
34.37/34.62	               (((f = (^[V_8:$o]: $false)) & (V_5 = X2)) | 
34.37/34.62	                ((f = ~) & (V_5 = X3)) | 
34.37/34.62	                ((f = (^[V_7:$o]: V_7)) & (V_5 = X4)) | 
34.37/34.62	                ((f = (^[V_6:$o]: $true)) & (V_5 = X5)))) =
34.37/34.62	         X3) | 
34.37/34.62	        (eps(^[V_9]:
34.37/34.62	               (((f = (^[V_12:$o]: $false)) & (V_9 = X2)) | 
34.37/34.62	                ((f = ~) & (V_9 = X3)) | 
34.37/34.62	                ((f = (^[V_11:$o]: V_11)) & (V_9 = X4)) | 
34.37/34.62	                ((f = (^[V_10:$o]: $true)) & (V_9 = X5)))) =
34.37/34.62	         X4) | 
34.37/34.62	        (eps(^[V_13]:
34.37/34.62	               (((f = (^[V_16:$o]: $false)) & (V_13 = X2)) | 
34.37/34.62	                ((f = ~) & (V_13 = X3)) | 
34.37/34.62	                ((f = (^[V_15:$o]: V_15)) & (V_13 = X4)) | 
34.37/34.62	                ((f = (^[V_14:$o]: $true)) & (V_13 = X5)))) =
34.37/34.62	         X5))))).
34.37/34.62	tff('1', plain,
34.37/34.62	    eps(
34.37/34.62	      (^[Y0 : $i]:
34.37/34.62	         (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	          ((f = ~) & (Y0 = sk_X3_))|((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	          ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	     != sk_X5_,
34.37/34.62	    inference('cnf', [status(esa)], [zf_stmt_1])).
34.37/34.62	tff('2', plain,
34.37/34.62	    (f != ~
34.37/34.62	     | eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	             ($true & (Y0 = sk_X3_))|
34.37/34.62	             ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	             ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	        != sk_X5_),
34.37/34.62	    inference('bool_case_simp', [status(thm)], ['1'])).
34.37/34.62	tff('3', plain,
34.37/34.62	    (f != ~
34.37/34.62	     | eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|(Y0 = sk_X3_)|
34.37/34.62	             ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	             ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	        != sk_X5_),
34.37/34.62	    inference('simplify boolean subterms', [status(thm)], ['2'])).
34.37/34.62	tff('4', plain, (f != ~) <= (~ (f = ~)),
34.37/34.62	    inference('split', [status(esa)], ['3'])).
34.37/34.62	tff('5', plain, (f('#fsk6') != (~ '#fsk6')) <= (~ (f = ~)),
34.37/34.62	    inference('neg_ext', [status(thm)], ['4'])).
34.37/34.62	tff('6', plain, ((~ f('#fsk6') | '#fsk6')) <= (~ (f = ~)),
34.37/34.62	    inference('cnf_fool', [status(thm)], ['5'])).
34.37/34.62	tff('7', plain, (~ f('#fsk6')) <= (~ (f('#fsk6'))),
34.37/34.62	    inference('split', [status(esa)], ['6'])).
34.37/34.62	tff('8', plain, (('#fsk6' | ~ f($false))) <= (~ (f('#fsk6'))),
34.37/34.62	    inference('bool_case_simp', [status(thm)], ['7'])).
34.37/34.62	tff('9', plain, ('#fsk6') | (f('#fsk6')) | ~ (f($false)),
34.37/34.62	    inference('split', [status(esa)], ['8'])).
34.37/34.62	tff('10', plain,
34.37/34.62	    (f = (^[Y0 : $o]: Y0)
34.37/34.62	     | eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	             ((f = ~) & (Y0 = sk_X3_))|($false & (Y0 = sk_X4_))|
34.37/34.62	             ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	        != sk_X5_),
34.37/34.62	    inference('bool_case_simp', [status(thm)], ['1'])).
34.37/34.62	tff('11', plain,
34.37/34.62	    (f = (^[Y0 : $o]: Y0)
34.37/34.62	     | eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	             ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	             ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	        != sk_X5_),
34.37/34.62	    inference('simplify boolean subterms', [status(thm)], ['10'])).
34.37/34.62	tff('12', plain,
34.37/34.62	    (eps(
34.37/34.62	       (^[Y0 : $i]:
34.37/34.62	          (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	           ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	           ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	      != sk_X5_)
34.37/34.62	      <= (~
34.37/34.62	          (eps(
34.37/34.62	             (^[Y0 : $i]:
34.37/34.62	                (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	                 ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                 ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	            = sk_X5_)),
34.37/34.62	    inference('split', [status(esa)], ['11'])).
34.37/34.62	tff('13', plain,
34.37/34.62	    (((f = (^[Y0 : $o]: $true))
34.37/34.62	      | eps(
34.37/34.62	          (^[Y0 : $i]:
34.37/34.62	             (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	              ((f = ~) & (Y0 = sk_X3_))|($false & (Y0 = sk_X5_)))))
34.37/34.62	         != sk_X5_))
34.37/34.62	      <= (~
34.37/34.62	          (eps(
34.37/34.62	             (^[Y0 : $i]:
34.37/34.62	                (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	                 ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                 ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	            = sk_X5_)),
34.37/34.62	    inference('fool_param', [status(thm)], ['12'])).
34.37/34.62	tff('14', plain,
34.37/34.62	    ((f = (^[Y0 : $o]: $true)
34.37/34.62	      | eps(
34.37/34.62	          (^[Y0 : $i]:
34.37/34.62	             (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	              ((f = ~) & (Y0 = sk_X3_))|($false & (Y0 = sk_X5_)))))
34.37/34.62	         != sk_X5_))
34.37/34.62	      <= (~
34.37/34.62	          (eps(
34.37/34.62	             (^[Y0 : $i]:
34.37/34.62	                (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	                 ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                 ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	            = sk_X5_)),
34.37/34.62	    inference('simplify nested equalities', [status(thm)], ['13'])).
34.37/34.62	tff('15', plain,
34.37/34.62	    ((f = (^[Y0 : $o]: $true)
34.37/34.62	      | eps(
34.37/34.62	          (^[Y0 : $i]:
34.37/34.62	             (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_)) |
34.37/34.62	              ((f = ~) & (Y0 = sk_X3_)))))
34.37/34.62	         != sk_X5_))
34.37/34.62	      <= (~
34.37/34.62	          (eps(
34.37/34.62	             (^[Y0 : $i]:
34.37/34.62	                (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	                 ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                 ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	            = sk_X5_)),
34.37/34.62	    inference('simplify boolean subterms', [status(thm)], ['14'])).
34.37/34.62	tff('16', plain,
34.37/34.62	    ((f != (^[Y0 : $o]: $false)
34.37/34.62	      | f = (^[Y0 : $o]: $true)
34.37/34.62	      | eps(
34.37/34.62	          (^[Y0 : $i]: (($true & (Y0 = sk_X2_)) | ((f = ~) & (Y0 = sk_X3_)))))
34.37/34.62	         != sk_X5_))
34.37/34.62	      <= (~
34.37/34.62	          (eps(
34.37/34.62	             (^[Y0 : $i]:
34.37/34.62	                (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	                 ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                 ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	            = sk_X5_)),
34.37/34.62	    inference('bool_case_simp', [status(thm)], ['15'])).
