TSTP Solution File: SET079-7 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET079-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n003.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 17:44:04 EDT 2024
% Result : Unsatisfiable 0.38s 0.60s
% Output : Proof 0.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET079-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n003.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 08:21:09 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.21/0.52 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.52 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.38/0.60 % SZS status Unsatisfiable for /export/starexec/sandbox2/tmp/tmp.PHS6MkgTGq/cvc5---1.0.5_22082.smt2
% 0.38/0.60 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.PHS6MkgTGq/cvc5---1.0.5_22082.smt2
% 0.38/0.61 (assume a0 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y))))
% 0.38/0.61 (assume a1 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y))))
% 0.38/0.61 (assume a2 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (tptp.subclass X Y))))
% 0.38/0.61 (assume a3 (forall ((X $$unsorted)) (tptp.subclass X tptp.universal_class)))
% 0.38/0.61 (assume a4 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.subclass X Y))))
% 0.38/0.61 (assume a5 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.subclass Y X))))
% 0.38/0.61 (assume a6 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.subclass Y X)) (= X Y))))
% 0.38/0.61 (assume a7 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))))
% 0.38/0.61 (assume a8 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))))
% 0.38/0.61 (assume a9 (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (tptp.member Y (tptp.unordered_pair X Y)))))
% 0.38/0.61 (assume a10 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)))
% 0.38/0.61 (assume a11 (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))))
% 0.38/0.61 (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))))
% 0.38/0.61 (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))))
% 0.38/0.61 (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))))
% 0.38/0.61 (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)))))
% 0.38/0.61 (assume a16 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= (tptp.ordered_pair (tptp.first Z) (tptp.second Z)) Z))))
% 0.38/0.61 (assume a17 (tptp.subclass tptp.element_relation (tptp.cross_product tptp.universal_class tptp.universal_class)))
% 0.38/0.61 (assume a18 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.element_relation)) (tptp.member X Y))))
% 0.38/0.61 (assume a19 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (tptp.member X Y)) (tptp.member (tptp.ordered_pair X Y) tptp.element_relation))))
% 0.38/0.61 (assume a20 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X))))
% 0.38/0.61 (assume a21 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z Y))))
% 0.38/0.61 (assume a22 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z X)) (not (tptp.member Z Y)) (tptp.member Z (tptp.intersection X Y)))))
% 0.38/0.61 (assume a23 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.complement X))) (not (tptp.member Z X)))))
% 0.38/0.61 (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))))
% 0.38/0.61 (assume a25 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.complement (tptp.intersection (tptp.complement X) (tptp.complement Y))) (tptp.union X Y))))
% 0.38/0.61 (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))))
% 0.38/0.61 (assume a27 (forall ((Xr $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.intersection Xr (tptp.cross_product X Y)) (tptp.restrict Xr X Y))))
% 0.38/0.61 (assume a28 (forall ((X $$unsorted) (Y $$unsorted) (Xr $$unsorted)) (= (tptp.intersection (tptp.cross_product X Y) Xr) (tptp.restrict Xr X Y))))
% 0.38/0.61 (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))))))
% 0.38/0.61 (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)))))
% 0.38/0.61 (assume a31 (forall ((X $$unsorted)) (tptp.subclass (tptp.rotate X) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))))
% 0.38/0.61 (assume a32 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.rotate X))) (tptp.member (tptp.ordered_pair (tptp.ordered_pair V W) U) X))))
% 0.38/0.61 (assume a33 (forall ((V $$unsorted) (W $$unsorted) (U $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair V W) U) X)) (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.rotate X)))))
% 0.38/0.61 (assume a34 (forall ((X $$unsorted)) (tptp.subclass (tptp.flip X) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))))
% 0.38/0.61 (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))))
% 0.38/0.61 (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)))))
% 0.38/0.61 (assume a37 (forall ((Y $$unsorted)) (= (tptp.domain_of (tptp.flip (tptp.cross_product Y tptp.universal_class))) (tptp.inverse Y))))
% 0.38/0.61 (assume a38 (forall ((Z $$unsorted)) (= (tptp.domain_of (tptp.inverse Z)) (tptp.range_of Z))))
