0.00/0.03	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.04	% Command    : do_CVC4 %s
0.03/0.24	% Computer   : n012.star.cs.uiowa.edu
0.03/0.24	% Model      : x86_64 x86_64
0.03/0.24	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.03/0.24	% Memory     : 32218.625MB
0.03/0.24	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.03/0.24	% CPULimit   : 300
0.03/0.24	% DateTime   : Sat Jul 14 04:19:55 CDT 2018
0.03/0.24	% CPUTime    : 
0.03/0.28	%----Proving without arithmetic mode
0.03/0.28	------- cvc4-fof casc j9 : /export/starexec/sandbox2/benchmark/theBenchmark.p at ...
0.03/0.28	--- Run --decision=internal --simplification=none --no-inst-no-entail --no-quant-cf --full-saturate-quant at 20...
20.85/27.48	--- Run --no-e-matching --full-saturate-quant at 20...
21.37/28.01	% SZS status Theorem for theBenchmark
21.37/28.01	% SZS output start Proof for theBenchmark
21.37/28.01	(skolem (forall ((X $$unsorted)) (or (not (inductive X)) (not (forall ((Y $$unsorted)) (or (not (inductive Y)) (subclass X Y)) )) (not (member X universal_class))) )
21.37/28.01	  ( skv_1 )
21.37/28.01	)
21.37/28.01	(skolem (forall ((XF $$unsorted)) (or (not (function XF)) (not (forall ((Y $$unsorted)) (or (not (member Y universal_class)) (member (apply XF Y) Y) (= null_class Y)) ))) )
21.37/28.01	  ( skv_2 )
21.37/28.01	)
21.37/28.01	(skolem (forall ((U $$unsorted)) (not (member U universal_class)) )
21.37/28.01	  ( skv_3 )
21.37/28.01	)
21.37/28.01	(skolem (forall ((U $$unsorted)) (or (not (disjoint U universal_class)) (not (member U universal_class))) )
21.37/28.01	  ( skv_4 )
21.37/28.01	)
21.37/28.01	(skolem (forall ((Z $$unsorted)) (not (member Z (cross_product universal_class universal_class))) )
21.37/28.01	  ( skv_5 )
21.37/28.01	)
21.37/28.01	(skolem (forall ((U $$unsorted)) (or (not (member U (cross_product universal_class universal_class))) (not (member U universal_class))) )
21.37/28.01	  ( skv_6 )
21.37/28.01	)
21.37/28.01	(skolem (let ((_let_0 (cross_product universal_class universal_class))) (forall ((U $$unsorted)) (or (not (disjoint U _let_0)) (not (member U _let_0)) (not (member U universal_class))) ))
21.37/28.01	  ( skv_7 )
21.37/28.01	)
21.37/28.01	(skolem (forall ((Z $$unsorted)) (not (member Z element_relation)) )
21.37/28.01	  ( skv_8 )
21.37/28.01	)
21.37/28.01	(skolem (forall ((U $$unsorted)) (or (not (member U universal_class)) (member U null_class)) )
21.37/28.01	  ( skv_9 )
21.37/28.01	)
21.37/28.01	(skolem (forall ((U $$unsorted)) (or (not (disjoint U element_relation)) (not (member U element_relation)) (not (member U universal_class))) )
21.37/28.01	  ( skv_10 )
21.37/28.01	)
21.37/28.01	(skolem (forall ((Z $$unsorted)) (not (member Z successor_relation)) )
21.37/28.01	  ( skv_11 )
21.37/28.01	)
21.37/28.01	(skolem (forall ((U $$unsorted)) (or (not (disjoint U successor_relation)) (not (member U successor_relation)) (not (member U universal_class))) )
21.37/28.01	  ( skv_12 )
21.37/28.01	)
21.37/28.01	(skolem (forall ((Z $$unsorted)) (not (member Z skv_1)) )
21.37/28.01	  ( skv_13 )
21.37/28.01	)
21.37/28.01	(skolem (forall ((U $$unsorted)) (or (not (member U null_class)) (member U (cross_product universal_class universal_class))) )
21.37/28.01	  ( skv_14 )
21.37/28.01	)
21.37/28.01	(skolem (forall ((U $$unsorted)) (or (not (member U element_relation)) (not (member U universal_class))) )
21.37/28.01	  ( skv_15 )
21.37/28.01	)
21.37/28.01	(skolem (forall ((U $$unsorted)) (or (not (disjoint U skv_1)) (not (member U skv_1)) (not (member U universal_class))) )
21.37/28.01	  ( skv_16 )
21.37/28.01	)
21.37/28.01	(skolem (forall ((Z $$unsorted)) (not (member Z skv_2)) )
21.37/28.01	  ( skv_17 )
21.37/28.01	)
21.37/28.01	(skolem (forall ((U $$unsorted)) (or (not (member U universal_class)) (member U (cross_product universal_class universal_class))) )
21.37/28.01	  ( skv_18 )
21.37/28.01	)
21.37/28.01	(skolem (forall ((U $$unsorted)) (or (not (member U element_relation)) (not (member U (cross_product universal_class universal_class)))) )
21.37/28.01	  ( skv_19 )
21.37/28.01	)
21.37/28.01	(skolem (forall ((U $$unsorted)) (or (not (disjoint U skv_2)) (not (member U skv_2)) (not (member U universal_class))) )
