%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM183-1 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n021.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 17:32:51 EDT 2024

% Result   : Unsatisfiable 20.85s 21.02s
% Output   : Proof 20.85s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14  % Problem    : NUM183-1 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.11/0.15  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n021.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Mon May 27 23:36:24 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.22/0.54  %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.55  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.61/10.84  --- Run --no-e-matching --full-saturate-quant at 5...
% 15.71/15.90  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.72/20.95  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 20.85/21.02  % SZS status Unsatisfiable for /export/starexec/sandbox/tmp/tmp.r6lfGkbp3Y/cvc5---1.0.5_5623.smt2
% 20.85/21.02  % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.r6lfGkbp3Y/cvc5---1.0.5_5623.smt2
% 20.85/21.03  (assume a0 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y))))
% 20.85/21.03  (assume a1 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y))))
% 20.85/21.03  (assume a2 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (tptp.subclass X Y))))
% 20.85/21.03  (assume a3 (forall ((X $$unsorted)) (tptp.subclass X tptp.universal_class)))
% 20.85/21.03  (assume a4 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.subclass X Y))))
% 20.85/21.03  (assume a5 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.subclass Y X))))
% 20.85/21.03  (assume a6 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.subclass Y X)) (= X Y))))
% 20.85/21.03  (assume a7 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))))
% 20.85/21.03  (assume a8 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))))
% 20.85/21.03  (assume a9 (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (tptp.member Y (tptp.unordered_pair X Y)))))
% 20.85/21.03  (assume a10 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)))
% 20.85/21.03  (assume a11 (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))))
% 20.85/21.03  (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))))
% 20.85/21.03  (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))))
% 20.85/21.03  (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))))
% 20.85/21.03  (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)))))
% 20.85/21.03  (assume a16 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= (tptp.ordered_pair (tptp.first Z) (tptp.second Z)) Z))))
% 20.85/21.03  (assume a17 (tptp.subclass tptp.element_relation (tptp.cross_product tptp.universal_class tptp.universal_class)))
% 20.85/21.03  (assume a18 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.element_relation)) (tptp.member X Y))))
% 20.85/21.03  (assume a19 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (tptp.member X Y)) (tptp.member (tptp.ordered_pair X Y) tptp.element_relation))))
% 20.85/21.03  (assume a20 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X))))
% 20.85/21.03  (assume a21 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z Y))))
% 20.85/21.03  (assume a22 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z X)) (not (tptp.member Z Y)) (tptp.member Z (tptp.intersection X Y)))))
% 20.85/21.03  (assume a23 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.complement X))) (not (tptp.member Z X)))))
% 20.85/21.03  (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))))
% 20.85/21.03  (assume a25 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.complement (tptp.intersection (tptp.complement X) (tptp.complement Y))) (tptp.union X Y))))
% 20.85/21.03  (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))))
% 20.85/21.03  (assume a27 (forall ((Xr $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.intersection Xr (tptp.cross_product X Y)) (tptp.restrict Xr X Y))))
% 20.85/21.03  (assume a28 (forall ((X $$unsorted) (Y $$unsorted) (Xr $$unsorted)) (= (tptp.intersection (tptp.cross_product X Y) Xr) (tptp.restrict Xr X Y))))
% 20.85/21.03  (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))))))
% 20.85/21.03  (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)))))
% 20.85/21.03  (assume a31 (forall ((X $$unsorted)) (tptp.subclass (tptp.rotate X) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))))
% 20.85/21.03  (assume a32 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.rotate X))) (tptp.member (tptp.ordered_pair (tptp.ordered_pair V W) U) X))))
% 20.85/21.03  (assume a33 (forall ((V $$unsorted) (W $$unsorted) (U $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair V W) U) X)) (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.rotate X)))))
% 20.85/21.03  (assume a34 (forall ((X $$unsorted)) (tptp.subclass (tptp.flip X) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))))
% 20.85/21.03  (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))))
% 20.85/21.03  (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)))))
% 20.85/21.03  (assume a37 (forall ((Y $$unsorted)) (= (tptp.domain_of (tptp.flip (tptp.cross_product Y tptp.universal_class))) (tptp.inverse Y))))
% 20.85/21.03  (assume a38 (forall ((Z $$unsorted)) (= (tptp.domain_of (tptp.inverse Z)) (tptp.range_of Z))))
% 20.85/21.03  (assume a39 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.first (tptp.not_subclass_element (tptp.restrict Z X (tptp.singleton Y)) tptp.null_class)) (tptp.domain Z X Y))))
% 20.85/21.03  (assume a40 (forall ((Z $$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))))
% 20.85/21.03  (assume a41 (forall ((Xr $$unsorted) (X $$unsorted)) (= (tptp.range_of (tptp.restrict Xr X tptp.universal_class)) (tptp.image Xr X))))
% 20.85/21.03  (assume a42 (forall ((X $$unsorted)) (= (tptp.union X (tptp.singleton X)) (tptp.successor X))))
% 20.85/21.03  (assume a43 (tptp.subclass tptp.successor_relation (tptp.cross_product tptp.universal_class tptp.universal_class)))
% 20.85/21.03  (assume a44 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.successor_relation)) (= (tptp.successor X) Y))))
% 20.85/21.03  (assume a45 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (tptp.successor X) Y)) (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product tptp.universal_class tptp.universal_class))) (tptp.member (tptp.ordered_pair X Y) tptp.successor_relation))))
% 20.85/21.03  (assume a46 (forall ((X $$unsorted)) (or (not (tptp.inductive X)) (tptp.member tptp.null_class X))))
% 20.85/21.03  (assume a47 (forall ((X $$unsorted)) (or (not (tptp.inductive X)) (tptp.subclass (tptp.image tptp.successor_relation X) X))))
% 20.85/21.03  (assume a48 (forall ((X $$unsorted)) (or (not (tptp.member tptp.null_class X)) (not (tptp.subclass (tptp.image tptp.successor_relation X) X)) (tptp.inductive X))))
% 20.85/21.03  (assume a49 (tptp.inductive tptp.omega))