34.37/34.62	tff('17', plain,
34.37/34.62	    ((f != (^[Y0 : $o]: $false)
34.37/34.62	      | f = (^[Y0 : $o]: $true)
34.37/34.62	      | eps((^[Y0 : $i]: ((Y0 = sk_X2_) | ((f = ~) & (Y0 = sk_X3_)))))
34.37/34.62	         != sk_X5_))
34.37/34.62	      <= (~
34.37/34.62	          (eps(
34.37/34.62	             (^[Y0 : $i]:
34.37/34.62	                (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	                 ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                 ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	            = sk_X5_)),
34.37/34.62	    inference('simplify boolean subterms', [status(thm)], ['16'])).
34.37/34.62	tff('18', plain,
34.37/34.62	    (f != (^[Y0 : $o]: $false)) <= (~ (f = (^[Y0 : $o]: $false))),
34.37/34.62	    inference('split', [status(esa)], ['17'])).
34.37/34.62	tff('19', plain,
34.37/34.62	    ![X1]:
34.37/34.62	      (~ (((f = (^[Y0 : $o]: $false)) & (X1 = sk_X2_))|
34.37/34.62	          ((f = ~) & (X1 = sk_X3_))|
34.37/34.62	          ((f = (^[Y0 : $o]: $true)) & (X1 = sk_X5_)))
34.37/34.62	       | (((f = (^[Y0 : $o]: $false)) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	                  ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X2_))|
34.37/34.62	          ((f = ~) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	                  ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X3_))|
34.37/34.62	          ((f = (^[Y0 : $o]: $true)) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	                  ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X5_)))),
34.37/34.62	    inference('inst_choice(^[Y0 : $i]:
34.37/34.62	   (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	    ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))',
34.37/34.62	              [status(thm)])).
34.37/34.62	tff('20', plain,
34.37/34.62	    ![X1]:
34.37/34.62	      (~ ((f = (^[Y0 : $o]: $false)) & (X1 = sk_X2_))
34.37/34.62	       | (((f = (^[Y0 : $o]: $false)) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	                  ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X2_))|
34.37/34.62	          ((f = ~) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	                  ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X3_))|
34.37/34.62	          ((f = (^[Y0 : $o]: $true)) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	                  ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X5_)))),
34.37/34.62	    inference('cnf_fool', [status(thm)], ['19'])).
34.37/34.62	tff('21', plain,
34.37/34.62	    ![X1]:
34.37/34.62	      (f != (^[Y0 : $o]: $false)
34.37/34.62	       | X1 != sk_X2_
34.37/34.62	       | (((f = (^[Y0 : $o]: $false)) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	                  ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X2_))|
34.37/34.62	          ((f = ~) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	                  ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X3_))|
34.37/34.62	          ((f = (^[Y0 : $o]: $true)) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	                  ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X5_)))),
34.37/34.62	    inference('cnf_fool', [status(thm)], ['20'])).
34.37/34.62	tff('22', plain,
34.37/34.62	    ((((f = (^[Y0 : $o]: $false)) &
34.37/34.62	       (eps(
34.37/34.62	          (^[Y0 : $i]:
34.37/34.62	             (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	              ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	              ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	        sk_X2_))|
34.37/34.62	      ((f = ~) &
34.37/34.62	       (eps(
34.37/34.62	          (^[Y0 : $i]:
34.37/34.62	             (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	              ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	              ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	        sk_X3_))|
34.37/34.62	      ((f = (^[Y0 : $o]: $true)) &
34.37/34.62	       (eps(
34.37/34.62	          (^[Y0 : $i]:
34.37/34.62	             (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	              ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	              ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	        sk_X5_)))
34.37/34.62	     | f != (^[Y0 : $o]: $false)),
34.37/34.62	    inference('simplify', [status(thm)], ['21'])).
34.37/34.62	tff('23', plain,
34.37/34.62	    (((f = (^[Y0 : $o]: $false)) &
34.37/34.62	      (eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	             ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	             ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	       sk_X2_))
34.37/34.62	     | ((f = ~) &
34.37/34.62	        (eps(
34.37/34.62	           (^[Y0 : $i]:
34.37/34.62	              (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	               ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	               ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	         sk_X3_))
34.37/34.62	     | ((f = (^[Y0 : $o]: $true)) &
34.37/34.62	        (eps(
34.37/34.62	           (^[Y0 : $i]:
34.37/34.62	              (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	               ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	               ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	         sk_X5_))
34.37/34.62	     | f != (^[Y0 : $o]: $false)),
34.37/34.62	    inference('cnf_fool', [status(thm)], ['22'])).
34.37/34.62	tff('24', plain,
34.37/34.62	    (eps(
34.37/34.62	       (^[Y0 : $i]:
34.37/34.62	          (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	           ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	           ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	      = sk_X2_
34.37/34.62	     | f != (^[Y0 : $o]: $false)
34.37/34.62	     | ((f = (^[Y0 : $o]: $true)) &
34.37/34.62	        (eps(
34.37/34.62	           (^[Y0 : $i]:
34.37/34.62	              (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	               ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	               ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	         sk_X5_))
34.37/34.62	     | ((f = ~) &
34.37/34.62	        (eps(
34.37/34.62	           (^[Y0 : $i]:
34.37/34.62	              (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	               ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	               ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	         sk_X3_))),
34.37/34.62	    inference('cnf_fool', [status(thm)], ['23'])).
34.37/34.62	tff('25', plain,
34.37/34.62	    (eps(
34.37/34.62	       (^[Y0 : $i]:
34.37/34.62	          (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	           ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	           ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	      = sk_X5_
34.37/34.62	     | ((f = ~) &
34.37/34.62	        (eps(
34.37/34.62	           (^[Y0 : $i]:
34.37/34.62	              (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	               ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	               ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	         sk_X3_))
34.37/34.62	     | f != (^[Y0 : $o]: $false)
34.37/34.62	     | eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	             ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	             ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	        = sk_X2_),
34.37/34.62	    inference('cnf_fool', [status(thm)], ['24'])).
34.37/34.62	tff('26', plain,
34.37/34.62	    (f = ~
34.37/34.62	     | eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	             ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	             ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	        = sk_X2_
34.37/34.62	     | f != (^[Y0 : $o]: $false)
34.37/34.62	     | eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	             ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	             ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	        = sk_X5_),
34.37/34.62	    inference('cnf_fool', [status(thm)], ['25'])).
34.37/34.62	tff('27', plain,
34.37/34.62	    (eps(
34.37/34.62	       (^[Y0 : $i]:
34.37/34.62	          (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	           ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	           ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	      = sk_X5_) | 
34.37/34.62	    (f = ~) | ~ (f = (^[Y0 : $o]: $false)) | 
34.37/34.62	    (eps(
34.37/34.62	       (^[Y0 : $i]:
34.37/34.62	          (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	           ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	           ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	      = sk_X2_),
34.37/34.62	    inference('split', [status(esa)], ['26'])).
34.37/34.62	tff('28', plain,
34.37/34.62	    eps(
34.37/34.62	      (^[Y0 : $i]:
34.37/34.62	         (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	          ((f = ~) & (Y0 = sk_X3_))|((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	          ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	     != sk_X2_,
34.37/34.62	    inference('cnf', [status(esa)], [zf_stmt_1])).
34.37/34.62	tff('29', plain,
34.37/34.62	    (f = (^[Y0 : $o]: Y0)
34.37/34.62	     | eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	             ((f = ~) & (Y0 = sk_X3_))|($false & (Y0 = sk_X4_))|
34.37/34.62	             ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	        != sk_X2_),
34.37/34.62	    inference('bool_case_simp', [status(thm)], ['28'])).
