%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET214-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n005.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed May 29 17:44:31 EDT 2024

% Result   : Unsatisfiable 1.06s 1.28s
% Output   : Proof 1.06s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SET214-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.12/0.15  % Command    : do_cvc5 %s %d
% 0.15/0.35  % Computer : n005.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Tue May 28 11:24:54 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.21/0.52  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.53  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.06/1.28  % SZS status Unsatisfiable for /export/starexec/sandbox2/tmp/tmp.YKj5FEdMQ5/cvc5---1.0.5_31398.smt2
% 1.06/1.28  % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.YKj5FEdMQ5/cvc5---1.0.5_31398.smt2
% 1.06/1.29  (assume a0 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y))))
% 1.06/1.29  (assume a1 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y))))
% 1.06/1.29  (assume a2 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (tptp.subclass X Y))))
% 1.06/1.29  (assume a3 (forall ((X $$unsorted)) (tptp.subclass X tptp.universal_class)))
% 1.06/1.29  (assume a4 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.subclass X Y))))
% 1.06/1.29  (assume a5 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.subclass Y X))))
% 1.06/1.29  (assume a6 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.subclass Y X)) (= X Y))))
% 1.06/1.29  (assume a7 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))))
% 1.06/1.29  (assume a8 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))))
% 1.06/1.29  (assume a9 (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (tptp.member Y (tptp.unordered_pair X Y)))))
% 1.06/1.29  (assume a10 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)))
% 1.06/1.29  (assume a11 (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))))
% 1.06/1.29  (assume a12 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))))
% 1.06/1.29  (assume a13 (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member U X))))
% 1.06/1.29  (assume a14 (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member V Y))))
% 1.06/1.29  (assume a15 (forall ((U $$unsorted) (X $$unsorted) (V $$unsorted) (Y $$unsorted)) (or (not (tptp.member U X)) (not (tptp.member V Y)) (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y)))))
% 1.06/1.29  (assume a16 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= (tptp.ordered_pair (tptp.first Z) (tptp.second Z)) Z))))
% 1.06/1.29  (assume a17 (tptp.subclass tptp.element_relation (tptp.cross_product tptp.universal_class tptp.universal_class)))
% 1.06/1.29  (assume a18 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.element_relation)) (tptp.member X Y))))
% 1.06/1.29  (assume a19 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (tptp.member X Y)) (tptp.member (tptp.ordered_pair X Y) tptp.element_relation))))
% 1.06/1.29  (assume a20 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X))))
% 1.06/1.29  (assume a21 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z Y))))
% 1.06/1.29  (assume a22 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z X)) (not (tptp.member Z Y)) (tptp.member Z (tptp.intersection X Y)))))
% 1.06/1.29  (assume a23 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.complement X))) (not (tptp.member Z X)))))
% 1.06/1.29  (assume a24 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z tptp.universal_class)) (tptp.member Z (tptp.complement X)) (tptp.member Z X))))
% 1.06/1.29  (assume a25 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.complement (tptp.intersection (tptp.complement X) (tptp.complement Y))) (tptp.union X Y))))
% 1.06/1.29  (assume a26 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection (tptp.complement (tptp.intersection X Y)) (tptp.complement (tptp.intersection (tptp.complement X) (tptp.complement Y)))) (tptp.symmetric_difference X Y))))
% 1.06/1.29  (assume a27 (forall ((Xr $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.intersection Xr (tptp.cross_product X Y)) (tptp.restrict Xr X Y))))
% 1.06/1.29  (assume a28 (forall ((X $$unsorted) (Y $$unsorted) (Xr $$unsorted)) (= (tptp.intersection (tptp.cross_product X Y) Xr) (tptp.restrict Xr X Y))))
% 1.06/1.29  (assume a29 (forall ((X $$unsorted) (Z $$unsorted)) (or (not (= (tptp.restrict X (tptp.singleton Z) tptp.universal_class) tptp.null_class)) (not (tptp.member Z (tptp.domain_of X))))))
% 1.06/1.29  (assume a30 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z tptp.universal_class)) (= (tptp.restrict X (tptp.singleton Z) tptp.universal_class) tptp.null_class) (tptp.member Z (tptp.domain_of X)))))
% 1.06/1.29  (assume a31 (forall ((X $$unsorted)) (tptp.subclass (tptp.rotate X) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))))
% 1.06/1.29  (assume a32 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.rotate X))) (tptp.member (tptp.ordered_pair (tptp.ordered_pair V W) U) X))))
% 1.06/1.29  (assume a33 (forall ((V $$unsorted) (W $$unsorted) (U $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair V W) U) X)) (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.rotate X)))))
% 1.06/1.29  (assume a34 (forall ((X $$unsorted)) (tptp.subclass (tptp.flip X) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))))
% 1.06/1.29  (assume a35 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.flip X))) (tptp.member (tptp.ordered_pair (tptp.ordered_pair V U) W) X))))
% 1.06/1.29  (assume a36 (forall ((V $$unsorted) (U $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair V U) W) X)) (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.flip X)))))
% 1.06/1.29  (assume a37 (forall ((Y $$unsorted)) (= (tptp.domain_of (tptp.flip (tptp.cross_product Y tptp.universal_class))) (tptp.inverse Y))))
% 1.06/1.29  (assume a38 (forall ((Z $$unsorted)) (= (tptp.domain_of (tptp.inverse Z)) (tptp.range_of Z))))
% 1.06/1.29  (assume a39 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.first (tptp.not_subclass_element (tptp.restrict Z X (tptp.singleton Y)) tptp.null_class)) (tptp.domain Z X Y))))
% 1.06/1.29  (assume a40 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.second (tptp.not_subclass_element (tptp.restrict Z (tptp.singleton X) Y) tptp.null_class)) (tptp.range Z X Y))))
% 1.06/1.29  (assume a41 (forall ((Xr $$unsorted) (X $$unsorted)) (= (tptp.range_of (tptp.restrict Xr X tptp.universal_class)) (tptp.image Xr X))))
% 1.06/1.29  (assume a42 (forall ((X $$unsorted)) (= (tptp.union X (tptp.singleton X)) (tptp.successor X))))
% 1.06/1.29  (assume a43 (tptp.subclass tptp.successor_relation (tptp.cross_product tptp.universal_class tptp.universal_class)))
% 1.06/1.29  (assume a44 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.successor_relation)) (= (tptp.successor X) Y))))
% 1.06/1.29  (assume a45 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (tptp.successor X) Y)) (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product tptp.universal_class tptp.universal_class))) (tptp.member (tptp.ordered_pair X Y) tptp.successor_relation))))
% 1.06/1.29  (assume a46 (forall ((X $$unsorted)) (or (not (tptp.inductive X)) (tptp.member tptp.null_class X))))
% 1.06/1.29  (assume a47 (forall ((X $$unsorted)) (or (not (tptp.inductive X)) (tptp.subclass (tptp.image tptp.successor_relation X) X))))
% 1.06/1.29  (assume a48 (forall ((X $$unsorted)) (or (not (tptp.member tptp.null_class X)) (not (tptp.subclass (tptp.image tptp.successor_relation X) X)) (tptp.inductive X))))
% 1.06/1.29  (assume a49 (tptp.inductive tptp.omega))
% 1.06/1.29  (assume a50 (forall ((Y $$unsorted)) (or (not (tptp.inductive Y)) (tptp.subclass tptp.omega Y))))
% 1.06/1.29  (assume a51 (tptp.member tptp.omega tptp.universal_class))