% 20.85/21.03  (assume a50 (forall ((Y $$unsorted)) (or (not (tptp.inductive Y)) (tptp.subclass tptp.omega Y))))
% 20.85/21.03  (assume a51 (tptp.member tptp.omega tptp.universal_class))
% 20.85/21.03  (assume a52 (forall ((X $$unsorted)) (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class X)) (tptp.sum_class X))))
% 20.85/21.03  (assume a53 (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.sum_class X) tptp.universal_class))))
% 20.85/21.03  (assume a54 (forall ((X $$unsorted)) (= (tptp.complement (tptp.image tptp.element_relation (tptp.complement X))) (tptp.power_class X))))
% 20.85/21.03  (assume a55 (forall ((U $$unsorted)) (or (not (tptp.member U tptp.universal_class)) (tptp.member (tptp.power_class U) tptp.universal_class))))
% 20.85/21.03  (assume a56 (forall ((Yr $$unsorted) (Xr $$unsorted)) (tptp.subclass (tptp.compose Yr Xr) (tptp.cross_product tptp.universal_class tptp.universal_class))))
% 20.85/21.03  (assume a57 (forall ((Y $$unsorted) (Z $$unsorted) (Yr $$unsorted) (Xr $$unsorted)) (or (not (tptp.member (tptp.ordered_pair Y Z) (tptp.compose Yr Xr))) (tptp.member Z (tptp.image Yr (tptp.image Xr (tptp.singleton Y)))))))
% 20.85/21.03  (assume a58 (forall ((Z $$unsorted) (Yr $$unsorted) (Xr $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.image Yr (tptp.image Xr (tptp.singleton Y))))) (not (tptp.member (tptp.ordered_pair Y Z) (tptp.cross_product tptp.universal_class tptp.universal_class))) (tptp.member (tptp.ordered_pair Y Z) (tptp.compose Yr Xr)))))
% 20.85/21.03  (assume a59 (forall ((X $$unsorted)) (or (not (tptp.single_valued_class X)) (tptp.subclass (tptp.compose X (tptp.inverse X)) tptp.identity_relation))))
% 20.85/21.03  (assume a60 (forall ((X $$unsorted)) (or (not (tptp.subclass (tptp.compose X (tptp.inverse X)) tptp.identity_relation)) (tptp.single_valued_class X))))
% 20.85/21.03  (assume a61 (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.subclass Xf (tptp.cross_product tptp.universal_class tptp.universal_class)))))
% 20.85/21.03  (assume a62 (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.subclass (tptp.compose Xf (tptp.inverse Xf)) tptp.identity_relation))))
% 20.85/21.03  (assume a63 (forall ((Xf $$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))))
% 20.85/21.03  (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))))
% 20.85/21.03  (assume a65 (forall ((X $$unsorted)) (or (= X tptp.null_class) (tptp.member (tptp.regular X) X))))
% 20.85/21.03  (assume a66 (forall ((X $$unsorted)) (or (= X tptp.null_class) (= (tptp.intersection X (tptp.regular X)) tptp.null_class))))
% 20.85/21.03  (assume a67 (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y))))
% 20.85/21.03  (assume a68 (tptp.function tptp.choice))
% 20.85/21.03  (assume a69 (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= Y tptp.null_class) (tptp.member (tptp.apply tptp.choice Y) Y))))
% 20.85/21.03  (assume a70 (forall ((Xf $$unsorted)) (or (not (tptp.one_to_one Xf)) (tptp.function Xf))))
% 20.85/21.03  (assume a71 (forall ((Xf $$unsorted)) (or (not (tptp.one_to_one Xf)) (tptp.function (tptp.inverse Xf)))))
% 20.85/21.03  (assume a72 (forall ((Xf $$unsorted)) (or (not (tptp.function (tptp.inverse Xf))) (not (tptp.function Xf)) (tptp.one_to_one Xf))))
% 20.85/21.03  (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))
% 20.85/21.03  (assume a74 (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation))
% 20.85/21.03  (assume a75 (forall ((Xr $$unsorted)) (= (tptp.complement (tptp.domain_of (tptp.intersection Xr tptp.identity_relation))) (tptp.diagonalise Xr))))
% 20.85/21.03  (assume a76 (forall ((X $$unsorted)) (= (tptp.intersection (tptp.domain_of X) (tptp.diagonalise (tptp.compose (tptp.inverse tptp.element_relation) X))) (tptp.cantor X))))
% 20.85/21.03  (assume a77 (forall ((Xf $$unsorted)) (or (not (tptp.operation Xf)) (tptp.function Xf))))
% 20.85/21.03  (assume a78 (forall ((Xf $$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)))))
% 20.85/21.03  (assume a79 (forall ((Xf $$unsorted)) (or (not (tptp.operation Xf)) (tptp.subclass (tptp.range_of Xf) (tptp.domain_of (tptp.domain_of Xf))))))
% 20.85/21.03  (assume a80 (forall ((Xf $$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))))
% 20.85/21.03  (assume a81 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (tptp.function Xh))))
% 20.85/21.03  (assume a82 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (= (tptp.domain_of (tptp.domain_of Xf1)) (tptp.domain_of Xh)))))
% 20.85/21.03  (assume a83 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (tptp.subclass (tptp.range_of Xh) (tptp.domain_of (tptp.domain_of Xf2))))))
% 20.85/21.03  (assume a84 (forall ((Xh $$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))))
% 20.85/21.03  (assume a85 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.operation Xf1))))
% 20.85/21.03  (assume a86 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.operation Xf2))))
% 20.85/21.03  (assume a87 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.compatible Xh Xf1 Xf2))))
% 20.85/21.03  (assume a88 (forall ((Xh $$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)))))))
% 20.85/21.03  (assume a89 (forall ((Xf1 $$unsorted) (Xf2 $$unsorted) (Xh $$unsorted)) (or (not (tptp.operation Xf1)) (not (tptp.operation Xf2)) (not (tptp.compatible Xh Xf1 Xf2)) (tptp.member (tptp.ordered_pair (tptp.not_homomorphism1 Xh Xf1 Xf2) (tptp.not_homomorphism2 Xh Xf1 Xf2)) (tptp.domain_of Xf1)) (tptp.homomorphism Xh Xf1 Xf2))))
% 20.85/21.03  (assume a90 (forall ((Xf1 $$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))))
% 20.85/21.03  (assume a91 (forall ((X $$unsorted)) (tptp.subclass (tptp.compose_class X) (tptp.cross_product tptp.universal_class tptp.universal_class))))
% 20.85/21.03  (assume a92 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair Y Z) (tptp.compose_class X))) (= (tptp.compose X Y) Z))))
% 20.85/21.03  (assume a93 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair Y Z) (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (= (tptp.compose X Y) Z)) (tptp.member (tptp.ordered_pair Y Z) (tptp.compose_class X)))))
% 20.85/21.03  (assume a94 (tptp.subclass tptp.composition_function (tptp.cross_product tptp.universal_class (tptp.cross_product tptp.universal_class tptp.universal_class))))
% 20.85/21.03  (assume a95 (forall ((X $$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))))
% 20.85/21.03  (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))))
% 20.85/21.03  (assume a97 (tptp.subclass tptp.domain_relation (tptp.cross_product tptp.universal_class tptp.universal_class)))
% 20.85/21.03  (assume a98 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.domain_relation)) (= (tptp.domain_of X) Y))))
% 20.85/21.03  (assume a99 (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.ordered_pair X (tptp.domain_of X)) tptp.domain_relation))))
% 20.85/21.03  (assume a100 (forall ((X $$unsorted)) (= (tptp.first (tptp.not_subclass_element (tptp.compose X (tptp.inverse X)) tptp.identity_relation)) (tptp.single_valued1 X))))