34.37/34.62	tff('30', plain,
34.37/34.62	    (f = (^[Y0 : $o]: Y0)
34.37/34.62	     | eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	             ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	             ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	        != sk_X2_),
34.37/34.62	    inference('simplify boolean subterms', [status(thm)], ['29'])).
34.37/34.62	tff('31', plain,
34.37/34.62	    (f = (^[Y0 : $o]: Y0)) | 
34.37/34.62	    ~
34.37/34.62	    (eps(
34.37/34.62	       (^[Y0 : $i]:
34.37/34.62	          (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	           ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	           ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	      = sk_X2_),
34.37/34.62	    inference('split', [status(esa)], ['30'])).
34.37/34.62	tff('32', plain,
34.37/34.62	    (f = (^[Y0 : $o]: Y0)) | 
34.37/34.62	    ~
34.37/34.62	    (eps(
34.37/34.62	       (^[Y0 : $i]:
34.37/34.62	          (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	           ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	           ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	      = sk_X5_),
34.37/34.62	    inference('split', [status(esa)], ['11'])).
34.37/34.62	tff('33', plain,
34.37/34.62	    (f = (^[Y0 : $o]: $false)
34.37/34.62	     | eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (($false & (Y0 = sk_X2_))|((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	             ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	             ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	        != sk_X5_),
34.37/34.62	    inference('bool_case_simp', [status(thm)], ['1'])).
34.37/34.62	tff('34', plain,
34.37/34.62	    (f = (^[Y0 : $o]: $false)
34.37/34.62	     | eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	             ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	             ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	        != sk_X5_),
34.37/34.62	    inference('simplify boolean subterms', [status(thm)], ['33'])).
34.37/34.62	tff('35', plain, (f = (^[Y0 : $o]: $false)) <= ((f = (^[Y0 : $o]: $false))),
34.37/34.62	    inference('split', [status(esa)], ['34'])).
34.37/34.62	tff('36', plain,
34.37/34.62	    (f = ~
34.37/34.62	     | eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	             ($false & (Y0 = sk_X3_))|
34.37/34.62	             ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	             ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	        != sk_X5_),
34.37/34.62	    inference('bool_case_simp', [status(thm)], ['1'])).
34.37/34.62	tff('37', plain,
34.37/34.62	    (f = ~
34.37/34.62	     | eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	             ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	             ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	        != sk_X5_),
34.37/34.62	    inference('simplify boolean subterms', [status(thm)], ['36'])).
34.37/34.62	tff('38', plain, (f = ~) <= ((f = ~)),
34.37/34.62	    inference('split', [status(esa)], ['37'])).
34.37/34.62	tff('39', plain,
34.37/34.62	    ((^[Y0 : $o]: $false) = ~) <= ((f = ~) & (f = (^[Y0 : $o]: $false))),
34.37/34.62	    inference('sup+', [status(thm)], ['35', '38'])).
34.37/34.62	tff('40', plain,
34.37/34.62	    (![X1 : $o]: (^[Y0 : $o]: $false)(X1) = (~ X1))
34.37/34.62	      <= ((f = ~) & (f = (^[Y0 : $o]: $false))),
34.37/34.62	    inference('ho_complete_eq', [status(thm)], ['39'])).
34.37/34.62	tff('41', plain,
34.37/34.62	    (![X1 : $o]: ~ (~ X1)) <= ((f = ~) & (f = (^[Y0 : $o]: $false))),
34.37/34.62	    inference('lambda-normalize', [status(thm)], ['40'])).
34.37/34.62	tff('42', plain, (![X0 : $o]: X0) <= ((f = ~) & (f = (^[Y0 : $o]: $false))),
34.37/34.62	    inference('cnf_otf', [status(thm)], ['41'])).
34.37/34.62	tff('43', plain, ~ (f = ~) | ~ (f = (^[Y0 : $o]: $false)),
34.37/34.62	    inference('simplify', [status(thm)], ['42'])).
34.37/34.62	tff('44', plain, (f = (^[Y0 : $o]: Y0)) <= ((f = (^[Y0 : $o]: Y0))),
34.37/34.62	    inference('split', [status(esa)], ['11'])).
34.37/34.62	tff('45', plain,
34.37/34.62	    (![X1 : $o]: f(X1) = (^[Y0 : $o]: Y0)(X1)) <= ((f = (^[Y0 : $o]: Y0))),
34.37/34.62	    inference('ho_complete_eq', [status(thm)], ['44'])).
34.37/34.62	tff('46', plain, (![X1 : $o]: f(X1) = X1) <= ((f = (^[Y0 : $o]: Y0))),
34.37/34.62	    inference('lambda-normalize', [status(thm)], ['45'])).
34.37/34.62	tff('47', plain, (![X1 : $o]: (f(X1) | ~ X1)) <= ((f = (^[Y0 : $o]: Y0))),
34.37/34.62	    inference('cnf_otf', [status(thm)], ['46'])).
34.37/34.62	tff('48', plain, (f($true)) <= ((f = (^[Y0 : $o]: Y0))),
34.37/34.62	    inference('fool.elim_var', [status(thm)], ['47'])).
34.37/34.62	tff('49', plain,
34.37/34.62	    (![X1 : $o]: f(X1) = (^[Y0 : $o]: $false)(X1))
34.37/34.62	      <= ((f = (^[Y0 : $o]: $false))),
34.37/34.62	    inference('ho_complete_eq', [status(thm)], ['35'])).
34.37/34.62	tff('50', plain, (![X1 : $o]: ~ f(X1)) <= ((f = (^[Y0 : $o]: $false))),
34.37/34.62	    inference('lambda-normalize', [status(thm)], ['49'])).
34.37/34.62	tff('51', plain, ~ (f = (^[Y0 : $o]: $false)) | ~ (f = (^[Y0 : $o]: Y0)),
34.37/34.62	    inference('sup-', [status(thm)], ['48', '50'])).
34.37/34.62	tff('52', plain, ~ (f = (^[Y0 : $o]: $false)),
34.37/34.62	    inference('sat_resolution', [status(thm)], ['27', '31', '32', '43', '51'])).
34.37/34.62	tff('53', plain, f != (^[Y0 : $o]: $false),
34.37/34.62	    inference('simpl_trail', [status(thm)], ['18', '52'])).
34.37/34.62	tff('54', plain, f('#fsk435') != (^[Y0 : $o]: $false)('#fsk435'),
34.37/34.62	    inference('neg_ext', [status(thm)], ['53'])).
34.37/34.62	tff('55', plain, f('#fsk435'),
34.37/34.62	    inference('lambda-normalize', [status(thm)], ['54'])).
34.37/34.62	tff('56', plain, ('#fsk435' | f($false)),
34.37/34.62	    inference('bool_case_simp', [status(thm)], ['55'])).
34.37/34.62	tff('57', plain, (f($false)) | ('#fsk435'),
34.37/34.62	    inference('split', [status(esa)], ['56'])).
34.37/34.62	tff('58', plain, (~ '#fsk435' | f($true)),
34.37/34.62	    inference('bool_case_simp', [status(thm)], ['55'])).
34.37/34.62	tff('59', plain, ~ ('#fsk435') | (f($true)),
34.37/34.62	    inference('split', [status(esa)], ['58'])).