% 1.06/1.29  (assume a52 (forall ((X $$unsorted)) (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class X)) (tptp.sum_class X))))
% 1.06/1.29  (assume a53 (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.sum_class X) tptp.universal_class))))
% 1.06/1.29  (assume a54 (forall ((X $$unsorted)) (= (tptp.complement (tptp.image tptp.element_relation (tptp.complement X))) (tptp.power_class X))))
% 1.06/1.29  (assume a55 (forall ((U $$unsorted)) (or (not (tptp.member U tptp.universal_class)) (tptp.member (tptp.power_class U) tptp.universal_class))))
% 1.06/1.29  (assume a56 (forall ((Yr $$unsorted) (Xr $$unsorted)) (tptp.subclass (tptp.compose Yr Xr) (tptp.cross_product tptp.universal_class tptp.universal_class))))
% 1.06/1.29  (assume a57 (forall ((Y $$unsorted) (Z $$unsorted) (Yr $$unsorted) (Xr $$unsorted)) (or (not (tptp.member (tptp.ordered_pair Y Z) (tptp.compose Yr Xr))) (tptp.member Z (tptp.image Yr (tptp.image Xr (tptp.singleton Y)))))))
% 1.06/1.29  (assume a58 (forall ((Z $$unsorted) (Yr $$unsorted) (Xr $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.image Yr (tptp.image Xr (tptp.singleton Y))))) (not (tptp.member (tptp.ordered_pair Y Z) (tptp.cross_product tptp.universal_class tptp.universal_class))) (tptp.member (tptp.ordered_pair Y Z) (tptp.compose Yr Xr)))))
% 1.06/1.29  (assume a59 (forall ((X $$unsorted)) (or (not (tptp.single_valued_class X)) (tptp.subclass (tptp.compose X (tptp.inverse X)) tptp.identity_relation))))
% 1.06/1.29  (assume a60 (forall ((X $$unsorted)) (or (not (tptp.subclass (tptp.compose X (tptp.inverse X)) tptp.identity_relation)) (tptp.single_valued_class X))))
% 1.06/1.29  (assume a61 (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.subclass Xf (tptp.cross_product tptp.universal_class tptp.universal_class)))))
% 1.06/1.29  (assume a62 (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.subclass (tptp.compose Xf (tptp.inverse Xf)) tptp.identity_relation))))
% 1.06/1.29  (assume a63 (forall ((Xf $$unsorted)) (or (not (tptp.subclass Xf (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (tptp.subclass (tptp.compose Xf (tptp.inverse Xf)) tptp.identity_relation)) (tptp.function Xf))))
% 1.06/1.29  (assume a64 (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.image Xf X) tptp.universal_class))))
% 1.06/1.29  (assume a65 (forall ((X $$unsorted)) (or (= X tptp.null_class) (tptp.member (tptp.regular X) X))))
% 1.06/1.29  (assume a66 (forall ((X $$unsorted)) (or (= X tptp.null_class) (= (tptp.intersection X (tptp.regular X)) tptp.null_class))))
% 1.06/1.29  (assume a67 (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y))))
% 1.06/1.29  (assume a68 (tptp.function tptp.choice))
% 1.06/1.29  (assume a69 (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= Y tptp.null_class) (tptp.member (tptp.apply tptp.choice Y) Y))))
% 1.06/1.29  (assume a70 (forall ((Xf $$unsorted)) (or (not (tptp.one_to_one Xf)) (tptp.function Xf))))
% 1.06/1.29  (assume a71 (forall ((Xf $$unsorted)) (or (not (tptp.one_to_one Xf)) (tptp.function (tptp.inverse Xf)))))
% 1.06/1.29  (assume a72 (forall ((Xf $$unsorted)) (or (not (tptp.function (tptp.inverse Xf))) (not (tptp.function Xf)) (tptp.one_to_one Xf))))
% 1.06/1.29  (assume a73 (= (tptp.intersection (tptp.cross_product tptp.universal_class tptp.universal_class) (tptp.intersection (tptp.cross_product tptp.universal_class tptp.universal_class) (tptp.complement (tptp.compose (tptp.complement tptp.element_relation) (tptp.inverse tptp.element_relation))))) tptp.subset_relation))
% 1.06/1.29  (assume a74 (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation))
% 1.06/1.29  (assume a75 (forall ((Xr $$unsorted)) (= (tptp.complement (tptp.domain_of (tptp.intersection Xr tptp.identity_relation))) (tptp.diagonalise Xr))))
% 1.06/1.29  (assume a76 (forall ((X $$unsorted)) (= (tptp.intersection (tptp.domain_of X) (tptp.diagonalise (tptp.compose (tptp.inverse tptp.element_relation) X))) (tptp.cantor X))))
% 1.06/1.29  (assume a77 (forall ((Xf $$unsorted)) (or (not (tptp.operation Xf)) (tptp.function Xf))))
% 1.06/1.29  (assume a78 (forall ((Xf $$unsorted)) (or (not (tptp.operation Xf)) (= (tptp.cross_product (tptp.domain_of (tptp.domain_of Xf)) (tptp.domain_of (tptp.domain_of Xf))) (tptp.domain_of Xf)))))
% 1.06/1.29  (assume a79 (forall ((Xf $$unsorted)) (or (not (tptp.operation Xf)) (tptp.subclass (tptp.range_of Xf) (tptp.domain_of (tptp.domain_of Xf))))))
% 1.06/1.29  (assume a80 (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (not (= (tptp.cross_product (tptp.domain_of (tptp.domain_of Xf)) (tptp.domain_of (tptp.domain_of Xf))) (tptp.domain_of Xf))) (not (tptp.subclass (tptp.range_of Xf) (tptp.domain_of (tptp.domain_of Xf)))) (tptp.operation Xf))))
% 1.06/1.29  (assume a81 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (tptp.function Xh))))
% 1.06/1.29  (assume a82 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (= (tptp.domain_of (tptp.domain_of Xf1)) (tptp.domain_of Xh)))))
% 1.06/1.29  (assume a83 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (tptp.subclass (tptp.range_of Xh) (tptp.domain_of (tptp.domain_of Xf2))))))
% 1.06/1.29  (assume a84 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.function Xh)) (not (= (tptp.domain_of (tptp.domain_of Xf1)) (tptp.domain_of Xh))) (not (tptp.subclass (tptp.range_of Xh) (tptp.domain_of (tptp.domain_of Xf2)))) (tptp.compatible Xh Xf1 Xf2))))
% 1.06/1.29  (assume a85 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.operation Xf1))))
% 1.06/1.29  (assume a86 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.operation Xf2))))
% 1.06/1.29  (assume a87 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.compatible Xh Xf1 Xf2))))
% 1.06/1.29  (assume a88 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (not (tptp.member (tptp.ordered_pair X Y) (tptp.domain_of Xf1))) (= (tptp.apply Xf2 (tptp.ordered_pair (tptp.apply Xh X) (tptp.apply Xh Y))) (tptp.apply Xh (tptp.apply Xf1 (tptp.ordered_pair X Y)))))))
% 1.06/1.29  (assume a89 (forall ((Xf1 $$unsorted) (Xf2 $$unsorted) (Xh $$unsorted)) (or (not (tptp.operation Xf1)) (not (tptp.operation Xf2)) (not (tptp.compatible Xh Xf1 Xf2)) (tptp.member (tptp.ordered_pair (tptp.not_homomorphism1 Xh Xf1 Xf2) (tptp.not_homomorphism2 Xh Xf1 Xf2)) (tptp.domain_of Xf1)) (tptp.homomorphism Xh Xf1 Xf2))))
% 1.06/1.29  (assume a90 (forall ((Xf1 $$unsorted) (Xf2 $$unsorted) (Xh $$unsorted)) (or (not (tptp.operation Xf1)) (not (tptp.operation Xf2)) (not (tptp.compatible Xh Xf1 Xf2)) (not (= (tptp.apply Xf2 (tptp.ordered_pair (tptp.apply Xh (tptp.not_homomorphism1 Xh Xf1 Xf2)) (tptp.apply Xh (tptp.not_homomorphism2 Xh Xf1 Xf2)))) (tptp.apply Xh (tptp.apply Xf1 (tptp.ordered_pair (tptp.not_homomorphism1 Xh Xf1 Xf2) (tptp.not_homomorphism2 Xh Xf1 Xf2)))))) (tptp.homomorphism Xh Xf1 Xf2))))
% 1.06/1.29  (assume a91 (forall ((X $$unsorted)) (tptp.subclass (tptp.compose_class X) (tptp.cross_product tptp.universal_class tptp.universal_class))))
% 1.06/1.29  (assume a92 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair Y Z) (tptp.compose_class X))) (= (tptp.compose X Y) Z))))
% 1.06/1.29  (assume a93 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair Y Z) (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (= (tptp.compose X Y) Z)) (tptp.member (tptp.ordered_pair Y Z) (tptp.compose_class X)))))
% 1.06/1.29  (assume a94 (tptp.subclass tptp.composition_function (tptp.cross_product tptp.universal_class (tptp.cross_product tptp.universal_class tptp.universal_class))))
% 1.06/1.29  (assume a95 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X (tptp.ordered_pair Y Z)) tptp.composition_function)) (= (tptp.compose X Y) Z))))
% 1.06/1.29  (assume a96 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product tptp.universal_class tptp.universal_class))) (tptp.member (tptp.ordered_pair X (tptp.ordered_pair Y (tptp.compose X Y))) tptp.composition_function))))