21.37/28.01	  ( skv_20 )
21.37/28.01	)
21.37/28.01	(skolem (forall ((Y $$unsorted)) (or (not (member null_class Y)) (not (member Y universal_class))) )
21.37/28.01	  ( skv_21 )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((X $$unsorted)) (not (member X null_class)) )
21.37/28.01	  ( null_class )
21.37/28.01	  ( universal_class )
21.37/28.01	  ( (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product (cross_product universal_class universal_class) universal_class) )
21.37/28.01	  ( successor_relation )
21.37/28.01	  ( element_relation )
21.37/28.01	  ( identity_relation )
21.37/28.01	  ( skv_1 )
21.37/28.01	  ( skv_5 )
21.37/28.01	  ( skv_8 )
21.37/28.01	  ( skv_11 )
21.37/28.01	  ( skv_14 )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (or (member Z Y) (member Z X)) (member Z (union X Y))) )
21.37/28.01	  ( null_class, null_class, null_class )
21.37/28.01	  ( null_class, null_class, universal_class )
21.37/28.01	  ( null_class, universal_class, null_class )
21.37/28.01	  ( null_class, universal_class, universal_class )
21.37/28.01	  ( universal_class, null_class, null_class )
21.37/28.01	  ( universal_class, null_class, universal_class )
21.37/28.01	  ( universal_class, universal_class, null_class )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((X $$unsorted)) (subclass X universal_class) )
21.37/28.01	  ( null_class )
21.37/28.01	  ( universal_class )
21.37/28.01	  ( (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product (cross_product universal_class universal_class) universal_class) )
21.37/28.01	  ( successor_relation )
21.37/28.01	  ( element_relation )
21.37/28.01	  ( identity_relation )
21.37/28.01	  ( (image successor_relation universal_class) )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((X $$unsorted)) (subclass (flip X) (cross_product (cross_product universal_class universal_class) universal_class)) )
21.37/28.01	  ( null_class )
21.37/28.01	  ( universal_class )
21.37/28.01	  ( (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product (cross_product universal_class universal_class) universal_class) )
21.37/28.01	  ( successor_relation )
21.37/28.01	  ( element_relation )
21.37/28.01	  ( identity_relation )
21.37/28.01	)
21.37/28.01	(instantiation (let ((_let_0 (ordered_pair (ordered_pair U V) W))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (= (member _let_0 (flip X)) (and (member _let_0 (cross_product (cross_product universal_class universal_class) universal_class)) (member (ordered_pair (ordered_pair V U) W) X))) ))
21.37/28.01	  ( null_class, null_class, null_class, null_class )
21.37/28.01	  ( null_class, null_class, null_class, universal_class )
21.37/28.01	  ( null_class, null_class, universal_class, null_class )
21.37/28.01	  ( null_class, null_class, universal_class, universal_class )
21.37/28.01	  ( null_class, universal_class, null_class, null_class )
21.37/28.01	  ( null_class, universal_class, null_class, universal_class )
21.37/28.01	  ( null_class, universal_class, universal_class, null_class )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((X $$unsorted)) (= (inductive X) (and (subclass (image successor_relation X) X) (member null_class X))) )
21.37/28.01	  ( null_class )
21.37/28.01	  ( universal_class )
21.37/28.01	  ( (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product (cross_product universal_class universal_class) universal_class) )
21.37/28.01	  ( successor_relation )
21.37/28.01	  ( element_relation )
21.37/28.01	  ( identity_relation )
21.37/28.01	  ( skv_1 )
21.37/28.01	)
21.37/28.01	(instantiation (let ((_let_0 (ordered_pair (ordered_pair U V) W))) (forall ((X $$unsorted) (U $$unsorted) (V $$unsorted) (W $$unsorted)) (= (and (member _let_0 (cross_product (cross_product universal_class universal_class) universal_class)) (member (ordered_pair (ordered_pair V W) U) X)) (member _let_0 (rotate X))) ))
21.37/28.01	  ( null_class, null_class, null_class, null_class )
21.37/28.01	  ( null_class, null_class, null_class, universal_class )
21.37/28.01	  ( null_class, null_class, universal_class, null_class )
21.37/28.01	  ( null_class, null_class, universal_class, universal_class )