34.37/34.62	tff('60', plain,
34.37/34.62	    (f != (^[Y0 : $o]: Y0)
34.37/34.62	     | eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	             ((f = ~) & (Y0 = sk_X3_))|($true & (Y0 = sk_X4_))|
34.37/34.62	             ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	        != sk_X5_),
34.37/34.62	    inference('bool_case_simp', [status(thm)], ['1'])).
34.37/34.62	tff('61', plain,
34.37/34.62	    (f != (^[Y0 : $o]: Y0)
34.37/34.62	     | eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	             ((f = ~) & (Y0 = sk_X3_))|(Y0 = sk_X4_)|
34.37/34.62	             ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	        != sk_X5_),
34.37/34.62	    inference('simplify boolean subterms', [status(thm)], ['60'])).
34.37/34.62	tff('62', plain, (f != (^[Y0 : $o]: Y0)) <= (~ (f = (^[Y0 : $o]: Y0))),
34.37/34.62	    inference('split', [status(esa)], ['61'])).
34.37/34.62	tff('63', plain,
34.37/34.62	    (f('#fsk5') != (^[Y0 : $o]: Y0)('#fsk5')) <= (~ (f = (^[Y0 : $o]: Y0))),
34.37/34.62	    inference('neg_ext', [status(thm)], ['62'])).
34.37/34.62	tff('64', plain, (f('#fsk5') != '#fsk5') <= (~ (f = (^[Y0 : $o]: Y0))),
34.37/34.62	    inference('lambda-normalize', [status(thm)], ['63'])).
34.37/34.62	tff('65', plain, (('#fsk5' | f($false))) <= (~ (f = (^[Y0 : $o]: Y0))),
34.37/34.62	    inference('bool_case_simp', [status(thm)], ['64'])).
34.37/34.62	tff('66', plain, ('#fsk5') | (f($false)) | (f = (^[Y0 : $o]: Y0)),
34.37/34.62	    inference('split', [status(esa)], ['65'])).
34.37/34.62	tff('67', plain,
34.37/34.62	    ![X1]:
34.37/34.62	      (~ (((f = ~) & (X1 = sk_X3_))|((f = (^[Y0 : $o]: Y0)) & (X1 = sk_X4_))|
34.37/34.62	          ((f = (^[Y0 : $o]: $true)) & (X1 = sk_X5_)))
34.37/34.62	       | (((f = ~) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X3_))|
34.37/34.62	          ((f = (^[Y0 : $o]: Y0)) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X4_))|
34.37/34.62	          ((f = (^[Y0 : $o]: $true)) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X5_)))),
34.37/34.62	    inference('inst_choice(^[Y0 : $i]:
34.37/34.62	   (((f = ~) & (Y0 = sk_X3_))|((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	    ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))',
34.37/34.62	              [status(thm)])).
34.37/34.62	tff('68', plain,
34.37/34.62	    ![X1]:
34.37/34.62	      (~ ((f = (^[Y0 : $o]: Y0)) & (X1 = sk_X4_))
34.37/34.62	       | (((f = ~) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X3_))|
34.37/34.62	          ((f = (^[Y0 : $o]: Y0)) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X4_))|
34.37/34.62	          ((f = (^[Y0 : $o]: $true)) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X5_)))),
34.37/34.62	    inference('cnf_fool', [status(thm)], ['67'])).
34.37/34.62	tff('69', plain,
34.37/34.62	    ![X1]:
34.37/34.62	      (f != (^[Y0 : $o]: Y0)
34.37/34.62	       | X1 != sk_X4_
34.37/34.62	       | (((f = ~) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X3_))|
34.37/34.62	          ((f = (^[Y0 : $o]: Y0)) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X4_))|
34.37/34.62	          ((f = (^[Y0 : $o]: $true)) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X5_)))),
34.37/34.62	    inference('cnf_fool', [status(thm)], ['68'])).
34.37/34.62	tff('70', plain,
34.37/34.62	    ((((f = ~) &
34.37/34.62	       (eps(
34.37/34.62	          (^[Y0 : $i]:
34.37/34.62	             (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	              ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	              ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	        sk_X3_))|
34.37/34.62	      ((f = (^[Y0 : $o]: Y0)) &
34.37/34.62	       (eps(
34.37/34.62	          (^[Y0 : $i]:
34.37/34.62	             (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	              ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	              ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	        sk_X4_))|
34.37/34.62	      ((f = (^[Y0 : $o]: $true)) &
34.37/34.62	       (eps(
34.37/34.62	          (^[Y0 : $i]:
34.37/34.62	             (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	              ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	              ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	        sk_X5_)))
34.37/34.62	     | f != (^[Y0 : $o]: Y0)),
34.37/34.62	    inference('simplify', [status(thm)], ['69'])).
34.37/34.62	tff('71', plain,
34.37/34.62	    (((f = ~) &
34.37/34.62	      (eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	             ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	             ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	       sk_X3_))
34.37/34.62	     | ((f = (^[Y0 : $o]: Y0)) &
34.37/34.62	        (eps(
34.37/34.62	           (^[Y0 : $i]:
34.37/34.62	              (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	               ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	               ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	         sk_X4_))
34.37/34.62	     | ((f = (^[Y0 : $o]: $true)) &
34.37/34.62	        (eps(
34.37/34.62	           (^[Y0 : $i]:
34.37/34.62	              (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	               ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	               ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	         sk_X5_))
34.37/34.62	     | f != (^[Y0 : $o]: Y0)),
34.37/34.62	    inference('cnf_fool', [status(thm)], ['70'])).
34.37/34.62	tff('72', plain,
34.37/34.62	    (eps(
34.37/34.62	       (^[Y0 : $i]:
34.37/34.62	          (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	           ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	           ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	      = sk_X3_
34.37/34.62	     | f != (^[Y0 : $o]: Y0)
34.37/34.62	     | ((f = (^[Y0 : $o]: $true)) &
34.37/34.62	        (eps(
34.37/34.62	           (^[Y0 : $i]:
34.37/34.62	              (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	               ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	               ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	         sk_X5_))
34.37/34.62	     | ((f = (^[Y0 : $o]: Y0)) &
34.37/34.62	        (eps(
34.37/34.62	           (^[Y0 : $i]:
34.37/34.62	              (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	               ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	               ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	         sk_X4_))),
34.37/34.62	    inference('cnf_fool', [status(thm)], ['71'])).
34.37/34.62	tff('73', plain,
34.37/34.62	    (eps(
34.37/34.62	       (^[Y0 : $i]:
34.37/34.62	          (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	           ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	           ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	      = sk_X5_
34.37/34.62	     | ((f = (^[Y0 : $o]: Y0)) &
34.37/34.62	        (eps(
34.37/34.62	           (^[Y0 : $i]:
34.37/34.62	              (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	               ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	               ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	         sk_X4_))
34.37/34.62	     | f != (^[Y0 : $o]: Y0)
34.37/34.62	     | eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	             ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	             ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	        = sk_X3_),
34.37/34.62	    inference('cnf_fool', [status(thm)], ['72'])).
34.37/34.62	tff('74', plain,
34.37/34.62	    (eps(
34.37/34.62	       (^[Y0 : $i]:
34.37/34.62	          (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	           ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	           ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	      = sk_X4_
34.37/34.62	     | eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	             ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	             ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	        = sk_X3_
34.37/34.62	     | f != (^[Y0 : $o]: Y0)
34.37/34.62	     | eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	             ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	             ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	        = sk_X5_),
34.37/34.62	    inference('cnf_fool', [status(thm)], ['73'])).