% 1.06/1.29  (assume a97 (tptp.subclass tptp.domain_relation (tptp.cross_product tptp.universal_class tptp.universal_class)))
% 1.06/1.29  (assume a98 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.domain_relation)) (= (tptp.domain_of X) Y))))
% 1.06/1.29  (assume a99 (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.ordered_pair X (tptp.domain_of X)) tptp.domain_relation))))
% 1.06/1.29  (assume a100 (forall ((X $$unsorted)) (= (tptp.first (tptp.not_subclass_element (tptp.compose X (tptp.inverse X)) tptp.identity_relation)) (tptp.single_valued1 X))))
% 1.06/1.29  (assume a101 (forall ((X $$unsorted)) (= (tptp.second (tptp.not_subclass_element (tptp.compose X (tptp.inverse X)) tptp.identity_relation)) (tptp.single_valued2 X))))
% 1.06/1.29  (assume a102 (forall ((X $$unsorted)) (= (tptp.domain X (tptp.image (tptp.inverse X) (tptp.singleton (tptp.single_valued1 X))) (tptp.single_valued2 X)) (tptp.single_valued3 X))))
% 1.06/1.29  (assume a103 (= (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation (tptp.complement tptp.identity_relation))) tptp.element_relation) tptp.singleton_relation))
% 1.06/1.29  (assume a104 (tptp.subclass tptp.application_function (tptp.cross_product tptp.universal_class (tptp.cross_product tptp.universal_class tptp.universal_class))))
% 1.06/1.29  (assume a105 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X (tptp.ordered_pair Y Z)) tptp.application_function)) (tptp.member Y (tptp.domain_of X)))))
% 1.06/1.29  (assume a106 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X (tptp.ordered_pair Y Z)) tptp.application_function)) (= (tptp.apply X Y) Z))))
% 1.06/1.29  (assume a107 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X (tptp.ordered_pair Y Z)) (tptp.cross_product tptp.universal_class (tptp.cross_product tptp.universal_class tptp.universal_class)))) (not (tptp.member Y (tptp.domain_of X))) (tptp.member (tptp.ordered_pair X (tptp.ordered_pair Y (tptp.apply X Y))) tptp.application_function))))
% 1.06/1.29  (assume a108 (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.function Xf))))
% 1.06/1.29  (assume a109 (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (= (tptp.domain_of Xf) X))))
% 1.06/1.29  (assume a110 (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.subclass (tptp.range_of Xf) Y))))
% 1.06/1.29  (assume a111 (forall ((Xf $$unsorted) (Y $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.subclass (tptp.range_of Xf) Y)) (tptp.maps Xf (tptp.domain_of Xf) Y))))
% 1.06/1.29  (assume a112 (not (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))
% 1.06/1.29  (step t1 (cl (=> (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X))) (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X)))) :rule implies_neg1)
% 1.06/1.29  (anchor :step t2)
% 1.06/1.29  (assume t2.a0 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X))))
% 1.06/1.29  (step t2.t1 (cl (or (not (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X)))) (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x)))) :rule forall_inst :args ((:= Z (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (:= X tptp.x) (:= Y tptp.y)))
% 1.06/1.29  (step t2.t2 (cl (not (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X)))) (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x))) :rule or :premises (t2.t1))
% 1.06/1.29  (step t2.t3 (cl (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x))) :rule resolution :premises (t2.t2 t2.a0))
% 1.06/1.29  (step t2 (cl (not (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X)))) (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x))) :rule subproof :discharge (t2.a0))
% 1.06/1.29  (step t3 (cl (=> (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X))) (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x))) (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x))) :rule resolution :premises (t1 t2))
% 1.06/1.29  (step t4 (cl (=> (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X))) (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x))) (not (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x)))) :rule implies_neg2)
% 1.06/1.29  (step t5 (cl (=> (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X))) (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x))) (=> (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X))) (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x)))) :rule resolution :premises (t3 t4))
% 1.06/1.29  (step t6 (cl (=> (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X))) (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x)))) :rule contraction :premises (t5))
% 1.06/1.29  (step t7 (cl (not (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X)))) (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x))) :rule implies :premises (t6))
% 1.06/1.29  (step t8 (cl (not (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x))) (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x)) :rule or_pos)
% 1.06/1.29  (step t9 (cl (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x) (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y))) (not (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x)))) :rule reordering :premises (t8))
% 1.06/1.29  (step t10 (cl (not (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x)) (not (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z)) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x)) (not (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z)) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z))) :rule or_pos)
% 1.06/1.29  (step t11 (cl (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x)) (not (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z)) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)) (not (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x)) (not (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z)) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z))))) :rule reordering :premises (t10))
% 1.06/1.29  (step t12 (cl (not (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z)) :rule or_pos)
% 1.06/1.29  (step t13 (cl (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z) (not (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z)))) :rule reordering :premises (t12))
% 1.06/1.29  (step t14 (cl (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (not (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) :rule and_neg)
% 1.06/1.29  (step t15 (cl (=> (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) :rule implies_neg1)
% 1.06/1.29  (anchor :step t16)
% 1.06/1.29  (assume t16.a0 (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)))
% 1.06/1.29  (assume t16.a1 (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))
% 1.06/1.29  (step t16.t1 (cl (=> (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) :rule implies_neg1)
% 1.06/1.29  (anchor :step t16.t2)
% 1.06/1.29  (assume t16.t2.a0 (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)))
% 1.06/1.29  (assume t16.t2.a1 (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))
% 1.06/1.29  (step t16.t2.t1 (cl (= (= (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) true) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)))) :rule equiv_simplify)
% 1.06/1.29  (step t16.t2.t2 (cl (not (= (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) true)) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) :rule equiv1 :premises (t16.t2.t1))
% 1.06/1.29  (step t16.t2.t3 (cl (= (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) :rule symm :premises (t16.t2.a1))
% 1.06/1.29  (step t16.t2.t4 (cl (= (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) :rule refl)
% 1.06/1.29  (step t16.t2.t5 (cl (= (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)))) :rule cong :premises (t16.t2.t3 t16.t2.t4))
% 1.06/1.29  (step t16.t2.t6 (cl (= (= (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) true) (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)))) :rule equiv_simplify)