% 0.38/0.61 (assume a39 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.first (tptp.not_subclass_element (tptp.restrict Z X (tptp.singleton Y)) tptp.null_class)) (tptp.domain Z X Y))))
% 0.38/0.61 (assume a40 (forall ((Z $$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))))
% 0.38/0.61 (assume a41 (forall ((Xr $$unsorted) (X $$unsorted)) (= (tptp.range_of (tptp.restrict Xr X tptp.universal_class)) (tptp.image Xr X))))
% 0.38/0.61 (assume a42 (forall ((X $$unsorted)) (= (tptp.union X (tptp.singleton X)) (tptp.successor X))))
% 0.38/0.61 (assume a43 (tptp.subclass tptp.successor_relation (tptp.cross_product tptp.universal_class tptp.universal_class)))
% 0.38/0.61 (assume a44 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.successor_relation)) (= (tptp.successor X) Y))))
% 0.38/0.61 (assume a45 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (tptp.successor X) Y)) (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product tptp.universal_class tptp.universal_class))) (tptp.member (tptp.ordered_pair X Y) tptp.successor_relation))))
% 0.38/0.61 (assume a46 (forall ((X $$unsorted)) (or (not (tptp.inductive X)) (tptp.member tptp.null_class X))))
% 0.38/0.61 (assume a47 (forall ((X $$unsorted)) (or (not (tptp.inductive X)) (tptp.subclass (tptp.image tptp.successor_relation X) X))))
% 0.38/0.61 (assume a48 (forall ((X $$unsorted)) (or (not (tptp.member tptp.null_class X)) (not (tptp.subclass (tptp.image tptp.successor_relation X) X)) (tptp.inductive X))))
% 0.38/0.61 (assume a49 (tptp.inductive tptp.omega))
% 0.38/0.61 (assume a50 (forall ((Y $$unsorted)) (or (not (tptp.inductive Y)) (tptp.subclass tptp.omega Y))))
% 0.38/0.61 (assume a51 (tptp.member tptp.omega tptp.universal_class))
% 0.38/0.61 (assume a52 (forall ((X $$unsorted)) (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class X)) (tptp.sum_class X))))
% 0.38/0.61 (assume a53 (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.sum_class X) tptp.universal_class))))
% 0.38/0.61 (assume a54 (forall ((X $$unsorted)) (= (tptp.complement (tptp.image tptp.element_relation (tptp.complement X))) (tptp.power_class X))))
% 0.38/0.61 (assume a55 (forall ((U $$unsorted)) (or (not (tptp.member U tptp.universal_class)) (tptp.member (tptp.power_class U) tptp.universal_class))))
% 0.38/0.61 (assume a56 (forall ((Yr $$unsorted) (Xr $$unsorted)) (tptp.subclass (tptp.compose Yr Xr) (tptp.cross_product tptp.universal_class tptp.universal_class))))
% 0.38/0.61 (assume a57 (forall ((Y $$unsorted) (Z $$unsorted) (Yr $$unsorted) (Xr $$unsorted)) (or (not (tptp.member (tptp.ordered_pair Y Z) (tptp.compose Yr Xr))) (tptp.member Z (tptp.image Yr (tptp.image Xr (tptp.singleton Y)))))))
% 0.38/0.61 (assume a58 (forall ((Z $$unsorted) (Yr $$unsorted) (Xr $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.image Yr (tptp.image Xr (tptp.singleton Y))))) (not (tptp.member (tptp.ordered_pair Y Z) (tptp.cross_product tptp.universal_class tptp.universal_class))) (tptp.member (tptp.ordered_pair Y Z) (tptp.compose Yr Xr)))))
% 0.38/0.61 (assume a59 (forall ((X $$unsorted)) (or (not (tptp.single_valued_class X)) (tptp.subclass (tptp.compose X (tptp.inverse X)) tptp.identity_relation))))
% 0.38/0.61 (assume a60 (forall ((X $$unsorted)) (or (not (tptp.subclass (tptp.compose X (tptp.inverse X)) tptp.identity_relation)) (tptp.single_valued_class X))))
% 0.38/0.61 (assume a61 (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.subclass Xf (tptp.cross_product tptp.universal_class tptp.universal_class)))))
% 0.38/0.61 (assume a62 (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.subclass (tptp.compose Xf (tptp.inverse Xf)) tptp.identity_relation))))
% 0.38/0.61 (assume a63 (forall ((Xf $$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))))
% 0.38/0.61 (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))))
% 0.38/0.61 (assume a65 (forall ((X $$unsorted)) (or (= X tptp.null_class) (tptp.member (tptp.regular X) X))))
% 0.38/0.61 (assume a66 (forall ((X $$unsorted)) (or (= X tptp.null_class) (= (tptp.intersection X (tptp.regular X)) tptp.null_class))))
% 0.38/0.61 (assume a67 (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y))))
% 0.38/0.61 (assume a68 (tptp.function tptp.choice))
% 0.38/0.61 (assume a69 (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= Y tptp.null_class) (tptp.member (tptp.apply tptp.choice Y) Y))))
% 0.38/0.61 (assume a70 (forall ((Xf $$unsorted)) (or (not (tptp.one_to_one Xf)) (tptp.function Xf))))
% 0.38/0.61 (assume a71 (forall ((Xf $$unsorted)) (or (not (tptp.one_to_one Xf)) (tptp.function (tptp.inverse Xf)))))
% 0.38/0.61 (assume a72 (forall ((Xf $$unsorted)) (or (not (tptp.function (tptp.inverse Xf))) (not (tptp.function Xf)) (tptp.one_to_one Xf))))
% 0.38/0.61 (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))
% 0.38/0.61 (assume a74 (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation))
% 0.38/0.61 (assume a75 (forall ((Xr $$unsorted)) (= (tptp.complement (tptp.domain_of (tptp.intersection Xr tptp.identity_relation))) (tptp.diagonalise Xr))))
% 0.38/0.61 (assume a76 (forall ((X $$unsorted)) (= (tptp.intersection (tptp.domain_of X) (tptp.diagonalise (tptp.compose (tptp.inverse tptp.element_relation) X))) (tptp.cantor X))))