% 20.85/21.03  (assume a101 (forall ((X $$unsorted)) (= (tptp.second (tptp.not_subclass_element (tptp.compose X (tptp.inverse X)) tptp.identity_relation)) (tptp.single_valued2 X))))
% 20.85/21.03  (assume a102 (forall ((X $$unsorted)) (= (tptp.domain X (tptp.image (tptp.inverse X) (tptp.singleton (tptp.single_valued1 X))) (tptp.single_valued2 X)) (tptp.single_valued3 X))))
% 20.85/21.03  (assume a103 (= (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation (tptp.complement tptp.identity_relation))) tptp.element_relation) tptp.singleton_relation))
% 20.85/21.03  (assume a104 (tptp.subclass tptp.application_function (tptp.cross_product tptp.universal_class (tptp.cross_product tptp.universal_class tptp.universal_class))))
% 20.85/21.03  (assume a105 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X (tptp.ordered_pair Y Z)) tptp.application_function)) (tptp.member Y (tptp.domain_of X)))))
% 20.85/21.03  (assume a106 (forall ((X $$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))))
% 20.85/21.03  (assume a107 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X (tptp.ordered_pair Y Z)) (tptp.cross_product tptp.universal_class (tptp.cross_product tptp.universal_class tptp.universal_class)))) (not (tptp.member Y (tptp.domain_of X))) (tptp.member (tptp.ordered_pair X (tptp.ordered_pair Y (tptp.apply X Y))) tptp.application_function))))
% 20.85/21.03  (assume a108 (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.function Xf))))
% 20.85/21.03  (assume a109 (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (= (tptp.domain_of Xf) X))))
% 20.85/21.03  (assume a110 (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.subclass (tptp.range_of Xf) Y))))
% 20.85/21.03  (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))))
% 20.85/21.03  (assume a112 (forall ((X $$unsorted)) (= (tptp.union X (tptp.inverse X)) (tptp.symmetrization_of X))))
% 20.85/21.03  (assume a113 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.irreflexive X Y)) (tptp.subclass (tptp.restrict X Y Y) (tptp.complement tptp.identity_relation)))))
% 20.85/21.03  (assume a114 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subclass (tptp.restrict X Y Y) (tptp.complement tptp.identity_relation))) (tptp.irreflexive X Y))))
% 20.85/21.03  (assume a115 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.connected X Y)) (tptp.subclass (tptp.cross_product Y Y) (tptp.union tptp.identity_relation (tptp.symmetrization_of X))))))
% 20.85/21.03  (assume a116 (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.subclass (tptp.cross_product Y Y) (tptp.union tptp.identity_relation (tptp.symmetrization_of X)))) (tptp.connected X Y))))
% 20.85/21.03  (assume a117 (forall ((Xr $$unsorted) (Y $$unsorted)) (or (not (tptp.transitive Xr Y)) (tptp.subclass (tptp.compose (tptp.restrict Xr Y Y) (tptp.restrict Xr Y Y)) (tptp.restrict Xr Y Y)))))
% 20.85/21.03  (assume a118 (forall ((Xr $$unsorted) (Y $$unsorted)) (or (not (tptp.subclass (tptp.compose (tptp.restrict Xr Y Y) (tptp.restrict Xr Y Y)) (tptp.restrict Xr Y Y))) (tptp.transitive Xr Y))))
% 20.85/21.03  (assume a119 (forall ((Xr $$unsorted) (Y $$unsorted)) (or (not (tptp.asymmetric Xr Y)) (= (tptp.restrict (tptp.intersection Xr (tptp.inverse Xr)) Y Y) tptp.null_class))))
% 20.85/21.03  (assume a120 (forall ((Xr $$unsorted) (Y $$unsorted)) (or (not (= (tptp.restrict (tptp.intersection Xr (tptp.inverse Xr)) Y Y) tptp.null_class)) (tptp.asymmetric Xr Y))))
% 20.85/21.03  (assume a121 (forall ((Xr $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.segment Xr Y Z) (tptp.domain_of (tptp.restrict Xr Y (tptp.singleton Z))))))
% 20.85/21.03  (assume a122 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.well_ordering X Y)) (tptp.connected X Y))))
% 20.85/21.03  (assume a123 (forall ((Xr $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.well_ordering Xr Y)) (not (tptp.subclass U Y)) (= U tptp.null_class) (tptp.member (tptp.least Xr U) U))))
% 20.85/21.03  (assume a124 (forall ((Xr $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.well_ordering Xr Y)) (not (tptp.subclass U Y)) (not (tptp.member V U)) (tptp.member (tptp.least Xr U) U))))
% 20.85/21.03  (assume a125 (forall ((Xr $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.well_ordering Xr Y)) (not (tptp.subclass U Y)) (= (tptp.segment Xr U (tptp.least Xr U)) tptp.null_class))))
% 20.85/21.03  (assume a126 (forall ((Xr $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.well_ordering Xr Y)) (not (tptp.subclass U Y)) (not (tptp.member V U)) (not (tptp.member (tptp.ordered_pair V (tptp.least Xr U)) Xr)))))
% 20.85/21.03  (assume a127 (forall ((Xr $$unsorted) (Y $$unsorted)) (or (not (tptp.connected Xr Y)) (not (= (tptp.not_well_ordering Xr Y) tptp.null_class)) (tptp.well_ordering Xr Y))))
% 20.85/21.03  (assume a128 (forall ((Xr $$unsorted) (Y $$unsorted)) (or (not (tptp.connected Xr Y)) (tptp.subclass (tptp.not_well_ordering Xr Y) Y) (tptp.well_ordering Xr Y))))
% 20.85/21.03  (assume a129 (forall ((V $$unsorted) (Xr $$unsorted) (Y $$unsorted)) (or (not (tptp.member V (tptp.not_well_ordering Xr Y))) (not (= (tptp.segment Xr (tptp.not_well_ordering Xr Y) V) tptp.null_class)) (not (tptp.connected Xr Y)) (tptp.well_ordering Xr Y))))
% 20.85/21.03  (assume a130 (forall ((Xr $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.section Xr Y Z)) (tptp.subclass Y Z))))
% 20.85/21.03  (assume a131 (forall ((Xr $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.section Xr Y Z)) (tptp.subclass (tptp.domain_of (tptp.restrict Xr Z Y)) Y))))
% 20.85/21.03  (assume a132 (forall ((Y $$unsorted) (Z $$unsorted) (Xr $$unsorted)) (or (not (tptp.subclass Y Z)) (not (tptp.subclass (tptp.domain_of (tptp.restrict Xr Z Y)) Y)) (tptp.section Xr Y Z))))
% 20.85/21.03  (assume a133 (forall ((X $$unsorted)) (or (not (tptp.member X tptp.ordinal_numbers)) (tptp.well_ordering tptp.element_relation X))))
% 20.85/21.03  (assume a134 (forall ((X $$unsorted)) (or (not (tptp.member X tptp.ordinal_numbers)) (tptp.subclass (tptp.sum_class X) X))))
% 20.85/21.03  (assume a135 (forall ((X $$unsorted)) (or (not (tptp.well_ordering tptp.element_relation X)) (not (tptp.subclass (tptp.sum_class X) X)) (not (tptp.member X tptp.universal_class)) (tptp.member X tptp.ordinal_numbers))))
% 20.85/21.03  (assume a136 (forall ((X $$unsorted)) (or (not (tptp.well_ordering tptp.element_relation X)) (not (tptp.subclass (tptp.sum_class X) X)) (tptp.member X tptp.ordinal_numbers) (= X tptp.ordinal_numbers))))
% 20.85/21.03  (assume a137 (= (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)) tptp.kind_1_ordinals))
% 20.85/21.03  (assume a138 (= (tptp.intersection (tptp.complement tptp.kind_1_ordinals) tptp.ordinal_numbers) tptp.limit_ordinals))
% 20.85/21.03  (assume a139 (forall ((X $$unsorted)) (tptp.subclass (tptp.rest_of X) (tptp.cross_product tptp.universal_class tptp.universal_class))))
% 20.85/21.03  (assume a140 (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.rest_of X))) (tptp.member U (tptp.domain_of X)))))