% 1.06/1.29  (step t16.t2.t7 (cl (= (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) true) (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)))) :rule equiv2 :premises (t16.t2.t6))
% 1.06/1.29  (step t16.t2.t8 (cl (= (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) true)) :rule resolution :premises (t16.t2.t7 t16.t2.a0))
% 1.06/1.29  (step t16.t2.t9 (cl (= (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) true)) :rule trans :premises (t16.t2.t5 t16.t2.t8))
% 1.06/1.29  (step t16.t2.t10 (cl (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) :rule resolution :premises (t16.t2.t2 t16.t2.t9))
% 1.06/1.29  (step t16.t2 (cl (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (not (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) :rule subproof :discharge (t16.t2.a0 t16.t2.a1))
% 1.06/1.29  (step t16.t3 (cl (not (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) :rule and_pos)
% 1.06/1.29  (step t16.t4 (cl (not (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) :rule and_pos)
% 1.06/1.29  (step t16.t5 (cl (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (not (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (not (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))))) :rule resolution :premises (t16.t2 t16.t3 t16.t4))
% 1.06/1.29  (step t16.t6 (cl (not (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (not (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) :rule reordering :premises (t16.t5))
% 1.06/1.29  (step t16.t7 (cl (not (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) :rule contraction :premises (t16.t6))
% 1.06/1.29  (step t16.t8 (cl (=> (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) :rule resolution :premises (t16.t1 t16.t7))
% 1.06/1.29  (step t16.t9 (cl (=> (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)))) :rule implies_neg2)
% 1.06/1.29  (step t16.t10 (cl (=> (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (=> (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)))) :rule resolution :premises (t16.t8 t16.t9))
% 1.06/1.29  (step t16.t11 (cl (=> (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)))) :rule contraction :premises (t16.t10))
% 1.06/1.29  (step t16.t12 (cl (not (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) :rule implies :premises (t16.t11))
% 1.06/1.29  (step t16.t13 (cl (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (not (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) :rule and_neg)
% 1.06/1.29  (step t16.t14 (cl (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) :rule resolution :premises (t16.t13 t16.a0 t16.a1))
% 1.06/1.29  (step t16.t15 (cl (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) :rule resolution :premises (t16.t12 t16.t14))
% 1.06/1.29  (step t16 (cl (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (not (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) :rule subproof :discharge (t16.a0 t16.a1))
% 1.06/1.29  (step t17 (cl (not (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) :rule and_pos)
% 1.06/1.29  (step t18 (cl (not (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) :rule and_pos)
% 1.06/1.29  (step t19 (cl (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (not (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (not (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))))) :rule resolution :premises (t16 t17 t18))
% 1.06/1.29  (step t20 (cl (not (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (not (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) :rule reordering :premises (t19))
% 1.06/1.29  (step t21 (cl (not (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) :rule contraction :premises (t20))
% 1.06/1.29  (step t22 (cl (=> (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) :rule resolution :premises (t15 t21))
% 1.06/1.29  (step t23 (cl (=> (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)))) :rule implies_neg2)
% 1.06/1.29  (step t24 (cl (=> (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (=> (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)))) :rule resolution :premises (t22 t23))
% 1.06/1.29  (step t25 (cl (=> (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)))) :rule contraction :premises (t24))
% 1.06/1.29  (step t26 (cl (not (and (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) :rule implies :premises (t25))
% 1.06/1.29  (step t27 (cl (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (not (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) :rule resolution :premises (t14 t26))
% 1.06/1.29  (step t28 (cl (not (or (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) :rule or_pos)
% 1.06/1.29  (step t29 (cl (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (not (or (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))) :rule reordering :premises (t28))
% 1.06/1.29  (step t30 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y))) (or (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y)))) :rule implies_neg1)
% 1.06/1.29  (anchor :step t31)
% 1.06/1.29  (assume t31.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y))))
% 1.06/1.29  (step t31.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y)))) (or (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))) :rule forall_inst :args ((:= X (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (:= Y (tptp.cross_product tptp.x tptp.z))))
% 1.06/1.29  (step t31.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y)))) (or (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) :rule or :premises (t31.t1))
% 1.06/1.29  (step t31.t3 (cl (or (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) :rule resolution :premises (t31.t2 t31.a0))
% 1.06/1.29  (step t31 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y)))) (or (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) :rule subproof :discharge (t31.a0))
% 1.06/1.29  (step t32 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y))) (or (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (or (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) :rule resolution :premises (t30 t31))
% 1.06/1.29  (step t33 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y))) (or (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (not (or (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))) :rule implies_neg2)
% 1.06/1.29  (step t34 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y))) (or (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y))) (or (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))) :rule resolution :premises (t32 t33))
% 1.06/1.29  (step t35 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y))) (or (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))) :rule contraction :premises (t34))
% 1.06/1.29  (step t36 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y)))) (or (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) :rule implies :premises (t35))
% 1.06/1.29  (step t37 (cl (or (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) :rule resolution :premises (t36 a1))
% 1.06/1.29  (step t38 (cl (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) :rule resolution :premises (t29 a112 t37))
% 1.06/1.29  (step t39 (cl (not (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) :rule or_pos)
% 1.06/1.29  (step t40 (cl (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))) (not (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))))) :rule reordering :premises (t39))
% 1.06/1.29  (step t41 (cl (=> (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= Z (tptp.ordered_pair (tptp.first Z) (tptp.second Z))))) (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= Z (tptp.ordered_pair (tptp.first Z) (tptp.second Z)))))) :rule implies_neg1)
% 1.06/1.29  (anchor :step t42)