21.37/28.01	  ( null_class, universal_class, null_class, null_class )
21.37/28.01	  ( null_class, universal_class, null_class, universal_class )
21.37/28.01	  ( null_class, universal_class, universal_class, null_class )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (and (member V Y) (member U X)) (member (ordered_pair U V) (cross_product X Y))) )
21.37/28.01	  ( null_class, null_class, null_class, null_class )
21.37/28.01	  ( null_class, null_class, null_class, universal_class )
21.37/28.01	  ( null_class, null_class, universal_class, null_class )
21.37/28.01	  ( null_class, null_class, universal_class, universal_class )
21.37/28.01	  ( null_class, universal_class, null_class, null_class )
21.37/28.01	  ( null_class, universal_class, null_class, universal_class )
21.37/28.01	  ( null_class, universal_class, universal_class, null_class )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((X $$unsorted) (Y $$unsorted)) (member (unordered_pair X Y) universal_class) )
21.37/28.01	  ( null_class, null_class )
21.37/28.01	  ( null_class, universal_class )
21.37/28.01	  ( null_class, (cross_product universal_class universal_class) )
21.37/28.01	  ( universal_class, null_class )
21.37/28.01	  ( universal_class, universal_class )
21.37/28.01	  ( universal_class, (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product universal_class universal_class), null_class )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((X $$unsorted)) (subclass (rotate X) (cross_product (cross_product universal_class universal_class) universal_class)) )
21.37/28.01	  ( null_class )
21.37/28.01	  ( universal_class )
21.37/28.01	  ( (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product (cross_product universal_class universal_class) universal_class) )
21.37/28.01	  ( successor_relation )
21.37/28.01	  ( element_relation )
21.37/28.01	  ( identity_relation )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((X $$unsorted) (Z $$unsorted)) (= (member Z (complement X)) (and (member Z universal_class) (not (member Z X)))) )
21.37/28.01	  ( null_class, null_class )
21.37/28.01	  ( null_class, universal_class )
21.37/28.01	  ( null_class, (cross_product universal_class universal_class) )
21.37/28.01	  ( universal_class, null_class )
21.37/28.01	  ( universal_class, universal_class )
21.37/28.01	  ( universal_class, (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product universal_class universal_class), null_class )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((XR $$unsorted) (YR $$unsorted) (U $$unsorted) (V $$unsorted)) (= (and (member V (image YR (image XR (singleton U)))) (member U universal_class)) (member (ordered_pair U V) (compose YR XR))) )
21.37/28.01	  ( null_class, null_class, null_class, null_class )
21.37/28.01	  ( null_class, null_class, null_class, universal_class )
21.37/28.01	  ( null_class, null_class, universal_class, null_class )
21.37/28.01	  ( null_class, null_class, universal_class, universal_class )
21.37/28.01	  ( null_class, universal_class, null_class, null_class )
21.37/28.01	  ( null_class, universal_class, null_class, universal_class )
21.37/28.01	  ( null_class, universal_class, universal_class, null_class )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (and (member Z X) (member Z Y)) (member Z (intersection X Y))) )
21.37/28.01	  ( null_class, null_class, null_class )
21.37/28.01	  ( null_class, null_class, universal_class )
21.37/28.01	  ( null_class, universal_class, null_class )
21.37/28.01	  ( null_class, universal_class, universal_class )
21.37/28.01	  ( universal_class, null_class, null_class )
21.37/28.01	  ( universal_class, null_class, universal_class )
21.37/28.01	  ( universal_class, universal_class, null_class )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((X $$unsorted) (Y $$unsorted)) (= (and (member Y universal_class) (member X Y)) (member (ordered_pair X Y) element_relation)) )
21.37/28.01	  ( null_class, null_class )
21.37/28.01	  ( null_class, universal_class )
21.37/28.01	  ( null_class, (cross_product universal_class universal_class) )
21.37/28.01	  ( universal_class, null_class )
21.37/28.01	  ( universal_class, universal_class )