% 20.85/21.03  (assume a141 (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.rest_of X))) (= (tptp.restrict X U tptp.universal_class) V))))
% 20.85/21.03  (assume a142 (forall ((U $$unsorted) (X $$unsorted) (V $$unsorted)) (or (not (tptp.member U (tptp.domain_of X))) (not (= (tptp.restrict X U tptp.universal_class) V)) (tptp.member (tptp.ordered_pair U V) (tptp.rest_of X)))))
% 20.85/21.03  (assume a143 (tptp.subclass tptp.rest_relation (tptp.cross_product tptp.universal_class tptp.universal_class)))
% 20.85/21.03  (assume a144 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.rest_relation)) (= (tptp.rest_of X) Y))))
% 20.85/21.03  (assume a145 (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.ordered_pair X (tptp.rest_of X)) tptp.rest_relation))))
% 20.85/21.03  (assume a146 (forall ((X $$unsorted) (Z $$unsorted)) (or (not (tptp.member X (tptp.recursion_equation_functions Z))) (tptp.function Z))))
% 20.85/21.03  (assume a147 (forall ((X $$unsorted) (Z $$unsorted)) (or (not (tptp.member X (tptp.recursion_equation_functions Z))) (tptp.function X))))
% 20.85/21.03  (assume a148 (forall ((X $$unsorted) (Z $$unsorted)) (or (not (tptp.member X (tptp.recursion_equation_functions Z))) (tptp.member (tptp.domain_of X) tptp.ordinal_numbers))))
% 20.85/21.03  (assume a149 (forall ((X $$unsorted) (Z $$unsorted)) (or (not (tptp.member X (tptp.recursion_equation_functions Z))) (= (tptp.compose Z (tptp.rest_of X)) X))))
% 20.85/21.03  (assume a150 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.function Z)) (not (tptp.function X)) (not (tptp.member (tptp.domain_of X) tptp.ordinal_numbers)) (not (= (tptp.compose Z (tptp.rest_of X)) X)) (tptp.member X (tptp.recursion_equation_functions Z)))))
% 20.85/21.03  (assume a151 (tptp.subclass tptp.union_of_range_map (tptp.cross_product tptp.universal_class tptp.universal_class)))
% 20.85/21.03  (assume a152 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.union_of_range_map)) (= (tptp.sum_class (tptp.range_of X)) Y))))
% 20.85/21.03  (assume a153 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (= (tptp.sum_class (tptp.range_of X)) Y)) (tptp.member (tptp.ordered_pair X Y) tptp.union_of_range_map))))
% 20.85/21.03  (assume a154 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.apply (tptp.recursion X tptp.successor_relation tptp.union_of_range_map) Y) (tptp.ordinal_add X Y))))
% 20.85/21.03  (assume a155 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.recursion tptp.null_class (tptp.apply tptp.add_relation X) tptp.union_of_range_map) (tptp.ordinal_multiply X Y))))
% 20.85/21.03  (assume a156 (forall ((X $$unsorted)) (or (not (tptp.member X tptp.omega)) (= (tptp.integer_of X) X))))
% 20.85/21.03  (assume a157 (forall ((X $$unsorted)) (or (tptp.member X tptp.omega) (= (tptp.integer_of X) tptp.null_class))))
% 20.85/21.03  (assume a158 (tptp.member tptp.x tptp.ordinal_numbers))
% 20.85/21.03  (assume a159 (not (tptp.member tptp.x tptp.kind_1_ordinals)))
% 20.85/21.03  (assume a160 (not (tptp.member tptp.x tptp.limit_ordinals)))
% 20.85/21.03  (step t1 (cl (=> (forall ((X $$unsorted)) (tptp.subclass X tptp.universal_class)) (tptp.subclass tptp.ordinal_numbers tptp.universal_class)) (forall ((X $$unsorted)) (tptp.subclass X tptp.universal_class))) :rule implies_neg1)
% 20.85/21.03  (anchor :step t2)
% 20.85/21.03  (assume t2.a0 (forall ((X $$unsorted)) (tptp.subclass X tptp.universal_class)))
% 20.85/21.03  (step t2.t1 (cl (or (not (forall ((X $$unsorted)) (tptp.subclass X tptp.universal_class))) (tptp.subclass tptp.ordinal_numbers tptp.universal_class))) :rule forall_inst :args ((:= X tptp.ordinal_numbers)))
% 20.85/21.03  (step t2.t2 (cl (not (forall ((X $$unsorted)) (tptp.subclass X tptp.universal_class))) (tptp.subclass tptp.ordinal_numbers tptp.universal_class)) :rule or :premises (t2.t1))
% 20.85/21.03  (step t2.t3 (cl (tptp.subclass tptp.ordinal_numbers tptp.universal_class)) :rule resolution :premises (t2.t2 t2.a0))
% 20.85/21.03  (step t2 (cl (not (forall ((X $$unsorted)) (tptp.subclass X tptp.universal_class))) (tptp.subclass tptp.ordinal_numbers tptp.universal_class)) :rule subproof :discharge (t2.a0))
% 20.85/21.03  (step t3 (cl (=> (forall ((X $$unsorted)) (tptp.subclass X tptp.universal_class)) (tptp.subclass tptp.ordinal_numbers tptp.universal_class)) (tptp.subclass tptp.ordinal_numbers tptp.universal_class)) :rule resolution :premises (t1 t2))
% 20.85/21.03  (step t4 (cl (=> (forall ((X $$unsorted)) (tptp.subclass X tptp.universal_class)) (tptp.subclass tptp.ordinal_numbers tptp.universal_class)) (not (tptp.subclass tptp.ordinal_numbers tptp.universal_class))) :rule implies_neg2)
% 20.85/21.03  (step t5 (cl (=> (forall ((X $$unsorted)) (tptp.subclass X tptp.universal_class)) (tptp.subclass tptp.ordinal_numbers tptp.universal_class)) (=> (forall ((X $$unsorted)) (tptp.subclass X tptp.universal_class)) (tptp.subclass tptp.ordinal_numbers tptp.universal_class))) :rule resolution :premises (t3 t4))
% 20.85/21.03  (step t6 (cl (=> (forall ((X $$unsorted)) (tptp.subclass X tptp.universal_class)) (tptp.subclass tptp.ordinal_numbers tptp.universal_class))) :rule contraction :premises (t5))
% 20.85/21.03  (step t7 (cl (not (forall ((X $$unsorted)) (tptp.subclass X tptp.universal_class))) (tptp.subclass tptp.ordinal_numbers tptp.universal_class)) :rule implies :premises (t6))
% 20.85/21.03  (step t8 (cl (not (or (not (tptp.subclass tptp.ordinal_numbers tptp.universal_class)) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x tptp.universal_class))) (not (tptp.subclass tptp.ordinal_numbers tptp.universal_class)) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x tptp.universal_class)) :rule or_pos)
% 20.85/21.03  (step t9 (cl (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x tptp.universal_class) (not (tptp.subclass tptp.ordinal_numbers tptp.universal_class)) (not (or (not (tptp.subclass tptp.ordinal_numbers tptp.universal_class)) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x tptp.universal_class)))) :rule reordering :premises (t8))
% 20.85/21.03  (step t10 (cl (not (or (not (tptp.member tptp.x tptp.universal_class)) (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))) (tptp.member tptp.x (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) (not (tptp.member tptp.x tptp.universal_class)) (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))) (tptp.member tptp.x (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))) :rule or_pos)
% 20.85/21.03  (step t11 (cl (tptp.member tptp.x (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) (not (tptp.member tptp.x tptp.universal_class)) (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))) (not (or (not (tptp.member tptp.x tptp.universal_class)) (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))) (tptp.member tptp.x (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))))) :rule reordering :premises (t10))