34.37/34.62	tff('75', plain,
34.37/34.62	    (eps(
34.37/34.62	       (^[Y0 : $i]:
34.37/34.62	          (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	           ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	           ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	      = sk_X3_) | 
34.37/34.62	    (eps(
34.37/34.62	       (^[Y0 : $i]:
34.37/34.62	          (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	           ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	           ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	      = sk_X4_) | 
34.37/34.62	    (eps(
34.37/34.62	       (^[Y0 : $i]:
34.37/34.62	          (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	           ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	           ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	      = sk_X5_) | 
34.37/34.62	    ~ (f = (^[Y0 : $o]: Y0)), inference('split', [status(esa)], ['74'])).
34.37/34.62	tff('76', plain,
34.37/34.62	    ~
34.37/34.62	    (eps(
34.37/34.62	       (^[Y0 : $i]:
34.37/34.62	          (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	           ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	           ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	      = sk_X5_) | 
34.37/34.62	    (f = (^[Y0 : $o]: $false)), inference('split', [status(esa)], ['34'])).
34.37/34.62	tff('77', plain,
34.37/34.62	    ~ (f = (^[Y0 : $o]: $false)) | 
34.37/34.62	    (eps(
34.37/34.62	       (^[Y0 : $i]:
34.37/34.62	          (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	           ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	           ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	      = sk_X5_) | 
34.37/34.62	    (f = ~) | 
34.37/34.62	    (eps(
34.37/34.62	       (^[Y0 : $i]:
34.37/34.62	          (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	           ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	           ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	      = sk_X2_),
34.37/34.62	    inference('split', [status(esa)], ['26'])).
34.37/34.62	tff('78', plain,
34.37/34.62	    ~
34.37/34.62	    (eps(
34.37/34.62	       (^[Y0 : $i]:
34.37/34.62	          (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	           ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	           ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	      = sk_X2_) | 
34.37/34.62	    (f = (^[Y0 : $o]: Y0)), inference('split', [status(esa)], ['30'])).
34.37/34.62	tff('79', plain,
34.37/34.62	    ~
34.37/34.62	    (eps(
34.37/34.62	       (^[Y0 : $i]:
34.37/34.62	          (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	           ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	           ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	      = sk_X5_) | 
34.37/34.62	    (f = (^[Y0 : $o]: Y0)), inference('split', [status(esa)], ['11'])).
34.37/34.62	tff('80', plain, ~ (f = (^[Y0 : $o]: $false)) | ~ (f = ~),
34.37/34.62	    inference('simplify', [status(thm)], ['42'])).
34.37/34.62	tff('81', plain, ~ (f = (^[Y0 : $o]: $false)),
34.37/34.62	    inference('sat_resolution', [status(thm)], ['77', '78', '79', '80', '51'])).
34.37/34.62	tff('82', plain,
34.37/34.62	    ~
34.37/34.62	    (eps(
34.37/34.62	       (^[Y0 : $i]:
34.37/34.62	          (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	           ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	           ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	      = sk_X5_),
34.37/34.62	    inference('sat_resolution', [status(thm)], ['76', '81'])).
34.37/34.62	tff('83', plain,
34.37/34.62	    eps(
34.37/34.62	      (^[Y0 : $i]:
34.37/34.62	         (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	          ((f = ~) & (Y0 = sk_X3_))|((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	          ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	     != sk_X4_,
34.37/34.62	    inference('cnf', [status(esa)], [zf_stmt_1])).
34.37/34.62	tff('84', plain,
34.37/34.62	    (f = (^[Y0 : $o]: $false)
34.37/34.62	     | eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (($false & (Y0 = sk_X2_))|((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	             ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	             ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	        != sk_X4_),
34.37/34.62	    inference('bool_case_simp', [status(thm)], ['83'])).
34.37/34.62	tff('85', plain,
34.37/34.62	    (f = (^[Y0 : $o]: $false)
34.37/34.62	     | eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	             ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	             ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	        != sk_X4_),
34.37/34.62	    inference('simplify boolean subterms', [status(thm)], ['84'])).
34.37/34.62	tff('86', plain,
34.37/34.62	    ~
34.37/34.62	    (eps(
34.37/34.62	       (^[Y0 : $i]:
34.37/34.62	          (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	           ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	           ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	      = sk_X4_) | 
34.37/34.62	    (f = (^[Y0 : $o]: $false)), inference('split', [status(esa)], ['85'])).
34.37/34.62	tff('87', plain,
34.37/34.62	    ~
34.37/34.62	    (eps(
34.37/34.62	       (^[Y0 : $i]:
34.37/34.62	          (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	           ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	           ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	      = sk_X4_),
34.37/34.62	    inference('sat_resolution', [status(thm)], ['86', '81'])).
34.37/34.62	tff('88', plain,
34.37/34.62	    eps(
34.37/34.62	      (^[Y0 : $i]:
34.37/34.62	         (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	          ((f = ~) & (Y0 = sk_X3_))|((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	          ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	     != sk_X3_,
34.37/34.62	    inference('cnf', [status(esa)], [zf_stmt_1])).
34.37/34.62	tff('89', plain,
34.37/34.62	    (f = (^[Y0 : $o]: $false)
34.37/34.62	     | eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (($false & (Y0 = sk_X2_))|((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	             ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	             ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	        != sk_X3_),
34.37/34.62	    inference('bool_case_simp', [status(thm)], ['88'])).
34.37/34.62	tff('90', plain,
34.37/34.62	    (f = (^[Y0 : $o]: $false)
34.37/34.62	     | eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	             ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	             ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	        != sk_X3_),
34.37/34.62	    inference('simplify boolean subterms', [status(thm)], ['89'])).
34.37/34.62	tff('91', plain,
34.37/34.62	    ~
34.37/34.62	    (eps(
34.37/34.62	       (^[Y0 : $i]:
34.37/34.62	          (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	           ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	           ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	      = sk_X3_) | 
34.37/34.62	    (f = (^[Y0 : $o]: $false)), inference('split', [status(esa)], ['90'])).
34.37/34.62	tff('92', plain,
34.37/34.62	    ~
34.37/34.62	    (eps(
34.37/34.62	       (^[Y0 : $i]:
34.37/34.62	          (((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	           ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	           ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	      = sk_X3_),
34.37/34.62	    inference('sat_resolution', [status(thm)], ['91', '81'])).
34.37/34.62	tff('93', plain, ~ (f = (^[Y0 : $o]: Y0)),
34.37/34.62	    inference('sat_resolution', [status(thm)], ['75', '82', '87', '92'])).
34.37/34.62	tff('94', plain, ((~ '#fsk5' | ~ f($true))) <= (~ (f = (^[Y0 : $o]: Y0))),
34.37/34.62	    inference('bool_case_simp', [status(thm)], ['64'])).
34.37/34.62	tff('95', plain, ~ (f($true)) | ~ ('#fsk5') | (f = (^[Y0 : $o]: Y0)),
34.37/34.62	    inference('split', [status(esa)], ['94'])).
34.37/34.62	tff('96', plain,
34.37/34.62	    (f != (^[Y0 : $o]: $true)
34.37/34.62	     | eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	             ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	             ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|($true & (Y0 = sk_X5_)))))
34.37/34.62	        != sk_X5_),
34.37/34.62	    inference('bool_case_simp', [status(thm)], ['1'])).