% 1.06/1.29  (assume t42.a0 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= Z (tptp.ordered_pair (tptp.first Z) (tptp.second Z))))))
% 1.06/1.29  (step t42.t1 (cl (or (not (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= Z (tptp.ordered_pair (tptp.first Z) (tptp.second Z)))))) (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))))) :rule forall_inst :args ((:= Z (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (:= X (tptp.intersection tptp.x tptp.y)) (:= Y tptp.z)))
% 1.06/1.29  (step t42.t2 (cl (not (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= Z (tptp.ordered_pair (tptp.first Z) (tptp.second Z)))))) (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) :rule or :premises (t42.t1))
% 1.06/1.29  (step t42.t3 (cl (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) :rule resolution :premises (t42.t2 t42.a0))
% 1.06/1.29  (step t42 (cl (not (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= Z (tptp.ordered_pair (tptp.first Z) (tptp.second Z)))))) (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) :rule subproof :discharge (t42.a0))
% 1.06/1.29  (step t43 (cl (=> (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= Z (tptp.ordered_pair (tptp.first Z) (tptp.second Z))))) (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) :rule resolution :premises (t41 t42))
% 1.06/1.29  (step t44 (cl (=> (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= Z (tptp.ordered_pair (tptp.first Z) (tptp.second Z))))) (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (not (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))))) :rule implies_neg2)
% 1.06/1.29  (step t45 (cl (=> (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= Z (tptp.ordered_pair (tptp.first Z) (tptp.second Z))))) (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (=> (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= Z (tptp.ordered_pair (tptp.first Z) (tptp.second Z))))) (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))))) :rule resolution :premises (t43 t44))
% 1.06/1.29  (step t46 (cl (=> (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= Z (tptp.ordered_pair (tptp.first Z) (tptp.second Z))))) (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))))) :rule contraction :premises (t45))
% 1.06/1.29  (step t47 (cl (not (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= Z (tptp.ordered_pair (tptp.first Z) (tptp.second Z)))))) (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) :rule implies :premises (t46))
% 1.06/1.29  (step t48 (cl (not (= (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= (tptp.ordered_pair (tptp.first Z) (tptp.second Z)) Z))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= Z (tptp.ordered_pair (tptp.first Z) (tptp.second Z))))))) (not (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= (tptp.ordered_pair (tptp.first Z) (tptp.second Z)) Z)))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= Z (tptp.ordered_pair (tptp.first Z) (tptp.second Z)))))) :rule equiv_pos2)
% 1.06/1.29  (anchor :step t49 :args ((Z $$unsorted) (:= Z Z) (X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 1.06/1.29  (step t49.t1 (cl (= Z Z)) :rule refl)
% 1.06/1.29  (step t49.t2 (cl (= X X)) :rule refl)
% 1.06/1.29  (step t49.t3 (cl (= Y Y)) :rule refl)
% 1.06/1.29  (step t49.t4 (cl (= (not (tptp.member Z (tptp.cross_product X Y))) (not (tptp.member Z (tptp.cross_product X Y))))) :rule refl)
% 1.06/1.29  (step t49.t5 (cl (= (= (tptp.ordered_pair (tptp.first Z) (tptp.second Z)) Z) (= Z (tptp.ordered_pair (tptp.first Z) (tptp.second Z))))) :rule all_simplify)
% 1.06/1.29  (step t49.t6 (cl (= (or (not (tptp.member Z (tptp.cross_product X Y))) (= (tptp.ordered_pair (tptp.first Z) (tptp.second Z)) Z)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= Z (tptp.ordered_pair (tptp.first Z) (tptp.second Z)))))) :rule cong :premises (t49.t4 t49.t5))
% 1.06/1.29  (step t49 (cl (= (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= (tptp.ordered_pair (tptp.first Z) (tptp.second Z)) Z))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= Z (tptp.ordered_pair (tptp.first Z) (tptp.second Z))))))) :rule bind)
% 1.06/1.29  (step t50 (cl (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= Z (tptp.ordered_pair (tptp.first Z) (tptp.second Z)))))) :rule resolution :premises (t48 t49 a16))
% 1.06/1.29  (step t51 (cl (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) :rule resolution :premises (t47 t50))
% 1.06/1.29  (step t52 (cl (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) :rule resolution :premises (t40 t38 t51))
% 1.06/1.29  (step t53 (cl (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) :rule resolution :premises (t27 t38 t52))
% 1.06/1.29  (step t54 (cl (=> (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member V Y))) (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z))) (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member V Y)))) :rule implies_neg1)
% 1.06/1.29  (anchor :step t55)
% 1.06/1.29  (assume t55.a0 (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member V Y))))
% 1.06/1.29  (step t55.t1 (cl (or (not (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member V Y)))) (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z)))) :rule forall_inst :args ((:= U (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (:= V (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (:= X (tptp.intersection tptp.x tptp.y)) (:= Y tptp.z)))
% 1.06/1.29  (step t55.t2 (cl (not (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member V Y)))) (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z))) :rule or :premises (t55.t1))
% 1.06/1.29  (step t55.t3 (cl (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z))) :rule resolution :premises (t55.t2 t55.a0))
% 1.06/1.29  (step t55 (cl (not (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member V Y)))) (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z))) :rule subproof :discharge (t55.a0))
% 1.06/1.29  (step t56 (cl (=> (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member V Y))) (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z))) (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z))) :rule resolution :premises (t54 t55))
% 1.06/1.29  (step t57 (cl (=> (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member V Y))) (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z))) (not (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z)))) :rule implies_neg2)
% 1.06/1.29  (step t58 (cl (=> (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member V Y))) (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z))) (=> (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member V Y))) (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z)))) :rule resolution :premises (t56 t57))
% 1.06/1.29  (step t59 (cl (=> (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member V Y))) (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z)))) :rule contraction :premises (t58))
% 1.06/1.29  (step t60 (cl (not (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member V Y)))) (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z))) :rule implies :premises (t59))
% 1.06/1.29  (step t61 (cl (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z))) :rule resolution :premises (t60 a14))
% 1.06/1.29  (step t62 (cl (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z)) :rule resolution :premises (t13 t53 t61))
% 1.06/1.29  (step t63 (cl (not (= (or (not (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) (not (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) (or (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)) (not (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))))) (not (or (not (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) (not (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z))))) (or (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)) (not (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z))))) :rule equiv_pos2)