21.37/28.01	  ( universal_class, (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product universal_class universal_class), null_class )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((XF $$unsorted)) (= (and (subclass XF (cross_product universal_class universal_class)) (subclass (compose XF (inverse XF)) identity_relation)) (function XF)) )
21.37/28.01	  ( null_class )
21.37/28.01	  ( universal_class )
21.37/28.01	  ( (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product (cross_product universal_class universal_class) universal_class) )
21.37/28.01	  ( successor_relation )
21.37/28.01	  ( element_relation )
21.37/28.01	  ( identity_relation )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((U $$unsorted) (X $$unsorted)) (= (member U (power_class X)) (and (subclass U X) (member U universal_class))) )
21.37/28.01	  ( null_class, null_class )
21.37/28.01	  ( null_class, universal_class )
21.37/28.01	  ( null_class, (cross_product universal_class universal_class) )
21.37/28.01	  ( universal_class, null_class )
21.37/28.01	  ( universal_class, universal_class )
21.37/28.01	  ( universal_class, (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product universal_class universal_class), null_class )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((X $$unsorted) (Y $$unsorted)) (= (and (subclass X Y) (subclass Y X)) (= X Y)) )
21.37/28.01	  ( null_class, null_class )
21.37/28.01	  ( null_class, universal_class )
21.37/28.01	  ( null_class, (cross_product universal_class universal_class) )
21.37/28.01	  ( null_class, (cross_product (cross_product universal_class universal_class) universal_class) )
21.37/28.01	  ( universal_class, (cross_product universal_class universal_class) )
21.37/28.01	  ( universal_class, (cross_product (cross_product universal_class universal_class) universal_class) )
21.37/28.01	  ( (cross_product universal_class universal_class), (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product universal_class universal_class), (cross_product (cross_product universal_class universal_class) universal_class) )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((XR $$unsorted) (YR $$unsorted)) (subclass (compose YR XR) (cross_product universal_class universal_class)) )
21.37/28.01	  ( null_class, null_class )
21.37/28.01	  ( null_class, universal_class )
21.37/28.01	  ( null_class, (cross_product universal_class universal_class) )
21.37/28.01	  ( universal_class, null_class )
21.37/28.01	  ( universal_class, universal_class )
21.37/28.01	  ( universal_class, (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product universal_class universal_class), null_class )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((X $$unsorted)) (= (union X (singleton X)) (successor X)) )
21.37/28.01	  ( null_class )
21.37/28.01	  ( universal_class )
21.37/28.01	  ( (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product (cross_product universal_class universal_class) universal_class) )
21.37/28.01	  ( successor_relation )
21.37/28.01	  ( element_relation )
21.37/28.01	  ( identity_relation )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (and (member U universal_class) (or (= U X) (= U Y))) (member U (unordered_pair X Y))) )
21.37/28.01	  ( null_class, null_class, null_class )
21.37/28.01	  ( null_class, null_class, universal_class )
21.37/28.01	  ( null_class, universal_class, null_class )
21.37/28.01	  ( null_class, universal_class, universal_class )
21.37/28.01	  ( universal_class, null_class, null_class )
21.37/28.01	  ( universal_class, null_class, universal_class )
21.37/28.01	  ( universal_class, universal_class, null_class )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((X $$unsorted) (Y $$unsorted)) (= (unordered_pair (singleton X) (unordered_pair X (singleton Y))) (ordered_pair X Y)) )
21.37/28.01	  ( null_class, null_class )
21.37/28.01	  ( null_class, universal_class )
21.37/28.01	  ( null_class, (cross_product universal_class universal_class) )
21.37/28.01	  ( universal_class, null_class )
21.37/28.01	  ( universal_class, universal_class )