34.37/34.62	tff('97', plain,
34.37/34.62	    (f != (^[Y0 : $o]: $true)
34.37/34.62	     | eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	             ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	             ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|(Y0 = sk_X5_))))
34.37/34.62	        != sk_X5_),
34.37/34.62	    inference('simplify boolean subterms', [status(thm)], ['96'])).
34.37/34.62	tff('98', plain, (f != (^[Y0 : $o]: $true)) <= (~ (f = (^[Y0 : $o]: $true))),
34.37/34.62	    inference('split', [status(esa)], ['97'])).
34.37/34.62	tff('99', plain,
34.37/34.62	    (f('#fsk8') != (^[Y0 : $o]: $true)('#fsk8'))
34.37/34.62	      <= (~ (f = (^[Y0 : $o]: $true))),
34.37/34.62	    inference('neg_ext', [status(thm)], ['98'])).
34.37/34.62	tff('100', plain, (~ f('#fsk8')) <= (~ (f = (^[Y0 : $o]: $true))),
34.37/34.62	    inference('lambda-normalize', [status(thm)], ['99'])).
34.37/34.62	tff('101', plain, (('#fsk8' | ~ f($false))) <= (~ (f = (^[Y0 : $o]: $true))),
34.37/34.62	    inference('bool_case_simp', [status(thm)], ['100'])).
34.37/34.62	tff('102', plain, ('#fsk8') | ~ (f($false)) | (f = (^[Y0 : $o]: $true)),
34.37/34.62	    inference('split', [status(esa)], ['101'])).
34.37/34.62	tff('103', plain,
34.37/34.62	    ((~ '#fsk8' | ~ f($true))) <= (~ (f = (^[Y0 : $o]: $true))),
34.37/34.62	    inference('bool_case_simp', [status(thm)], ['100'])).
34.37/34.62	tff('104', plain, ~ (f($true)) | ~ ('#fsk8') | (f = (^[Y0 : $o]: $true)),
34.37/34.62	    inference('split', [status(esa)], ['103'])).
34.37/34.62	tff('105', plain, ~ (f($true)) | ~ (f($false)) | (f = (^[Y0 : $o]: $true)),
34.37/34.62	    inference('sat_resolution', [status(thm)], ['102', '104'])).
34.37/34.62	tff('106', plain,
34.37/34.62	    (f = (^[Y0 : $o]: $true)
34.37/34.62	     | eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	             ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	             ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_))|
34.37/34.62	             ($false & (Y0 = sk_X5_)))))
34.37/34.62	        != sk_X5_),
34.37/34.62	    inference('bool_case_simp', [status(thm)], ['1'])).
34.37/34.62	tff('107', plain,
34.37/34.62	    (f = (^[Y0 : $o]: $true)
34.37/34.62	     | eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	             ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	             ((f = (^[Y1 : $o]: Y1)) & (Y0 = sk_X4_)))))
34.37/34.62	        != sk_X5_),
34.37/34.62	    inference('simplify boolean subterms', [status(thm)], ['106'])).
34.37/34.62	tff('108', plain, (f = (^[Y0 : $o]: $true)) <= ((f = (^[Y0 : $o]: $true))),
34.37/34.62	    inference('split', [status(esa)], ['107'])).
34.37/34.62	tff('109', plain,
34.37/34.62	    (![X1 : $o]: f(X1) = (^[Y0 : $o]: $true)(X1))
34.37/34.62	      <= ((f = (^[Y0 : $o]: $true))),
34.37/34.62	    inference('ho_complete_eq', [status(thm)], ['108'])).
34.37/34.62	tff('110', plain, (![X1 : $o]: f(X1)) <= ((f = (^[Y0 : $o]: $true))),
34.37/34.62	    inference('lambda-normalize', [status(thm)], ['109'])).
34.37/34.62	tff('111', plain, ~ (f = (^[Y0 : $o]: $true)) | ~ (f = (^[Y0 : $o]: $false)),
34.37/34.62	    inference('sup-', [status(thm)], ['110', '50'])).
34.37/34.62	tff('112', plain,
34.37/34.62	    ![X1]:
34.37/34.62	      (~ ((f = (^[Y0 : $o]: $true)) & (X1 = sk_X5_))
34.37/34.62	       | (((f = (^[Y0 : $o]: $false)) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	                  ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X2_))|
34.37/34.62	          ((f = ~) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	                  ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X3_))|
34.37/34.62	          ((f = (^[Y0 : $o]: $true)) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	                  ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X5_)))),
34.37/34.62	    inference('cnf_fool', [status(thm)], ['19'])).
34.37/34.62	tff('113', plain,
34.37/34.62	    ![X1]:
34.37/34.62	      (f != (^[Y0 : $o]: $true)
34.37/34.62	       | X1 != sk_X5_
34.37/34.62	       | (((f = (^[Y0 : $o]: $false)) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	                  ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X2_))|
34.37/34.62	          ((f = ~) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	                  ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X3_))|
34.37/34.62	          ((f = (^[Y0 : $o]: $true)) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	                  ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X5_)))),
34.37/34.62	    inference('cnf_fool', [status(thm)], ['112'])).
34.37/34.62	tff('114', plain,
34.37/34.62	    ((((f = (^[Y0 : $o]: $false)) &
34.37/34.62	       (eps(
34.37/34.62	          (^[Y0 : $i]:
34.37/34.62	             (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	              ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	              ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	        sk_X2_))|
34.37/34.62	      ((f = ~) &
34.37/34.62	       (eps(
34.37/34.62	          (^[Y0 : $i]:
34.37/34.62	             (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	              ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	              ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	        sk_X3_))|
34.37/34.62	      ((f = (^[Y0 : $o]: $true)) &
34.37/34.62	       (eps(
34.37/34.62	          (^[Y0 : $i]:
34.37/34.62	             (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	              ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	              ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	        sk_X5_)))
34.37/34.62	     | f != (^[Y0 : $o]: $true)),
34.37/34.62	    inference('simplify', [status(thm)], ['113'])).
34.37/34.62	tff('115', plain,
34.37/34.62	    (((f = (^[Y0 : $o]: $false)) &
34.37/34.62	      (eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	             ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	             ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	       sk_X2_))
34.37/34.62	     | ((f = ~) &
34.37/34.62	        (eps(
34.37/34.62	           (^[Y0 : $i]:
34.37/34.62	              (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	               ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	               ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	         sk_X3_))
34.37/34.62	     | ((f = (^[Y0 : $o]: $true)) &
34.37/34.62	        (eps(
34.37/34.62	           (^[Y0 : $i]:
34.37/34.62	              (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	               ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	               ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	         sk_X5_))
34.37/34.62	     | f != (^[Y0 : $o]: $true)),
34.37/34.62	    inference('cnf_fool', [status(thm)], ['114'])).
34.37/34.62	tff('116', plain,
34.37/34.62	    (f = (^[Y0 : $o]: $false)
34.37/34.62	     | f != (^[Y0 : $o]: $true)
34.37/34.62	     | ((f = (^[Y0 : $o]: $true)) &
34.37/34.62	        (eps(
34.37/34.62	           (^[Y0 : $i]:
34.37/34.62	              (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	               ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	               ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	         sk_X5_))
34.37/34.62	     | ((f = ~) &
34.37/34.62	        (eps(
34.37/34.62	           (^[Y0 : $i]:
34.37/34.62	              (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	               ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	               ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	         sk_X3_))),
34.37/34.62	    inference('cnf_fool', [status(thm)], ['115'])).