% 1.06/1.29  (step t64 (cl (= (= (= (not (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) true) (= (not (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))))) :rule equiv_simplify)
% 1.06/1.29  (step t65 (cl (not (= (= (not (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) true)) (= (not (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) :rule equiv1 :premises (t64))
% 1.06/1.29  (step t66 (cl (= (= (not (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)) (not (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))))))) :rule all_simplify)
% 1.06/1.29  (step t67 (cl (= (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)) (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) :rule refl)
% 1.06/1.29  (step t68 (cl (= (not (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) :rule all_simplify)
% 1.06/1.29  (step t69 (cl (= (= (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)) (not (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))))) (= (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)) (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))))) :rule cong :premises (t67 t68))
% 1.06/1.29  (step t70 (cl (= (= (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)) (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) true)) :rule all_simplify)
% 1.06/1.29  (step t71 (cl (= (= (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)) (not (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))))) true)) :rule trans :premises (t69 t70))
% 1.06/1.29  (step t72 (cl (= (= (not (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) true)) :rule trans :premises (t66 t71))
% 1.06/1.29  (step t73 (cl (= (not (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) :rule resolution :premises (t65 t72))
% 1.06/1.29  (step t74 (cl (= (not (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))))) :rule refl)
% 1.06/1.29  (step t75 (cl (= (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z))))) :rule refl)
% 1.06/1.29  (step t76 (cl (= (or (not (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) (not (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) (or (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)) (not (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))))) :rule cong :premises (t73 t74 t75))
% 1.06/1.29  (step t77 (cl (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) (not (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) :rule and_neg)
% 1.06/1.29  (step t78 (cl (=> (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) :rule implies_neg1)
% 1.06/1.29  (anchor :step t79)
% 1.06/1.29  (assume t79.a0 (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))))
% 1.06/1.29  (assume t79.a1 (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))
% 1.06/1.29  (step t79.t1 (cl (=> (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) :rule implies_neg1)
% 1.06/1.29  (anchor :step t79.t2)
% 1.06/1.29  (assume t79.t2.a0 (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))))
% 1.06/1.29  (assume t79.t2.a1 (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))
% 1.06/1.29  (step t79.t2.t1 (cl (= (= (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)) false) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z))))) :rule equiv_simplify)
% 1.06/1.29  (step t79.t2.t2 (cl (not (= (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)) false)) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) :rule equiv1 :premises (t79.t2.t1))
% 1.06/1.29  (step t79.t2.t3 (cl (= (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) :rule symm :premises (t79.t2.a1))
% 1.06/1.29  (step t79.t2.t4 (cl (= (tptp.cross_product tptp.x tptp.z) (tptp.cross_product tptp.x tptp.z))) :rule refl)
% 1.06/1.29  (step t79.t2.t5 (cl (= (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)) (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) :rule cong :premises (t79.t2.t3 t79.t2.t4))
% 1.06/1.29  (step t79.t2.t6 (cl (= (= (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)) false) (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))))) :rule equiv_simplify)
% 1.06/1.29  (step t79.t2.t7 (cl (= (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)) false) (not (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))))) :rule equiv2 :premises (t79.t2.t6))
% 1.06/1.29  (step t79.t2.t8 (cl (not (not (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))))) (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) :rule not_not)
% 1.06/1.29  (step t79.t2.t9 (cl (= (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)) false) (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) :rule resolution :premises (t79.t2.t7 t79.t2.t8))
% 1.06/1.29  (step t79.t2.t10 (cl (= (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)) false)) :rule resolution :premises (t79.t2.t9 t79.t2.a0))
% 1.06/1.29  (step t79.t2.t11 (cl (= (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)) false)) :rule trans :premises (t79.t2.t5 t79.t2.t10))
% 1.06/1.29  (step t79.t2.t12 (cl (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) :rule resolution :premises (t79.t2.t2 t79.t2.t11))
% 1.06/1.29  (step t79.t2 (cl (not (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) (not (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) :rule subproof :discharge (t79.t2.a0 t79.t2.a1))
% 1.06/1.29  (step t79.t3 (cl (not (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) :rule and_pos)
% 1.06/1.29  (step t79.t4 (cl (not (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) :rule and_pos)
% 1.06/1.29  (step t79.t5 (cl (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z))) (not (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (not (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))))) :rule resolution :premises (t79.t2 t79.t3 t79.t4))
% 1.06/1.29  (step t79.t6 (cl (not (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (not (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) :rule reordering :premises (t79.t5))
% 1.06/1.29  (step t79.t7 (cl (not (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) :rule contraction :premises (t79.t6))
% 1.06/1.29  (step t79.t8 (cl (=> (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) :rule resolution :premises (t79.t1 t79.t7))
% 1.06/1.29  (step t79.t9 (cl (=> (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) (not (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z))))) :rule implies_neg2)
% 1.06/1.29  (step t79.t10 (cl (=> (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) (=> (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z))))) :rule resolution :premises (t79.t8 t79.t9))
% 1.06/1.29  (step t79.t11 (cl (=> (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z))))) :rule contraction :premises (t79.t10))
% 1.06/1.29  (step t79.t12 (cl (not (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) :rule implies :premises (t79.t11))
% 1.06/1.29  (step t79.t13 (cl (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) (not (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) :rule and_neg)
% 1.06/1.29  (step t79.t14 (cl (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) :rule resolution :premises (t79.t13 t79.a0 t79.a1))
% 1.06/1.29  (step t79.t15 (cl (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) :rule resolution :premises (t79.t12 t79.t14))
% 1.06/1.29  (step t79 (cl (not (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) (not (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) :rule subproof :discharge (t79.a0 t79.a1))
% 1.06/1.29  (step t80 (cl (not (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) :rule and_pos)
% 1.06/1.29  (step t81 (cl (not (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) :rule and_pos)