% 20.85/21.03  (step t12 (cl (not (= (not (tptp.member tptp.x tptp.kind_1_ordinals)) (not (tptp.member tptp.x (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))))) (not (not (tptp.member tptp.x tptp.kind_1_ordinals))) (not (tptp.member tptp.x (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) :rule equiv_pos2)
% 20.85/21.03  (step t13 (cl (= tptp.x tptp.x)) :rule refl)
% 20.85/21.03  (step t14 (cl (and (= tptp.limit_ordinals (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers)) (= tptp.kind_1_ordinals (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) (= tptp.singleton_relation (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation (tptp.complement (tptp.intersection (tptp.inverse (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.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.element_relation)) (= tptp.identity_relation (tptp.intersection (tptp.inverse (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.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 (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))))))) (not (= tptp.limit_ordinals (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers))) (not (= tptp.kind_1_ordinals (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))) (not (= tptp.singleton_relation (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation (tptp.complement (tptp.intersection (tptp.inverse (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.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.element_relation))) (not (= tptp.identity_relation (tptp.intersection (tptp.inverse (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.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)))))))) (not (= tptp.subset_relation (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)))))))) :rule and_neg)
% 20.85/21.03  (step t15 (cl (not (= (= tptp.limit_ordinals (tptp.intersection (tptp.complement tptp.kind_1_ordinals) tptp.ordinal_numbers)) (= tptp.limit_ordinals (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers)))) (not (= tptp.limit_ordinals (tptp.intersection (tptp.complement tptp.kind_1_ordinals) tptp.ordinal_numbers))) (= tptp.limit_ordinals (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers))) :rule equiv_pos2)
% 20.85/21.03  (step t16 (cl (= tptp.limit_ordinals tptp.limit_ordinals)) :rule refl)
% 20.85/21.03  (step t17 (cl (and (= tptp.kind_1_ordinals (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) (= tptp.singleton_relation (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation (tptp.complement (tptp.intersection (tptp.inverse (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.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.element_relation)) (= tptp.identity_relation (tptp.intersection (tptp.inverse (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.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 (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))))))) (not (= tptp.kind_1_ordinals (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))) (not (= tptp.singleton_relation (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation (tptp.complement (tptp.intersection (tptp.inverse (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.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.element_relation))) (not (= tptp.identity_relation (tptp.intersection (tptp.inverse (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.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)))))))) (not (= tptp.subset_relation (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)))))))) :rule and_neg)
% 20.85/21.03  (step t18 (cl (= tptp.kind_1_ordinals (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))) :rule symm :premises (a137))
% 20.85/21.03  (step t19 (cl (not (= (= tptp.singleton_relation (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation (tptp.complement tptp.identity_relation))) tptp.element_relation)) (= tptp.singleton_relation (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation (tptp.complement (tptp.intersection (tptp.inverse (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.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.element_relation)))) (not (= tptp.singleton_relation (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation (tptp.complement tptp.identity_relation))) tptp.element_relation))) (= tptp.singleton_relation (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation (tptp.complement (tptp.intersection (tptp.inverse (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.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.element_relation))) :rule equiv_pos2)
% 20.85/21.03  (step t20 (cl (= tptp.singleton_relation tptp.singleton_relation)) :rule refl)
% 20.85/21.03  (step t21 (cl (= tptp.element_relation tptp.element_relation)) :rule refl)
% 20.85/21.03  (step t22 (cl (and (= tptp.identity_relation (tptp.intersection (tptp.inverse (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.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 (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))))))) (not (= tptp.identity_relation (tptp.intersection (tptp.inverse (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.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)))))))) (not (= tptp.subset_relation (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)))))))) :rule and_neg)
% 20.85/21.03  (step t23 (cl (not (= (= tptp.identity_relation (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation)) (= tptp.identity_relation (tptp.intersection (tptp.inverse (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.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))))))))) (not (= tptp.identity_relation (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation))) (= tptp.identity_relation (tptp.intersection (tptp.inverse (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.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)))))))) :rule equiv_pos2)
% 20.85/21.03  (step t24 (cl (= tptp.identity_relation tptp.identity_relation)) :rule refl)
% 20.85/21.03  (step t25 (cl (= tptp.subset_relation (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))))))) :rule symm :premises (a73))
% 20.85/21.03  (step t26 (cl (= (tptp.inverse tptp.subset_relation) (tptp.inverse (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)))))))) :rule cong :premises (t25))
% 20.85/21.03  (step t27 (cl (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) (tptp.intersection (tptp.inverse (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.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)))))))) :rule cong :premises (t26 t25))
% 20.85/21.03  (step t28 (cl (= (= tptp.identity_relation (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation)) (= tptp.identity_relation (tptp.intersection (tptp.inverse (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.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))))))))) :rule cong :premises (t24 t27))
% 20.85/21.03  (step t29 (cl (= tptp.identity_relation (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation))) :rule symm :premises (a74))