34.37/34.62	tff('117', plain,
34.37/34.62	    (eps(
34.37/34.62	       (^[Y0 : $i]:
34.37/34.62	          (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	           ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	           ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	      = sk_X5_
34.37/34.62	     | ((f = ~) &
34.37/34.62	        (eps(
34.37/34.62	           (^[Y0 : $i]:
34.37/34.62	              (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	               ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	               ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	         sk_X3_))
34.37/34.62	     | f != (^[Y0 : $o]: $true)
34.37/34.62	     | f = (^[Y0 : $o]: $false)),
34.37/34.62	    inference('cnf_fool', [status(thm)], ['116'])).
34.37/34.62	tff('118', plain,
34.37/34.62	    (f = ~
34.37/34.62	     | f = (^[Y0 : $o]: $false)
34.37/34.62	     | f != (^[Y0 : $o]: $true)
34.37/34.62	     | eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	             ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	             ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	        = sk_X5_),
34.37/34.62	    inference('cnf_fool', [status(thm)], ['117'])).
34.37/34.62	tff('119', plain,
34.37/34.62	    ~ (f = (^[Y0 : $o]: $true)) | 
34.37/34.62	    (eps(
34.37/34.62	       (^[Y0 : $i]:
34.37/34.62	          (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	           ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	           ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	      = sk_X5_) | 
34.37/34.62	    (f = ~) | (f = (^[Y0 : $o]: $false)),
34.37/34.62	    inference('split', [status(esa)], ['118'])).
34.37/34.62	tff('120', plain,
34.37/34.62	    ((^[Y0 : $o]: $true) = ~) <= ((f = ~) & (f = (^[Y0 : $o]: $true))),
34.37/34.62	    inference('sup+', [status(thm)], ['108', '38'])).
34.37/34.62	tff('121', plain,
34.37/34.62	    (![X1 : $o]: (^[Y0 : $o]: $true)(X1) = (~ X1))
34.37/34.62	      <= ((f = ~) & (f = (^[Y0 : $o]: $true))),
34.37/34.62	    inference('ho_complete_eq', [status(thm)], ['120'])).
34.37/34.62	tff('122', plain,
34.37/34.62	    (![X1 : $o]: (~ X1)) <= ((f = ~) & (f = (^[Y0 : $o]: $true))),
34.37/34.62	    inference('lambda-normalize', [status(thm)], ['121'])).
34.37/34.62	tff('123', plain,
34.37/34.62	    (![X0 : $o]: ~ X0) <= ((f = ~) & (f = (^[Y0 : $o]: $true))),
34.37/34.62	    inference('cnf_otf', [status(thm)], ['122'])).
34.37/34.62	tff('124', plain, ~ (f = (^[Y0 : $o]: $true)) | ~ (f = ~),
34.37/34.62	    inference('sup+', [status(thm)], ['123', '110'])).
34.37/34.62	tff('125', plain, (![X0 : $o]: (X0 | ~ f(X0))) <= ((f = (^[Y0 : $o]: Y0))),
34.37/34.62	    inference('cnf_otf', [status(thm)], ['46'])).
34.37/34.62	tff('126', plain, (~ f($false)) <= ((f = (^[Y0 : $o]: Y0))),
34.37/34.62	    inference('simplify', [status(thm)], ['125'])).
34.37/34.62	tff('127', plain, ~ (f = (^[Y0 : $o]: $true)) | ~ (f = (^[Y0 : $o]: Y0)),
34.37/34.62	    inference('sup-', [status(thm)], ['110', '126'])).
34.37/34.62	tff('128', plain, ~ (f = (^[Y0 : $o]: $true)) | (f = (^[Y0 : $o]: $false)),
34.37/34.62	    inference('sat_resolution', [status(thm)], ['79', '119', '124', '127'])).
34.37/34.62	tff('129', plain, ~ (f = (^[Y0 : $o]: $true)),
34.37/34.62	    inference('sat_resolution', [status(thm)], ['111', '128'])).
34.37/34.62	tff('130', plain, ~ (f($true)),
34.37/34.62	    inference('sat_resolution', [status(thm)],
34.37/34.62	              ['66', '93', '95', '93', '105', '129'])).
34.37/34.62	tff('131', plain, ~ ('#fsk435'),
34.37/34.62	    inference('sat_resolution', [status(thm)], ['59', '130'])).
34.37/34.62	tff('132', plain, (f($false)),
34.37/34.62	    inference('sat_resolution', [status(thm)], ['57', '131'])).
34.37/34.62	tff('133', plain, ('#fsk6') <= (('#fsk6')),
34.37/34.62	    inference('split', [status(esa)], ['8'])).
34.37/34.62	tff('134', plain, ((f('#fsk6') | ~ '#fsk6')) <= (~ (f = ~)),
34.37/34.62	    inference('cnf_fool', [status(thm)], ['5'])).
34.37/34.62	tff('135', plain, (f('#fsk6')) <= ((f('#fsk6'))),
34.37/34.62	    inference('split', [status(esa)], ['134'])).
34.37/34.62	tff('136', plain, (f($true)) <= ((f('#fsk6')) & ('#fsk6')),
34.37/34.62	    inference('sup+', [status(thm)], ['133', '135'])).
34.37/34.62	tff('137', plain, (~ f($true)) <= (~ (f($true))),
34.37/34.62	    inference('split', [status(esa)], ['103'])).
34.37/34.62	tff('138', plain, ~ ('#fsk6') | ~ (f('#fsk6')) | (f($true)),
34.37/34.62	    inference('sup-', [status(thm)], ['136', '137'])).
34.37/34.62	tff('139', plain, ('#fsk6') | ~ (f('#fsk6')) | (f = ~),
34.37/34.62	    inference('split', [status(esa)], ['6'])).
34.37/34.62	tff('140', plain,
34.37/34.62	    (f = (^[Y0 : $o]: Y0)
34.37/34.62	     | eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	             ((f = ~) & (Y0 = sk_X3_))|($false & (Y0 = sk_X4_))|
34.37/34.62	             ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	        != sk_X3_),
34.37/34.62	    inference('bool_case_simp', [status(thm)], ['88'])).
34.37/34.62	tff('141', plain,
34.37/34.62	    (f = (^[Y0 : $o]: Y0)
34.37/34.62	     | eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	             ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	             ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	        != sk_X3_),
34.37/34.62	    inference('simplify boolean subterms', [status(thm)], ['140'])).
34.37/34.62	tff('142', plain,
34.37/34.62	    ~
34.37/34.62	    (eps(
34.37/34.62	       (^[Y0 : $i]:
34.37/34.62	          (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	           ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	           ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.62	      = sk_X3_) | 
34.37/34.62	    (f = (^[Y0 : $o]: Y0)), inference('split', [status(esa)], ['141'])).
34.37/34.62	tff('143', plain,
34.37/34.62	    (~ = (^[Y0 : $o]: Y0)) <= ((f = (^[Y0 : $o]: Y0)) & (f = ~)),
34.37/34.62	    inference('sup+', [status(thm)], ['38', '44'])).
34.37/34.62	tff('144', plain,
34.37/34.62	    (![X1 : $o]: (~ X1) = (^[Y0 : $o]: Y0)(X1))
34.37/34.62	      <= ((f = (^[Y0 : $o]: Y0)) & (f = ~)),
34.37/34.62	    inference('ho_complete_eq', [status(thm)], ['143'])).