% 1.06/1.29  (step t82 (cl (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z))) (not (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (not (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))))) :rule resolution :premises (t79 t80 t81))
% 1.06/1.29  (step t83 (cl (not (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (not (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) :rule reordering :premises (t82))
% 1.06/1.29  (step t84 (cl (not (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) :rule contraction :premises (t83))
% 1.06/1.29  (step t85 (cl (=> (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) :rule resolution :premises (t78 t84))
% 1.06/1.29  (step t86 (cl (=> (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) (not (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z))))) :rule implies_neg2)
% 1.06/1.29  (step t87 (cl (=> (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) (=> (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z))))) :rule resolution :premises (t85 t86))
% 1.06/1.29  (step t88 (cl (=> (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z))))) :rule contraction :premises (t87))
% 1.06/1.29  (step t89 (cl (not (and (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) :rule implies :premises (t88))
% 1.06/1.29  (step t90 (cl (not (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) (not (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) :rule resolution :premises (t77 t89))
% 1.06/1.29  (step t91 (cl (or (not (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) (not (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) (not (not (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))))) :rule or_neg)
% 1.06/1.29  (step t92 (cl (or (not (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) (not (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) (not (not (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))))) :rule or_neg)
% 1.06/1.29  (step t93 (cl (or (not (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) (not (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) (not (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z))))) :rule or_neg)
% 1.06/1.29  (step t94 (cl (or (not (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) (not (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) (or (not (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) (not (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) (or (not (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) (not (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z))))) :rule resolution :premises (t90 t91 t92 t93))
% 1.06/1.29  (step t95 (cl (or (not (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) (not (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z))))) :rule contraction :premises (t94))
% 1.06/1.29  (step t96 (cl (or (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)) (not (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z))))) :rule resolution :premises (t63 t76 t95))
% 1.06/1.29  (step t97 (cl (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)) (not (= (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) :rule or :premises (t96))
% 1.06/1.29  (step t98 (cl (not (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) :rule or_pos)
% 1.06/1.29  (step t99 (cl (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (not (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))) :rule reordering :premises (t98))
% 1.06/1.29  (step t100 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (tptp.subclass X Y))) (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (tptp.subclass X Y)))) :rule implies_neg1)
% 1.06/1.29  (anchor :step t101)
% 1.06/1.29  (assume t101.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (tptp.subclass X Y))))
% 1.06/1.29  (step t101.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (tptp.subclass X Y)))) (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))) :rule forall_inst :args ((:= X (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z)) (:= Y (tptp.cross_product tptp.x tptp.z))))
% 1.06/1.29  (step t101.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (tptp.subclass X Y)))) (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) :rule or :premises (t101.t1))
% 1.06/1.29  (step t101.t3 (cl (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) :rule resolution :premises (t101.t2 t101.a0))
% 1.06/1.29  (step t101 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (tptp.subclass X Y)))) (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) :rule subproof :discharge (t101.a0))
% 1.06/1.29  (step t102 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (tptp.subclass X Y))) (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) :rule resolution :premises (t100 t101))
% 1.06/1.29  (step t103 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (tptp.subclass X Y))) (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (not (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))) :rule implies_neg2)
% 1.06/1.29  (step t104 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (tptp.subclass X Y))) (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (tptp.subclass X Y))) (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))) :rule resolution :premises (t102 t103))
% 1.06/1.29  (step t105 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (tptp.subclass X Y))) (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))))) :rule contraction :premises (t104))
% 1.06/1.29  (step t106 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (tptp.subclass X Y)))) (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) :rule implies :premises (t105))
% 1.06/1.29  (step t107 (cl (or (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z))) (tptp.subclass (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) :rule resolution :premises (t106 a2))
% 1.06/1.29  (step t108 (cl (not (tptp.member (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)) (tptp.cross_product tptp.x tptp.z)))) :rule resolution :premises (t99 a112 t107))
% 1.06/1.29  (step t109 (cl (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) :rule resolution :premises (t97 t108 t52))
% 1.06/1.29  (step t110 (cl (=> (forall ((U $$unsorted) (X $$unsorted) (V $$unsorted) (Y $$unsorted)) (or (not (tptp.member U X)) (not (tptp.member V Y)) (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y)))) (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x)) (not (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z)) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) (forall ((U $$unsorted) (X $$unsorted) (V $$unsorted) (Y $$unsorted)) (or (not (tptp.member U X)) (not (tptp.member V Y)) (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))))) :rule implies_neg1)
% 1.06/1.29  (anchor :step t111)
% 1.06/1.29  (assume t111.a0 (forall ((U $$unsorted) (X $$unsorted) (V $$unsorted) (Y $$unsorted)) (or (not (tptp.member U X)) (not (tptp.member V Y)) (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y)))))
% 1.06/1.29  (step t111.t1 (cl (or (not (forall ((U $$unsorted) (X $$unsorted) (V $$unsorted) (Y $$unsorted)) (or (not (tptp.member U X)) (not (tptp.member V Y)) (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))))) (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x)) (not (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z)) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z))))) :rule forall_inst :args ((:= U (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (:= X tptp.x) (:= V (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (:= Y tptp.z)))
% 1.06/1.29  (step t111.t2 (cl (not (forall ((U $$unsorted) (X $$unsorted) (V $$unsorted) (Y $$unsorted)) (or (not (tptp.member U X)) (not (tptp.member V Y)) (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))))) (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x)) (not (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z)) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) :rule or :premises (t111.t1))