% 0.38/0.61 (assume a77 (forall ((Xf $$unsorted)) (or (not (tptp.operation Xf)) (tptp.function Xf))))
% 0.38/0.61 (assume a78 (forall ((Xf $$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)))))
% 0.38/0.61 (assume a79 (forall ((Xf $$unsorted)) (or (not (tptp.operation Xf)) (tptp.subclass (tptp.range_of Xf) (tptp.domain_of (tptp.domain_of Xf))))))
% 0.38/0.61 (assume a80 (forall ((Xf $$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))))
% 0.38/0.61 (assume a81 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (tptp.function Xh))))
% 0.38/0.61 (assume a82 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (= (tptp.domain_of (tptp.domain_of Xf1)) (tptp.domain_of Xh)))))
% 0.38/0.61 (assume a83 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (tptp.subclass (tptp.range_of Xh) (tptp.domain_of (tptp.domain_of Xf2))))))
% 0.38/0.61 (assume a84 (forall ((Xh $$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))))
% 0.38/0.61 (assume a85 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.operation Xf1))))
% 0.38/0.61 (assume a86 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.operation Xf2))))
% 0.38/0.61 (assume a87 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.compatible Xh Xf1 Xf2))))
% 0.38/0.61 (assume a88 (forall ((Xh $$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)))))))
% 0.38/0.61 (assume a89 (forall ((Xf1 $$unsorted) (Xf2 $$unsorted) (Xh $$unsorted)) (or (not (tptp.operation Xf1)) (not (tptp.operation Xf2)) (not (tptp.compatible Xh Xf1 Xf2)) (tptp.member (tptp.ordered_pair (tptp.not_homomorphism1 Xh Xf1 Xf2) (tptp.not_homomorphism2 Xh Xf1 Xf2)) (tptp.domain_of Xf1)) (tptp.homomorphism Xh Xf1 Xf2))))
% 0.38/0.61 (assume a90 (forall ((Xf1 $$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))))
% 0.38/0.61 (assume a91 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product U V))) (tptp.member X (tptp.unordered_pair X Y)))))
% 0.38/0.61 (assume a92 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product U V))) (tptp.member Y (tptp.unordered_pair X Y)))))
% 0.38/0.61 (assume a93 (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 tptp.universal_class))))
% 0.38/0.61 (assume a94 (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 tptp.universal_class))))
% 0.38/0.61 (assume a95 (forall ((X $$unsorted)) (tptp.subclass X X)))
% 0.38/0.61 (assume a96 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.subclass Y Z)) (tptp.subclass X Z))))
% 0.38/0.61 (assume a97 (forall ((X $$unsorted) (Y $$unsorted)) (or (= X Y) (tptp.member (tptp.not_subclass_element X Y) X) (tptp.member (tptp.not_subclass_element Y X) Y))))
% 0.38/0.61 (assume a98 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (= X Y) (tptp.member (tptp.not_subclass_element Y X) Y))))
% 0.38/0.61 (assume a99 (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element Y X) X)) (= X Y) (tptp.member (tptp.not_subclass_element X Y) X))))
% 0.38/0.61 (assume a100 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (not (tptp.member (tptp.not_subclass_element Y X) X)) (= X Y))))
% 0.38/0.61 (assume a101 (forall ((Y $$unsorted) (X $$unsorted)) (not (tptp.member Y (tptp.intersection (tptp.complement X) X)))))
% 0.38/0.61 (assume a102 (forall ((Z $$unsorted)) (not (tptp.member Z tptp.null_class))))
% 0.38/0.61 (assume a103 (forall ((X $$unsorted)) (tptp.subclass tptp.null_class X)))
% 0.38/0.61 (assume a104 (forall ((X $$unsorted)) (or (not (tptp.subclass X tptp.null_class)) (= X tptp.null_class))))
% 0.38/0.61 (assume a105 (forall ((Z $$unsorted)) (or (= Z tptp.null_class) (tptp.member (tptp.not_subclass_element Z tptp.null_class) Z))))
% 0.38/0.61 (assume a106 (tptp.member tptp.null_class tptp.universal_class))
% 0.38/0.61 (assume a107 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair X Y) (tptp.unordered_pair Y X))))
% 0.38/0.61 (assume a108 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.subclass (tptp.singleton X) (tptp.unordered_pair X Y))))
% 0.38/0.61 (assume a109 (forall ((Y $$unsorted) (X $$unsorted)) (tptp.subclass (tptp.singleton Y) (tptp.unordered_pair X Y))))
% 0.38/0.61 (assume a110 (forall ((Y $$unsorted) (X $$unsorted)) (or (tptp.member Y tptp.universal_class) (= (tptp.unordered_pair X Y) (tptp.singleton X)))))
% 0.38/0.61 (assume a111 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member X tptp.universal_class) (= (tptp.unordered_pair X Y) (tptp.singleton Y)))))
% 0.38/0.61 (assume a112 (forall ((X $$unsorted) (Y $$unsorted)) (or (= (tptp.unordered_pair X Y) tptp.null_class) (tptp.member X tptp.universal_class) (tptp.member Y tptp.universal_class))))
% 0.38/0.61 (assume a113 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (= (tptp.unordered_pair X Y) (tptp.unordered_pair X Z))) (not (tptp.member (tptp.ordered_pair Y Z) (tptp.cross_product tptp.universal_class tptp.universal_class))) (= Y Z))))
% 0.38/0.61 (assume a114 (forall ((X $$unsorted) (Z $$unsorted) (Y $$unsorted)) (or (not (= (tptp.unordered_pair X Z) (tptp.unordered_pair Y Z))) (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product tptp.universal_class tptp.universal_class))) (= X Y))))