34.37/34.62	tff('145', plain,
34.37/34.62	    (![X1 : $o]: (~ X1) = X1) <= ((f = (^[Y0 : $o]: Y0)) & (f = ~)),
34.37/34.62	    inference('lambda-normalize', [status(thm)], ['144'])).
34.37/34.62	tff('146', plain,
34.37/34.62	    (![X0 : $o]: (X0 | X0)) <= ((f = (^[Y0 : $o]: Y0)) & (f = ~)),
34.37/34.62	    inference('cnf_otf', [status(thm)], ['145'])).
34.37/34.62	tff('147', plain, ~ (f = ~) | ~ (f = (^[Y0 : $o]: Y0)),
34.37/34.62	    inference('simplify', [status(thm)], ['146'])).
34.37/34.62	tff('148', plain,
34.37/34.62	    ![X1]:
34.37/34.62	      (~ ((f = ~) & (X1 = sk_X3_))
34.37/34.62	       | (((f = (^[Y0 : $o]: $false)) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	                  ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X2_))|
34.37/34.62	          ((f = ~) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	                  ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X3_))|
34.37/34.62	          ((f = (^[Y0 : $o]: $true)) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	                  ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X5_)))),
34.37/34.62	    inference('cnf_fool', [status(thm)], ['19'])).
34.37/34.62	tff('149', plain,
34.37/34.62	    ![X1]:
34.37/34.62	      (f != ~
34.37/34.62	       | X1 != sk_X3_
34.37/34.62	       | (((f = (^[Y0 : $o]: $false)) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	                  ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X2_))|
34.37/34.62	          ((f = ~) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	                  ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X3_))|
34.37/34.62	          ((f = (^[Y0 : $o]: $true)) &
34.37/34.62	           (eps(
34.37/34.62	              (^[Y0 : $i]:
34.37/34.62	                 (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	                  ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	                  ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	            sk_X5_)))),
34.37/34.62	    inference('cnf_fool', [status(thm)], ['148'])).
34.37/34.62	tff('150', plain,
34.37/34.62	    ((((f = (^[Y0 : $o]: $false)) &
34.37/34.62	       (eps(
34.37/34.62	          (^[Y0 : $i]:
34.37/34.62	             (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	              ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	              ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	        sk_X2_))|
34.37/34.62	      ((f = ~) &
34.37/34.62	       (eps(
34.37/34.62	          (^[Y0 : $i]:
34.37/34.62	             (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	              ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	              ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	        sk_X3_))|
34.37/34.62	      ((f = (^[Y0 : $o]: $true)) &
34.37/34.62	       (eps(
34.37/34.62	          (^[Y0 : $i]:
34.37/34.62	             (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	              ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	              ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	        sk_X5_)))
34.37/34.62	     | f != ~),
34.37/34.62	    inference('simplify', [status(thm)], ['149'])).
34.37/34.62	tff('151', plain,
34.37/34.62	    (((f = (^[Y0 : $o]: $false)) &
34.37/34.62	      (eps(
34.37/34.62	         (^[Y0 : $i]:
34.37/34.62	            (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	             ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	             ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	       sk_X2_))
34.37/34.62	     | ((f = ~) &
34.37/34.62	        (eps(
34.37/34.62	           (^[Y0 : $i]:
34.37/34.62	              (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	               ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	               ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	         sk_X3_))
34.37/34.62	     | ((f = (^[Y0 : $o]: $true)) &
34.37/34.62	        (eps(
34.37/34.62	           (^[Y0 : $i]:
34.37/34.62	              (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	               ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	               ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	         sk_X5_))
34.37/34.62	     | f != ~),
34.37/34.62	    inference('cnf_fool', [status(thm)], ['150'])).
34.37/34.62	tff('152', plain,
34.37/34.62	    (f = (^[Y0 : $o]: $false)
34.37/34.62	     | f != ~
34.37/34.62	     | ((f = (^[Y0 : $o]: $true)) &
34.37/34.62	        (eps(
34.37/34.62	           (^[Y0 : $i]:
34.37/34.62	              (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	               ((f = ~) & (Y0 = sk_X3_))|
34.37/34.62	               ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.62	         sk_X5_))
34.37/34.62	     | ((f = ~) &
34.37/34.62	        (eps(
34.37/34.62	           (^[Y0 : $i]:
34.37/34.62	              (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.62	               ((f = ~) & (Y0 = sk_X3_))|
34.37/34.63	               ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.63	         sk_X3_))),
34.37/34.63	    inference('cnf_fool', [status(thm)], ['151'])).
34.37/34.63	tff('153', plain,
34.37/34.63	    (f = (^[Y0 : $o]: $true)
34.37/34.63	     | ((f = ~) &
34.37/34.63	        (eps(
34.37/34.63	           (^[Y0 : $i]:
34.37/34.63	              (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.63	               ((f = ~) & (Y0 = sk_X3_))|
34.37/34.63	               ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_))))) =
34.37/34.63	         sk_X3_))
34.37/34.63	     | f != ~
34.37/34.63	     | f = (^[Y0 : $o]: $false)),
34.37/34.63	    inference('cnf_fool', [status(thm)], ['152'])).
34.37/34.63	tff('154', plain,
34.37/34.63	    (eps(
34.37/34.63	       (^[Y0 : $i]:
34.37/34.63	          (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.63	           ((f = ~) & (Y0 = sk_X3_))|
34.37/34.63	           ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.63	      = sk_X3_
34.37/34.63	     | f = (^[Y0 : $o]: $false)
34.37/34.63	     | f != ~
34.37/34.63	     | f = (^[Y0 : $o]: $true)),
34.37/34.63	    inference('cnf_fool', [status(thm)], ['153'])).
34.37/34.63	tff('155', plain,
34.37/34.63	    ~ (f = ~) | 
34.37/34.63	    (eps(
34.37/34.63	       (^[Y0 : $i]:
34.37/34.63	          (((f = (^[Y1 : $o]: $false)) & (Y0 = sk_X2_))|
34.37/34.63	           ((f = ~) & (Y0 = sk_X3_))|
34.37/34.63	           ((f = (^[Y1 : $o]: $true)) & (Y0 = sk_X5_)))))
34.37/34.63	      = sk_X3_) | 
34.37/34.63	    (f = (^[Y0 : $o]: $false)) | (f = (^[Y0 : $o]: $true)),
34.37/34.63	    inference('split', [status(esa)], ['154'])).
34.37/34.63	tff('156', plain, ~ (f = ~),
34.37/34.63	    inference('sat_resolution', [status(thm)],
34.37/34.63	              ['142', '147', '155', '81', '129'])).
34.37/34.63	tff('157', plain, ~ (f('#fsk6')),
34.37/34.63	    inference('sat_resolution', [status(thm)], ['138', '130', '139', '156'])).
34.37/34.63	tff('158', plain, ~ ('#fsk6') | (f('#fsk6')) | (f = ~),
34.37/34.63	    inference('split', [status(esa)], ['134'])).
34.37/34.63	tff('159', plain, ~ ('#fsk6'),
34.37/34.63	    inference('sat_resolution', [status(thm)], ['158', '156', '157'])).
34.37/34.63	tff('160', plain, $false,
34.37/34.63	    inference('sat_resolution', [status(thm)], ['9', '132', '157', '159'])).
34.37/34.63	
34.37/34.63	% SZS output end Refutation
34.37/34.63	% Zipperpin 1.5 exiting
34.37/34.63	EOF