% 1.06/1.29  (step t111.t3 (cl (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x)) (not (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z)) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) :rule resolution :premises (t111.t2 t111.a0))
% 1.06/1.29  (step t111 (cl (not (forall ((U $$unsorted) (X $$unsorted) (V $$unsorted) (Y $$unsorted)) (or (not (tptp.member U X)) (not (tptp.member V Y)) (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))))) (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x)) (not (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z)) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) :rule subproof :discharge (t111.a0))
% 1.06/1.29  (step t112 (cl (=> (forall ((U $$unsorted) (X $$unsorted) (V $$unsorted) (Y $$unsorted)) (or (not (tptp.member U X)) (not (tptp.member V Y)) (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y)))) (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x)) (not (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z)) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x)) (not (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z)) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) :rule resolution :premises (t110 t111))
% 1.06/1.29  (step t113 (cl (=> (forall ((U $$unsorted) (X $$unsorted) (V $$unsorted) (Y $$unsorted)) (or (not (tptp.member U X)) (not (tptp.member V Y)) (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y)))) (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x)) (not (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z)) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) (not (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x)) (not (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z)) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z))))) :rule implies_neg2)
% 1.06/1.29  (step t114 (cl (=> (forall ((U $$unsorted) (X $$unsorted) (V $$unsorted) (Y $$unsorted)) (or (not (tptp.member U X)) (not (tptp.member V Y)) (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y)))) (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x)) (not (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z)) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) (=> (forall ((U $$unsorted) (X $$unsorted) (V $$unsorted) (Y $$unsorted)) (or (not (tptp.member U X)) (not (tptp.member V Y)) (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y)))) (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x)) (not (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z)) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z))))) :rule resolution :premises (t112 t113))
% 1.06/1.29  (step t115 (cl (=> (forall ((U $$unsorted) (X $$unsorted) (V $$unsorted) (Y $$unsorted)) (or (not (tptp.member U X)) (not (tptp.member V Y)) (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y)))) (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x)) (not (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z)) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z))))) :rule contraction :premises (t114))
% 1.06/1.29  (step t116 (cl (not (forall ((U $$unsorted) (X $$unsorted) (V $$unsorted) (Y $$unsorted)) (or (not (tptp.member U X)) (not (tptp.member V Y)) (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))))) (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x)) (not (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z)) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) :rule implies :premises (t115))
% 1.06/1.29  (step t117 (cl (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x)) (not (tptp.member (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.z)) (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product tptp.x tptp.z)))) :rule resolution :premises (t116 a15))
% 1.06/1.29  (step t118 (cl (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x))) :rule resolution :premises (t11 t62 t109 t117))
% 1.06/1.29  (step t119 (cl (not (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y)))) (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y))) :rule or_pos)
% 1.06/1.29  (step t120 (cl (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y)) (not (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y))))) :rule reordering :premises (t119))
% 1.06/1.29  (step t121 (cl (=> (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member U X))) (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y)))) (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member U X)))) :rule implies_neg1)
% 1.06/1.29  (anchor :step t122)
% 1.06/1.29  (assume t122.a0 (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member U X))))
% 1.06/1.29  (step t122.t1 (cl (or (not (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member U X)))) (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y))))) :rule forall_inst :args ((:= U (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (:= V (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (:= X (tptp.intersection tptp.x tptp.y)) (:= Y tptp.z)))
% 1.06/1.29  (step t122.t2 (cl (not (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member U X)))) (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y)))) :rule or :premises (t122.t1))
% 1.06/1.29  (step t122.t3 (cl (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y)))) :rule resolution :premises (t122.t2 t122.a0))
% 1.06/1.29  (step t122 (cl (not (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member U X)))) (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y)))) :rule subproof :discharge (t122.a0))
% 1.06/1.29  (step t123 (cl (=> (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member U X))) (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y)))) (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y)))) :rule resolution :premises (t121 t122))
% 1.06/1.29  (step t124 (cl (=> (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member U X))) (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y)))) (not (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y))))) :rule implies_neg2)
% 1.06/1.29  (step t125 (cl (=> (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member U X))) (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y)))) (=> (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member U X))) (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y))))) :rule resolution :premises (t123 t124))
% 1.06/1.29  (step t126 (cl (=> (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member U X))) (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y))))) :rule contraction :premises (t125))
% 1.06/1.29  (step t127 (cl (not (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member U X)))) (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y)))) :rule implies :premises (t126))
% 1.06/1.29  (step t128 (cl (or (not (tptp.member (tptp.ordered_pair (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.second (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z)))) (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y)))) :rule resolution :premises (t127 a13))
% 1.06/1.29  (step t129 (cl (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y))) :rule resolution :premises (t120 t53 t128))
% 1.06/1.29  (step t130 (cl (not (or (not (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) (tptp.intersection tptp.x tptp.y))) (tptp.member (tptp.first (tptp.not_subclass_element (tptp.cross_product (tptp.intersection tptp.x tptp.y) tptp.z) (tptp.cross_product tptp.x tptp.z))) tptp.x)))) :rule resolution :premises (t9 t118 t129))
% 1.06/1.29  (step t131 (cl) :rule resolution :premises (t7 t130 a20))
% 1.06/1.29  
% 1.06/1.30  % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.YKj5FEdMQ5/cvc5---1.0.5_31398.smt2
% 1.06/1.30  % cvc5---1.0.5 exiting
% 1.06/1.30  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------