% 0.38/0.61 (assume a115 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (not (= (tptp.unordered_pair X Y) tptp.null_class)))))
% 0.38/0.61 (assume a116 (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (not (= (tptp.unordered_pair X Y) tptp.null_class)))))
% 0.38/0.61 (assume a117 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product U V))) (not (= (tptp.unordered_pair X Y) tptp.null_class)))))
% 0.38/0.61 (assume a118 (forall ((X $$unsorted) (Z $$unsorted) (Y $$unsorted)) (or (not (tptp.member X Z)) (not (tptp.member Y Z)) (tptp.subclass (tptp.unordered_pair X Y) Z))))
% 0.38/0.61 (assume a119 (forall ((X $$unsorted)) (tptp.member (tptp.singleton X) tptp.universal_class)))
% 0.38/0.61 (assume a120 (forall ((Y $$unsorted) (X $$unsorted)) (tptp.member (tptp.singleton Y) (tptp.unordered_pair X (tptp.singleton Y)))))
% 0.38/0.61 (assume a121 (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.singleton X)))))
% 0.38/0.61 (assume a122 (tptp.member tptp.x tptp.universal_class))
% 0.38/0.61 (assume a123 (= (tptp.singleton tptp.x) tptp.null_class))
% 0.38/0.61 (step t1 (cl (not (= (or (not (= tptp.null_class (tptp.singleton tptp.x))) (not (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x))) (not (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) (or (not (= tptp.null_class (tptp.singleton tptp.x))) (not (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x))) (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) (not (or (not (= tptp.null_class (tptp.singleton tptp.x))) (not (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x))) (not (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))))) (or (not (= tptp.null_class (tptp.singleton tptp.x))) (not (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x))) (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) :rule equiv_pos2)
% 0.38/0.61 (step t2 (cl (= (not (= tptp.null_class (tptp.singleton tptp.x))) (not (= tptp.null_class (tptp.singleton tptp.x))))) :rule refl)
% 0.38/0.61 (step t3 (cl (= (not (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x))) (not (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x))))) :rule refl)
% 0.38/0.61 (step t4 (cl (= (= (= (not (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) true) (= (not (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) :rule equiv_simplify)
% 0.38/0.61 (step t5 (cl (not (= (= (not (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) true)) (= (not (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) :rule equiv1 :premises (t4))
% 0.38/0.61 (step t6 (cl (= (= (not (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)) (not (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))))) :rule all_simplify)
% 0.38/0.61 (step t7 (cl (= (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) :rule refl)
% 0.38/0.61 (step t8 (cl (= (not (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) :rule all_simplify)
% 0.38/0.61 (step t9 (cl (= (= (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)) (not (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) (= (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) :rule cong :premises (t7 t8))
% 0.38/0.61 (step t10 (cl (= (= (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) true)) :rule all_simplify)
% 0.38/0.61 (step t11 (cl (= (= (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)) (not (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) true)) :rule trans :premises (t9 t10))
% 0.38/0.61 (step t12 (cl (= (= (not (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) true)) :rule trans :premises (t6 t11))
% 0.38/0.61 (step t13 (cl (= (not (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) :rule resolution :premises (t5 t12))
% 0.38/0.61 (step t14 (cl (= (or (not (= tptp.null_class (tptp.singleton tptp.x))) (not (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x))) (not (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) (or (not (= tptp.null_class (tptp.singleton tptp.x))) (not (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x))) (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) :rule cong :premises (t2 t3 t13))
% 0.38/0.61 (step t15 (cl (not (= (=> (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x)))) (not (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))))) (not (=> (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x))))) (not (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))))) :rule equiv_pos2)
% 0.38/0.61 (step t16 (cl (= (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))))) :rule refl)
% 0.38/0.61 (step t17 (cl (= (= (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x))) false) (not (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x)))))) :rule equiv_simplify)
% 0.38/0.61 (step t18 (cl (= (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x))) false) (not (not (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x)))))) :rule equiv2 :premises (t17))