21.37/28.01	  ( universal_class, (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product universal_class universal_class), null_class )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (member Z (cross_product X Y))) (= Z (ordered_pair (first Z) (second Z)))) )
21.37/28.01	  ( null_class, null_class, null_class )
21.37/28.01	  ( null_class, null_class, universal_class )
21.37/28.01	  ( null_class, null_class, (cross_product universal_class universal_class) )
21.37/28.01	  ( null_class, universal_class, null_class )
21.37/28.01	  ( null_class, universal_class, universal_class )
21.37/28.01	  ( universal_class, null_class, null_class )
21.37/28.01	  ( universal_class, null_class, universal_class )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((X $$unsorted)) (= (unordered_pair X X) (singleton X)) )
21.37/28.01	  ( null_class )
21.37/28.01	  ( universal_class )
21.37/28.01	  ( (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product (cross_product universal_class universal_class) universal_class) )
21.37/28.01	  ( successor_relation )
21.37/28.01	  ( element_relation )
21.37/28.01	  ( identity_relation )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((X $$unsorted) (Y $$unsorted)) (= (subclass X Y) (forall ((U $$unsorted)) (or (not (member U X)) (member U Y)) )) )
21.37/28.01	  ( null_class, null_class )
21.37/28.01	  ( null_class, universal_class )
21.37/28.01	  ( null_class, (cross_product universal_class universal_class) )
21.37/28.01	  ( universal_class, null_class )
21.37/28.01	  ( universal_class, universal_class )
21.37/28.01	  ( universal_class, (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product universal_class universal_class), null_class )
21.37/28.01	  ( (cross_product universal_class universal_class), universal_class )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((X $$unsorted) (Y $$unsorted)) (= (and (member Y universal_class) (= Y (successor X)) (member X universal_class)) (member (ordered_pair X Y) successor_relation)) )
21.37/28.01	  ( null_class, null_class )
21.37/28.01	  ( null_class, universal_class )
21.37/28.01	  ( null_class, (cross_product universal_class universal_class) )
21.37/28.01	  ( universal_class, null_class )
21.37/28.01	  ( universal_class, universal_class )
21.37/28.01	  ( universal_class, (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product universal_class universal_class), null_class )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((X $$unsorted) (XF $$unsorted)) (or (not (function XF)) (not (member X universal_class)) (member (image XF X) universal_class)) )
21.37/28.01	  ( null_class, null_class )
21.37/28.01	  ( (cross_product universal_class universal_class), universal_class )
21.37/28.01	  ( (cross_product (cross_product universal_class universal_class) universal_class), (cross_product universal_class universal_class) )
21.37/28.01	  ( successor_relation, (cross_product (cross_product universal_class universal_class) universal_class) )
21.37/28.01	  ( element_relation, successor_relation )
21.37/28.01	  ( identity_relation, element_relation )
21.37/28.01	  ( skv_1, identity_relation )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((X $$unsorted) (XR $$unsorted) (Y $$unsorted)) (= (restrict XR X Y) (intersection XR (cross_product X Y))) )
21.37/28.01	  ( null_class, null_class, null_class )
21.37/28.01	  ( null_class, null_class, universal_class )
21.37/28.01	  ( null_class, universal_class, null_class )
21.37/28.01	  ( null_class, universal_class, universal_class )
21.37/28.01	  ( universal_class, null_class, null_class )
21.37/28.01	  ( universal_class, null_class, universal_class )
21.37/28.01	  ( universal_class, universal_class, null_class )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((X $$unsorted)) (or (not (member X universal_class)) (member (sum_class X) universal_class)) )
21.37/28.01	  ( null_class )
21.37/28.01	  ( (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product (cross_product universal_class universal_class) universal_class) )
21.37/28.01	  ( successor_relation )
21.37/28.01	  ( element_relation )
21.37/28.01	  ( identity_relation )