% 20.85/21.03  (step t30 (cl (= tptp.identity_relation (tptp.intersection (tptp.inverse (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.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)))))))) :rule resolution :premises (t23 t28 t29))
% 20.85/21.03  (step t31 (cl (= tptp.subset_relation (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))))))) :rule symm :premises (a73))
% 20.85/21.03  (step t32 (cl (and (= tptp.identity_relation (tptp.intersection (tptp.inverse (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.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 (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)))))))) :rule resolution :premises (t22 t30 t31))
% 20.85/21.03  (step t33 (cl (= tptp.identity_relation (tptp.intersection (tptp.inverse (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.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)))))))) :rule and :premises (t32))
% 20.85/21.03  (step t34 (cl (= (tptp.complement tptp.identity_relation) (tptp.complement (tptp.intersection (tptp.inverse (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.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))))))))) :rule cong :premises (t33))
% 20.85/21.03  (step t35 (cl (= (tptp.compose tptp.element_relation (tptp.complement tptp.identity_relation)) (tptp.compose tptp.element_relation (tptp.complement (tptp.intersection (tptp.inverse (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.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)))))))))) :rule cong :premises (t21 t34))
% 20.85/21.03  (step t36 (cl (= (tptp.complement (tptp.compose tptp.element_relation (tptp.complement tptp.identity_relation))) (tptp.complement (tptp.compose tptp.element_relation (tptp.complement (tptp.intersection (tptp.inverse (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.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))))))))))) :rule cong :premises (t35))
% 20.85/21.03  (step t37 (cl (= (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation (tptp.complement tptp.identity_relation))) tptp.element_relation) (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation (tptp.complement (tptp.intersection (tptp.inverse (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.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.element_relation))) :rule cong :premises (t36 t21))
% 20.85/21.03  (step t38 (cl (= (= tptp.singleton_relation (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation (tptp.complement tptp.identity_relation))) tptp.element_relation)) (= tptp.singleton_relation (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation (tptp.complement (tptp.intersection (tptp.inverse (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.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.element_relation)))) :rule cong :premises (t20 t37))
% 20.85/21.03  (step t39 (cl (= tptp.singleton_relation (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation (tptp.complement tptp.identity_relation))) tptp.element_relation))) :rule symm :premises (a103))
% 20.85/21.03  (step t40 (cl (= tptp.singleton_relation (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation (tptp.complement (tptp.intersection (tptp.inverse (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.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.element_relation))) :rule resolution :premises (t19 t38 t39))
% 20.85/21.03  (step t41 (cl (and (= tptp.kind_1_ordinals (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) (= tptp.singleton_relation (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation (tptp.complement (tptp.intersection (tptp.inverse (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.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.element_relation)) (= tptp.identity_relation (tptp.intersection (tptp.inverse (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.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 (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)))))))) :rule resolution :premises (t17 t18 t40 t30 t31))
% 20.85/21.03  (step t42 (cl (= tptp.kind_1_ordinals (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))) :rule and :premises (t41))
% 20.85/21.03  (step t43 (cl (= (tptp.complement tptp.kind_1_ordinals) (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) :rule cong :premises (t42))
% 20.85/21.03  (step t44 (cl (= tptp.ordinal_numbers tptp.ordinal_numbers)) :rule refl)
% 20.85/21.03  (step t45 (cl (= (tptp.intersection (tptp.complement tptp.kind_1_ordinals) tptp.ordinal_numbers) (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers))) :rule cong :premises (t43 t44))
% 20.85/21.03  (step t46 (cl (= (= tptp.limit_ordinals (tptp.intersection (tptp.complement tptp.kind_1_ordinals) tptp.ordinal_numbers)) (= tptp.limit_ordinals (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers)))) :rule cong :premises (t16 t45))
% 20.85/21.03  (step t47 (cl (= tptp.limit_ordinals (tptp.intersection (tptp.complement tptp.kind_1_ordinals) tptp.ordinal_numbers))) :rule symm :premises (a138))
% 20.85/21.03  (step t48 (cl (= tptp.limit_ordinals (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers))) :rule resolution :premises (t15 t46 t47))
% 20.85/21.03  (step t49 (cl (and (= tptp.limit_ordinals (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers)) (= tptp.kind_1_ordinals (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) (= tptp.singleton_relation (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation (tptp.complement (tptp.intersection (tptp.inverse (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.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.element_relation)) (= tptp.identity_relation (tptp.intersection (tptp.inverse (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.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 (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)))))))) :rule resolution :premises (t14 t48 t18 t40 t30 t31))
% 20.85/21.03  (step t50 (cl (= tptp.kind_1_ordinals (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))) :rule and :premises (t49))
% 20.85/21.03  (step t51 (cl (= (tptp.member tptp.x tptp.kind_1_ordinals) (tptp.member tptp.x (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) :rule cong :premises (t13 t50))
% 20.85/21.03  (step t52 (cl (= (not (tptp.member tptp.x tptp.kind_1_ordinals)) (not (tptp.member tptp.x (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))))) :rule cong :premises (t51))
% 20.85/21.03  (step t53 (cl (not (tptp.member tptp.x (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) :rule resolution :premises (t12 t52 a159))
% 20.85/21.03  (step t54 (cl (not (or (not (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers)))) (not (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers))) :rule or_pos)
% 20.85/21.03  (step t55 (cl (tptp.member tptp.x (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers)) (not (tptp.member tptp.x tptp.ordinal_numbers)) (not (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) (not (or (not (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers))))) :rule reordering :premises (t54))