% 0.38/0.61 (step t19 (cl (not (not (not (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x)))))) (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x)))) :rule not_not)
% 0.38/0.61 (step t20 (cl (= (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x))) false) (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x)))) :rule resolution :premises (t18 t19))
% 0.38/0.61 (step t21 (cl (=> (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x))) false) (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x)))) :rule implies_neg1)
% 0.38/0.61 (anchor :step t22)
% 0.38/0.61 (assume t22.a0 (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))
% 0.38/0.61 (assume t22.a1 (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)))
% 0.38/0.61 (assume t22.a2 (= tptp.null_class (tptp.singleton tptp.x)))
% 0.38/0.61 (step t22.t1 (cl (not (= (= true false) false)) (not (= true false)) false) :rule equiv_pos2)
% 0.38/0.61 (step t22.t2 (cl (= (= true false) false)) :rule all_simplify)
% 0.38/0.61 (step t22.t3 (cl (= (= (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)) true) (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) :rule equiv_simplify)
% 0.38/0.61 (step t22.t4 (cl (= (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)) true) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) :rule equiv2 :premises (t22.t3))
% 0.38/0.61 (step t22.t5 (cl (= (tptp.singleton tptp.x) tptp.null_class)) :rule symm :premises (t22.a2))
% 0.38/0.61 (step t22.t6 (cl (= tptp.null_class (tptp.singleton tptp.x))) :rule symm :premises (t22.t5))
% 0.38/0.61 (step t22.t7 (cl (= (tptp.unordered_pair tptp.x tptp.x) (tptp.singleton tptp.x))) :rule symm :premises (t22.a1))
% 0.38/0.61 (step t22.t8 (cl (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x))) :rule symm :premises (t22.t7))
% 0.38/0.61 (step t22.t9 (cl (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) :rule trans :premises (t22.t6 t22.t8))
% 0.38/0.61 (step t22.t10 (cl (= (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)) true)) :rule resolution :premises (t22.t4 t22.t9))
% 0.38/0.61 (step t22.t11 (cl (= true (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) :rule symm :premises (t22.t10))
% 0.38/0.61 (step t22.t12 (cl (= (= (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)) false) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) :rule equiv_simplify)
% 0.38/0.61 (step t22.t13 (cl (= (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)) false) (not (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) :rule equiv2 :premises (t22.t12))
% 0.38/0.61 (step t22.t14 (cl (not (not (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) :rule not_not)
% 0.38/0.61 (step t22.t15 (cl (= (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)) false) (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) :rule resolution :premises (t22.t13 t22.t14))
% 0.38/0.61 (step t22.t16 (cl (= (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)) false)) :rule resolution :premises (t22.t15 t22.a0))
% 0.38/0.61 (step t22.t17 (cl (= true false)) :rule trans :premises (t22.t11 t22.t16))
% 0.38/0.61 (step t22.t18 (cl false) :rule resolution :premises (t22.t1 t22.t2 t22.t17))
% 0.38/0.61 (step t22 (cl (not (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) (not (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x))) (not (= tptp.null_class (tptp.singleton tptp.x))) false) :rule subproof :discharge (t22.a0 t22.a1 t22.a2))
% 0.38/0.61 (step t23 (cl (not (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x)))) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) :rule and_pos)
% 0.38/0.61 (step t24 (cl (not (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x)))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x))) :rule and_pos)
% 0.38/0.61 (step t25 (cl (not (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x)))) (= tptp.null_class (tptp.singleton tptp.x))) :rule and_pos)
% 0.38/0.61 (step t26 (cl false (not (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x)))) (not (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x)))) (not (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x))))) :rule resolution :premises (t22 t23 t24 t25))
% 0.38/0.61 (step t27 (cl (not (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x)))) (not (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x)))) (not (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x)))) false) :rule reordering :premises (t26))
% 0.38/0.61 (step t28 (cl (not (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x)))) false) :rule contraction :premises (t27))
% 0.38/0.61 (step t29 (cl (=> (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x))) false) false) :rule resolution :premises (t21 t28))
% 0.38/0.61 (step t30 (cl (=> (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x))) false) (not false)) :rule implies_neg2)
% 0.38/0.61 (step t31 (cl (=> (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x))) false) (=> (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x))) false)) :rule resolution :premises (t29 t30))