21.37/28.01	  ( skv_1 )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((U $$unsorted)) (or (not (member U universal_class)) (member (power_class U) universal_class)) )
21.37/28.01	  ( null_class )
21.37/28.01	  ( (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product (cross_product universal_class universal_class) universal_class) )
21.37/28.01	  ( successor_relation )
21.37/28.01	  ( element_relation )
21.37/28.01	  ( identity_relation )
21.37/28.01	  ( skv_1 )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((X $$unsorted) (Z $$unsorted)) (= (and (member Z universal_class) (not (= null_class (restrict X (singleton Z) universal_class)))) (member Z (domain_of X))) )
21.37/28.01	  ( null_class, null_class )
21.37/28.01	  ( null_class, universal_class )
21.37/28.01	  ( null_class, (cross_product universal_class universal_class) )
21.37/28.01	  ( universal_class, null_class )
21.37/28.01	  ( universal_class, universal_class )
21.37/28.01	  ( universal_class, (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product universal_class universal_class), null_class )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((Z $$unsorted)) (= (range_of Z) (domain_of (inverse Z))) )
21.37/28.01	  ( null_class )
21.37/28.01	  ( universal_class )
21.37/28.01	  ( (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product (cross_product universal_class universal_class) universal_class) )
21.37/28.01	  ( successor_relation )
21.37/28.01	  ( element_relation )
21.37/28.01	  ( identity_relation )
21.37/28.01	)
21.37/28.01	(instantiation (let ((_let_0 (ordered_pair X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (member Y universal_class)) (not (member X universal_class)) (and (= X (first _let_0)) (= Y (second _let_0)))) ))
21.37/28.01	  ( null_class, null_class )
21.37/28.01	  ( (cross_product universal_class universal_class), (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product (cross_product universal_class universal_class) universal_class), (cross_product (cross_product universal_class universal_class) universal_class) )
21.37/28.01	  ( successor_relation, successor_relation )
21.37/28.01	  ( element_relation, element_relation )
21.37/28.01	  ( identity_relation, identity_relation )
21.37/28.01	  ( skv_1, skv_1 )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((Y $$unsorted)) (= (domain_of (flip (cross_product Y universal_class))) (inverse Y)) )
21.37/28.01	  ( null_class )
21.37/28.01	  ( universal_class )
21.37/28.01	  ( (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product (cross_product universal_class universal_class) universal_class) )
21.37/28.01	  ( successor_relation )
21.37/28.01	  ( element_relation )
21.37/28.01	  ( identity_relation )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((X $$unsorted) (XR $$unsorted)) (= (range_of (restrict XR X universal_class)) (image XR X)) )
21.37/28.01	  ( null_class, null_class )
21.37/28.01	  ( null_class, universal_class )
21.37/28.01	  ( null_class, (cross_product universal_class universal_class) )
21.37/28.01	  ( universal_class, null_class )
21.37/28.01	  ( universal_class, universal_class )
21.37/28.01	  ( universal_class, (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product universal_class universal_class), null_class )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((U $$unsorted) (X $$unsorted)) (= (member U (sum_class X)) (not (forall ((Y $$unsorted)) (or (not (member U Y)) (not (member Y X))) ))) )
21.37/28.01	  ( null_class, null_class )
21.37/28.01	  ( null_class, universal_class )
21.37/28.01	  ( null_class, (cross_product universal_class universal_class) )
21.37/28.01	  ( universal_class, null_class )
21.37/28.01	  ( universal_class, universal_class )
21.37/28.01	  ( universal_class, (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product universal_class universal_class), null_class )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((Z $$unsorted)) (= (not (forall ((X $$unsorted)) (or (not (member X universal_class)) (not (= Z (ordered_pair X X)))) )) (member Z identity_relation)) )
21.37/28.01	  ( null_class )
21.37/28.01	  ( universal_class )
21.37/28.01	  ( (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product (cross_product universal_class universal_class) universal_class) )