% 20.85/21.03  (step t56 (cl (not (= (not (tptp.member tptp.x tptp.limit_ordinals)) (not (tptp.member tptp.x (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers))))) (not (not (tptp.member tptp.x tptp.limit_ordinals))) (not (tptp.member tptp.x (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers)))) :rule equiv_pos2)
% 20.85/21.03  (step t57 (cl (= tptp.x tptp.x)) :rule refl)
% 20.85/21.03  (step t58 (cl (= tptp.limit_ordinals (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers))) :rule and :premises (t49))
% 20.85/21.03  (step t59 (cl (= (tptp.member tptp.x tptp.limit_ordinals) (tptp.member tptp.x (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers)))) :rule cong :premises (t57 t58))
% 20.85/21.03  (step t60 (cl (= (not (tptp.member tptp.x tptp.limit_ordinals)) (not (tptp.member tptp.x (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers))))) :rule cong :premises (t59))
% 20.85/21.03  (step t61 (cl (not (tptp.member tptp.x (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers)))) :rule resolution :premises (t56 t60 a160))
% 20.85/21.03  (step t62 (cl (=> (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)))) (or (not (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers)))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z X)) (not (tptp.member Z Y)) (tptp.member Z (tptp.intersection X Y))))) :rule implies_neg1)
% 20.85/21.03  (anchor :step t63)
% 20.85/21.03  (assume t63.a0 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z X)) (not (tptp.member Z Y)) (tptp.member Z (tptp.intersection X Y)))))
% 20.85/21.03  (step t63.t1 (cl (or (not (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z X)) (not (tptp.member Z Y)) (tptp.member Z (tptp.intersection X Y))))) (or (not (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers))))) :rule forall_inst :args ((:= Z tptp.x) (:= X (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))) (:= Y tptp.ordinal_numbers)))
% 20.85/21.03  (step t63.t2 (cl (not (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z X)) (not (tptp.member Z Y)) (tptp.member Z (tptp.intersection X Y))))) (or (not (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers)))) :rule or :premises (t63.t1))
% 20.85/21.03  (step t63.t3 (cl (or (not (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers)))) :rule resolution :premises (t63.t2 t63.a0))
% 20.85/21.03  (step t63 (cl (not (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z X)) (not (tptp.member Z Y)) (tptp.member Z (tptp.intersection X Y))))) (or (not (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers)))) :rule subproof :discharge (t63.a0))
% 20.85/21.03  (step t64 (cl (=> (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z X)) (not (tptp.member Z Y)) (tptp.member Z (tptp.intersection X Y)))) (or (not (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers)))) (or (not (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers)))) :rule resolution :premises (t62 t63))
% 20.85/21.03  (step t65 (cl (=> (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z X)) (not (tptp.member Z Y)) (tptp.member Z (tptp.intersection X Y)))) (or (not (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers)))) (not (or (not (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers))))) :rule implies_neg2)
% 20.85/21.03  (step t66 (cl (=> (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z X)) (not (tptp.member Z Y)) (tptp.member Z (tptp.intersection X Y)))) (or (not (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers)))) (=> (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z X)) (not (tptp.member Z Y)) (tptp.member Z (tptp.intersection X Y)))) (or (not (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers))))) :rule resolution :premises (t64 t65))
% 20.85/21.03  (step t67 (cl (=> (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z X)) (not (tptp.member Z Y)) (tptp.member Z (tptp.intersection X Y)))) (or (not (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers))))) :rule contraction :premises (t66))
% 20.85/21.03  (step t68 (cl (not (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z X)) (not (tptp.member Z Y)) (tptp.member Z (tptp.intersection X Y))))) (or (not (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers)))) :rule implies :premises (t67))
% 20.85/21.03  (step t69 (cl (or (not (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x (tptp.intersection (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))) tptp.ordinal_numbers)))) :rule resolution :premises (t68 a22))
% 20.85/21.03  (step t70 (cl (not (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))))) :rule resolution :premises (t55 t61 a158 t69))
% 20.85/21.03  (step t71 (cl (=> (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z tptp.universal_class)) (tptp.member Z (tptp.complement X)) (tptp.member Z X))) (or (not (tptp.member tptp.x tptp.universal_class)) (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))) (tptp.member tptp.x (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z tptp.universal_class)) (tptp.member Z (tptp.complement X)) (tptp.member Z X)))) :rule implies_neg1)
% 20.85/21.03  (anchor :step t72)
% 20.85/21.03  (assume t72.a0 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z tptp.universal_class)) (tptp.member Z (tptp.complement X)) (tptp.member Z X))))
% 20.85/21.03  (step t72.t1 (cl (or (not (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z tptp.universal_class)) (tptp.member Z (tptp.complement X)) (tptp.member Z X)))) (or (not (tptp.member tptp.x tptp.universal_class)) (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))) (tptp.member tptp.x (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))))) :rule forall_inst :args ((:= Z tptp.x) (:= X (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))))
% 20.85/21.03  (step t72.t2 (cl (not (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z tptp.universal_class)) (tptp.member Z (tptp.complement X)) (tptp.member Z X)))) (or (not (tptp.member tptp.x tptp.universal_class)) (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))) (tptp.member tptp.x (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) :rule or :premises (t72.t1))
% 20.85/21.03  (step t72.t3 (cl (or (not (tptp.member tptp.x tptp.universal_class)) (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))) (tptp.member tptp.x (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) :rule resolution :premises (t72.t2 t72.a0))
% 20.85/21.03  (step t72 (cl (not (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z tptp.universal_class)) (tptp.member Z (tptp.complement X)) (tptp.member Z X)))) (or (not (tptp.member tptp.x tptp.universal_class)) (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))) (tptp.member tptp.x (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) :rule subproof :discharge (t72.a0))