% 0.38/0.61 (step t32 (cl (=> (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x))) false)) :rule contraction :premises (t31))
% 0.38/0.61 (step t33 (cl (= (=> (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x))) false) (not (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x)))))) :rule implies_simplify)
% 0.38/0.61 (step t34 (cl (not (=> (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x))) false)) (not (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x))))) :rule equiv1 :premises (t33))
% 0.38/0.61 (step t35 (cl (not (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x))))) :rule resolution :premises (t32 t34))
% 0.38/0.61 (step t36 (cl (= (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x))) false)) :rule resolution :premises (t20 t35))
% 0.38/0.61 (step t37 (cl (= (=> (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x)))) (=> (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) false))) :rule cong :premises (t16 t36))
% 0.38/0.61 (step t38 (cl (= (=> (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) false) (not (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))))) :rule all_simplify)
% 0.38/0.61 (step t39 (cl (= (=> (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x)))) (not (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))))) :rule trans :premises (t37 t38))
% 0.38/0.61 (step t40 (cl (=> (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x)))) (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) :rule implies_neg1)
% 0.38/0.61 (anchor :step t41)
% 0.38/0.61 (assume t41.a0 (= tptp.null_class (tptp.singleton tptp.x)))
% 0.38/0.61 (assume t41.a1 (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)))
% 0.38/0.61 (assume t41.a2 (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))
% 0.38/0.61 (step t41.t1 (cl (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x))) (not (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) (not (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x))) (not (= tptp.null_class (tptp.singleton tptp.x)))) :rule and_neg)
% 0.38/0.61 (step t41.t2 (cl (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x)))) :rule resolution :premises (t41.t1 t41.a2 t41.a1 t41.a0))
% 0.38/0.61 (step t41 (cl (not (= tptp.null_class (tptp.singleton tptp.x))) (not (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x))) (not (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x)))) :rule subproof :discharge (t41.a0 t41.a1 t41.a2))
% 0.38/0.61 (step t42 (cl (not (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) (= tptp.null_class (tptp.singleton tptp.x))) :rule and_pos)
% 0.38/0.61 (step t43 (cl (not (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x))) :rule and_pos)
% 0.38/0.61 (step t44 (cl (not (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) :rule and_pos)
% 0.38/0.61 (step t45 (cl (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x))) (not (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) (not (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) (not (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))))) :rule resolution :premises (t41 t42 t43 t44))
% 0.38/0.61 (step t46 (cl (not (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) (not (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) (not (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x)))) :rule reordering :premises (t45))
% 0.38/0.61 (step t47 (cl (not (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x)))) :rule contraction :premises (t46))
% 0.38/0.61 (step t48 (cl (=> (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x)))) (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x)))) :rule resolution :premises (t40 t47))
% 0.38/0.61 (step t49 (cl (=> (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x)))) (not (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x))))) :rule implies_neg2)
% 0.38/0.61 (step t50 (cl (=> (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x)))) (=> (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x))))) :rule resolution :premises (t48 t49))
% 0.38/0.61 (step t51 (cl (=> (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) (and (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (= tptp.null_class (tptp.singleton tptp.x))))) :rule contraction :premises (t50))
% 0.38/0.61 (step t52 (cl (not (and (= tptp.null_class (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))))) :rule resolution :premises (t15 t39 t51))
% 0.38/0.61 (step t53 (cl (not (= tptp.null_class (tptp.singleton tptp.x))) (not (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x))) (not (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) :rule not_and :premises (t52))
% 0.38/0.61 (step t54 (cl (or (not (= tptp.null_class (tptp.singleton tptp.x))) (not (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x))) (not (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) (not (not (= tptp.null_class (tptp.singleton tptp.x))))) :rule or_neg)
% 0.38/0.61 (step t55 (cl (or (not (= tptp.null_class (tptp.singleton tptp.x))) (not (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x))) (not (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) (not (not (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x))))) :rule or_neg)