21.37/28.01	  ( successor_relation )
21.37/28.01	  ( element_relation )
21.37/28.01	  ( identity_relation )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((X $$unsorted)) (or (= null_class X) (not (forall ((U $$unsorted)) (or (not (disjoint U X)) (not (member U X)) (not (member U universal_class))) ))) )
21.37/28.01	  ( universal_class )
21.37/28.01	  ( (cross_product universal_class universal_class) )
21.37/28.01	  ( successor_relation )
21.37/28.01	  ( element_relation )
21.37/28.01	  ( skv_1 )
21.37/28.01	  ( skv_2 )
21.37/28.01	  ( (successor null_class) )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((XF $$unsorted) (Y $$unsorted)) (= (apply XF Y) (sum_class (image XF (singleton Y)))) )
21.37/28.01	  ( null_class, null_class )
21.37/28.01	  ( null_class, universal_class )
21.37/28.01	  ( null_class, (cross_product universal_class universal_class) )
21.37/28.01	  ( universal_class, null_class )
21.37/28.01	  ( universal_class, universal_class )
21.37/28.01	  ( universal_class, (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product universal_class universal_class), null_class )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((X $$unsorted) (Y $$unsorted)) (= (forall ((U $$unsorted)) (or (not (member U Y)) (not (member U X))) ) (disjoint X Y)) )
21.37/28.01	  ( universal_class, universal_class )
21.37/28.01	  ( universal_class, (cross_product universal_class universal_class) )
21.37/28.01	  ( universal_class, element_relation )
21.37/28.01	  ( (cross_product universal_class universal_class), universal_class )
21.37/28.01	  ( (cross_product universal_class universal_class), (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product universal_class universal_class), element_relation )
21.37/28.01	  ( element_relation, universal_class )
21.37/28.01	  ( skv_4, universal_class )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((X $$unsorted)) (not (forall ((Z $$unsorted)) (not (member Z X)) )) )
21.37/28.01	  ( null_class )
21.37/28.01	  ( universal_class )
21.37/28.01	  ( (cross_product universal_class universal_class) )
21.37/28.01	  ( successor_relation )
21.37/28.01	  ( element_relation )
21.37/28.01	  ( skv_1 )
21.37/28.01	  ( skv_2 )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((Y $$unsorted)) (or (not (inductive Y)) (subclass skv_1 Y)) )
21.37/28.01	  ( null_class )
21.37/28.01	  ( universal_class )
21.37/28.01	  ( (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product (cross_product universal_class universal_class) universal_class) )
21.37/28.01	  ( successor_relation )
21.37/28.01	  ( element_relation )
21.37/28.01	  ( identity_relation )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((Y $$unsorted)) (or (not (member Y universal_class)) (member (apply skv_2 Y) Y) (= null_class Y)) )
21.37/28.01	  ( null_class )
21.37/28.01	  ( universal_class )
21.37/28.01	  ( (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product (cross_product universal_class universal_class) universal_class) )
21.37/28.01	  ( successor_relation )
21.37/28.01	  ( element_relation )
21.37/28.01	  ( identity_relation )
21.37/28.01	  ( skv_1 )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((Y $$unsorted)) (or (not (member null_class Y)) (not (member Y null_class))) )
21.37/28.01	  ( (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product (cross_product universal_class universal_class) universal_class) )
21.37/28.01	  ( successor_relation )
21.37/28.01	  ( element_relation )
21.37/28.01	  ( skv_2 )
21.37/28.01	  ( (image successor_relation skv_1) )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((X $$unsorted)) (or (not (member X universal_class)) (not (= null_class (ordered_pair X X)))) )
21.37/28.01	  ( (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product (cross_product universal_class universal_class) universal_class) )
21.37/28.01	  ( successor_relation )
21.37/28.01	  ( element_relation )
21.37/28.01	  ( identity_relation )
21.37/28.01	  ( skv_1 )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((U $$unsorted)) (or (not (member U universal_class)) (not (member U skv_4))) )