% 20.85/21.03  (step t73 (cl (=> (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z tptp.universal_class)) (tptp.member Z (tptp.complement X)) (tptp.member Z X))) (or (not (tptp.member tptp.x tptp.universal_class)) (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))) (tptp.member tptp.x (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) (or (not (tptp.member tptp.x tptp.universal_class)) (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))) (tptp.member tptp.x (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) :rule resolution :premises (t71 t72))
% 20.85/21.03  (step t74 (cl (=> (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z tptp.universal_class)) (tptp.member Z (tptp.complement X)) (tptp.member Z X))) (or (not (tptp.member tptp.x tptp.universal_class)) (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))) (tptp.member tptp.x (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) (not (or (not (tptp.member tptp.x tptp.universal_class)) (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))) (tptp.member tptp.x (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))))) :rule implies_neg2)
% 20.85/21.03  (step t75 (cl (=> (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z tptp.universal_class)) (tptp.member Z (tptp.complement X)) (tptp.member Z X))) (or (not (tptp.member tptp.x tptp.universal_class)) (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))) (tptp.member tptp.x (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) (=> (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z tptp.universal_class)) (tptp.member Z (tptp.complement X)) (tptp.member Z X))) (or (not (tptp.member tptp.x tptp.universal_class)) (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))) (tptp.member tptp.x (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))))) :rule resolution :premises (t73 t74))
% 20.85/21.03  (step t76 (cl (=> (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z tptp.universal_class)) (tptp.member Z (tptp.complement X)) (tptp.member Z X))) (or (not (tptp.member tptp.x tptp.universal_class)) (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))) (tptp.member tptp.x (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))))) :rule contraction :premises (t75))
% 20.85/21.03  (step t77 (cl (not (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z tptp.universal_class)) (tptp.member Z (tptp.complement X)) (tptp.member Z X)))) (or (not (tptp.member tptp.x tptp.universal_class)) (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))) (tptp.member tptp.x (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) :rule implies :premises (t76))
% 20.85/21.03  (step t78 (cl (or (not (tptp.member tptp.x tptp.universal_class)) (tptp.member tptp.x (tptp.complement (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)))) (tptp.member tptp.x (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers))))) :rule resolution :premises (t77 a24))
% 20.85/21.03  (step t79 (cl (not (tptp.member tptp.x tptp.universal_class))) :rule resolution :premises (t11 t53 t70 t78))
% 20.85/21.03  (step t80 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y))) (or (not (tptp.subclass tptp.ordinal_numbers tptp.universal_class)) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x tptp.universal_class))) (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y)))) :rule implies_neg1)
% 20.85/21.03  (anchor :step t81)
% 20.85/21.03  (assume t81.a0 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y))))
% 20.85/21.03  (step t81.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y)))) (or (not (tptp.subclass tptp.ordinal_numbers tptp.universal_class)) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x tptp.universal_class)))) :rule forall_inst :args ((:= X tptp.ordinal_numbers) (:= Y tptp.universal_class) (:= U tptp.x)))
% 20.85/21.03  (step t81.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y)))) (or (not (tptp.subclass tptp.ordinal_numbers tptp.universal_class)) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x tptp.universal_class))) :rule or :premises (t81.t1))
% 20.85/21.03  (step t81.t3 (cl (or (not (tptp.subclass tptp.ordinal_numbers tptp.universal_class)) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x tptp.universal_class))) :rule resolution :premises (t81.t2 t81.a0))
% 20.85/21.03  (step t81 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y)))) (or (not (tptp.subclass tptp.ordinal_numbers tptp.universal_class)) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x tptp.universal_class))) :rule subproof :discharge (t81.a0))
% 20.85/21.03  (step t82 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y))) (or (not (tptp.subclass tptp.ordinal_numbers tptp.universal_class)) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x tptp.universal_class))) (or (not (tptp.subclass tptp.ordinal_numbers tptp.universal_class)) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x tptp.universal_class))) :rule resolution :premises (t80 t81))
% 20.85/21.03  (step t83 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y))) (or (not (tptp.subclass tptp.ordinal_numbers tptp.universal_class)) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x tptp.universal_class))) (not (or (not (tptp.subclass tptp.ordinal_numbers tptp.universal_class)) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x tptp.universal_class)))) :rule implies_neg2)
% 20.85/21.03  (step t84 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y))) (or (not (tptp.subclass tptp.ordinal_numbers tptp.universal_class)) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x tptp.universal_class))) (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y))) (or (not (tptp.subclass tptp.ordinal_numbers tptp.universal_class)) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x tptp.universal_class)))) :rule resolution :premises (t82 t83))
% 20.85/21.03  (step t85 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y))) (or (not (tptp.subclass tptp.ordinal_numbers tptp.universal_class)) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x tptp.universal_class)))) :rule contraction :premises (t84))
% 20.85/21.03  (step t86 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y)))) (or (not (tptp.subclass tptp.ordinal_numbers tptp.universal_class)) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x tptp.universal_class))) :rule implies :premises (t85))
% 20.85/21.03  (step t87 (cl (or (not (tptp.subclass tptp.ordinal_numbers tptp.universal_class)) (not (tptp.member tptp.x tptp.ordinal_numbers)) (tptp.member tptp.x tptp.universal_class))) :rule resolution :premises (t86 a0))
% 20.85/21.03  (step t88 (cl (not (tptp.subclass tptp.ordinal_numbers tptp.universal_class))) :rule resolution :premises (t9 a158 t79 t87))
% 20.85/21.03  (step t89 (cl) :rule resolution :premises (t7 t88 a3))
% 20.85/21.03  
% 20.85/21.03  % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.r6lfGkbp3Y/cvc5---1.0.5_5623.smt2
% 20.87/21.03  % cvc5---1.0.5 exiting
% 20.87/21.04  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------