% 0.38/0.61 (step t56 (cl (or (not (= tptp.null_class (tptp.singleton tptp.x))) (not (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x))) (not (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) (not (not (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))))) :rule or_neg)
% 0.38/0.61 (step t57 (cl (or (not (= tptp.null_class (tptp.singleton tptp.x))) (not (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x))) (not (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) (or (not (= tptp.null_class (tptp.singleton tptp.x))) (not (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x))) (not (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) (or (not (= tptp.null_class (tptp.singleton tptp.x))) (not (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x))) (not (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))))) :rule resolution :premises (t53 t54 t55 t56))
% 0.38/0.61 (step t58 (cl (or (not (= tptp.null_class (tptp.singleton tptp.x))) (not (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x))) (not (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))))) :rule contraction :premises (t57))
% 0.38/0.61 (step t59 (cl (or (not (= tptp.null_class (tptp.singleton tptp.x))) (not (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x))) (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) :rule resolution :premises (t1 t14 t58))
% 0.38/0.61 (step t60 (cl (not (= tptp.null_class (tptp.singleton tptp.x))) (not (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x))) (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) :rule or :premises (t59))
% 0.38/0.61 (step t61 (cl (not (or (not (tptp.member tptp.x tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) (not (tptp.member tptp.x tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) :rule or_pos)
% 0.38/0.61 (step t62 (cl (not (tptp.member tptp.x tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))) (not (or (not (tptp.member tptp.x tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))))) :rule reordering :premises (t61))
% 0.38/0.61 (step t63 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair X Y))))) (or (not (tptp.member tptp.x tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair X Y)))))) :rule implies_neg1)
% 0.38/0.61 (anchor :step t64)
% 0.38/0.61 (assume t64.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair X Y))))))
% 0.38/0.61 (step t64.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair X Y)))))) (or (not (tptp.member tptp.x tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))))) :rule forall_inst :args ((:= X tptp.x) (:= Y tptp.x)))
% 0.38/0.61 (step t64.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair X Y)))))) (or (not (tptp.member tptp.x tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) :rule or :premises (t64.t1))
% 0.38/0.61 (step t64.t3 (cl (or (not (tptp.member tptp.x tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) :rule resolution :premises (t64.t2 t64.a0))
% 0.38/0.61 (step t64 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair X Y)))))) (or (not (tptp.member tptp.x tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) :rule subproof :discharge (t64.a0))
% 0.38/0.61 (step t65 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair X Y))))) (or (not (tptp.member tptp.x tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) (or (not (tptp.member tptp.x tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) :rule resolution :premises (t63 t64))
% 0.38/0.61 (step t66 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair X Y))))) (or (not (tptp.member tptp.x tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) (not (or (not (tptp.member tptp.x tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))))) :rule implies_neg2)
% 0.38/0.61 (step t67 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair X Y))))) (or (not (tptp.member tptp.x tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair X Y))))) (or (not (tptp.member tptp.x tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))))) :rule resolution :premises (t65 t66))
% 0.38/0.61 (step t68 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair X Y))))) (or (not (tptp.member tptp.x tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))))) :rule contraction :premises (t67))
% 0.38/0.61 (step t69 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair X Y)))))) (or (not (tptp.member tptp.x tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) :rule implies :premises (t68))
% 0.38/0.61 (step t70 (cl (not (= (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (not (= (tptp.unordered_pair X Y) tptp.null_class)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair X Y))))))) (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (not (= (tptp.unordered_pair X Y) tptp.null_class))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair X Y)))))) :rule equiv_pos2)
% 0.38/0.61 (anchor :step t71 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 0.38/0.61 (step t71.t1 (cl (= X X)) :rule refl)