21.37/28.01	  ( (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product (cross_product universal_class universal_class) universal_class) )
21.37/28.01	  ( successor_relation )
21.37/28.01	  ( element_relation )
21.37/28.01	  ( identity_relation )
21.37/28.01	  ( skv_1 )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((U $$unsorted)) (or (not (member U null_class)) (member U universal_class)) )
21.37/28.01	  ( (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product (cross_product universal_class universal_class) universal_class) )
21.37/28.01	  ( successor_relation )
21.37/28.01	  ( element_relation )
21.37/28.01	  ( identity_relation )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((Y $$unsorted)) (or (not (member null_class Y)) (not (member Y universal_class))) )
21.37/28.01	  ( (cross_product (cross_product universal_class universal_class) universal_class) )
21.37/28.01	  ( successor_relation )
21.37/28.01	  ( element_relation )
21.37/28.01	  ( skv_1 )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((X $$unsorted)) (or (not (member X universal_class)) (not (= universal_class (ordered_pair X X)))) )
21.37/28.01	  ( (cross_product (cross_product universal_class universal_class) universal_class) )
21.37/28.01	  ( successor_relation )
21.37/28.01	  ( element_relation )
21.37/28.01	  ( identity_relation )
21.37/28.01	  ( skv_1 )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((Y $$unsorted)) (or (not (member universal_class Y)) (not (member Y null_class))) )
21.37/28.01	  ( (cross_product (cross_product universal_class universal_class) universal_class) )
21.37/28.01	  ( successor_relation )
21.37/28.01	  ( skv_2 )
21.37/28.01	  ( (image successor_relation skv_1) )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((X $$unsorted)) (or (not (member X universal_class)) (not (= (cross_product universal_class universal_class) (ordered_pair X X)))) )
21.37/28.01	  ( successor_relation )
21.37/28.01	  ( element_relation )
21.37/28.01	  ( identity_relation )
21.37/28.01	  ( skv_1 )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((U $$unsorted)) (or (not (member U (cross_product universal_class universal_class))) (member U universal_class)) )
21.37/28.01	  ( universal_class )
21.37/28.01	  ( (cross_product universal_class universal_class) )
21.37/28.01	  ( (cross_product (cross_product universal_class universal_class) universal_class) )
21.37/28.01	  ( successor_relation )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((Y $$unsorted)) (or (not (member universal_class Y)) (not (member Y universal_class))) )
21.37/28.01	  ( element_relation )
21.37/28.01	  ( skv_1 )
21.37/28.01	  ( (image successor_relation skv_1) )
21.37/28.01	)
21.37/28.01	(instantiation (forall ((X $$unsorted)) (or (not (member X universal_class)) (not (= (cross_product (cross_product universal_class universal_class) universal_class) (ordered_pair X X)))) )
21.37/28.01	  ( element_relation )
21.37/28.01	  ( identity_relation )
21.37/28.01	  ( skv_1 )
21.37/28.02	)
21.37/28.02	(instantiation (forall ((U $$unsorted)) (or (not (member U null_class)) (member U (cross_product universal_class universal_class))) )
21.37/28.02	  ( element_relation )
21.37/28.02	  ( identity_relation )
21.37/28.02	)
21.37/28.02	(instantiation (forall ((Y $$unsorted)) (or (not (member null_class Y)) (not (member Y (cross_product universal_class universal_class)))) )
21.37/28.02	  ( skv_1 )
21.37/28.02	  ( (image successor_relation skv_1) )
21.37/28.02	)
21.37/28.02	(instantiation (forall ((X $$unsorted)) (or (not (member X universal_class)) (not (= successor_relation (ordered_pair X X)))) )
21.37/28.02	  ( identity_relation )
21.37/28.02	  ( skv_1 )
21.37/28.02	)
21.37/28.02	(instantiation (forall ((Y $$unsorted)) (or (not (member universal_class Y)) (not (member Y (cross_product universal_class universal_class)))) )
21.37/28.02	  ( (image successor_relation skv_1) )
21.37/28.02	)
21.37/28.02	(instantiation (forall ((X $$unsorted)) (or (not (member X universal_class)) (not (= element_relation (ordered_pair X X)))) )
21.37/28.02	  ( skv_1 )
21.37/28.02	)
21.37/28.02	% SZS output end Proof for theBenchmark
21.37/28.02	EOF