% 0.38/0.61 (step t71.t2 (cl (= Y Y)) :rule refl)
% 0.38/0.61 (step t71.t3 (cl (= (not (tptp.member X tptp.universal_class)) (not (tptp.member X tptp.universal_class)))) :rule refl)
% 0.38/0.61 (step t71.t4 (cl (= (= (tptp.unordered_pair X Y) tptp.null_class) (= tptp.null_class (tptp.unordered_pair X Y)))) :rule all_simplify)
% 0.38/0.61 (step t71.t5 (cl (= (not (= (tptp.unordered_pair X Y) tptp.null_class)) (not (= tptp.null_class (tptp.unordered_pair X Y))))) :rule cong :premises (t71.t4))
% 0.38/0.61 (step t71.t6 (cl (= (or (not (tptp.member X tptp.universal_class)) (not (= (tptp.unordered_pair X Y) tptp.null_class))) (or (not (tptp.member X tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair X Y)))))) :rule cong :premises (t71.t3 t71.t5))
% 0.38/0.61 (step t71 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (not (= (tptp.unordered_pair X Y) tptp.null_class)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair X Y))))))) :rule bind)
% 0.38/0.61 (step t72 (cl (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair X Y)))))) :rule resolution :premises (t70 t71 a115))
% 0.38/0.61 (step t73 (cl (or (not (tptp.member tptp.x tptp.universal_class)) (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x))))) :rule resolution :premises (t69 t72))
% 0.38/0.61 (step t74 (cl (not (= tptp.null_class (tptp.unordered_pair tptp.x tptp.x)))) :rule resolution :premises (t62 a122 t73))
% 0.38/0.61 (step t75 (cl (not (= (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair tptp.x tptp.x) (tptp.singleton tptp.x))) (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x))))) (not (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair tptp.x tptp.x) (tptp.singleton tptp.x)))) (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)))) :rule equiv_pos2)
% 0.38/0.61 (step t76 (cl (= (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))))) :rule refl)
% 0.38/0.61 (step t77 (cl (= (= (tptp.unordered_pair tptp.x tptp.x) (tptp.singleton tptp.x)) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)))) :rule all_simplify)
% 0.38/0.61 (step t78 (cl (= (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair tptp.x tptp.x) (tptp.singleton tptp.x))) (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x))))) :rule cong :premises (t76 t77))
% 0.38/0.61 (step t79 (cl (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair tptp.x tptp.x) (tptp.singleton tptp.x))) (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X)))) :rule implies_neg1)
% 0.38/0.61 (anchor :step t80)
% 0.38/0.61 (assume t80.a0 (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))))
% 0.38/0.61 (step t80.t1 (cl (or (not (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X)))) (= (tptp.unordered_pair tptp.x tptp.x) (tptp.singleton tptp.x)))) :rule forall_inst :args ((:= X tptp.x)))
% 0.38/0.61 (step t80.t2 (cl (not (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X)))) (= (tptp.unordered_pair tptp.x tptp.x) (tptp.singleton tptp.x))) :rule or :premises (t80.t1))
% 0.38/0.61 (step t80.t3 (cl (= (tptp.unordered_pair tptp.x tptp.x) (tptp.singleton tptp.x))) :rule resolution :premises (t80.t2 t80.a0))
% 0.38/0.61 (step t80 (cl (not (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X)))) (= (tptp.unordered_pair tptp.x tptp.x) (tptp.singleton tptp.x))) :rule subproof :discharge (t80.a0))
% 0.38/0.61 (step t81 (cl (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair tptp.x tptp.x) (tptp.singleton tptp.x))) (= (tptp.unordered_pair tptp.x tptp.x) (tptp.singleton tptp.x))) :rule resolution :premises (t79 t80))
% 0.38/0.61 (step t82 (cl (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair tptp.x tptp.x) (tptp.singleton tptp.x))) (not (= (tptp.unordered_pair tptp.x tptp.x) (tptp.singleton tptp.x)))) :rule implies_neg2)
% 0.38/0.61 (step t83 (cl (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair tptp.x tptp.x) (tptp.singleton tptp.x))) (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair tptp.x tptp.x) (tptp.singleton tptp.x)))) :rule resolution :premises (t81 t82))
% 0.38/0.61 (step t84 (cl (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair tptp.x tptp.x) (tptp.singleton tptp.x)))) :rule contraction :premises (t83))
% 0.38/0.61 (step t85 (cl (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x)))) :rule resolution :premises (t75 t78 t84))
% 0.38/0.61 (step t86 (cl (not (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X)))) (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x))) :rule implies :premises (t85))
% 0.38/0.61 (step t87 (cl (= (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.x))) :rule resolution :premises (t86 a11))
% 0.38/0.61 (step t88 (cl (= tptp.null_class (tptp.singleton tptp.x))) :rule symm :premises (a123))
% 0.38/0.61 (step t89 (cl) :rule resolution :premises (t60 t74 t87 t88))
% 0.38/0.61
% 0.38/0.61 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.PHS6MkgTGq/cvc5---1.0.5_22082.smt2
% 0.38/0.62 % cvc5---1.0.5 exiting
% 0.38/0.62 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------